Particle Physics Planet

December 18, 2014

The n-Category Cafe

Effective Sample Size

On a scale of 0 to 10, how much does the average citizen of the Republic of Elbonia trust the president?

You’re conducting a survey to find out, and you’ve calculated that in order to get the precision you want, you’re going to need a sample of 100 statistically independent individuals. Now you have to decide how to do this.

You could stand in the central square of the capital city and survey the next 100 people who walk by. But these opinions won’t be independent: probably politics in the capital isn’t representative of politics in Elbonia as a whole.

So you consider travelling to 100 different locations in the country and asking one Elbonian at each. But apart from anything else, this is far too expensive for you to do.

Maybe a compromise would be OK. You could go to 10 locations and ask… 20 people at each? 30? How many would you need in order to match the precision of 100 independent individuals — to have an “effective sample size” of 100?

The answer turns out to be closely connected to a quantity I’ve written about many times before: magnitude. Let me explain…

The general situation is that we have a large population of individuals (in this case, Elbonians), and with each there is associated a real number (in this case, their level of trust in the president). So we have a probability distribution, and we’re interested in discovering some statistic $\theta \theta$ (in this case, the mean, but it might instead be the median or the variance or the 90th percentile). We do this by taking some sample of $nn$ individuals, and then doing something with the sampled data to produce an estimate of $\theta \theta$.

The “something” we do with the sampled data is called an estimator. So, an estimator is a real-valued function on the set of possible sample data. For instance, if you’re trying to estimate the mean of the population, and we denote the sample data by ${Y}_{1},\dots ,{Y}_{n}Y_1, \ldots, Y_n$, then the obvious estimator for the population mean would be just the sample mean,

$\frac{1}{n}{Y}_{1}+\cdots +\frac{1}{n}{Y}_{n}. \frac\left\{1\right\}\left\{n\right\} Y_1 + \cdots + \frac\left\{1\right\}\left\{n\right\} Y_n. $

But it’s important to realize that the best estimator for a given statistic of the population (such as the mean) needn’t be that same statistic applied to the sample. For example, suppose we wish to know the mean mass of men from Mali. Unfortunately, we’ve only weighed three men from Mali, and two of them are brothers. You could use

$\frac{1}{3}{Y}_{1}+\frac{1}{3}{Y}_{2}+\frac{1}{3}{Y}_{3} \frac\left\{1\right\}\left\{3\right\} Y_1 + \frac\left\{1\right\}\left\{3\right\} Y_2 + \frac\left\{1\right\}\left\{3\right\} Y_3 $

as your estimator, but since body mass is somewhat genetic, that would give undue importance to one particular family. At the opposite extreme, you could use

$\frac{1}{2}{Y}_{1}+\frac{1}{4}{Y}_{2}+\frac{1}{4}{Y}_{3} \frac\left\{1\right\}\left\{2\right\} Y_1 + \frac\left\{1\right\}\left\{4\right\} Y_2 + \frac\left\{1\right\}\left\{4\right\} Y_3 $

(where ${Y}_{1}Y_1$ is the mass of the non-brother). But that would be going too far, as it gives the non-brother as much importance as the two brothers put together. Probably the best answer is somewhere in between. Exactly where in between depends on the correlation between masses of brothers, which is a quantity we might reasonably estimate from data gathered elsewhere in the world.

(There’s a deliberate echo here of something I wrote previously: in what proportions should we sow poppies, Polish wheat and Persian wheat in order to maximize biological diversity? The similarity is no coincidence.)

There are several qualities we might seek in an estimator. I’ll focus on two.

• High precision   The precision of an estimator is the reciprocal of its variance. To make sense of this, you have to realize that estimators are random variables too! An estimator with high precision, or low variance, is not much changed by the effects of randomness. It will give more or less the same answer if you run it multiple times.

For instance, suppose we’ve decided to do the Elbonian survey by asking 30 people in each of the 5 biggest cities and 20 people from each of 3 chosen villages, then taking some specific weighted mean of the resulting data. If that’s a high-precision estimator, it will give more or less the same final answer no matter which specific Elbonians happen to have been stopped by the pollsters.

• Unbiased   An estimator of some statistic is unbiased if its expected value is equal to that statistic for the population.

For example, suppose we’re trying to estimate the variance of some distribution. If our sample consists of a measly two individuals, then the variance of the sample is likely to be much less than the variance of the population. After all, with only two individuals observed, we’ve barely begun to glimpse the full variation of the population as a whole. It can actually be shown that with a sample size of two, the expected value of the sample variance is half the population variance. So the sample variance is a biased estimator of the population variance, but twice the sample variance is an unbiased estimator.

(Being unbiased is perhaps a less crucial property of an estimator than it might at first appear. Suppose the boss of a chain of pizza takeaways wants to know the average size of pizzas ordered. “Size” could be measured by diameter — what you order by — or area — what you eat. But since the relationship between diameter and area is quadratic rather than linear, an unbiased estimator of one will be a biased estimator of the other.)

No matter what statistic you’re trying to estimate, you can talk about the “effective sample size” of an estimator. But for simplicity, I’ll only talk about estimating the mean.

Here’s a loose definition:

The effective sample size of an estimator of the population mean is the number ${n}_{\mathrm{eff}}n_\left\{eff\right\}$ with the property that our estimator has the same precision (or variance) as the estimator got by sampling ${n}_{\mathrm{eff}}n_\left\{eff\right\}$ independent individuals.

Let’s unpack that.

Suppose we choose $nn$ individuals at random from the population (with replacement, if you care). So we have independent, identically distributed random variables ${Y}_{1},\dots ,{Y}_{n}Y_1, \ldots, Y_n$. As above, we take the sample mean

$\frac{1}{n}{Y}_{1}+\cdots +\frac{1}{n}{Y}_{n} \frac\left\{1\right\}\left\{n\right\} Y_1 + \cdots + \frac\left\{1\right\}\left\{n\right\} Y_n $

as our estimator of the population mean. Since variance is additive for independent random variables, the variance of this estimator is

$n\cdot \mathrm{Var}\left(\frac{1}{n}{Y}_{1}\right)=n\cdot \frac{1}{{n}^{2}}\mathrm{Var}\left({Y}_{1}\right)=\frac{{\sigma }^{2}}{n} n \cdot Var\Bigl\left( \frac\left\{1\right\}\left\{n\right\} Y_1 \Bigr\right) = n \cdot \frac\left\{1\right\}\left\{n^2\right\} Var\left(Y_1\right) = \frac\left\{\sigma^2\right\}\left\{n\right\} $

where ${\sigma }^{2}\sigma^2$ is the population variance. The precision of the estimator is, therefore, $n/{\sigma }^{2}n/\sigma^2$. That makes sense: as your sample size $nn$ increases, the precision of your estimate increases too.

Now, suppose we have some other estimator $\stackrel{^}{\mu }\hat\left\{\mu\right\}$ of the population mean. It’s a random variable, so it has a variance $\mathrm{Var}\left(\stackrel{^}{\mu }\right)Var\left(\hat\left\{\mu\right\}\right)$. The effective sample size of the estimator $\stackrel{^}{\mu }\hat\left\{\mu\right\}$ is the number ${n}_{\mathrm{eff}}n_\left\{eff\right\}$ satisfying

${\sigma }^{2}/{n}_{\mathrm{eff}}=\mathrm{Var}\left(\stackrel{^}{\mu }\right). \sigma^2/n_\left\{eff\right\} = Var\left(\hat\left\{\mu\right\}\right). $

This doesn’t entirely make sense, as the unique number ${n}_{\mathrm{eff}}n_\left\{eff\right\}$ satisfying this equation needn’t be an integer, so we can’t sensibly talk about a sample of size ${n}_{\mathrm{eff}}n_\left\{eff\right\}$. Nevertheless, we can absolutely rigorously define the effective sample size of our estimator $\stackrel{^}{\mu }\hat\left\{\mu\right\}$ as

${n}_{\mathrm{eff}}={\sigma }^{2}/Var\left(\stackrel{^}{\mu }\right). n_\left\{eff\right\} = \sigma^2/\Var\left(\hat\left\{\mu\right\}\right). $

And that’s the definition. Differently put,

$\text{effective sample size}=\text{precision}×\text{population variance}. \text\left\{effective sample size\right\} = \text\left\{precision \right\} \times \text\left\{population variance\right\}. $

Trivial examples   If $\stackrel{^}{\mu }\hat\left\{\mu\right\}$ is the mean value of $nn$ uncorrelated individuals, then the effective sample size is $nn$. If $\stackrel{^}{\mu }\hat\left\{\mu\right\}$ is the mean value of $nn$ extremely highly correlated individuals, then the variance of the estimator is little less than the variance of a single individual, so the effective sample size is little more than $11$.

Now, suppose our pollsters have come back from their trips to various parts of Elbonia. Together, they’ve asked $nn$ individuals how much they trust the president. We want to take that data and use it to estimate the population mean — that is, the mean level of trust in the president across Elbonia — in as precise a way as possible.

We’re going to restrict ourselves to unbiased estimators, so that the expected value of the estimator is the population mean. We’re also going to consider only linear estimators: those of the form

${a}_{1}{Y}_{1}+\cdots +{a}_{n}{Y}_{n} a_1 Y_1 + \cdots + a_n Y_n $

where ${Y}_{1},\dots ,{Y}_{n}Y_1, \ldots, Y_n$ are the trust levels expressed by the $nn$ Elbonians surveyed.

Question:

What choice of unbiased linear estimator maximizes the effective sample size?

To answer this, we need to recall some basic statistical notions…

Correlation and covariance

Variance is a quadratic form, and covariance is the corresponding bilinear form. That is, take two random variables $XX$ and $YY$, with respective means ${\mu }_{X}\mu_X$ and ${\mu }_{Y}\mu_Y$. Then their covariance is

$\mathrm{Cov}\left(X,Y\right)=E\left(\left(X-{\mu }_{X}\right)\left(Y-{\mu }_{Y}\right)\right). Cov\left(X, Y\right) = E\left(\left(X - \mu_X\right)\left(Y - \mu_Y\right)\right). $

This is bilinear in $XX$ and $YY$, and $\mathrm{Cov}\left(X,X\right)=\mathrm{Var}\left(X\right)Cov\left(X, X\right) = Var\left(X\right)$.

$\mathrm{Cov}\left(X,Y\right)Cov\left(X, Y\right)$ is bounded above and below by $±{\sigma }_{X}{\sigma }_{Y}\pm \sigma_X \sigma_Y$, the product of the standard deviations. It’s natural to normalize, dividing through by ${\sigma }_{X}{\sigma }_{Y}\sigma_X \sigma_Y$ to obtain a number between $-1-1$ and $11$. This gives the correlation coefficient

${\rho }_{X,Y}=\frac{\mathrm{Cov}\left(X,Y\right)}{{\sigma }_{X}{\sigma }_{Y}}\in \left[-1,1\right]. \rho_\left\{X, Y\right\} = \frac\left\{Cov\left(X, Y\right)\right\}\left\{\sigma_X\sigma_Y\right\} \in \left[-1, 1\right]. $

Alternatively, we can first scale $XX$ and $YY$ to have variance $11$, then take the covariance, and this also gives the correlation:

${\rho }_{X,Y}=\mathrm{Cov}\left(X/{\sigma }_{X},Y/{\sigma }_{Y}\right). \rho_\left\{X, Y\right\} = Cov\left(X/\sigma_X, Y/\sigma_Y\right). $

Now suppose we have $nn$ random variables, ${Y}_{1},\dots ,{Y}_{n}Y_1, \ldots, Y_n$. The correlation matrix $RR$ is the $n×nn \times n$ matrix whose $\left(i,j\right)\left(i, j\right)$-entry is ${\rho }_{{Y}_{i},{Y}_{j}}\rho_\left\{Y_i, Y_j\right\}$. Correlation matrices have some easily-proved properties:

• The entries are all in $\left[-1,1\right]\left[-1, 1\right]$.

• The diagonal entries are all $11$.

• The matrix is symmetric.

• The matrix is positive semidefinite. That’s because the corresponding quadratic form is $\left({a}_{1},\dots ,{a}_{n}\right)↦\mathrm{Var}\left(\sum {a}_{i}{Y}_{i}/{\sigma }_{i}\right)\left(a_1, \ldots, a_n\right) \mapsto Var\left(\sum a_i Y_i/\sigma_i\right)$, and variances are nonnegative.

And actually, it’s not so hard to prove that any matrix with these properties is the correlation matrix of some sequence of random variables.

In what follows, for simplicity, I’ll quietly assume that the correlation matrices we encounter are strictly positive definite. This only amounts to assuming that no linear combination of the ${Y}_{i}Y_i$s has variance zero — in other words, that there are no exact linear relationships between the random variables involved.

Back to the main question

Here’s where we got to. We surveyed $nn$ individuals from our population, giving $nn$ identically distributed but not necessarily independent random variables ${Y}_{1},\dots ,{Y}_{n}Y_1, \ldots, Y_n$. Some of them will be correlated because of geographical clustering.

We’re trying to use this data to estimate the population mean in as precise a way as possible. Specifically, we’re looking for numbers ${a}_{1},\dots ,{a}_{n}a_1, \ldots, a_n$ such that the linear estimator $\sum {a}_{i}{Y}_{i}\sum a_i Y_i$ is unbiased and has the maximum possible effective sample size.

The effective sample size was defined as ${n}_{\mathrm{eff}}={\sigma }^{2}/\mathrm{Var}\left(\sum {a}_{i}{Y}_{i}\right)n_\left\{eff\right\} = \sigma^2/Var\left(\sum a_i Y_i\right)$, where ${\sigma }^{2}\sigma^2$ is the variance of the distribution we’re drawing from. Now we need to work out the variance in the denominator.

Let $RR$ denote the correlation matrix of ${Y}_{1},\dots ,{Y}_{n}Y_1, \ldots, Y_n$. I said a moment ago that $\left({a}_{1},\dots ,{a}_{n}\right)↦\mathrm{Var}\left(\sum {a}_{i}{Y}_{i}\right)\left(a_1, \ldots, a_n\right) \mapsto Var \left(\sum a_i Y_i\right)$ is the quadratic form corresponding to the bilinear form represented by the covariance matrix. Since each ${Y}_{i}Y_i$ has variance ${\sigma }^{2}\sigma^2$, the covariance matrix is just ${\sigma }^{2}\sigma^2$ times the correlation matrix $RR$. Hence

$\mathrm{Var}\left({a}_{1}{Y}_{1}+\cdots +{a}_{n}{Y}_{n}\right)={\sigma }^{2}\cdot {a}^{*}Ra Var\left(a_1 Y_1 + \cdots + a_n Y_n\right) = \sigma^2 \cdot a^\ast R a $

where $*\ast$ denotes a transpose and $a=\left({a}_{1},\dots ,{a}_{n}\right)a = \left(a_1, \ldots, a_n\right)$.

So, the effective sample size of our estimator is

$1/{a}^{*}Ra. 1/a^\ast R a. $

We also wanted our estimator to be unbiased. Its expected value is

$E\left({a}_{1}{Y}_{1}+\cdots +{a}_{n}{Y}_{n}\right)=\left({a}_{1}+\cdots +{a}_{n}\right)\mu E\left(a_1 Y_1 + \cdots + a_n Y_n\right) = \left(a_1 + \cdots + a_n\right) \mu $

where $\mu \mu$ is the population mean. So, we need $\sum {a}_{i}=1\sum a_i = 1$.

Putting this together, the maximum possible effective sample size among all unbiased linear estimators is

$\mathrm{sup}\left\{\frac{1}{{a}^{*}Ra}\phantom{\rule{thinmathspace}{0ex}}:\phantom{\rule{thinmathspace}{0ex}}a\in {ℝ}^{n},\phantom{\rule{thinmathspace}{0ex}}\sum {a}_{i}=1\right\}. \sup \Bigl\\left\{ \frac\left\{1\right\}\left\{a^\ast R a\right\} \, : \, a \in \mathbb\left\{R\right\}^n, \, \sum a_i = 1 \Bigr\\right\}. $

Which $a\in {ℝ}^{n}a \in \mathbb\left\{R\right\}^n$ achieves this maximum, and what is the maximum possible effective sample size? That’s easy, and in fact it’s something that’s appeared many times at this blog before…

The magnitude of a matrix

The magnitude $|R||R|$ of an invertible $n×nn \times n$ matrix $RR$ is the sum of all ${n}^{2}n^2$ entries of ${R}^{-1}R^\left\{-1\right\}$. To calculate it, you don’t need to go as far as inverting $RR$. It’s much easier to find the unique column vector $ww$ satisfying

$Rw=\left(\begin{array}{c}1\\ ⋮\\ 1\end{array}\right) R w = \begin\left\{pmatrix\right\} 1 \\ \vdots \\ 1 \end\left\{pmatrix\right\} $

(the weighting of $RR$), then calculate ${\sum }_{i}{w}_{i}\sum_i w_i$. This sum is the magnitude of $RR$, since ${w}_{i}w_i$ is the $ii$th row-sum of ${R}^{-1}R^\left\{-1\right\}$.

Most of what I’ve written about magnitude has been in the situation where we start with a finite metric space $X=\left\{{x}_{1},\dots ,{x}_{n}\right\}X = \\left\{x_1, \ldots, x_n\\right\}$, and we use the matrix $ZZ$ with entries ${Z}_{ij}=\mathrm{exp}\left(-d\left({x}_{i},{x}_{j}\right)\right)Z_\left\{i j\right\} = exp\left(-d\left(x_i, x_j\right)\right)$. This turns out to give interesting information about $XX$. In the metric situation, the entries of the matrix $ZZ$ are between $00$ and $11$. Often $ZZ$ is positive definite (e.g. when $X\subset {ℝ}^{n}X \subset \mathbb\left\{R\right\}^n$), as correlation matrices are.

When $RR$ is positive definite, there’s a third way to describe the magnitude:

$|R|=\mathrm{sup}\left\{\frac{1}{{a}^{*}Ra}\phantom{\rule{thinmathspace}{0ex}}:\phantom{\rule{thinmathspace}{0ex}}a\in {ℝ}^{n},\phantom{\rule{thinmathspace}{0ex}}\sum {a}_{i}=1\right\}. |R| = \sup \Bigl\\left\{ \frac\left\{1\right\}\left\{a^\ast R a\right\} \, : \, a \in \mathbb\left\{R\right\}^n, \, \sum a_i = 1 \Bigr\\right\}. $

The supremum is attained just when $a=w/|R|a = w/|R|$, and the proof is a simple application of the Cauchy–Schwarz inequality.

But that supremum is exactly the expression we had for maximum effective sample size! So:

The maximum possible value of ${n}_{\mathrm{eff}}n_\left\{eff\right\}$ is $|R||R|$.

Or more wordily:

The maximum effective sample size of an unbiased linear estimator of the mean is the magnitude of the sample correlation matrix.

Or wordily but approximately:

Effective sample size $==$ magnitude of correlation matrix.

Moreover, we know how to attain that maximum. It’s attained if and only if our estimator is

$\frac{1}{|R|}\left({w}_{1}{Y}_{1}+\cdots +{w}_{n}{Y}_{n}\right) \frac\left\{1\right\}\left\{|R|\right\} \left(w_1 Y_1 + \cdots + w_n Y_n\right) $

where $w=\left({w}_{1},\dots ,{w}_{n}\right)w = \left(w_1, \ldots, w_n\right)$ is the weighting of the correlation matrix.

I’m not too sure where this “result” — observation, really — comes from. I learned it from the statistician Paul Blackwell at Sheffield, who, like me, had been reading this paper:

Andrew Solow and Stephen Polasky, Measuring biological diversity. Environmental and Ecological Statistics 1 (1994), 95–103.

In turn, Solow and Polasky refer to this:

Morris Eaton, A group action on covariances with applications to the comparison of linear normal experiments. In: Moshe Shaked and Y.L. Tong (eds.), Stochastic inequalities: Papers from the AMS-IMS-SIAM Joint Summer Research Conference held in Seattle, Washington, July 1991, Institute of Mathematical Statistics Lecture Notes — Monograph Series, Volume 22, 1992.

But the result is so simple that I’d imagine it’s much older. I’ve been wondering whether it’s essentially the Gauss-Markov theorem; I thought it was, then I thought it wasn’t. Does anyone know?

The surprising behaviour of effective sample size

You might expect the effective size of a sample of $nn$ individuals to be at most $nn$. It’s not.

You might expect the effective sample size to go down as the correlations within the sample go up. It doesn’t.

This behaviour appears in even the simplest nontrivial example:

Example   Suppose our sample consists of just two individuals. Call the sampled values ${Y}_{1}Y_1$ and ${Y}_{2}Y_2$, and write the correlation matrix as $R=\left(\begin{array}{cc}1& \rho \\ \rho & 1\end{array}\right). R = \begin\left\{pmatrix\right\} 1 & \rho \\ \rho & 1 \end\left\{pmatrix\right\}. $ Then the maximum-precision unbiased linear estimator is $\frac{1}{2}\left({Y}_{1}+{Y}_{2}\right)\frac\left\{1\right\}\left\{2\right\}\left(Y_1 + Y_2\right)$, and its effective sample size is $|R|=\frac{2}{1+\rho }. |R| = \frac\left\{2\right\}\left\{1 + \rho\right\}. $ As the correlation $\rho \rho$ between the two variables increases from $00$ to $11$, the effective sample size decreases from $22$ to $11$, as you’d expect.

But when $\rho <0\rho \lt 0$, the effective sample size is greater than 2. In fact, as $\rho \to -1\rho \to -1$, the effective sample size tends to $\infty \infty$. That’s intuitively plausible. For if $\rho \rho$ is close to $-1-1$ then, writing ${Y}_{1}=\mu +{\epsilon }_{1}Y_1 = \mu + \varepsilon_1$ and ${Y}_{2}=\mu +{\epsilon }_{2}Y_2 = \mu + \varepsilon_2$, we have ${\epsilon }_{1}\approx -{\epsilon }_{2}\varepsilon_1 \approx -\varepsilon_2$, and so $\frac{1}{2}\left({Y}_{1}+{Y}_{2}\right)\frac\left\{1\right\}\left\{2\right\}\left(Y_1 + Y_2\right)$ is a very good estimator of $\mu \mu$. In the extreme, when $\rho =-1\rho = -1$, it’s an exact estimator of $\mu \mu$ — it’s infinitely precise.

The fact that the effective sample size can be greater than the actual sample size seems to be very well known. For instance, there’s a whole page about it in the documentation for Q, which is apparently “analysis software for market research”.

What’s interesting is that this doesn’t only occur when some of the variables are negatively correlated. It can also happen when all the correlations are nonnegative, as in the following example from the paper by Eaton cited above.

Example Consider the correlation matrix $R=\left(\begin{array}{ccc}1& 0& \rho \\ 0& 1& \rho \\ \rho & \rho & 1\end{array}\right) R = \begin\left\{pmatrix\right\} 1 &0 &\rho \\ 0 &1 &\rho \\ \rho &\rho &1 \end\left\{pmatrix\right\} $ where $0\le \rho <\sqrt{2}/2=0.707\dots 0 \leq \rho \lt \sqrt\left\{2\right\}/2 = 0.707\ldots$. This is positive definite, so it’s the correlation matrix of some random variables ${Y}_{1},{Y}_{2},{Y}_{3}Y_1, Y_2, Y_3$.

A routine computation shows that $|R|=\frac{3-4\rho }{1-2{\rho }^{2}}. |R| = \frac\left\{3 - 4\rho\right\}\left\{1 - 2\rho^2\right\}. $ As we’ve shown, this is the effective sample size of a maximum-precision unbiased linear estimator of the mean.

When $\rho =0\rho = 0$, it’s $33$, as you’d expect: the variables are uncorrelated. As $\rho \rho$ increases, $|R||R|$ decreases, again as you’d expect: more correlation between the variables leads to a smaller effective sample size. This behaviour continues until $\rho =1/2\rho = 1/2$, where $|R|=2|R| = 2$.

But then something strange happens. As $\rho \rho$ increases from $1/21/2$ to $\sqrt{2}/2\sqrt\left\{2\right\}/2$, the effective sample size increases from $22$ to $\infty \infty$. Increasing the correlation increases the effective sample size. For instance, when $\rho =0.7\rho = 0.7$, we have $|R|=10|R| = 10$ — the maximum-precision estimator is as precise as if we’d chosen $1010$ independent individuals. For that value of $\rho \rho$, the maximum-precision estimator turns out to be $\frac{3}{2}{Y}_{1}+\frac{3}{2}{Y}_{2}-2{Y}_{3}. \frac\left\{3\right\}\left\{2\right\} Y_1 + \frac\left\{3\right\}\left\{2\right\} Y_2 - 2 Y_3. $ Go figure!

These examples may seem counterintuitive, but Eaton cautions us to beware of our feeble intuitions:

These examples show that our rather vague intuitive feeling that “positive correlation tends to decrease information content in an experiment” is very far from the truth, even for rather simple normal experiments with three observations.

This is very like the fact that a metric space with $nn$ points can have magnitude (“effective number of points”) greater than $nn$, even if the associated matrix $ZZ$ is positive definite.

Anyone with any statistical knowledge who’s still reading will easily have picked up on the fact that I’m a total amateur. If that’s you, I’d love to hear your comments!

Jaques Distler - Musings

Smoke Signals, Morse Code or ... ?

It seemed like a straightforward question. If you use Apple’s Contacts.app to store your contacts, you’ve surely noticed this behaviour: some of your contacts auto-magically sprout clickable links for Facetime video/audio chats, with no intervention on your part. I was curious enough to submit a query about it, via Apple’s Support Site:

Contacts.app seems to know whether each of my contacts has registered their email for FaceTime, even if I have NEVER tried to facetime with them (or call their cell-phone or …). How does it do this? Are all of the email addresses in my addressbook automatically uploaded to Apple’s servers? If so, how do I turn this off, as it seems to be a MASSIVE invasion of my privacy.

That was a month and a half ago (2014/11/02). Today, I received a response:

Dear Jacques,

Thank you for your recent email.

We sincerely understand your frustration and apologize for any inconvenience this has caused you. We understand you have questions and concerns about your contacts and FaceTime. Because of the nature and complexity of this issue, Apple does not offer this type of assistance or support through written correspondence.

support.apple.com/kb/HE57

Thank you, Apple Customer Care

Can it really be that the explanation is too complex for “written correspondence”? What other communication method would be more adequate?

Or maybe one of you know the answer. How does Contacts.app determine which of the email addresses in my addressbook have been registered for Facetime?

The n-Category Cafe

Welcome, Qiaochu!

I’m delighted to announce that Qiaochu Yuan has joined us as a host of the $nn$-Category Café. Qiaochu is a grad student at Berkeley, who you’ll quite likely already know from his blog Annoying Precision or from his very wide and energetic activity at MathOverflow.

Welcome, Qiaochu!

CERN Bulletin

AXEL-2015 - Introduction To Particle Accelerators | starting 19 January

CERN Technical Training 2015: Learning for the LHC

AXEL-2015 is a lecture series on particle accelerators, given at CERN within the framework of the 2014 Technical Training Programme. As part of the BE Department’s Operations Group Shutdown Lecture series, the general accelerator physics module has been organised since 2003 as a joint venture between the BE Department and Technical Training, and is open to the general CERN community.

The AXEL-2015 course is designed for technicians who are operating an accelerator or whose work is closely linked to accelerators, but it is also open to technicians, engineers, and physicists interested in this field. The course does not require any prior knowledge of accelerators. However, some basic knowledge of trigonometry, matrices and differential equations and some basic knowledge of magnetism would be an advantage.

The series will consists of 10 one-hour sessions (Monday 19 January 2015 – Friday 23 January 2015, from 9 a.m. to 10.15 a.m. and from 10.45 a.m. to 12 noon), and will be delivered in English with questions and answers also possible in French. The lecturer is Rende Steerenberg, Deputy Group Leader of the BE Operations Group and PS Section Leader. The programme will cover: basic mathematics; transverse optics; lattice calculations; resonances; longitudinal motion; leptons; transfer lines, injection and ejection; longitudinal and transverse beam instabilities.

Registration is required for this course. Participation in all lectures is encouraged to allow people to gain the maximum benefit; registered participants will be invited and attendance will be recorded in their personal training records. If you are interested in AXEL-2015, please talk to your supervisor and/or your Departmental Training Officer. Register online via the training catalogue. The detailed program is available on the AXEL-2015 webpage, accessible at http://www.cern.ch/TechnicalTraining/

Organizers:
Rende Steerenberg, BE-OP 79086/164518
Technical Training, HR-LD 74924

CERN Bulletin

Administrative Circular No. 2 (Rev. 6) – Recruitment, appointment and possible developments regarding the contractual position of staff members (1 January 2015)

Administrative Circular No. 2 (Rev. 6) entitled "Recruitment, appointment and possible developments regarding the contractual position of staff members", approved by the Director-General following discussion in the Standing Concertation Committee meeting on 27 November 2014 is available on the Human Resources Department website.

It cancels and replaces Administrative Circular No. 2 (Rev. 5) entitled "Recruitment, appointment and possible developments regarding the contractual position of staff members" of September 2011.

This circular was revised in order to improve the effectiveness of the career transition measures, in particular by expanding the scope of the programme to include also career transition within the Organization and by placing emphasis on career orientation and job search.

Administrative Circular No. 2 will be further revised next year with the adoption of the new contract policy, subject to approval of the relevant amendments by all competent bodies.

HR Department

Peter Coles - In the Dark

That Was The REF That Was..

I feel obliged to comment on the results of the 2014 Research Excellence Framework (REF) that were announced today. Actually, I knew about them yesterday but the news was under embargo until one minute past midnight by which time I was tucked up in bed.

The results for the two Units of Assessment relevant to the School of Mathematical and Physical Sciences are available online here for Mathematical Sciences and here for Physics and Astronomy.

To give some background: the overall REF score for a Department is obtained by adding three different components: outputs (quality of research papers); impact (referrring to the impact beyond academia); and environment (which measures such things as grant income, numbers of PhD students and general infrastructure). These are weighted at 65%, 20% and 15% respectively.

Scores are assigned to these categories, e.g. for submitted outputs (usually four per staff member) on a scale of 4* (world-leading), 3* (internationally excellent), 2* (internationally recognised), 1* (nationally recognised) and unclassified and impact on a scale 4* (outstanding), 3* (very considerable), 2* (considerable), 1* (recognised but modest) and unclassified. Impact cases had to be submitted based on the number of staff submitted: two up to 15 staff, three between 15 and 25 and increasing in a like manner with increasing numbers.

The REF will control the allocation of funding in a manner yet to be decided in detail, but it is generally thought that anything scoring 2* or less will attract no funding (so the phrase “internationally recognised” really means “worthless” in the REF, as does “considerable” when applied to impact). It is also thought likely that funding will be heavily weighted towards 4* , perhaps with a ratio of 9:1 between 4* and 3*.

We knew that this REF would be difficult for the School and our fears were born out for both the Department of Mathematics or the Department of Physics and Astronomy because both departments grew considerably (by about 50%) during the course of 2013, largely in response to increased student numbers. New staff can bring outputs from elsewhere, but not impact. The research underpinning the impact has to have been done by staff working in the institution in question. And therein lies the rub for Sussex…

To take the Department of Physics and Astronomy, as an example, last year we increased staff numbers from about 23 to about 38. But the 15 new staff members could not bring any impact with them. Lacking sufficient impact cases to submit more, we were obliged to restrict our submission to fewer than 25. To make matters worse our impact cases were not graded very highly, with only 13.3% of the submission graded 4* and 13.4% graded 3*.

The outputs from Physics & Astronomy at Sussex were very good, with 93% graded 3* or 4*. That’s a higher fraction than Oxford, Cambridge, Imperial College and UCL in fact, and with a Grade Point Average of 3.10. Most other departments submitted very good outputs so the output scores are very highly bunched and a small difference in GPA means a large number of places in the rankings. The impact scores, however, have a much wider dispersion, with the result that despite the relatively small percentage contribution they have a large effect on overall rankings. As a consequence, overall, Sussex Physics & Astronomy slipped down from 14th in the RAE to 34th place in the REF (based on a Grade Point Average). Disappointing to say the least, but we’re not the only fallers. In the 2008 RAE the top-rated physics department was Lancaster; this time round they are 27th.

I now find myself in a situation eerily reminiscent of that I found myself facing in Cardiff after the 2008 Research Assessment Exercise, the forerunner of the REF. Having been through that experience I’m a hardened to disappointments and at least can take heart from Cardiff’s performance this time round. Spirits were very low there after the RAE, but a thorough post-mortem, asture investment in new research areas, and determined preparations for this REF has paid dividends: they have climbed to 6th place this time round. That gives me the chance not only to congratulate my former colleagues there for their excellent result but also to use them as an example for what we at Sussex have to do for next time. An even more remarkable success story is Strathclyde, 34th in the last RAE and now top of the REF table. Congratulations to them too!

Fortunately our strategy is already in hand. The new staff have already started working towards the next REF (widely thought to be likely to happen in 2020) and we are about to start a brand new research activity in experimental physics next year. We will be in a much better position to generate research impact as we diversify our portfolio so that it is not as strongly dominated by “blue skies” research, such as particle physics and astronomy, for which it is much harder to demonstrate economic impact.

I was fully aware of the challenges facing Physics & Astronomy at Sussex when I moved here in February 2013, but with the REF submission made later the same year there was little I could do to alter the situation. Fortunately the University of Sussex management realises that we have to play a long game in Physics and has been very supportive of our continued strategic growth. The result of the 2014 REF result is a setback but it does demonstrate that the stategy we have already embarked upon is the right one.

Roll on 2020!

Symmetrybreaking - Fermilab/SLAC

Physicist turned carbon-catcher

Particle physics inspires Arizona State University professor Klaus Lackner's work on climate change.

In the early 2000s, physicist Klaus Lackner decided to change fields based on one powerful idea: that we can pull carbon out of the air fast enough to counter global warming.

Carbon in the air predominantly exists as carbon dioxide, a greenhouse gas that traps heat in the atmosphere. Climate scientists agree that increasing levels of carbon dioxide are contributing to climate change. Around the world, scientists are searching for ways to control greenhouse gas emissions.

So how did a physicist transition from hunting the smallest fundamental particles to capturing relatively large molecules like carbon dioxide?

It started with a concept paper Lackner co-wrote in 1995 about a solar-powered self-replicating machine that might pull carbon from the air. The idea was mostly an “exciting thought experiment” to Lackner, he says.

But the real turning point came four years later at a science fair, where Lackner’s teenage daughter Claire used a fish pump to move air past a filament coated with sodium hydroxide. The powerful base captured half of the acidic carbon dioxide, earned her first place, and encouraged her father to apply his physics training to make the process more efficient.

“As a particle physicist, you are thinking about complicated systems and looking for symmetries that hold them all together,” Lackner says. “This back-and-forth between thinking big and pulling on it till you get it right, that comes from physics training.”

As a result, in 2008, Lackner revealed his “mechanical tree,” a device that captures carbon from the ambient air in a rinsable filter, eliminating the need for an expensive pump.

A physicist by training

Lackner spent 13 years working on carbon capture and energy at Columbia before taking his current position as head of Arizona State University’s Center for Negative Carbon Emissions. Through it all, his physics training has always shaped his scientific outlook and work.

As a teenager in Germany, Lackner was inspired by American physicist George Gamov’s popular book One, Two, Three…Infinity. He enrolled in the Heidelberg University physics program in the 1960s, where he received his PhD in particle physics.

Over his career, Lackner worked with some of the biggest names in science. At Heidelberg he studied under Nobel Laureate Hans Jensen, recognized for his “shell” explanation of the atom’s nucleus. An invite from Murray Gell-Mann, who won a Nobel for his work classifying elementary particles and their interactions, brought Lackner to Caltech. There, Lackner investigated that subatomic particle’s fractional charge with George Zweig, famous for his work on the quark model independent of Gell-Mann.

“I loved coming to Caltech,” says Lackner. “Even if you were a young postdoc, you were taken seriously. It was strictly just the message that you had to defend and explain. I found that exhilarating.”

Lackner transferred to SLAC National Accelerator Laboratory and later to Los Alamos National Laboratory. While there, he worked with Nobel laureate Martin Perl on a SLAC-based large-scale search for isolated, uncoupled quarks.

During nearly two decades at Los Alamos, Lackner tackled a variety of research projects, including on fluid dynamics—something he says stimulated him to think more about energy.

Changing gears

Columbia University hired Lackner in 2001, where he joined well-known climate scientist Wally Broecker.

“Klaus is the most brilliant person I have ever dealt with,” Broecker says. “I always say the world is really lucky that Klaus is putting his energy into air capture.”

While he had success with theory and demonstration, Lackner’s attempts to commercialize his mechanical tree and bring it to scale have so far been unsuccessful. The economic atmosphere, which included the 2008 market crash, was not conducive to air capture enterprises, he says. Nevertheless, Broecker calls Lackner’s work critical.

“By the time we do get our energy from non-fossil fuels—if the models are anywhere near right—we are going to have to pull down the carbon dioxide level in the atmosphere,” Broecker says. “It seems to me the only way to do that is something like what Klaus is doing.”

At ASU, Lackner intends to continue his carbon capture and other Columbia University investigations, such as how to make a liquid fuel from captured carbon. He says finding space to do his work has been much easier in the desert around Phoenix than it ever was in Upper Manhattan.

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More Bang for your Buck: Getting the Most out of Your Transit Light Curves
Title: How low can you go? The photoeccentric effect for planets of various sizes
Authors: Ellen Price, Leslie Rogers, John Johnson, Rebekah Dawson
First Author’s Institution: California Institute of Technology

I often think that all 3,000+ exoplanets that have been discovered are a lot like most people’s facebook friends. C’mon… Do you actually know all 3,000 of them? But who can blame you. You met them once years ago and now there isn’t enough time in a day or month or even in a year to comb through everyone’s profile and figure out whom you care about and whom you don’t. Well it seems like exoplanet scientists are having a similar problem. According to the Exoplanet Orbit Database, there are 3,303 planet candidates. For planet candidates, the following is true:

1. The Kepler Mission has observed each planet passing in front of its parent star and has obtained a light curve (see transit method)
2. From each light curve, scientists can determine each planet’s radius and orbital period
3. Additional observations must be done in order to confirm each planet’s existence and/or to get additional planet properties.

A planet’s radius and orbital period gives us about as much information as looking at someone’s profile picture. You get a general feeling for it’s size and hotness. Ideally, though, we’d like to know how dense the planet is, and how it moves around its parent star. For that, bullet #3 indicates we’d need additional observations. Like vetting through facebook friends, it’s just not practical or physically possible to try and follow up all 3,000+ planets to determine whom we care about and whom we don’t. In fact, for some of the more distant Kepler planets, not even the world’s largest telescopes could obtain data with high enough precision to derive a parameter such as orbital eccentricity. Therefore, it would be infinitely more practical if we could figure out a way to strip out more than just planet radius and orbital period from the Kepler light curves. In today’s astrobite, Price et al. do just that by discussing a new technique to determine eccentricities of planets from Kepler transiting exoplanets, which they have coined the “photoeccentric effect”.

Photoeccentric Effect

Figure 1. Cartoon drawing of the transit method taken from JPL. The numbers above represent key states in a transit when the planet is 1) out of transit, 2) in ingress 3) in transit. If we kept going, (4) would be in egress and (5) would be out of transit again. Because the light curve is a function of time, we can measure the time spent in each of these phases.

For those who are new to the transit method let’s quickly revisit some jargon. Looking at figure 1, there are three main events we want to internalize: 1) before the planet approaches the star it is “out of transit”, 2) when the planet is passing into/out of the disk of the star, it is in “ingress/egress” and 3) when the planet is in front of the star it is “in transit”. The planet in figure 1 has a perfectly circular orbit (zero eccentricity). Now, imagine stretching the planet’s orbit toward you in attempt to increase the eccentricity and think about how that might affect the planet’s light curve. As it turns out (and like everything in life), those slight deviations in the light curves can be described by a set of equations and voilà! The photoeccentric effect was born. Well… Not that easy. A little more magic is required to actually figure out the eccentricity from the equations. The good news is, this technique was proven to work on Kepler’s biggest (think jupiter-sized) planets two years ago by two of the authors on this paper (Dawson & Johnson). Price et al. take that same technique and try to figure out if we can pin down eccentricities of some of the smallest sized planets. Because let’s face it, those are the only ones we care about anyways (kidding!!).

Methods

In order to calculate the eccentricity, Price et. al. define a parameter, g, which describes how much a light curve deviates from the ideal, circular-orbit light curve shown in Figure 1. The parameter, g is a function of eccentricity, e, and ω, the argument of periastron (g(e, ω)). It is also a separate function of six different parameters we should be familiar with by now: transit depth, ingress/egress duration, transit duration, orbital period, radius of the star, semi-major axis of the planet (g(δ, τ, T, P, R*, a)). Now we have two equations and eight unknowns. So what do we do? Cry? No! Because we already said that δ, τ, T, P, R*, and a can all be measured directly from the light curve and our parameter g, can be determined. Now we just have one equation g(e, ω) with two unknowns. Price et. al. use Bayesian statistics to nail down the eccentricities. I refer the reader to this astrobite, which gives a great break down of Bayesian statistics for those that are interested.

Results

Figure 2. To the right are the results for HAT-P-2b and to the left are the results for GJ 436b. P(e) is the posterior probability distribution (see Bayesian statistics). The arrows represent the known eccentricities for each planet and the red dashed lines represent the range of statistically viable eccentricities derived from the Price et. al. model. If the model worked correctly, the measured value should fall somewhere in between the red dashed lines. Main point: Price et. al. accurately determines eccentricity for GJ 436b but not HAT-P-2b.

Price et. al. find that for smaller and smaller planets, the uncertainty in their calculation of eccentricity increases. Why is this? Well, for smaller and smaller planets, the light curve starts to resemble a useless flat line and it gets more and more difficult to determine δ, τ, T, P, R*, and a. And because we used those parameters to determine g, it directly effects our calculation of eccentricity. Figure 2 shows results for the cases of two different planets: HAT-P-2b (left) and GJ 436b (right). In both figures the arrow indicates the known value of the eccentricity. If our statistics was correct, the measured values should lie within the red dashed lines, which represent statistically viable solutions of the eccentricity. Therefore, Price et. al. were able to get eccentricities for GJ 426b but not HAT-P-2b. They ultimately find that their method works well for both very large eccentricities and very small eccentricities (GJ 436b has a low eccentricity), but not well for intermediate eccentricities (HAT-P-2b).

In the end this is a fantastic result. We are one step closer to unraveling the wealth of information that might be hidden deep within our 3,303 facebook friendly exoplanets.

Emily Lakdawalla - The Planetary Society Blog

Infinite Visions, One Planetary Society
Three weeks ago, we launched a social media campaign hoping to engage the public in space exploration. What we achieved was more than we expected—our Infinite Visions campaign reached more than 2.5 million people in 47 countries.

December 17, 2014

Emily Lakdawalla - The Planetary Society Blog

NASA Delays Asteroid Redirect Mission Concept Selection until 2015
NASA's efforts to capture a near-Earth asteroid and tow it back to lunar orbit will have to wait a little bit longer for a final mission concept.

Christian P. Robert - xi'an's og

full Bayesian significance test

Among the many comments (thanks!) I received when posting our Testing via mixture estimation paper came the suggestion to relate this approach to the notion of full Bayesian significance test (FBST) developed by (Julio, not Hal) Stern and Pereira, from São Paulo, Brazil. I thus had a look at this alternative and read the Bayesian Analysis paper they published in 2008, as well as a paper recently published in Logic Journal of IGPL. (I could not find what the IGPL stands for.) The central notion in these papers is the e-value, which provides the posterior probability that the posterior density is larger than the largest posterior density over the null set. This definition bothers me, first because the null set has a measure equal to zero under an absolutely continuous prior (BA, p.82). Hence the posterior density is defined in an arbitrary manner over the null set and the maximum is itself arbitrary. (An issue that invalidates my 1993 version of the Lindley-Jeffreys paradox!) And second because it considers the posterior probability of an event that does not exist a priori, being conditional on the data. This sounds in fact quite similar to Statistical Inference, Murray Aitkin’s (2009) book using a posterior distribution of the likelihood function. With the same drawback of using the data twice. And the other issues discussed in our commentary of the book. (As a side-much-on-the-side remark, the authors incidentally  forgot me when citing our 1992 Annals of Statistics paper about decision theory on accuracy estimators..!)

Filed under: Books, Statistics Tagged: Bayes factor, Bayesian Analysis, Bayesian model choice, e-values, full Bayesian significance test, logic journal of the IGPL, measure theory, Murray Aitkin, p-values, São Paulo, statistical inference

Jester - Resonaances

Planck: what's new
Slides from the recent Planck collaboration meeting are now available online. One can find there preliminary results that include an input from Planck's measurements of the polarization of the  Cosmic Microwave Background (some which were previously available via the legendary press release in French). I already wrote about the new  important limits on dark matter annihilation cross section. Here I picked up a few more things that may be of interest for a garden variety particle physicist.

• ΛCDM.
Here is a summary of Planck's best fit parameters of the standard cosmological model with and without the polarization info:

Note that the temperature-only numbers are slightly different than in the 2013 release, because of improved calibration and foreground cleaning.  Frustratingly, ΛCDM remains  solid. The polarization data do not change the overall picture, but they shrink some errors considerably. The Hubble parameter remains at a low value; the previous tension with Ia supernovae observations seems to be partly resolved and blamed on systematics on the supernovae side.  For the large scale structure fans, the parameter σ8 characterizing matter fluctuations today remains at a high value, in some tension with weak lensing and cluster counts.
• Neff.
There are also better limits on deviations from ΛCDM. One interesting result is the new improved constraint on the effective number of neutrinos, Neff in short. The way this result is presented may be confusing.  We know perfectly well there are exactly 3 light active (interacting via weak force) neutrinos; this has been established in the 90s at the LEP collider, and Planck has little to add in this respect. Heavy neutrinos, whether active or sterile, would not show in this measurement at all.  For light sterile neutrinos, Neff implies an upper bound on the mixing angle with the active ones. The real importance of  Neff lies in that it counts any light particles (other than photons) contributing to the energy density of the universe at the time of CMB decoupling. Outside the standard model neutrinos, other theorized particles could contribute any real positive number to Neff, depending on their temperature and spin. A few years ago there have been consistent hints of Neff  much larger 3, which would imply physics beyond the standard model. Alas, Planck has shot down these claims. The latest number combining Planck and Baryon Acoustic Oscillations is Neff =3.04±0.18, spot on 3.046 expected from the standard model neutrinos.  This represents an important constraint on any new physics model with very light (less than eV) particles.
• Σmν.
The limit on the sum of the neutrino masses keeps improving and gets into a really interesting regime. Recall that, from oscillation experiments, we can extract the neutrino mass differences: Δm32 ≈ 0.05 eV and Δm12≈0.009 eV up to a sign, but we don't know their absolute masses.  Planck and others have already excluded the possibility that all 3 neutrinos have approximately the same mass. Now they are not far from probing the so-called inverted hierarchy, where two neutrinos have approximately the same mass and the 3rd is much lighter, in which case Σmν ≈ 0.1 eV. Planck and Baryon Acoustic Oscillations set the limit Σmν < 0.16 eV at 95% CL, however this result is not strongly advertised because it is sensitive to the value of the Hubble parameter. Including non-Planck measurements leads to a weaker, more conservative limit Σmν < 0.23 eV, the same as quoted in the 2013 release.
• CνB.
For dessert, something cool. So far we could observe the cosmic neutrino background only through its contribution to the  energy density of radiation in the early universe. This affects observables that can be inferred from the CMB acoustic peaks, such as the Hubble expansion rate or the time of matter-radiation equality. Planck, for the first time, probes the properties of the CνB. Namely, it measures the  effective sound speed ceff and viscosity cvis parameters, which affect the growth of perturbations in the CνB. Free-streaming particles like the neutrinos should have ceff^2 =  cvis^2 = 1/3, while Planck measures ceff^2 = 0.3256±0.0063 and  cvis^2 = 0.336±0.039. The result is unsurprising, but it may help constraining some more exotic models of neutrino interactions.

To summarize, Planck continues to deliver disappointing results, and there's still more to follow ;)

ZapperZ - Physics and Physicists

Defending The Integrety Of Physics
The suggestion made by a few theorists that theoretical physics, at least some aspect of it, should be accepted merely based on "aesthetics" and not from experimental verification is downright STUPID! This is highlighted in the opinion piece published in Nature recently (I don't know how long this article is available online for free, so read it now!).

This year, debates in physics circles took a worrying turn. Faced with difficulties in applying fundamental theories to the observed Universe, some researchers called for a change in how theoretical physics is done. They began to argue — explicitly — that if a theory is sufficiently elegant and explanatory, it need not be tested experimentally, breaking with centuries of philosophical tradition of defining scientific knowledge as empirical. We disagree. As the philosopher of science Karl Popper argued: a theory must be falsifiable to be scientific.

Without experimental verification, then such ideas are no longer physics but rather, a religion. You accept things purely on a matter of faith, or beauty, or elegance, etc.. without being able to empirically show that it is valid.

I will fight tooth and nail to make sure physics doesn't go into that rout. If these theorists want to pursue such a thing, then they should stop calling themselves physicists and start their own religion.

Zz.

Emily Lakdawalla - The Planetary Society Blog

SpaceX to Attempt First-Ever Ocean Barge Rocket Landing
This Friday, SpaceX will attempt what no agency or company has done before: land a used rocket stage on a floating ocean platform.

arXiv blog

How Mobile Phone Data Reveals Food Consumption Patterns in Central Africa

Food shortages in developing countries have always been difficult to monitor in real time. But mobile phone data is changing that, say demographers.

An increasingly important side-effect of the mobile phone revolution is that the big data it generates has become a high-resolution microscope for examining the nature of society. Various teams have shown how mobile phone data reveals patterns of commuting, criminal activity and even human reproductive strategies.

Symmetrybreaking - Fermilab/SLAC

LHC filled with liquid helium

The Large Hadron Collider is now cooled to nearly its operational temperature.

The Large Hadron Collider isn’t just a cool particle accelerator. It's the coldest.

Last week the cryogenics team at CERN finished filling the eight curved sections of the LHC with liquid helium. The LHC ring is now cooled to below 4 kelvin (minus 452 degrees Fahrenheit).

This cool-down is an important milestone in preparing the LHC for its spring 2015 restart, after which physicists plan to use it to produce the highest-energy particle collisions ever achieved on Earth.

“We are delighted that the LHC is now cold again,” says Beate Heinemann, the deputy leader of the ATLAS experiment and a physicist with the University of California, Berkeley, and Lawrence Berkeley National Laboratory. “We are getting very excited about the high-energy run starting in spring next year, which will open the possibility of finding new particles which were just out of reach.”

The LHC uses more than 1000 superconducting dipole magnets to bend high-energy particles around its circumference. These superconducting magnets are made from a special material that, when cooled close to absolute zero (minus 460 degrees Fahrenheit), can maintain a high electrical current with zero electrical resistance.

“These magnets have to produce an extremely strong magnetic field to bend the particles, which are moving at very close to the speed of light,” says Mike Lamont, the head of LHC operations. “The magnets are powered with high electrical currents whenever beam is circulating. Room-temperature electromagnets would be unable to support the currents required.”

To get the 16 miles of LHC magnets close to absolute zero, engineers slowly inject helium into a special cryogenic system surrounding the magnets and gradually reduce the temperature over the course of several months at a rate of one sector cooled per month. As the temperature drops, the helium becomes liquid and acts as a cold shell to keep the magnets at their operational temperature.

“Helium is a special element because it only becomes a liquid below 5 kelvin,” says Laurent Tavian, the group leader of the CERN cryogenics team. “It is also the only element which is not solid at very low temperature, and it is naturally inert—meaning we can easily store it and never have to worry about it becoming flammable.”

The first sector cool-down started in May 2014. Engineers first pre-cooled the helium using 9000 metric tons of liquid nitrogen. After the pre-cooling, engineers injected the helium into the accelerator.

“Filling the entire accelerator requires 130 metric tons of helium, which we received from our supplier at a rate of around one truckload every week,” Tavian says.

In January CERN engineers plan to have the entire accelerator cooled to its nominal operating temperature of 1.9 kelvin (minus 456 degrees Fahrenheit), colder than outer space.

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Peter Coles - In the Dark

Well, not long now until the announcement of the results of the 2014 Research Excellence Framework are known publicly. I’ll post something in the way of a personal reflection tomorrow, as long as I haven’t thrown myself off Brighton Pier by then. In the meantime, I couldn’t resist sharing this brilliant parody of Wilfred Owen I found via Twitter…

Originally posted on Stumbling with Confidence:

(This has been written as the momentous results of the Research Excellence Framework, known to all and sundry as the dreaded REF, are about to be announced, and as careers hang in the balance depending on who are the winners and losers.)

(with apologies to Wilfred Owen)

What lasting hell for these who try as authors?
Only the monstrous anger of the dons.
Only the stuttering academic’s crippled cursor
Can patter out career horizons.
No metrics now for them; no citations nor reviews;
Nor any voice of warning save the choirs, –
The shrill, demented choirs of wailing peers;
And lost opportunities calling them from sad HEIs.
What meetings may be held to speed them all?
Not in the hand of managers but in their eyes
Shall shine the unholy glimmers of goodbyes.
The cost of student fees shall be their pall;
Their inheritance the frustrations…

View original 11 more words

Tommaso Dorigo - Scientificblogging

New Limits On VY Production From CDF: Good, But Also Disappointing
Alas, for once I must say I am not completely happy of one new result by the CDF collaboration - the experiment to which I devoted 18 years of my research time, and where I learned almost everything I know about experimental particle physics.

December 16, 2014

Christian P. Robert - xi'an's og

Topological sensitivity analysis for systems biology

Michael Stumpf sent me Topological sensitivity analysis for systems biology, written by Ann Babtie and Paul Kirk,  en avant-première before it came out in PNAS and I read it during the trip to NIPS in Montréal. (The paper is published in open access, so everyone can read it now!) The topic is quite central to a lot of debates about climate change, economics, ecology, finance, &tc., namely to assess the impact of using the wrong model to draw conclusions and make decisions about a real phenomenon. (Which reminded me of the distinction between mechanical and phenomenological models stressed by Michael Blum in his NIPS talk.) And it is of much interest from a Bayesian point of view since assessing the worth of a model requires modelling the “outside” of a model, using for instance Gaussian processes as in the talk Tony O’Hagan gave in Warwick earlier this term. I would even go as far as saying that the issue of assessing [and compensating for] how wrong a model is, given available data, may be the (single) most under-assessed issue in statistics. We (statisticians) have yet to reach our Boxian era.

In Babtie et al., the space or universe of models is represented by network topologies, each defining the set of “parents” in a semi-Markov representation of the (dynamic) model. At which stage Gaussian processes are also called for help. Alternative models are ranked in terms of fit according to a distance between simulated data from the original model (sounds like a form of ABC?!). Obviously, there is a limitation in the number and variety of models considered this way, I mean there are still assumptions made on the possible models, while this number of models is increasing quickly with the number of nodes. As pointed out in the paper (see, e.g., Fig.4), the method has a parametric bootstrap flavour, to some extent.

What is unclear is how one can conduct Bayesian inference with such a collection of models. Unless all models share the same “real” parameters, which sounds unlikely. The paper mentions using uniform prior on all parameters, but this is difficult to advocate in a general setting. Another point concerns the quantification of how much one can trust a given model, since it does not seem models are penalised by a prior probability. Hence they all are treated identically. This is a limitation of the approach (or an indication that it is only a preliminary step in the evaluation of models) in that some models within a large enough collection will eventually provide an estimate that differs from those produced by the other models. So the assessment may become altogether highly pessimistic for this very reason.

“If our parameters have a real, biophysical interpretation, we therefore need to be very careful not to assert that we know the true values of these quantities in the underlying system, just because–for a given model–we can pin them down with relative certainty.”

In addition to its relevance for moving towards approximate models and approximate inference, and in continuation of yesterday’s theme, the paper calls for nested sampling to generate samples from the posterior(s) and to compute the evidence associated with each model. (I realised I had missed this earlier paper by Michael and co-authors on nested sampling for system biology.) There is no discussion in the paper on why nested sampling was selected, compared with, say, a random walk Metropolis-Hastings algorithm. Unless it is used in a fully automated way,  but the paper is rather terse on that issue… And running either approach on 10⁷ models in comparison sounds like an awful lot of work!!! Using importance [sampling] nested sampling as we proposed with Nicolas Chopin could be a way to speed up this exploration if all parameters are identical between all or most models.

Filed under: Books, Statistics, Travel, University life Tagged: Gaussian processes, model choice, model validation, nested sampling, network, PNAS, topology

Sean Carroll - Preposterous Universe

Guest Post: Chip Sebens on the Many-Interacting-Worlds Approach to Quantum Mechanics

I got to know Charles “Chip” Sebens back in 2012, when he emailed to ask if he could spend the summer at Caltech. Chip is a graduate student in the philosophy department at the University of Michigan, and like many philosophers of physics, knows the technical background behind relativity and quantum mechanics very well. Chip had funding from NSF, and I like talking to philosophers, so I said why not?

We had an extremely productive summer, focusing on our different stances toward quantum mechanics. At the time I was a casual adherent of the Everett (many-worlds) formulation, but had never thought about it carefully. Chip was skeptical, in particular because he thought there were good reasons to believe that EQM should predict equal probabilities for being on any branch of the wave function, rather than the amplitude-squared probabilities of the real-world Born Rule. Fortunately, I won, although the reason I won was mostly because Chip figured out what was going on. We ended up writing a paper explaining why the Born Rule naturally emerges from EQM under some simple assumptions. Now I have graduated from being a casual adherent to a slightly more serious one.

But that doesn’t mean Everett is right, and it’s worth looking at other formulations. Chip was good enough to accept my request that he write a guest blog post about another approach that’s been in the news lately: a “Newtonian” or “Many-Interacting-Worlds” formulation of quantum mechanics, which he has helped to pioneer.

In Newtonian physics objects always have definite locations. They are never in two places at once. To determine how an object will move one simply needs to add up the various forces acting on it and from these calculate the object’s acceleration. This framework is generally taken to be inadequate for explaining the quantum behavior of subatomic particles like electrons and protons. We are told that quantum theory requires us to revise this classical picture of the world, but what picture of reality is supposed to take its place is unclear. There is little consensus on many foundational questions: Is quantum randomness fundamental or a result of our ignorance? Do electrons have well-defined properties before measurement? Is the Schrödinger equation always obeyed? Are there parallel universes?

Some of us feel that the theory is understood well enough to be getting on with. Even though we might not know what electrons are up to when no one is looking, we know how to apply the theory to make predictions for the results of experiments. Much progress has been made―observe the wonder of the standard model―without answering these foundational questions. Perhaps one day with insight gained from new physics we can return to these basic questions. I will call those with such a mindset the doers. Richard Feynman was a doer:

“It will be difficult. But the difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, ‘But how can it be like that?’ which is a reflection of uncontrolled but utterly vain desire to see it in terms of something familiar. I will not describe it in terms of an analogy with something familiar; I will simply describe it. … I think I can safely say that nobody understands quantum mechanics. … Do not keep saying to yourself, if you can possibly avoid it, ‘But how can it be like that?’ because you will get ‘down the drain’, into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.”

-Feynman, The Character of Physical Law (chapter 6, pg. 129)

In contrast to the doers, there are the dreamers. Dreamers, although they may often use the theory without worrying about its foundations, are unsatisfied with standard presentations of quantum mechanics. They want to know “how it can be like that” and have offered a variety of alternative ways of filling in the details. Doers denigrate the dreamers for being unproductive, getting lost “down the drain.” Dreamers criticize the doers for giving up on one of the central goals of physics, understanding nature, to focus exclusively on another, controlling it. But even by the lights of the doer’s primary mission―being able to make accurate predictions for a wide variety of experiments―there are reasons to dream:

“Suppose you have two theories, A and B, which look completely different psychologically, with different ideas in them and so on, but that all consequences that are computed from each are exactly the same, and both agree with experiment. … how are we going to decide which one is right? There is no way by science, because they both agree with experiment to the same extent. … However, for psychological reasons, in order to guess new theories, these two things may be very far from equivalent, because one gives a man different ideas from the other. By putting the theory in a certain kind of framework you get an idea of what to change. … Therefore psychologically we must keep all the theories in our heads, and every theoretical physicist who is any good knows six or seven different theoretical representations for exactly the same physics.”

-Feynman, The Character of Physical Law (chapter 7, pg. 168)

In the spirit of finding alternative versions of quantum mechanics―whether they agree exactly or only approximately on experimental consequences―let me describe an exciting new option which has recently been proposed by Hall, Deckert, and Wiseman (in Physical Review X) and myself (forthcoming in Philosophy of Science), receiving media attention in: Nature, New Scientist, Cosmos, Huffington Post, Huffington Post Blog, FQXi podcast… Somewhat similar ideas have been put forward by Böstrom, Schiff and Poirier, and Tipler. The new approach seeks to take seriously quantum theory’s hydrodynamic formulation which was developed by Erwin Madelung in the 1920s. Although the proposal is distinct from the many-worlds interpretation, it also involves the postulation of parallel universes. The proposed multiverse picture is not the quantum mechanics of college textbooks, but just because the theory looks so “completely different psychologically” it might aid the development of new physics or new calculational techniques (even if this radical picture of reality ultimately turns out to be incorrect).

Let’s begin with an entirely reasonable question a dreamer might ask about quantum mechanics.

“I understand water waves and sound waves. These waves are made of particles. A sound wave is a compression wave that results from particles of air bunching up in certain regions and vacating other. Waves play a central role in quantum mechanics. Is it possible to understand these waves as being made of some things?”

There are a variety of reasons to think the answer is no, but they can be overcome. In quantum mechanics, the state of a system is described by a wave function Ψ. Consider a single particle in the famous double-slit experiment. In this experiment the one particle initially passes through both slits (in its quantum way) and then at the end is observed hitting somewhere on a screen. The state of the particle is described by a wave function which assigns a complex number to each point in space at each time. The wave function is initially centered on the two slits. Then, as the particle approaches the detection screen, an interference pattern emerges; the particle behaves like a wave.

Figure 1: The evolution of Ψ with the amount of color proportional to the amplitude (a.k.a. magnitude) and the hue indicating the phase of Ψ.

There’s a problem with thinking of the wave as made of something: the wave function assigns strange complex numbers to points in space instead of familiar real numbers. This can be resolved by focusing on |Ψ|2, the squared amplitude of the wave function, which is always a positive real number.

Figure 2: The evolution of |Ψ|2.

We normally think of |Ψ|2 as giving the probability of finding the particle somewhere. But, to entertain the dreamer’s idea about quantum waves, let’s instead think of |Ψ|2 as giving a density of particles. Whereas figure 2 is normally interpreted as showing the evolution of the probability distribution for a single particle, instead understand it as showing the distribution of a large number of particles: initially bunched up at the two slits and later spread out in bands at the detector (figure 3). Although I won’t go into the details here, we can actually understand the way that wave changes in time as resulting from interactions between these particles, from the particles pushing each other around. The Schrödinger equation, which is normally used to describe the way the wave function changes, is then viewed as consequence of this interaction.

Figure 3: The evolution of particles with |Ψ|2 as the density. This animation is meant to help visualize the idea, but don’t take the precise motions of the particles too seriously. Although we know how the particles move en masse, we don’t know precisely how individual particles move.

In solving the problem about complex numbers, we’ve created two new problems: How can there really be a large number of particles if we only ever see one show up on the detector at the end? If |Ψ|2 is now telling us about densities and not probabilities, what does it have to do with probabilities?

Removing a simplification in the standard story will help. Instead of focusing on the wave function of a single particle, let’s consider all particles at once. To describe the state of a collection of particles it turns out we can’t just give each particle its own wave function. This would miss out on an important feature of quantum mechanics: entanglement. The state of one particle may be inextricably linked to the state of another. Instead of having a wave function for each particle, a single universal wave function describes the collection of particles.

The universal wave function takes as input a position for each particle as well as the time. The position of a single particle is given by a point in familiar three dimensional space. The positions of all particles can be given by a single point in a very high dimensional space, configuration space: the first three dimensions of configuration space give the position of particle 1, the next three give the position of particle 2, etc. The universal wave function Ψ assigns a complex number to each point of configuration space at each time.  |Ψ|2 then assigns a positive real number to each point of configuration space (at each time). Can we understand this as a density of some things?

A single point in configuration space specifies the locations of all particles, a way all things might be arranged, a way the world might be. If there is only one world, then only one point in configuration space is special: it accurately captures where all the particles are. If there are many worlds, then many points in configuration space are special: each accurately captures where the particles are in some world. We could describe how densely packed these special points are, which regions of configuration space contain many worlds and which regions contain few. We can understand |Ψ|2 as giving the density of worlds in configuration space. This might seem radical, but it is the natural extension of the answer to the dreamer’s question depicted in figure 3.

Now that we have moved to a theory with many worlds, the first problem above can be answered: The reason that we only see one particle hit the detector in the double-slit experiment is that only one of the particles in figure 3 is in our world. When the particles hit the detection screen at the end we only see our own. The rest of the particles, though not part of our world, do interact with ours. They are responsible for the swerves in our particle’s trajectory. (Because of this feature, Hall, Deckert, and Wiseman have coined the name “Many Interacting Worlds” for the approach.)

Figure 4: The evolution of particles in figure 3 with the particle that lives in our world highlighted.

No matter how knowledgeable and observant you are, you cannot know precisely where every single particle in the universe is located. Put another way, you don’t know where our world is located in configuration space. Since the regions of configuration space where |Ψ|2 is large have more worlds in them and more people like you wondering which world they’re in, you should expect to be in a region of configuration space where|Ψ|2 is large. (Aside: this strategy of counting each copy of oneself as equally likely is not so plausible in the old many-worlds interpretation.) Thus the connection between |Ψ|2 and probability is not a fundamental postulate of the theory, but a result of proper reasoning given this picture of reality.

There is of course much more to the story than what’s been said here. One particularly intriguing consequence of the new approach is that the three sentence characterization of Newtonian physics with which this post began is met. In that sense, this theory makes quantum mechanics look like classical physics. For this reason, in my paper I gave the theory the name “Newtonian Quantum Mechanics.”

Emily Lakdawalla - The Planetary Society Blog

Like A Bad Penny: Methane on Mars
With the announcement of Curiosity's detection of methane on Mars, Nicholas Heavens gives us a guide to the history of methane detection on Mars, a discussion of its scientific significance, and a few things to consider when hearing about and asking about the detection.

The n-Category Cafe

Turing's Legacy

You’ve probably heard about The Imitation Game, a film about Alan Turing’s life starring Benedict Cumberbatch. Maybe you’ve seen it.

On Sunday, the Edinburgh Filmhouse hosted a special event, “The Maths Behind The Imitation Game”, organized by Edinburgh undergraduates and the department’s Mathematics Engagement Officer, Julia Collins. To my surprise, it was packed out, with a hundred or so people in the audience, and more queuing for returns. Someone did a great job on publicity.

The event consisted of three talks, followed by Q&A. I gave one of them. Later, Julia wrote a blog post on each talk — these are nicely-written, and say much more than I’m going to say here.

• John Longley from Informatics spoke on computability and abstract notions of computation. Julia’s write-up is here.

• I spoke on the legacy of Turing’s code-breaking work at Bletchley Park, comparing and contrasting things then and now. The notes for my talk are here, and Julia’s post on it is here.

• Jamie Davies, an expert on the formation of tissues in mammals, spoke on the aspect of Turing’s work that’s perhaps least familiar to pure mathematicians: pattern formation and morphogenesis. For instance, you once consisted of just a single pair of cells. How did something so simple know how to develop into something as complex as you? Julia’s post is here.

Symmetrybreaking - Fermilab/SLAC

Deck the halls with Nobel physicists

Symmetry presents a physics twist on the craft of cutting paper snowflakes.

If you’re looking for a way to decorate for the holidays while also proudly declaring your love of science, symmetry has got your back. Below you’ll find templates for paper snowflakes with winners of the Nobel Prize in Physics incorporated into the designs.

With the help of a printer, paper, an X-acto knife (preferably with some sharp replacement blades at the ready) and a cutting board or mat, you can transform your home into a flurry of famous physicists.

Simply download the snowflake templates, print them out, follow the folding instructions, and cut out the gray areas, making sure to cut through every layer of paper (but not your fingers!). Then unfold the paper and revel in your creation.

Practice makes perfect, but remember, no two snowflakes are supposed to be alike anyway.

Albert Einstein

Energy and mass may be equivalent, but this Albert Einstein snowflake is beyond compare.

Marie Curie

Double Nobel Laureate Marie Curie radiates charm in this snowflake design.

Erwin Schrödinger

Is it an Erwin Schrödinger snowflake with cats on it, or is it a cat snowflake with Erwin Schrödingers on it? You won’t know until you make it.

For advanced snowflake-making techniques, see our instructional video.

Like what you see? Sign up for a free subscription to symmetry!

Peter Coles - In the Dark

Contact

As I mentioned in my previous post, yesterday evening  I attended the opening of a new show at the Fondation Louis Vuitton in Paris. The first thing to say is that the Fondation Louis Vuitton building, designed by Frank Gehry, is an absolutely amazing structure. It was dark and rainy when I arrived there yesterday and I failed to get any decent pictures of the outside but if you google around you will see what I mean. The interior of the building is an extraordinary as the outside; indeed, it’s such a complex topology that the distinction between inside and outside gets completely lost. It’s definitely a work of art in its own right and enormous fun to wander around, although some of the terraces and balconies are not suitable for those of us who are afraid of heights especially since the only barriers are transparent.

Anyway, the installation I mainly went to see, by Olafur Eliasson,  called Contact, is built around two large spaces on the lower ground floor of the Fondation Louis Vuitton building. The first room is semi-circular in shape and darkened. Along what would be the diameter were it a full circle there is a mirror, just in front of the centre of which there is a bright light surrounded by metallic structure in the form of a mesh. The light illuminates a strip of the circular wall, with darkness above and below, and not only casts a shadow of the mesh against the curved wall but also does the same for the people in the room. The radius of the semicircle is about 25 metres so the room can accommodate many people.

First impressions entering this space are quite strange. First, the room seems to be exactly circular. Then you realise there is a mirror and the mixture of geometrical and human shadows on the circular section of wall. Once you have taken in the true geometry, however, there is stull the fun of watching how people behave within it. Like many of Olafur’s works, this one is as much created by the people who enter the room as it is by the artist.

My phone wasn’t really up to taking pictures of this – and in any case it’s something to be experience rather than seen in a photograph, but here are some attempts. In this one,  very large shadow in the middle is mine:

The second room is a quadrant rather than a semicircle, with mirrors along the two straight edges creating the impression of a complete circle. This time, instead of a single point of light in the centre there is a horizontal illuminated stripe of an intense orange-red which, in the mirrors, creates in the viewer the impression of being in the middle of a ring of light.

My first impression when I entered this part of the installation was to recall some of the lighting effects near the end of the film Close Encounters of the Third Kind:

This is evocative of attempts that have been made from time to time to construct cosmological models with a compact topology, such as a finite flat space with its edges identified to form a torus.

In between these two large spaces there are a number of smaller pieces involving curved mirrors devices that invert and otherwise distort the images of people moving around inside the exhibition, one in particular producing an amazing holographic effect. Knowing how these things work does not diminish their power to amaze and to make you want to reach out and try to touch what is not really there..

Anyway, that’s all just a taster. You really have to see it to appreciate it. It’s a show that asks very interesting questions about we use light in order to perceive space and indeed how we construct space itself through our own imagination.

Lubos Motl - string vacua and pheno

Landscape of some M-theory $$G_2$$ compactifications: 50 million shapes
The first hep-th paper today is
The Landscape of M-theory Compactifications on Seven-Manifolds with $$G_2$$ Holonomy
by David Morrison and James Halverson. The most important classes or descriptions of superstring/M-theory compactifications (or solutions) that produce realistic physics are
1. heterotic $$E_8\times E_8$$ strings on Calabi-Yau three-folds, string theorists' oldest promising horse
2. heterotic Hořava-Witten M-theory limit with the same gauge group, on Calabi-Yaus times a line interval
3. type IIB flux vacua – almost equivalently, F-theory on Calabi-Yau four-folds – with the notorious $$10^{500}$$ landscape
4. type IIA string theory with D6-branes plus orientifolds or similar braneworlds
5. M-theory on $$G_2$$ holonomy manifolds
There are various relationships and dualities between these groups that connect all of them to a rather tight network. All these compactifications yield $$\NNN=1$$ supersymmetry in $$d=4$$ at some point which is then expected to be spontaneously broken.

Halverson and Morrison focus on the last group, the $$G_2$$ compactifications, although they don't consider "quite" realistic compactifications. To have non-Abelian gauge groups like the Standard Model's $$SU(3)\times SU(2)\times U(1)$$, one needs singular seven-dimensional $$G_2$$ holonomy manifolds: the singularities are needed for the non-Abelian enhanced group.

They are satisfied with smooth manifolds whose gauge group in $$d=4$$ is non-Abelian, namely $$U(1)^3$$.

Recall that $$G_2$$ is the "smallest" among five simple exceptional Lie groups – the others are $$F_4,E_6,E_7,E_8$$. $$G_2$$ is a subgroup of $$SO(7)$$, the group rotating a 7-dimensional Euclidean space, but instead of allowing all 21 $$SO(7)$$ generators, $$G_2$$ only allows 2/3 of them, namely 14, those that preserve the multiplication table between the 7 imaginary units in the Cayley algebra (also known as octonions).

It's a beautiful structure. The preservation of the multiplication table, the antisymmetric tensor $$m_{ijk}$$ where $$i,j,k\in \{1,2,\dots , 7\}$$, is equivalent to the preservation of a spinor $$s$$ in the 8-dimensional real spinor representation of $$Spin(7)$$. After all,$m_{ijk} = s^T \gamma_{[i} \gamma_j \gamma_{k]} s.$ And it's this conservation of "one spinor among eight" that is responsible for preserving one eighth of the original 32 real supercharges in M-theory. We are left with 4 unbroken supercharges or $$\NNN=1$$ in $$d=4$$.

Pretty much all the other groups deal with six-dimensional compact manifolds of the "hidden dimensions". In the M-theory case, we have eleven dimensions in total which is why the $$G_2$$ holonomy manifolds are seven-dimensional. So the dimensionality is higher than for the 6-dimensional manifolds in string theory.

You may say that having a "higher number of dimensions", like in M-theory, means to "do a better job in translating the physics to geometry". We are geometrizing a higher percentage of the physical properties of the geometrization – which some people could consider to be a "clear aesthetic advantage". And the $$G_2$$ compactifications treat this maximum number of (seven) compactified dimensions on equal footing which may be said to be "nice", too. More physical properties deciding about the particle spectrum are encoded in the geometric shapes of the compatified 7 dimensions; fewer of them are carried by "matter fields" or "branes" living on top of the compactified dimensions. All these comments are mine but I guess that string theorists including the authors of this paper would generally endorse my observations.

(The type IIB vacua may also be viewed as "12-dimensional" F-theory on 8-dimensional manifolds, Calabi-Yau four-folds, and in some sense, because of these 8 extra dimensions, F-theory geometrizes even a "higher fraction of physics" than M-theory. It may translate some fluxes to a topology change of the 8-dimensional manifold. But unlike M-theory's 7 dimensions, the 8 dimensions in F-theory are not treated on completely equal footing – two of them have to be an infinitesimal toroidal fiber.)

These differences have an impact on the counting of the number of vacua. You have heard that the type IIB flux vacua lead to $$10^{500}$$ different solutions of string theory. They are built by adding fluxes and branes to the compactified dimensions. The fluxes and branes are "decorations" of a geometry that is given to start with. But the number of topologically distinct 6-dimensional manifolds used in these games is of order 30,000 (at least if we assume that each choice of the Hodge numbers $$h^{1,1}$$ and $$h^{1,2}$$ produces a unique topology which I believe is close to the truth because if there were a huge excess, almost all arrangements of these small enough Hodge numbers would be realized by a known topology which is known not to be the case), even though this upper class may be built in many ways, sometimes from millions of building blocks. On the other hand, the decoration may be added on top of the geometry in "googol to the fifth or so" different ways.

As I said, M-theory has "more dimensions of the underlying geometry" and "fewer decorations". Instead of 30,000 different topologies, they show that some recent construction produces something like 500 million different topologies, i.e. half a billion of allowed seven-dimensional manifolds that are so qualitatively different that they can't be connected with each other continuously, through non-singular intermediate manifolds. But there's nothing much to add (matter fields' backgrounds, fluxes, branes) here, so this is pretty much the final number of the vacua. (The four-form fluxes $$G_4$$ over 4-cycles of the manifold may be nonzero but for any allowed compactification, its cousin with $$G_4$$ equal to zero is allowed, too. And nonzero values of $$G_4$$ qualitatively change the story on moduli stabilization – by adding a superpotential term that most researchers seem to find unattractive, at least now.)

The 500-million class of seven-dimensional $$G_2$$ compactifications was constructed by Kovalev (and those who fixed some of his errors and extended the method). The method is known as TCS, the "twisted connected sum". One starts with two Calabi-Yau three-folds times a circle, twists them, and glues them in such a way that the final result is guaranteed to have $$G_2$$ holonomy. It's probably no coincidence that 500 million is very close to the number of "subsets with two elements" of a set with 30,000 elements. The information carried by the topology of a $$G_2$$ holonomy manifold could be very close (the same? Probably not) to the information carried by two Calabi-Yau three-folds.

It seems to me that this method betrays some dependence on the complex geometry and Calabi-Yaus. This is sort of an undemocratic situation. The laymen often dislike complex numbers and fail to realize that complex numbers are more fundamental in natural mathematics (e.g. calculus and higher-dimensional geometry) than e.g. real numbers. However, professional mathematicians do not suffer from this problem, of course. They do realize that complex numbers are more natural. And I would argue that the complex geometries and other things may even be "overstudied" relatively to other things.

My feeling is that the pairing of the dimensions into "complex dimensions", something that is a part of the Calabi-Yau manifolds, is intrinsically linked to the supersymmetry as realized in perturbative string theory because the field $$B_{\mu\nu}$$ coupled to the fundamental strings' world sheets has two indices, just like the metric tensor. That's why they're naturally combined into some complex tensors with two indices and why the spacetime dimensions end up paired. The "complex-like" character of D-brane gauge groups, like $$U(N)$$, is probably a sign of the same character of perturbative string theory that loves bilinear invariants and therefore complex numbers. Lots of things are known and solvable.

On the other hand, M-theory likes compactifications with holonomies like $$G_2$$ that also has a cubic (or quartic, it's equivalent) invariant, a higher-than-bilinear one. Enhanced gauge groups from singularities are not just $$U(N)$$-like, membranes are coupled to a 3-form gauge potential $$C_{\lambda\mu\nu}$$, not a 2-form gauge potential $$B_{\mu\nu}$$, and this is one of the sources of the cubic and higher-order structures. That's a heuristic argument why exceptional Lie groups and other things that go "beyond complex numbers" are more frequently encountered in M-theory but not in perturbative string theory.

The exceptional Lie groups and cubic invariants are perhaps "more exceptional" and "harder to solve" which is why our knowledge of the M-theory compactifications and $$G_2$$ holonomy manifolds is probably less complete than in the case of the Calabi-Yau manifolds. Perturbative methods are usually inapplicable because there's no solvable "zeroth order approximation": M-theory wants couplings of order one and the dilaton or the string coupling is no longer adjustable (because the extra dimension whose size dictates the dilaton has been used as one dimension, some material to construct the 7-dimensional geometry from which it cannot be separated).

And we usually reduce the $$G_2$$ manifolds – which are odd-dimensional and therefore obviously not complex – to some complex manifolds. Couldn't we discuss these manifolds without any reference to the complex ones? One may have a feeling that it should be possible, for the sake of democracy – the classes of the vacua have the same $$\NNN=1$$ supersymmetry and may be expected to be treated more democratically – but this feeling may be wrong, too. Maybe the exceptional groups and M-theory should be viewed as some "strange derivatives" of the classical groups and string theory based on bilinear things, after all, and the democracy between the descriptions is an illusion.

Back to the paper.

They discuss these 500 million $$G_2$$ manifolds and various membrane instantons and topological transitions in between them, along with the spectra of the models and the Higgs vs Coulomb branches. Most of this work deals with non-singular $$G_2$$ manifolds that produce Abelian gauge groups in $$d=4$$ only but in this context, it's natural to expect that insights about the compactifications that allow the Standard Model or GUT gauge groups, for example, are "special cases" of the constructions above – or "special cases of a generalization" of the TCS construction that also allows singularities.

Concerning the right compactification, I think it is "very likely" that our Universe allows a description in terms of one of the five compactifications mentioned at the top. The anthropic people think that the class with the "overwhelming majority of the solutions", the type IIB flux vacua, is almost inevitably the most relevant one. But I completely disagree. There's no rational argument linking "the number of solutions in a class" with the "probability that the class contains the right compactification".

I think it is much more rational to say that each of the five classes above has about 20% probability of being relevant. That is my idea about the fair Bayesian inference: each comparably simple, qualitatively different hypothesis (in this case, each of the 5 classes of stringy compactifications) should be assigned the same or comparable prior probability, otherwise we are biased. (The correct vacuum may also allow two or many different dual descriptions.) If the "last 20%" are relevant and our world is a $$G_2$$ compactification of M-theory, it may ultimately be sufficient to eliminate about 500 million compactifications in total and pick the right one that passes some tests. It's plausible that the right compactification could be found if that's true. It may end up looking very special for some reason, too.

We don't know yet but I think it's obviously right to try to get as far as we can because the 5 descriptions of superstring/M-theory mentioned at the top seem to be the contemporary physicists' only strong candidates for a theory of Nature that goes beyond an effective quantum field theory and this situation hasn't changed for a decade or two.

December 15, 2014

Christian P. Robert - xi'an's og

an extension of nested sampling

I was reading [in the Paris métro] Hastings-Metropolis algorithm on Markov chains for small-probability estimation, arXived a few weeks ago by François Bachoc, Lionel Lenôtre, and Achref Bachouch, when I came upon their first algorithm that reminded me much of nested sampling: the following was proposed by Guyader et al. in 2011,

To approximate a tail probability P(H(X)>h),

• start from an iid sample of size N from the reference distribution;
• at each iteration m, select the point x with the smallest H(x)=ξ and replace it with a new point y simulated under the constraint H(y)≥ξ;
• stop when all points in the sample are such that H(X)>h;
• take

$\left(1-\dfrac{1}{N}\right)^{m-1}$

as the unbiased estimator of P(H(X)>h).

Hence, except for the stopping rule, this is the same implementation as nested sampling. Furthermore, Guyader et al. (2011) also take advantage of the bested sampling fact that, if direct simulation under the constraint H(y)≥ξ is infeasible, simulating via one single step of a Metropolis-Hastings algorithm is as valid as direct simulation. (I could not access the paper, but the reference list of Guyader et al. (2011) includes both original papers by John Skilling, so the connection must be made in the paper.) What I find most interesting in this algorithm is that it even achieves unbiasedness (even in the MCMC case!).

Filed under: Books, Statistics, University life Tagged: arXiv, extreme value theory, Hastings-Metropolis sampler, Metropolis-Hastings algorithms, nested sampling, Poisson process, rare events, unbiasedness

Characterizing Cepheid Light Curves
Title: New NIR light-curve templates for classical Cepheids

Authors: L. Inno et al.

Institution of First Author: Department of Physics, University of Rome Tor Vergata

Distance is a tricky thing to measure in astronomy. We can’t use tape measures or rulers, and even more sophisticated methods like laser ranging are only good for the very nearest of neighbors, like the moon. To figure out how far away other astrophysical objects are, astronomers use the cosmic distance ladder. The cosmic distance ladder starts with objects that are close enough for us to get direct measures on their distance (usually though parallax) and then uses those fundamental distances to calibrate the distance farther out. Each successive measurement of distance from a new phenomena builds upon the measurements before it, hence the name. One type of distance indicator we use are standard candles (there are ‘standard rulers’ as well, but those are less common). Standard candles have a known intrinsic luminosity, so we can determine their distances from how bright we observe them to be.

Henrietta Swan Leavitt

Cepheids, which have been previously been mentioned in several astrobites, are stars that vary in magnitude in a periodic fashion. Cepheid luminosities are proportional to the lengths of their periods, something known as the period-luminosity relation (first discovered by the brilliant Henrietta Leavitt while she was working as a human “computer” at the Harvard College Observatory), which makes them good standard candles. Since an object’s brightness depends on its distance from us, we can generally only measure intrinsic luminosities if we know how far away it is. With Cepheids, however, we can measure their periods to determine their intrinsic luminosities, and from there determine their distances. They are also especially important because they are one of the first “rungs” in the cosmic distance ladder.

Figure 1: This is figure 5 from Madore & Freedman 1991. It shows the variations in the amplitude and the phase at which the Cepheid reaches maximum light across many different bands. The top light curves are at ultraviolet and optical wavelengths, and the bottom few in red and near-infrared, out to 2.2 microns for the K band. Note the distinctive ‘sawtooth’ shape in the shorter wavelengths, which becomes more sinusoidal at longer wavelengths.

Characterizing Cepheids

Measuring the mean magnitude or period of a Cepheid, however, can be a pretty demanding task in its own right. A Cepheid’s light curve looks different in different wavelengths (as shown in Figure 1, taken from Madore and Freedman 1991). The shorter-wavelength bands like the B and V-bands have light curves with larger amplitudes of variation and more asymmetry than the light curves in longer-wavelength near-infrared bands like J, H, and K. This makes it easier to detect and characterize the Cepheids in the B and V bands, but harder to accurately determine the mean magnitude of a Cepheid in those wavelengths, since we have to know accurately what phase of the light curve we are observing in order to get a good measurement of the mean magnitude. In practice, we often want to use measure the periods using light curves from shorter wavelengths and measure the mean magnitudes using light curves from longer wavelengths.

Figure 1: Figure 4 from the paper, showing the merged Cepheid light curves and templates in ten period bins for fundamental mode Cepheids (Cepheids that pulse without any stationary radial ‘nodes’). The P refers to the range in period in days and J, H, and K are three wavelength bands, with K, the longest, at 2.2 microns. The green line indicates the multi Gaussian templates and the red line the Fourier series templates.

Near infrared (NIR) observations, however, are costlier than optical observations because it is more difficult to remove the background sky from NIR observations and because the camera technology is not as advanced in the infrared as it is in the optical. As a result, we have fewer observations of Cepheids in those wavelengths. This is where light curve templates can help us. We’ve already mentioned that a there’s a relationship between a Cepheid’s period and luminosity, but the shape of a Cepheid light curve is also related to its period. By putting together observations of many Cepheids, we can create template light curves that accurately predict the shape of a Cepheid’s light curve for a given period and in a given wavelength. Then, using the templates, we can get an estimate of a Cepheid’s mean magnitude in the NIR with just one observation.

New NIR Light Curve Templates

Figure 3: Figure 11 from the paper, which shows the improvements in the residuals of their templates (red and green) over older NIR templates (blue). Delta J is the difference in the J-band between the true mean magnitude and the and the mean magnitude computed using the J-band templates and a single mock observation. The red and green indicate the different fit functions they used for their templates while the blue points are residuals from a set of NIR templates from 2005. The bin numbers just indicate the period duration they tested. The red and green points have a mean of zero (less than 0.001 mag) and uncorrelated residuals, whereas the blue points have a mean of about 0.001 mag and suffer from non-symmetric, phase-dependent residuals not present in the former two.

The authors of today’s paper have created new NIR Cepheid light curve templates that can be used in helping us measure the magnitudes, and thus, distances to Cepheids much more accurately. The templates cover a wide range of periods – from 1 to 100 days – and are based on a sample of 200 Cepheids (over 3 times the number used previously in making NIR templates).

Traditionally, the periods have been measured from the maximum of one period to the maximum of the next, but this can introduce significant errors for Cepheids whose light curves look like they have double or flatter peaks (a result of the Hertzsprung Progression) because it is difficult to determine exactly when they are at maximum light. The authors of today’s paper take a different approach: they make use of the ‘sawtooth’ shape of the light curves (as seen in Figure 2), where the brightness of the star increases rapidly. Using this steep rise to anchor the period is more accurate than using the peak. This method also allowed the authors of today’s paper to eliminate the phase-dependent residuals present in previous templates. Finally, in addition to fitting the light curves with (a more commonly-used) seventh-order Fourier series, the authors also tried fits using multiple period Gaussians. The period Gaussian functions allow them to get good fits with fewer parameters (from 15 to 9) and to be less sensitive to spurious features in the data.

Upon applying their NIR templates to a single NIR observation, the authors are able to provide mean magnitudes that are 80% more accurate than a mean magnitude estimated from just one data point. This brings the average error in magnitude to less than 0.02 mag. This error is less than the intrinsic scatter of the period-luminosity relation, so it means that these templates allow the mean magnitude of a Cepheid to be measured to the precision limit with just one NIR observation. The results of this paper will bring us closer than ever to accurate determinations of distance.

Emily Lakdawalla - The Planetary Society Blog

Reporting from the 2014 Fall Meeting of the American Geophysical Union
In San Francisco, in an annual tradition, more than 20,000 geologists are descending on the Moscone Center. I'll be attending #AGU14 this week, but you can also watch press briefings and many of the sessions online.

Peter Coles - In the Dark

Arrivé à Paris

Well, here I am in a misty and murky and rather cold Paris. My first trip on the Eurostar from St Pancras as it happens. I’ve used the train to get to Paris before, but the last time was a long time ago when it departed from a temporary station at Waterloo. Anyway, there’s a direct train from Brighton to St Pancras International. Although it was about half an hour late, I still had time for a bite to eat before boarding. The train was pretty full, but ran on time and I got into Gare du Nord just before 4pm local time. A short (and inexpensive) trip on the Metro brought me to the hotel where I’ll be staying the night.

There is a conference going on in Paris this week about Planck but that’s not why I’m here. In fact I’m attending the opening of “Contact”, an exhibition by Olafur Eliasson at the Fondation Louis Vuitton.

I was toying with the idea of combining this event with the Planck meeting, but (a) I’ve got too much to do to stay for the whole week and (b) I don’t think there’ll be much new at the Planck meeting anyway.

Anyway, Olafur very kindly asked me to write something for the  catalogue, as the exhibition has something of an astronomical theme and I guess that’s why I got the VIP invitation. There’s something called a cocktail dinatoire afterwards which I presume involves large amounts of alcohol. That may fortify me for the impending REF results, which are due out later this week..

Anyway, I’ll post about the exhibition if I get time tomorrow morning before the  journey home. It doesn’t open for the general public until Wednesday 17th December, by the way, in case you’re in Paris and thinking of taking a look for yourself.

arXiv blog

Why Neural Networks Look Set to Thrash the Best Human Go Players for the First Time

One of the last bastions of human mastery over computers is about to fall to the relentless onslaught of machine learning algorithms.

Computers are rapidly beginning to outperform humans in more or less every area of endeavor. For example, machine vision experts recently unveiled an algorithm that outperforms humans in face recognition. Similar algorithms are beginning to match humans at object recognition too. And human chess players long ago gave up the fight to beat computers.

Jester - Resonaances

Update on the bananas
One of the most interesting physics stories of this year was the discovery of an unidentified 3.5 keV x-ray  emission line from galactic clusters. This so-called bulbulon can be interpreted as a signal of a sterile neutrino dark matter particle decaying into an active neutrino and  a photon. Some time ago I wrote about the banana paper that questioned the dark matter origin of the signal. Much has happened since, and I owe you an update. The current experimental situation is summarized in this plot:

To be more specific, here's what's happening.

•  Several groups searching for the 3.5 keV emission have reported negative results. One of those searched for the signal in dwarf galaxies, which offer a  much cleaner environment allowing for a more reliable detection. No signal was found, although the limits do not exclude conclusively the original bulbulon claim. Another study looked for the signal in multiple galaxies. Again, no signal was found, but this time the reported limits are in severe tension with the sterile neutrino interpretation of the bulbulon. Yet another study failed to find the 3.5 keV line in  Coma, Virgo and Ophiuchus clusters, although they detect it in the Perseus cluster. Finally, the banana group analyzed the morphology of the 3.5 keV emission from the Galactic center and Perseus and found it incompatible with dark matter decay.
• The discussion about the existence of the 3.5 keV emission from the Andromeda galaxy is  ongoing. The conclusions seem to depend on the strategy to determine the continuum x-ray emission. Using data from the XMM satellite, the banana group fits the background in the 3-4 keV range  and does not find the line, whereas this paper argues it is more kosher to fit in the 2-8 keV range, in which case the line can be detected in exactly the same dataset. It is not obvious who is right, although the fact that the significance of the signal depends so strongly on the background fitting procedure is not encouraging.
• The main battle rages on around K-XVIII (X-n stands for the X atom stripped of n-1 electrons; thus, K-XVIII is the potassium ion with 2 electrons). This little bastard has emission lines at 3.47 keV and 3.51 keV which could account for the bulbulon signal. In the original paper, the bulbuline group invokes a model of plasma emission that allows them to constrain  the flux due to the K-XVIII emission from  the  measured ratios of the strong S-XVI/S-XV and Ca-XX/Ca-XIX lines. The banana paper argued that the bulbuline model is unrealistic as it  gives inconsistent predictions for some plasma line ratios. The bulbuline group pointed out that the banana group used wrong numbers to estimate the line emission strenghts. The banana group maintains that their conclusions still hold when the error is corrected. It all boils down to the question whether the allowed range for the K-XVIII emission strength assumed by the bulbine group is conservative enough. Explaining the 3.5 keV feature solely by K-XVIII requires assuming element abundance ratios that are very different than the solar one, which may or may not be realistic.
•  On the other hand, both groups have converged on the subject of chlorine. In the banana  paper it  was pointed out that the 3.5 keV line may be due to the Cl-XVII (hydrogen-like chlorine ion) Lyman-β transition which happens to be at 3.51 keV. However the bulbuline group subsequently derived limits on the corresponding Lyman-α line at 2.96 keV. From these limits, one can deduce in a fairly model-independent way that the contribution of Cl-XVII Lyman-β transition is negligible.

To clarify the situation we need more replies to comments on replies, and maybe also  better data from future x-ray satellite missions. The significance of the detection depends, more than we'd wish, on dirty astrophysics involved in modeling the standard x-ray emission from galactic plasma. It seems unlikely that the sterile neutrino model with the originally reported parameters will stand, as it is in tension with several other analyses. The probability of the 3.5 keV signal being of dark matter origin is certainly much lower than a few months ago. But the jury is still out, and it's not impossible to imagine that more data and more analyses will tip the scales the other way.

Further reading: how to protect yourself from someone attacking you with a banana.

CERN Bulletin

Service availability during the annual closure 2014/2015

Flying Free: A Supermassive Black Hole Kicked Out Of Its Galaxy
Authors: Michael Koss, Laura Blecha, Richard Mushotzky, Chao Ling Hung, Sylvain Veilleux, Benny Trakhtenbrot, Kevin Schawinski, Daniel Stern, Nathan Smith, Yanxia Li, Allison Man, Alexei V. Filippenko, Jon C. Mauerhan, Kris Stanek, David Sanders
Title: SDSS1133: An Unusually Persistent Transient in a Nearby Dwarf Galaxy
First Author’s Institution: ETH Zurich

The space between galaxies, long thought to be a  near empty void, is now rapidly being revealed to be home to a host of astronomical phenomena. We’ve seen stars flying free of their galaxies, and discovered that the Universe is built on a cosmic web  of dark matter. Now astronomers may have added a new type of intergalactic resident to the list: a super-massive black hole, a million times the mass of the Sun, kicked out from its home galaxy.

The search for such evicted black holes was prompted by the budding field studying gravitational waves, ripples in space time caused by the interactions of massive objects. Some theories suggested that in a merger between two super massive black holes, which are thought to be present at the core of most, if not all, galaxies, the resulting gravitational waves would carry away some of the momentum in the collision. If this caused the remaining momentum to be asymmetric, the newly merged black hole could be given a “kick,” a substantial increase in speed in one direction. Depending on the mass of the host galaxy, this could be enough to throw the black hole out into intergalactic space.

The immense gravity of the black hole means that it would carry with it an accretion disc of gas and dust. As the material in the disc fell on to the black hole, the released energy would shine out across a huge wavelength range. This means that, if the gravitational wave theories are correct, we should be able to observe such objects from the Earth.

However so far, with the exception of a few tentative candidates,  the search for escaped black holes has drawn a blank. The authors of this paper think they may have finally found one.

Top: The candidate escaped back hole, SDSS1133, and its host galaxy, Mrk 177, observed in two different telescope filters. Bottom: A close up of the centre of Mrk 177, with signs of two separate cores created in the events leading up to the expulsion of the black hole.

The authors concentrated their search around dwarf galaxies, as the lower mass of the galaxy should make it easier for a black hole to escape to an observable distance. Their candidate ejected black hole is a bright point of light known as SDSS1133, which sits about two and a half thousand light years from a nearby dwarf galaxy, Mrk 117. This had been observed before now, but, thanks to a non detection in 2005, had been classified as a supernova.

To show that this diagnosis was incorrect and that SDSS1133 was actually escaped black hole, the authors amassed a host of observations stretching back as far as 1950. Combining them with their own data allowed them to see how the brightness of SDSS1133 had changed over the past 63 years. Whereas a supernova should quickly fade away, SDSS1133 had stayed bright for all of that time- in fact it had even got brighter in some observations. The bright, near constant light from the object, which was constrained to an area no larger than a few tens of light years, was entirely consistent with SDSS1133 being an escaped black hole, together with its accretion disc.

In addition to the half-century’s worth of images, the authors also took several spectra of the object. Using Keck, one of the largest telescopes in the world, they found a number of features that matched observation of black holes at the cores of many other galaxies. Emission lines from super-hot iron and calcium matched what was expected from an active black hole, and the lack of features that would have been observed if stars had been present supported the idea that this particular black hole was alone in space.

More spectra of SD1133, obtained at different times over the past decade, could provide one final test. By measuring the width of the emission lines the authors could work out the Doppler shift of the material in the accretion disc, which is induced by the orbital velocity of the disc around the black hole. The orbital velocity is proportional to the mass of the back hole, so these measurements can be used to get a rough idea of that mass. If each spectrum had given a different result for the mass of the black hole then the hypotheses that this was a lone black hole would be in doubt. In the end, the answer came out the same each time- roughly one million times the mass of the Sun.

So have the authors found the first super massive black hole to be kicked out of its galaxy? The observations seem to match it, but there is another possible explanation. Giant stars known as luminous blue variable stars (LBVs), such as the famous Eta Carinae, share many similar observational properties with active back holes. If such a star had been ejected from Mrk 117, then exploded in a supernova, it could match all of the observations of SDSS1133. It would, however, be the longest-lived LBV known, with an unusually bright supernova finishing it off.

The authors conclude that, whilst SDSS1133 could be just an ejected LBV, the bulk of the evidence is in favour of it being the first discovery of a super massive back hole kicked out of its home galaxy. Continued observations of the object will be tested against predictions of how such lonely black holes should evolve, allowing astronomers to solve the mystery for good.

Astronomical Fashion & Design Gifts from Startorialist
For the past year, astronomers Summer Ash and Emily Rice have been scouring the web for all things space when it comes to clothes, accessories, and furnishings and posting them to their blog: Startoralist. They post about everything from astronaut nutcrackers to galaxy painted Doc Martins to nail polish inspired by Neil deGrasse Tyson, but they especially try to highlight designs directly related to the Universe as we know, love, and study it.

We at Astrobites invited Summer to create a holiday gift guide for the stylish and savvy star-lovers in all our lives. Here are her top picks:

Snuggle up with your favorite planet in the comfort of your own bed with these Celestial Buddies.

There’s a moon and a comet but no Pluto. Sick burn.

When ever your data starts getting you down, punch the Universe back with amazing throw pillows by Dia Misuraca.

Cuddle up with NGC 2403.

What’s it like to eat dinner on Mars? We don’t know, but with these solar system plates you can at least eat dinner off of Mars.

Eat your astronaut ice cream in style.

Show your planet love on your feet with these socks from MoMA. Choice of Earth, Venus, or Jupiter.

Venus socks keep your feet toasty, but not at a realistic 450 C.

Prefer your socks to be a little bit out there? These universe socks should do the trick.

The average temperature of the universe is 2.73K. These socks will keep your feet warmer than that.

Cosmic Converse let you strut around and in the Universe at the same time!

This shoe runs half a size large. Perhaps because of inflation?

Pretty much everything from the Lost in Space Etsy store is amazing, but we especially love these “spacelet bracelets” (also customizable).

No word on if you can customize Pluto into a planetary bangle.

Portable and wearable telescope for the astronomer that is always observing.

Make sure you find some good dark sky.

Swatch watches inspired by the celestial sphere.

Accuracy may be relative.

Space up your daily look with these specialty hair bows.

These are also available as bow ties!

Or with these awesome scarves from Slow Factory featuring real NASA Images.

10% of your purchase goes to help refugee women in the Middle East.

This original illustration is adapted from an 1822 star chart.

Let everyone know how “Hubble Gotchu” with this graphic print HST tee.

Hand screen-printed!

If you have any future plans of hitchhiking through the galaxy, you probably need one of these backpacks from SprialUK.

Shipping world-wide!

And if you really want to dress the part, you’ll need a proper “space suit” like these from ShadowplayNYC.

Shirt + scarf for your full-coverage nebula print needs.

Summer Ash is the Director of Outreach for Columbia University’s Department of Astronomy. She is also the “In-House Astrophysicist” for The Rachel Maddow Show and tweets as @Summer_Ash

December 14, 2014

Christian P. Robert - xi'an's og

NIPS 2014

Second and last day of the NIPS workshops! The collection of topics was quite broad and would have made my choosing an ordeal, except that I was invited to give a talk at the probabilistic programming workshop, solving my dilemma… The first talk by Kathleen Fisher was quite enjoyable in that it gave a conceptual discussion of the motivations for probabilistic languages, drawing an analogy with the early days of computer programming that saw a separation between higher level computer languages and machine programming, with a compiler interface. And calling for a similar separation between the models faced by statistical inference and machine-learning and the corresponding code, if I understood her correctly. This was connected with Frank Wood’s talk of the previous day where he illustrated the concept through a generation of computer codes to approximately generate from standard distributions like Normal or Poisson. Approximately as in ABC, which is why the organisers invited me to talk in this session. However, I was a wee bit lost in the following talks and presumably lost part of my audience during my talk, as I realised later to my dismay when someone told me he had not perceived the distinction between the trees in the random forest procedure and the phylogenetic trees in the population genetic application. Still, while it had for me a sort of Twilight Zone feeling of having stepped in another dimension, attending this workshop was an worthwhile experiment as an eye-opener into a highly different albeit connected field, where code and simulator may take the place of a likelihood function… To the point of defining Hamiltonian Monte Carlo directly on the former, as Vikash Mansinghka showed me at the break.

I completed the day with the final talks in the variational inference workshop, if only to get back on firmer ground! Apart from attending my third talk by Vikash in the conference (but on a completely different topic on variational approximations for discrete particle-ar distributions), a talk by Tim Salimans linked MCMC and variational approximations, using MCMC and HMC to derive variational bounds. (He did not expand on the opposite use of variational approximations to build better proposals.) Overall, I found these two days and my first NIPS conference quite exciting, if somewhat overpowering, with a different atmosphere and a different pace compared with (small or large) statistical meetings. (And a staggering gender imbalance!)

Filed under: Kids, pictures, Statistics, Travel, University life Tagged: ABC, Andrey Markov, Canada, compiler, Montréal, mug, NIPS 2014, phylogenetic tree, population genetics, probabilistic programming, random forests, variational Bayes methods

Peter Coles - In the Dark

Parisian Thoroughfare

Ahead of my short trip to Paris tomorrow, of which more anon, I thought I’d post this wonderful performance by quintessential bebop pianist Bud Powell of his own composition, Parisian Thoroughfare. This track comes from the same B;ue Note album The Amazing Bud Powell as the version of Over The Rainbow I posted recently, which is one of the most played on my iPod. I hope you like this,

Clifford V. Johnson - Asymptotia

Results of a College Education?
One of my favourite Mark Twain sayings: "cauliflower is nothing but cabbage with a college education". Spotted these in the Hollywood farmer's market on Sunday: [...] Click to continue reading this post

Happy Birthday Astrobites–a look back at our first four years

Yes, this cake is from 2011. Is that too old to eat?

November 29th, 2010 was the date when the concept of Astrobites was first discussed among a group of (then) first year astronomy graduate students at Harvard.  Over the next few weeks, our first several posts were published on the old version of our site.

In the four years since those days, we’ve published more than a thousand posts covering the latest research results in astronomy, news about our field, classic papers, our personal experiences as graduate students, our readers’ own research, and more.

First and foremost, we want to take this occasion to thank all the graduate student authors, guest posters, readers, and supporters that have made this long and continuing project possible.  We give a special thanks to the Harvard Department of Astronomy, the American Astronomical Society, and to our current and past webhosts (VoxCharta and Harvard Research Computing) for their support.  Perhaps most of all, we need to thank the hundreds of remarkable astronomers who have produced the original research that we have taken such pleasure in reporting on these past years.

But let’s also take this occasion to look back at how we’ve grown and evolved over the years, with congratulations to everyone involved as we continue our work together:

How we’ve grown

Not unlike a human child or a class II young stellar object, Astrobites has grown rapidly and substantially since its birth.  (Fortunately, the timescale for our growth is probably more like the human child.)

Principally, we’ve grown as a student organization.  From the seven Harvard students who started the site, we’ve grown to a collaboration of 62 students from around the world.  Our most recent class of authors, joining us this past October, numbers twelve strong and hail from Ohio to Zurich.

Of course, we’ve all each grown professionally in this time as well.  Not a few of us have graduated and taken up post-doctoral posts or found careers outside of academia.  You can read work by several of our alumns in Astronomy and Sky and Telescope Magazines, on Universe Today, FiveThirtyEight, and one of our own recently joined the AAS press office.

Map of astrobites readership by city from the month of November, 2014.

We’ve been delighted to see our vision for graduate student-led science communication projects pollinate and expand.  Sister sites to astrobites have popped up in other fields, such as Oceanbites, Chembites, and Particlebites.  The Communicating Science workshop series (ComSciCon) that several of our members founded in 2012 has flourished, with 9 national and local events around the country completed or announced.

Finally, it’s been a pleasure to serve, hear from, interact with, and learn about the readers who visit astrobites from around the world (four thousand per week according to our site analytics).  Our most recent readership survey shows us that about 20% of these readers are undergraduate students and 40% are graduate students, exactly the young scientists that we started astrobites to support as they begin their careers in research.  Indeed, 80% of our student readership is pursuing a career in research, while 20% are focused on other goals including outreach and education.

Somewhat to our surprise these past four years, our readership continues to be in no small part composed of non-students, including practicing researchers (12%), educators (6%), and astronomy enthusiasts (17%).  We’re glad that our work has broader impacts than to serve purely as an educational resource.

Kirit Karkare’s route to the South Pole. He cautions that the Mercator projection makes this route look more inefficient than it really is.

In our most recent reader survey, we asked you to tell us your favorite posts from our first thousand published on astrobites.  We’ll share a small selection of these here:

The five part personal research narrative and travelogue of Astrobites author Kirit Karkare on his way to work on BICEP2 at the South Pole remains a favorite.  Kirit’s gorgeous photographs from New Zealand and the Pole can’t hurt.

A number of international students wrote in thanks of Elisabeth Newton’s recent piece, Applying to grad school in the US: a timeline.  We certainly hoped this compendium of information would be invaluable for American undergraduates, but perhaps didn’t realize how especially scarce this information is to those seeking to come here from abroad.

Alice Olmstead clearly touched a nerve with her personal and heartfelt narrative of her decision to transition from a career in research to education.  One reader who wrote in called it “eye-opening.”

Another reader harked way back to one of my own favorite posts from our first year, A Day in the lives of astronomy grad students.  We featured a tableau of everyday stories from graduate students at universities around the world.  I think this remains one of the most realistic resources on the web for students trying to understand what it really means to be a scientist.

Several of you wrote in to highlight Yuan-Sen Ting’s brilliant guest series of astrophysical classics posts on Neutral Hydrogen in the Universe, featuring screenshots of Yuan-Sen’s interactive lyman alpha forest simulator that he later published through EdX.  Guest author Andrew Pontzen also published a great series of interactive cosmological simulations on our site.

Our favorite posts

Sukrit Ranjan boldly explores Mars, Utah.

Recently, we also asked Astrobites authors new and old to reflect back on their own favorite posts from the past several years.  Reflecting our authors’ varied interests, and the diverse subjects we’ve covered on the site over the years, these posts spanned the gamut of astrophysical research.

On the subject of galaxies, Chris Faesi highlighted his review of the relation between gas density and star formation rate and Anna Rosen picked her coverage of recent research in globular cluster dynamics.

In stellar astronomy, Elisa Chisari linked to her writing on the sun’s potential use as a gravitational wave detector and Meredith Rawls offered a look at some consequences of binary common envelope evolution.  Brett Deaton recently wrote about the beautiful imagery that would result from a binary black hole merger.

For the cosmologically minded reader, Andrew Emerick has covered hydrodynamic simulations of the universe and Josh Fuchs wrote about groundbreaking work on the use of white dwarfs as cosmic clocks.

Closer to home, Nick Ballering suggested his piece covering the new hypothesis on the formation mechanism for the dramatically different morphology between the near and far side of our own Moon.  Perhaps the most dynamic sub-field in astronomy over the years we’ve been writing has been exoplanets, and our extensive coverage (nearly 200 posts and counting)  has reflected this.  Ben Montet pointed to his excellent methodological review of how to model correlated noise, for example in exoplanet transit signals.

The oldest of this bunch was Sukrit Ranjan’s 2011 remembrance of his own journey to (an analog) Mars in 2011, which is just the second of three travelogue pieces we’ll list here.  The most recent was Ashley Villar’s piece from just last week, exploring new Kepler observations of the Blazhko effect in RR Lyrae variable stars.

The Internet’s favorite posts

A view from Adele Plunkett’s tour of the ALMA facilty.

And just for fun, let’s look back at the most popular articles we’ve ever posted according to the all-seeing eye of Google Analytics:

1. ALMA: An antenna array is a successful mix of apples and oranges by Adele Plunkett
2. How to use SAO ds9 to examine astronomical images by Nathan Sanders
3. What do we want graduate school to be? by the Astrobites collaboration
4. The verbal GRE: dirty secrets on its role in grad school admission by Zachary Slepian
5. Arecibo detects a fast radio burst by Yvette Cendes
6. Installing and running Gadget-2 by Nathan Goldbaum
7. The first discovery of a Thorne–Żytkow Object? by Yvette Cendes
8. Kepler’s Habitable Worlds by Lauren Weiss
9. Running your first SPH simulation by Nathan Goldbaum
10. The Impossible Star by Korey Haynes

Each of these has received more than 9,000 unique visitors since we started tracking in September, 2011.  For context, the American Astronomical Society has a total membership of 7,000 (with about half that being active participants at meetings, etc.) and astronomy papers typically receive <200 reads in their first year after publication according to data on ADS Labs.

Our goals and our future

Astrobites’ fundamental goals have not changed since it was launched four years ago.  We remain committed to providing an educational resource for your students pursuing careers in research, and to provide writing, outreach, and leadership experience to scientists during their graduate careers.

I would note that, although it’s fun to look at the “top ten” list above, none of us are keeping track of the pageview statistics for Astrobites regularly.  Unlike much of the modern news media, our editorial direction is completely independent of readership metrics.  We’re writing about the things that interest us and that we think will be valuable to our readers.  We’ve never shown ads on the site, and all our authors volunteer their time.

In a media environment that is increasingly corporate sponsored; integrated with advertising; and, in some cases, in danger of sacrificing its objectivity; we think that these operating principles are important for our project.  We’re so glad to know that others do, too.

Clifford V. Johnson - Asymptotia

Tiger’s Jaw
One of the many plants* that look a lot happier after the much-needed rain... [...] Click to continue reading this post

December 13, 2014

Sean Carroll - Preposterous Universe

Slow Life

Watch and savor this remarkable video by Daniel Stoupin. It shows tiny marine animals in motion — motions that are typically so slow that we would never notice, here enormously sped-up so that humans can appreciate them.

Slow Life from Daniel Stoupin on Vimeo.

I found it at this blog post by Peter Godfrey-Smith, a philosopher of biology. He notes that some kinds of basic processes, like breathing, are likely common to creatures that live at all different timescales; but others, like reaching out and grasping things, might not be open to creatures in the slow domain. Which raises the question: what kinds of motion are available to slow life that we fast-movers can’t experience?

Not all timescales are created equal. In the real world, the size of atoms sets a fundamental length, and chemical reactions set fundamental times, out of which everything larger is composed. We will never find a naturally-occurring life form, here on Earth or elsewhere in the universe, whose heart beats once per zeptosecond. But who knows? Maybe there are beings whose “hearts” beat once per millennium.

Quantum Diaries

New books for the physics fan

These recently published popular science books will help you catch up on particle physics news, knowledge and history. Image: Artwork Sandbox Studio, Chicago, with Ana Kova

Looking to stay current on your particle physics knowledge? Here are 10 recent popular science books you might want to check out.

1. Faraday, Maxwell and the Electromagnetic Field: How Two Men Revolutionized Physics

Nancy Forbes, Basil Mahon

Classical unified field theory came from the realization that electricity, magnetism and light all can be explained with a single electromagnetic field.

There is no modern physics without classical unified field theory—heck, there are no electronics without classical unified field theory—and there is no classical unified field theory without Michael Faraday (1791-1867) and James Clerk Maxwell (1831-1879).

The unlikely partners, born four decades apart, shared the achievement of upending a view of the world that had prevailed since Isaac Newton.

“The extraordinary idea put forward by Faraday and Maxwell was that space itself acted as a repository of energy and a transmitter of forces,” write Nancy Forbes and Basil Mahon in Faraday, Maxwell and the Electromagnetic Field: How Two Men Revolutionized Physics.

Faraday was largely self-taught and made important realizations without the benefit of a formal education in mathematics, while Maxwell was regarded as among the most brilliant mathematical physicists of his time. This double biography examines their differing lives and explains how their combined work paved the way for modern physics.

2. The Cosmic Cocktail: Three Parts Dark Matter

Katherine Freese

In The Cosmic Cocktail: Three Parts Dark Matter, physicist Katherine Freese explores the critical place dark matter occupies in our understanding of the cosmos.

It has yet to be observed directly. But, she tells us, dark matter’s day of reckoning might not be far off.

“Some new particles, unlike any from our daily experience, might be tearing through the galaxy,” she writes. “Scientists have already found hints of detection in their experiments… The nature of dark matter is one of the greatest puzzles of modern science, and it is a puzzle we are on the verge of solving.”

Freese, now the new director of the Nordic Institute for Theoretical Physics in Stockholm, admits to spending a disproportionate amount of time on the dance floor of nearby Studio 54 when she should have been focused on her doctoral studies at Columbia University. But she also tells a compelling history of the search for dark matter, from the cantankerous Fritz Zwicky’s early predictions in the 1930s to hopes for an appearance when the Large Hadron Collider fires up again in 2015.

3. The Large Hadron Collider: The Extraordinary Story of the Higgs Boson and Other Stuff that will Blow Your Mind

Don Lincoln

“My goal was to give readers an inside account of the hunt and discovery,” says Fermilab scientist Don Lincoln, a member of CERN’s CMS experiment, of his latest book, The Large Hadron Collider: The Extraordinary Story of the Higgs Boson and Other Stuff that will Blow Your Mind. “Almost all of the similar books have been written by non-physicists and theorists. I went to all the meetings, so I have a unique perspective.”

In the book, Lincoln describes the process of the discovery of the Higgs boson—and explains that it is not the end of the story.

Even though the widely celebrated appearance of the Higgs particle confirmed theorists’ predictions, Lincoln maintains that the relatively light mass of the Higgs raises enough questions to keep physicists awake at night.

“The measurement is quite inconsistent with the Standard Model and the quantum corrections,” he says. “This absolutely screams that there is something still to be found and this could be supersymmetry, extra dimensions, composite Higgs bosons or some other kind of new physics. In short, we know there is something big we’re missing.”

4. The Most Wanted Particle: The Inside Story of the Hunt for the Higgs, the Heart of the Future of Physics

Jon Butterworth

“I wanted it to give readers a sense of what it really feels like to work in a big experiment at such an amazing time and what it meant,” says University College London physicist Jon Butterworth of his book The Most Wanted Particle: The Inside Story of the Hunt for the Higgs, the Heart of the Future of Physics. “This meant occasionally the physics had to go a bit deeper than the common analogies, but also there is a lot of non-physics story which hopefully captures the real-time excitement.”

Butterworth, who works on the ATLAS experiment at CERN, uses a personalized approach to convey a sense of scene. In one chapter, he describes explaining the Higgs discovery to British TV reporter Tom Clarke while the two shoot pool.

He also uses his current hometown in England to describe his workplace at CERN, comparing the size of the Large Hadron Collider tunnel to the size of the London Underground.

The book, released in the UK in May under the title Smashing Physics: Inside the World’s Biggest Experiment, will be released in the US in January 2015.

5. The Perfect Wave: With Neutrinos at the Boundary of Space and Time

Heinrich Pas

Heinrich Pas, a theorist at the Technical University of Dortmund in Germany, studies neutrinos, particles that seem to defy the rules but may hold answers to the deepest questions of the universe.

In The Perfect Wave: With Neutrinos at the Boundary of Space and Time, Pas explains how powerful processes in the cosmos—from the fusion that lights the sun to the magnificent explosions of supernovae—are bound up in the workings of the mysterious particles.

“It is a story of an elementary particle that, just like the Silver Surfer in the superhero cartoons, surfs to the boundaries of knowledge, of the universe and of time itself,” Pas writes. “A story that captivates you as it sucks you into a maelstrom like an oversized wonderland. Jump on your board and hold tight.”

6. The Science of Interstellar

Kip Thorne

Kip S. Thorne, the Feynman Professor of Theoretical Physics Emeritus at Caltech, served as the executive producer for scientific credibility (and flexibility) on the space epic Interstellar. He explains that work in the book The Science of Interstellar.

In the film, astronaut Cooper (Matthew McConaughey) takes leaps and bounds over, under, around and through black holes and wormholes on his quest to find a refugee planet for the population of Earth, whose food supply is devastated by global blight.

Thorne writes that “[s]ome of the science is known to be true, some of it is an educated guess, and some is speculation.”

But he takes all of it seriously; Thorne and his colleagues even wrote a scientific paper based on their computer simulations of the movie’s black hole.

7. The Singular Universe and the Reality of Time

Roberto Mangabeira Unger, Lee Smolin

Physicist Lee Smolin of Canada’s Perimeter Institute for Theoretical Physics, author of the controversial book The Trouble With Physics, collaborated with philosopher and politician Roberto Mangabeira Unger on the new book The Singular Universe and the Reality of Time.

In it, Smolin and Unger argue against the idea of the multiverse and declare that it is time to view the cosmos as being governed by laws that are evolving rather than laws that are immutable. They contend that, “everything changes sooner or later, including change itself. The laws of nature are not exempt from this impermanence.”

8. Time in Powers of Ten: Natural Phenomena and their Timescales

Gerard ‘t Hooft, Stefan Vandoren

In Time in Powers of Ten: Natural Phenomena and their Timescales, Nobel Laureate Gerard ‘t Hooft and theorist Stefan Vandoren, both of Utrecht University in the Netherlands, step back and forth in time from the minutest fractions of a second to the age of the universe and beyond. Observations range from the orbits and rotations of planets and stars, down to the decay times of atoms and elementary particles and back to geological time scales.

“The smallest matter mankind has studied moves considerably faster than the quickest computing processes of the most expeditious machine; while on the other side of the timescale we see planets, stars and entire galaxies of unimaginably old age, some billions of years,” ‘t Hooft and Vandoren write. “Scientists believe they know almost exactly how old the universe is, but even its seemingly eternal lifetime does not constitute a limit for physicists’ research.”

9. Travelling to Infinity: The True Story Behind the Theory of Everything

Jane Hawking

In Travelling to Infinity: The True Story Behind the Theory of Everything, readers are introduced to a young, floppy-haired Stephen Hawking through the eyes of his first wife, Jane Hawking (née Wilde). Hawking published versions of this book in both 1999 and 2007, and the book was reissued this year to accompany the film adaptation, The Theory of Everything.

In the book, Jane describes an early impression of Stephen from a New Year’s party in 1963: “Clearly here was someone, like me, who tended to stumble through life and managed to see the funny side of situations. Someone who, like me, was fairly shy, yet not averse to sharing his opinions, someone who unlike me had developed a sense of his own worth and had the effrontery to convey it.”

Here is a love story in which love is not enough. Hawking leaves and marries one of the nurses who tended him. Jane marries an old family friend. The two have reconciled and are on amicable terms—a good thing when the person writing your life story is your former spouse.

10. What If? Serious Scientific Answers to Absurd Hypothetical Questions

Randall Munroe

Randall Munroe’s stick-figure web comic strip, xkcd, comes with a warning: “This comic occasionally contains strong language (which may be unsuitable for children), unusual humor (which may be unsuitable for adults), and advanced mathematics (which may be unsuitable for liberal-arts majors).”

There are no dumb questions, only humorous and provocative answers from Munroe, a former NASA roboticist, in his book What If? Serious Scientific Answers to Absurd Hypothetical Questions. For example:

“Q – What would happen if the Earth and all terrestrial objects stopped spinning, but the atmosphere retained its velocity?

“A – Nearly everyone would die. THEN things would get interesting…”

In “What If?” what seems like the end is often just the beginning.

Mike Perricone

Tommaso Dorigo - Scientificblogging

The Plot Of The Week: Higgs Decays To WW In ATLAS
The latest paper by the ATLAS Collaboration is a very detailed report of the search for Higgs boson decays to W boson pairs in Run 1 data. The H->WW* process contributes significantly to the total bounty of Higgs boson candidates that the two CERN experiments have been able to collect in the 2011 7-TeV and 2012 8-TeV proton-proton collisions, but the presence of neutrinos in the final state prevents the clean reconstruction of an invariant mass peak, hence the WW* final state has remained a bit "in the shadows" with respect to the cherished ZZ* and gamma-gamma final states.

December 12, 2014

Quantum Diaries

How to make a neutrino beam

Ingredients for a neutrino beam: speedy protons, target, magnetic horn, decay pipe, absorbers. Image adapted from Fermilab

Fermilab is in the middle of expanding its neutrino program and is developing new detectors to study these ghostly particles. With its exquisite particle accelerator complex, Fermilab is capable of creating very intense beams of neutrinos.

Our neutrino recipe starts with a tank of hydrogen. The hydrogen atoms are fed an extra electron to make them negatively charged, allowing them to be accelerated. Once the charged atoms are accelerated, all of the electrons are ripped off, leaving a beam of positive protons. The protons are extracted into either the Booster Neutrino Beamline (BNB) or are further accelerated and extracted into the Neutrino Main Injector beamline (NuMI). Fermilab is the only laboratory with two neutrino beams. Our two beams have different energies, which allows us to study different properties of the neutrinos.

In the BNB, these protons smash into a target to break up the strong bonds of the quarks inside the proton. These collisions are so violent that they produce new quarks from their excess energy. These quarks immediately form together again into lighter composite short-lived particles called pions and kaons.

Since the pions and kaons emerge at different directions and speeds, they need to be herded together. As a bugle tunes your breath into musical notes, a horn of a different type rounds up and focuses the pions and kaons. The BNB horn looks roughly like the bell of a six-foot long bugle. It produces an electric field that in turn generates a funnel-like magnetic field, which directs all of the dispersed pions and kaons of positive electric charge straight ahead. Particles with negative charges get defocused. By switching the direction of the electric field, we can focus the negatively charged particles while defocusing the positive charges.

The focused particles in the BNB beam travel through a 50-meter long tunnel. This is where the magic happens. In this empty tunnel, the pions and kaons decay in flight into neutrinos, electrons and muons. At the end of the decay tunnel is a wall of steel and concrete to stop and absorb any particle that is not a neutrino. Because neutrinos interact so rarely, they easily whiz through the absorbers and on towards the experiments. And that’s the basic formula to make a beam of neutrinos!

A single neutrino beamline can support many experiments because the neutrinos interact too rarely to get “used up.” The BNB feeds neutrinos to MicroBooNE, and most of them go on through to the other side towards the MiniBooNE detector. Similarly, most of those go on through the other side as well and continue traveling to infinity and beyond. Detectors located in this beam measure neutrino oscillations and their interactions.

The NuMI beamline is designed similarly, but uses a different target material, two focusing horns, and a 675-meter decay pipe. The spacing between the two NuMI horns is adjustable, allowing fine-tuning of the neutrino beam energy. The NuMI beamline has higher-energy neutrinos than the BNB and thus studies different properties of neutrino oscillations.

The NuMI beamline feeds neutrinos to the MINERvA experiment and on through to the MINOS near detector. The NuMI beamline then continues about 450 miles through Earth on toward the MINOS far detector in the Soudan mine in Minnesota. By the time the beam reaches the far detector, it is about 20 miles in diameter! By having a near and far detector, we are able to observe neutrino flavor oscillations by measuring how much of the beam is electron neutrino flavor and muon neutrino flavor at each of these two detectors.

The last of the big Fermilab neutrino experiments is NOvA. Its near detector is off to the side of the NuMI beam and measures neutrinos only with a specific range of direction and energy. The NOvA far detector is positioned to measure the neutrinos with the same properties at a greater distance, about 500 miles away in Ash River, Minnesota. By placing the NOvA detectors 3 degrees to the side of the beam’s center, NOvA will get to make more precise oscillation measurements for a range of neutrino energies.

As more experiments are designed with more demanding requirements, Fermilab may expect to see more neutrino beamline R&D and the construction of new beamlines.

Tia Miceli

Sean Carroll - Preposterous Universe

Where Have We Tested Gravity?

General relativity is a rich theory that makes a wide variety of experimental predictions. It’s been tested many ways, and always seems to pass with flying colors. But there’s always the possibility that a different test in a new regime will reveal some anomalous behavior, which would open the door to a revolution in our understanding of gravity. (I didn’t say it was a likely possibility, but you don’t know until you try.)

Not every experiment tests different things; sometimes one set of observations is done with a novel technique, but is actually just re-examining a physical regime that has already been well-explored. So it’s interesting to have a handle on what regimes we have already tested. For GR, that’s not such an easy question; it’s difficult to compare tests like gravitational redshift, the binary pulsar, and Big Bang nucleosynthesis.

So it’s good to see a new paper that at least takes a stab at putting it all together:

Linking Tests of Gravity On All Scales: from the Strong-Field Regime to Cosmology
Tessa Baker, Dimitrios Psaltis, Constantinos Skordis

The current effort to test General Relativity employs multiple disparate formalisms for different observables, obscuring the relations between laboratory, astrophysical and cosmological constraints. To remedy this situation, we develop a parameter space for comparing tests of gravity on all scales in the universe. In particular, we present new methods for linking cosmological large-scale structure, the Cosmic Microwave Background and gravitational waves with classic PPN tests of gravity. Diagrams of this gravitational parameter space reveal a noticeable untested regime. The untested window, which separates small-scale systems from the troubled cosmological regime, could potentially hide the onset of corrections to General Relativity.

The idea is to find a simple way of characterizing different tests of GR so that they can be directly compared. This will always be something of an art as well as a science — the metric tensor has ten independent parameters (six of which are physical, given four coordinates we can choose), and there are a lot of ways they can combine together, so there’s little hope of a parameterization that is both easy to grasp and covers all bases.

Still, you can make some reasonable assumptions and see whether you make progress. Baker et al. have defined two parameters: the “Potential” ε, which roughly tells you how deep the gravitational well is, and the “Curvature” ξ, which tells you how strongly the field is changing through space. Again — these are reasonable things to look at, but not really comprehensive. Nevertheless, you can make a nice plot that shows where different experimental constraints lie in your new parameter space.

The nice thing is that there’s a lot of parameter space that is unexplored! You can think of this plot as a finding chart for experimenters who want to dream up new ways to test our best understanding of gravity in new regimes.

One caveat: it would be extremely surprising indeed if gravity didn’t conform to GR in these regimes. The philosophy of effective field theory gives us a very definite expectation for where our theories should break down: on length scales shorter than where we have tested the theory. It would be weird, although certainly not impossible, for a theory of gravity to work with exquisite precision in our Solar System, but break down on the scales of galaxies or cosmology. It’s not impossible, but that fact should weigh heavily in one’s personal Bayesian priors for finding new physics in this kind of regime. Just another way that Nature makes life challenging for we poor human physicists.

arXiv blog

RoboBrain: The World's First Knowledge Engine For Robots

If you have a question, you can ask Google or Bing or any number of online databases. Now robots have their own knowledge database

One of the most exciting changes influencing modern life is the ability to search and interact with information on a scale that has never been possible before. All this is thanks to a convergence of technologies that have resulted in services such as Google Now, Siri, Wikipedia and IBM’s Watson supercomputer.

CERN Bulletin

Fabiola Gianotti signs her contract as CERN's new Director- General

Today, 12 December 2014, Fabiola Gianotti signed her five-year contract as the new CERN Director-General. Her mandate will begin on 1 January 2016.

Fabiola Gianotti (left) and President of CERN Council Agnieszka Zalewska (right) after the signature of the contract.

The Italian physicist, Fabiola Gianotti was appointed as the Organization’s next Director-General at the 173rd Closed Session of the CERN Council on 4 November. The appointment was formalised this week at the December session of Council.

More news from this week Council meetings can be found here.

CERN Bulletin

2015 Executive Committee: the strength of continuity
The year 2015 will see few changes in the composition of the Executive Committee. On the one hand, Oliver Boetcher enters and becomes the representative of the Staff Association in the Management Board of EN Department. On the other hand, Jaap Panman, who will retire in 2015, leaves the Committee at the end of 2014. We would like to thank Joël Lahaye, who was the departmental representative for EN in 2014, and Jaap for their contributions. The other members of the Committee continue to assume their respective duties, thus ensuring that your Staff Association will have a solid, experienced, effective and cohesive team to cope with the challenges of the new year, with, among others, the key issues of pensions and the 2015 five-yearly review. Your staff delegates hope to be able to count on the active support of all of you to defend the interests of the personnel, past, present, and future, and their families. Sandrine BAUDAT FP Member Oliver BOETCHER EN Member Rachel BRAY GS Member Caroline CAZENOVES TE Communication officer Flavio COSTA IT Member Nicolas DELRUELLE TE Member Juan GARCIA PEREZ TE Secretary Michel GOOSSENS IT President Céline GROBON PH Vice-president Lynda LEROUX HR Member Michael LUDWIG BE Member Alessandro RAIMONDO GS Vice-president, Treasurer Almudena SOLERO DG Training Officer Sébastien ÉVRARD EN Permanent guest Frédéric GALLEAZZI EN Permanent guest Joël LAHAYE EN Permanent guest Yves SILLANOLI TE Permanent guest In italic departmental representatives

Clifford V. Johnson - Asymptotia

The Universe Lives!
(Seems a highly appropriate title to use when up at 4:00am listening to the excellent violent wind and rain storm that's going on outside.) This is mostly a note for fans of the show The Universe, on the History channel, or H2, and channels by other names internationally. I just wanted to say that the show is going to carry on, with a new season coming out early next year! I mention this because it looked for a while (at least a few times) like there wouldn't be another season (after a solid 7 or 8 seasons over as many years), and then at the last minute they greenlit that short season that aired earlier this year with the subtitle "Ancient Mysteries Explained" or something worrying like that (because it sounds a lot like the "Ancient Aliens" show which, well, I'd rather it did not sound anything like...) Then it was not clear again whether that was just a last hurrah or not... Well, it was not, since we've been shooting for several episodes this last month or so! Looks like there will be at least a short season coming, with the same subtitle. I've done some work on a few segments that will appear in two or three episodes. They wanted me to do more but I had a rather busy period coming up and so declined to do any more shooting days after November, so I'll be somewhat fleeting in my appearances, but hope that the physics I did get to talk about is clear and interesting - assuming they use those bits at all (you can never tell). My favourite day was when we were out at Zuma Beach, which I think I mentioned in a short post a while back. The episode focuses on contrasts between Astronomy and Astrology, which is certainly a good topic! I came up with a fun analogy with which to explain a certain idea and we enlisted a group [...] Click to continue reading this post

December 11, 2014

Tommaso Dorigo - Scientificblogging

Travel Blog
While I do intend to update this blog today or tomorrow with a report on a nice new measurement, my blogging activities have generally slowed down a bit this week, as I am traveling. On Monday I flew from Venice to Paris and then to Miami (in a brand new A380 - that was the first time for me on that giant plane). On the next day I flew to Cancun, and then headed to Playa del Carmen where I am currently staying.

Tommaso Dorigo - Scientificblogging

Travel Blog
While I do intend to update this blog today or tomorrow on a nice new measurement, my blogging activities have generally slowed down a bit this week, as I am traveling. On Monday I flew from Venice to Paris and then to Miami (in a brand new A380 - that was the first time for me on that giant plane). On the next day I flew to Cancun, and then headed to Playa del Carmen where I am currently staying.

Tommaso Dorigo - Scientificblogging

Travel Blog
While I do intend to update this blog today or tomorrow on a nice new measurement, my blogging activities have generally slowed down a bit this week, as I am traveling. On Monday I flew from Venice to Paris and then to Miami (in a brand new A380 - that was the first time for me on that giant plane). On the next day I flew to Cancun, and then headed to Playa del Carmen where I am currently staying.

Symmetrybreaking - Fermilab/SLAC

A giant neutrino detector is traveling by truck from the Italian Gran Sasso laboratories to CERN to get ready for a new life.

On Tuesday night a 600-metric-tonne particle detector became the world’s largest neutrino experiment currently on an international road trip.

The ICARUS T600 neutrino detector—the world’s largest liquid-argon neutrino experiment—is on its way from the INFN Gran Sasso laboratories in Italy to European research center CERN on the border of France and Switzerland. Once it arrives at CERN, it will undergo upgrades to prepare it for a second life.

“ICARUS is presently the state-of-the-art technology,” says Nobel Laureate Carlo Rubbia, the leader of the ICARUS experiment. “Its success has demonstrated the enormous potentials of this detector technique… Most of the ICARUS developments have become part of the liquid-argon technology that is now being used is most of the other, more recent projects.”

Since 2010, the ICARUS experiment has studied neutrinos streaming about 450 miles straight through the Earth from CERN to Gran Sasso. Neutrinos come in three types, called flavors, and they switch flavors as they travel. The ICARUS experiment was set up to study those flavor oscillations. Its detector, which works like a huge, three-dimensional camera that visualizes subatomic events, has recorded several thousand neutrino interactions.

Scientists see more experiments in the detector’s future, possibly using a powerful beam of neutrinos already in operation at Fermi National Accelerator Laboratory near Chicago.

The detector is 6 meters wide, 18 meters long and 4 meters high. When in operation, it is filled with ultra-pure liquid argon and about 52,000 wires, which collect signals from particles and can reconstruct 3-D images of a what happens when a neutrino knocks an electron off of an atom of argon.

To prepare the sensitive detector for transport, workers moved its inner chamber on sleds into a shipping container, says Chiara Zarra, the ICARUS movement and transportation coordinator. But getting the experiment out of its home was a challenge, she says. The laboratory layout had changed since ICARUS was first installed, and there were multiple other experiments to maneuver through. A team from CERN helped with planning by creating 3-D simulations of the operation.

Over the course of about a week, the detector will travel on a special equipment transporter through Rome, Genoa and Turin. After that it will cross the Alps through the Mont Blanc tunnel on its way to Geneva.

Like what you see? Sign up for a free subscription to symmetry!

The n-Category Cafe

Integral Octonions (Part 11)

Take a bunch of equal-sized solid balls in 8 dimensions. Pick one… and then get as many others to touch it as you can.

You can get 240 balls to touch it — no more. And unlike in 3 dimensions, there’s no ‘wiggle room’: you’re forced into a specific arrangement of balls, apart from your ability to rotate the whole configuration.

You can continue packing balls so that each ball touches 240 others — and unlike in 3 dimensions, there’s no choice about how to do it: their centers are forced to lie at a lattice of points called the E8 lattice.

If we pick a point in this lattice, it has 240 nearest neighbors. Let’s call these the first shell. It has 2160 second-nearest neighbors. Let’s call these the second shell.

And here’s what fascinates me now…

You can take the first shell, rotate it, and expand it so that the resulting 240 points form a subset of the second shell!

In fact, there are 270 different subsets of this type. And if you pick two of them that happen to be disjoint, you can use them to create a copy of the Leech lattice inside ${\mathrm{E}}_{8}\oplus {\mathrm{E}}_{8}\oplus {\mathrm{E}}_{8}\mathrm\left\{E\right\}_8 \oplus \mathrm\left\{E\right\}_8 \oplus \mathrm\left\{E\right\}_8$ — that is, the direct sum of three copies of the ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ lattice!

There are exactly 17,280 ways to pick two disjoint subsets of this type. And each way gives a distinct embedding of the Leech lattice in ${\mathrm{E}}_{8}\oplus {\mathrm{E}}_{8}\oplus {\mathrm{E}}_{8}\mathrm\left\{E\right\}_8 \oplus \mathrm\left\{E\right\}_8 \oplus \mathrm\left\{E\right\}_8$.

We’re seeing some big numbers here! Some seem harder to understand than others. Though it’s not easy to prove that the ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ lattice gives the largest number of balls that can touch a given central one in 8 dimensions, it’s easy to check by hand that it has 240 points in the first shell, and 2160 in the second shell. This is old, well-known stuff.

Greg Egan discovered the other two numbers using computer calculations. By now we understand one of them fairly well: we found a simple construction that gives 270 subsets of the second shell that are rotated, rescaled versions of the first shell. The construction is nice, because it involves the Fano plane: the projective plane over the field with 2 elements! So, I’ll explain that today.

The number 17,280 remains mysterious.

Why 270?

I want to show you that there are at least 270 subsets of the second shell of the ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ lattice that are rotated, rescaled copies of the first shell. In fact that’s the exact number — but I only know that because I trust Egan’s computing skills. We did, however, figure out a very pretty proof that there are at least 270. Here are the key steps:

1. There’s a rotational symmetry of the ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ lattice mapping any point of the first shell to any point to any other point, and similarly for the second shell.
2. There are 240 points in the first shell.
3. There are 2160 points in the second shell.
4. There are 30 rotated, expanded copies of the first shell containing your favorite point in the second shell.

Item 1 lets us exploit symmetry. Since your favorite point in the second shell is just like any other point, we can construct 30 × 2160 rotated, expanded copies of the first shell in the second shell. But these copies are not all distinct: if we counted them by naive multiplication, we would be overcounting by a factor of 240, since each has 240 points. So, the correct count is

$30×2160/240=30×9=270 30 \times 2160 / 240 = 30 \times 9 = 270 $

as desired.

Why are items 1-4 true?

In Part 4 and Part 5 of these series we saw that the points in the first shell are the vertices of a highly symmetrical polytope, the E8 root polytope. We saw that this polytope has 240 vertices, 2160 7-orthoplex faces, and 17,280 7-simplex faces. Remember, an n-orthoplex is the $nn$-dimensional generalization of an octahedron:

while an n-simplex is the $nn$-dimensional generalization of a tetrahedron:

General facts about Coxeter groups, reviewed in Part 5, imply that the symmetries of the ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ root polytope act transitively on its vertices, its 7-orthoplex faces and its 7-simplex faces. We also saw that each 7-orthoplex face has a vector in the second shell as its outward-pointing normal. Thus there are 2160 points in the second shell, and the symmetries act transitively on these too. This takes care of items 1-3.

So, the only really new fact is item 4: there are 30 rotated, expanded copies of the first shell containing a chosen point in the second shell! This is what I want to show. More precisely, I’ll show that there are at least 30. So far I only know there are at most 30 thanks to Egan’s computer search. We can probably dream up a proof, but we haven’t gotten around to it.

Why 30?

Remember the standard description of the ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ lattice. Define a half-integer to be an integer plus $\frac{1}{2}\frac\left\{1\right\}\left\{2\right\}$. The ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ lattice consists of all 8-tuples of real numbers

$\left({x}_{0},{x}_{1},{x}_{2},{x}_{3},{x}_{4},{x}_{5},{x}_{6},{x}_{7}\right) \left(x_0, x_1, x_2, x_3, x_4, x_5, x_6, x_7\right) $

such that

• the ${x}_{i}x_i$ are either all integers or all half-integers, and
• the sum of all the ${x}_{i}x_i$ is even.

The shortest nonzero vectors in this lattice — the vectors in the first shell — have length $\sqrt{2}\sqrt\left\{2\right\}$, like this:

$\left(1,1,0,0,0,0,0,0\right) \left(1,1,0,0,0,0,0,0\right) $

The second shortest nonzero vectors — the vectors in the second shell — have length $22$, like this:

$\left(1,1,1,1,0,0,0,0\right) \left(1,1,1,1,0,0,0,0\right) $

So, we have the opportunity to find an expanded copy of ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ lattice, dilated by a factor of $\sqrt{2}\sqrt\left\{2\right\}$, inside the ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ lattice.

Our goal is to find 30 such copies containing our favorite point in the second shell. Let’s take this as our favorite:

$\left(2,0,0,0,0,0,0,0\right) \left(2,0,0,0,0,0,0,0\right) $

And here’s the cool part: there’s one such copy for each way to give the set

$\left\{1,2,3,4,5,6,7\right\} \\left\{1,2,3,4,5,6,7\\right\} $

the structure of a projective plane!

Up to isomorphism there’s just one projective plane of order 7: the projective plane over the field of 2 elements, called the Fano plane. It has 7 points and 7 lines, 3 points on each line and 3 lines through each point:

It’s a projective plane in the axiomatic sense: each pair of distinct points lies on a unique line, and each pair of distinct lines intersects in a unique point.

So, how many projective plane structures are there on the set

$\left\{1,2,3,4,5,6,7\right\}? \\left\{1,2,3,4,5,6,7\\right\} ? $

We get one from any way of labelling the diagram above by numbers from 1 to 7. There are $7!7!$ of these labellings. However, not every one gives a distinct Fano plane structure, since the Fano plane has symmetries. Its symmetry group is famous: it’s the second smallest nonabelian simple group, and it has 168 elements. So, we get

$\frac{7!}{168}=\frac{1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7}{24\cdot 7}=30 \frac\left\{7!\right\}\left\{168\right\} = \frac\left\{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7\right\}\left\{24 \cdot 7\right\} = 30 $

different Fano plane structures on the set

$\left\{1,2,3,4,5,6,7\right\} \\left\{1,2,3,4,5,6,7\\right\} $

How can we use one of these Fano plane structures to find an expanded copy of the ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ lattice inside the ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ lattice?

Let ${e}_{i}e_i$ be the $ii$th basis vector of ${ℝ}^{8}\mathbb\left\{R\right\}^8$, where $i=0,1,2,3,4,5,6,7i = 0,1,2,3,4,5,6,7$. We form the lattice consisting of all integer linear combinations of:

• the vectors $2{e}_{i}2e_i$,
• the vectors $±{e}_{0}±{e}_{i}±{e}_{j}±{e}_{k} \pm e_0 \pm e_i \pm e_j \pm e_k $ where $i,j,ki,j,k$ lie on some line in the Fano plane,
• the vectors $±{e}_{p}±{e}_{q}±{e}_{r}±{e}_{s} \pm e_p \pm e_q \pm e_r \pm e_s $ where $p,q,r,sp,q,r,s$ all lie off some line in the Fano plane.

Pondering the discussion of ‘Kirmse integers’ in Part 6, you’ll see this lattice is a rotated copy of the ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ lattice, rescaled by a factor of $\sqrt{2}\sqrt\left\{2\right\}$. However, you can also immediately see that it’s a sublattice of the ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ lattice as defined above!

With a bit more work, you can see that each different projective plane structure on $\left\{1,2,3,4,5,6,7\right\}\\left\{1,2,3,4,5,6,7\\right\}$ gives a different lattice of this sort. So, we get 30 of them.

Since each such lattice consists of linear combinations of its shortest vectors, we get 30 distinct subsets of the second shell that are rotated, rescaled copies of the first shell. Moreover, all these contain our favorite point in the second shell,

$2{e}_{0}=\left(2,0,0,0,0,0,0,0\right) 2e_0 = \left(2,0,0,0,0,0,0,0\right) $

Why 17,280?

So, I’ve shown how to construct at least 270 subsets of the second shell of the ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ lattice that are rotated, rescaled copies of the first shell. And in fact, that’s all there are.

I said any way to pick two of these 270 subsets that are disjoint gives a copy of the Leech lattice inside ${\mathrm{E}}_{8}\oplus {\mathrm{E}}_{8}\oplus {\mathrm{E}}_{8}\mathrm\left\{E\right\}_8 \oplus \mathrm\left\{E\right\}_8 \oplus \mathrm\left\{E\right\}_8$. Egan explained how this works in Part 9.

But why are there 17,280 ways to choose two disjoint subsets of this sort? We don’t have a proof yet; his computer calculations just reveal that it’s true. Since

$270×64={3}^{3}×10×{4}^{3}={12}^{3}×10=17,280 270 \times 64 = 3^3 \times 10 \times 4^3 = 12^3 \times 10 = 17,280 $

it would suffice to check that for each of our 270 subsets we can find 64 others that are disjoint from it. And indeed, his computer calculations verify this, and have told us a lot about what these 64 are like. But we haven’t yet turned this into a human-readable proof that there are 64.

Another thing he checked that each of these 17,280 disjoint pairs gives a distinct sublattice of ${\mathrm{E}}_{8}\oplus {\mathrm{E}}_{8}\oplus {\mathrm{E}}_{8}\mathrm\left\{E\right\}_8 \oplus \mathrm\left\{E\right\}_8 \oplus \mathrm\left\{E\right\}_8$. So, this procedure gives 17,280 distinct copies of the Leech lattice sitting in here. But again, this deserves a nice proof.

By the way: it’s not as if we’re short of Leech lattices sitting inside ${\mathrm{E}}_{8}\oplus {\mathrm{E}}_{8}\oplus {\mathrm{E}}_{8}\mathrm\left\{E\right\}_8 \oplus \mathrm\left\{E\right\}_8 \oplus \mathrm\left\{E\right\}_8$. In Part 10 we saw, without any computer assistance, that there are at least 244,035,421. However, the ones obtained by the construction we’re discussing now are especially nice: for example, we’ve seen they give Jordan subrings of the exceptional Jordan algebra. So I think these are worth understanding in more detail.

And besides, they’re leading us into fun questions about the geometry of the ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ lattice! Any excuse for thinking about ${\mathrm{E}}_{8}\mathrm\left\{E\right\}_8$ is a good thing as far as I’m concerned. It’s endlessly rewarding in its beauty: today we’ve seen how the Fano plane is hiding inside it, in a rather abstract way. Of course, we already knew the Fano plane was involved in defining octonion multiplication — but nothing today required octonion multiplication. To define the product of octonions we need to orient the lines of the Fano plane, breaking its symmetry group — but today we didn’t need to do this!

The n-Category Cafe

A Categorical Understanding of the Proof of Cantor-Schröder-Bernstein?

Over the past year I have become increasingly fascinated by set theory and logic. So this morning when I was meant to be preparing a talk, I instead found myself thinking about the Cantor–Schröder–Bernstein theorem.

Theorem (Cantor–Schröder–Bernstein). Let $AA$ and $BB$ be sets. If there exist injections $f:A\to Bf \colon A \to B$ and $g:B\to Ag \colon B \to A$, then $|A|=|B||A|=|B|$.

This is an incredibly powerful tool for proving that two sets have the same cardinality. (Exercise: use CSB to prove that $|ℕ|=|ℚ||\mathbb\left\{N\right\}|=|\mathbb\left\{Q\right\}|$ and that $|P\left(ℕ\right)|=|ℝ||P\left(\mathbb\left\{N\right\}\right)|=|\mathbb\left\{R\right\}|$.) Earlier this fall, I taught a proof of this result that I learned from Peter Johnstone’s Notes on logic and set theory. The question that’s distracting me is this: how categorical is this argument?

Proof of Cantor–Schröder–Bernstein

Let me start by describing the proof I have in mind. The hope is that $ff$ and $gg$ might be used to construct a bijection $A\cong BA \cong B$ in the following manner: by finding subsets ${A}^{*}\subset AA^\ast \subset A$ and ${B}^{*}\subset BB^\ast \subset B$ so that $ff$ defines a bijection between ${A}^{*}A^\ast$ and its image, the complement of ${B}^{*}B^\ast$, and $gg$ defines a bijection between ${B}^{*}B^\ast$ and its image, the complement of ${A}^{*}A^\ast$.

The first trick — and this is the part that I do not understood categorically — is that a pair of subsets with the above property is encoded by a fixed point to the function

$h:P\left(A\right)\to P\left(A\right)h \colon P\left(A\right) \to P\left(A\right)$ defined by $h\left(X\right)=A\g\left(B\f\left(A\right)\right).h\left(X\right) = A \backslash g\left(B \backslash f\left(A\right)\right).$

Here I’m thinking of the powerset $P\left(A\right)P\left(A\right)$ as a poset, ordered by inclusion, and indeed $hh$ is a functor: $X\subset Y\subset AX \subset Y \subset A$ implies that $h\left(X\right)\subset h\left(Y\right)h\left(X\right) \subset h\left(Y\right)$. Now the second trick is to remember that a terminal coalgebra for an endofunctor, if it exists, defines a fixed point.

Here the coalgebras are just those subsets $XX$ with the property that $X\subset h\left(X\right)X \subset h\left(X\right)$. Let $𝒞\subset P\left(A\right)\mathcal\left\{C\right\} \subset P\left(A\right)$ be the subposet of coalgebras (if you will, defined by the forming the inserter of the identity and $hh$). I don’t know whether it is a priori clear that $𝒞\mathcal\left\{C\right\}$ has a terminal object, but if it does, then it is given by forming the union

$C=\cup \left\{X\subset A\mid X\subset h\left(X\right)\right\}. C = \cup \\left\{X \subset A \mid X \subset h\left(X\right)\\right\}.$

And indeed this works: it’s easy to check that $C\subset h\left(C\right)C \subset h\left(C\right)$ and moreover that this inclusion is an equality. The bijection $A\cong BA \cong B$ is defined by $ff$ applied to $CC$ and $gg$ applied to the complement of $f\left(C\right)f\left(C\right)$.

Alternatively, we could apply a theorem of Adámek to form the terminal coalgebra: it is the limit of the inverse sequence

$\cdots \subset {h}^{3}\left(A\right)\subset {h}^{2}\left(A\right)\subset h\left(A\right)\subset A \cdots \subset h^3\left(A\right) \subset h^2\left(A\right) \subset h\left(A\right) \subset A$

defined by repeatedly applying the endofunctor $hh$ to the terminal object $A\in P\left(A\right)A \in P\left(A\right)$. Because $P\left(A\right)P\left(A\right)$ is complete, this limit must exist.

This construction seems to be related to the other standard proof of Cantor–Schröder–Bernstein, which Wikipedia tells me is due to Julius König. The injections $ff$ and $gg$ and their partially-defined inverses define a partition of $A\bigsqcup BA \sqcup B$ into disjoint infinite (possibly repeating) chains of elements contained alternately in $AA$ and in $BB$

$\cdots a,f\left(a\right),g\left(f\left(a\right)\right),f\left(g\left(f\left(a\right)\right),\dots \cdots a , f\left(a\right), g\left(f\left(a\right)\right), f\left(g\left(f\left(a\right)\right), \ldots $

that terminate at the left whenever there is an element that is not in the image of $ff$ or $gg$. For those elements in chains that terminate at the left at an element of $AA$ (resp. $BB$), $ff$ (resp. $gg$) is used to define the bijection. For the remaining chains, either $ff$ or $gg$ may be used.

Arguing inductively by cases, you can see that the limit of the inverse sequence, i.e., the terminal coalgebra of $hh$ is the union of those elements $a\in Aa \in A$ that appear in chains that either terminate at an element of $AA$ or continue forever (possibly repeating) in both directions. (Side question: is there a slick way to demonstrate this?) This argument tells us that the terminal coalgebra is the maximal fixed point of $hh$, but in general it isn’t the only one. The minimal fixed point consists only of those elements in chains that terminate at an element of $AA$ on the left.

So, how categorical is this argument? Am I seeing terminal coalgebras just because I learned this proof from a category theorist? Or is this interpretation less superficial than the way I am presenting it?

Concluding remarks:

• The $nn$Lab explains that a dual version of this proof holds in any boolean topos, but not in all toposes, because the argument given above requires the law of the excluded middle.

• A category theorist might ask whether Cantor–Schröder–Bernstein holds in other categories. For those wishing to dive into that rabbit hole, I recommend starting here.

December 10, 2014

Symmetrybreaking - Fermilab/SLAC

First LHC magnets prepped for restart

A first set of superconducting magnets has passed the test and is ready for the Large Hadron Collider to restart in spring.

This week, one-eighth of the LHC dipole magnets reached the energy they’ll need to operate in 2015.

Engineers at CERN powered 154 superconducting magnets to a current of around 11,000 amps. This is about a thousand times greater than an average household appliance and is required to make the 50-foot-long electromagnets powerful enough to bend particles moving close to the speed of light around the curves of the LHC.

“Over the summer we plan to ramp up the LHC to the highest energy ever achieved in a collider experiment,” says Mirko Pojer, an LHC engineer-in-charge and co-leader of the magnet re-commissioning team. “But before we do that, we need to make sure that our magnets are primed and ready for the job.”

From 2010 to 2013, the LHC produced proton-proton collisions of up to 8 trillion electronvolts. This first run allowed physicist to probe a previously inaccessible realm of physics and discover the Higgs boson. But the LHC is designed to operate at even higher energies, and physicists are eager to see what might be hiding just out of reach.

“We had a very successful first run and made a huge discovery, but we want to keep probing,” says Greg Rakness, a UCLA researcher and CMS run coordinator. “The exciting thing about the next run is that we have no idea what we could find, because we have never been able to access this energy realm before.”

To prepare the LHC for 13 trillion electronvolt proton-proton collisions, CERN shut down the machine for almost two years for upgrades and repairs. This involved reinforcing almost 1700 magnet interconnections, including more than 10,000 superconducting splices.

Now that that work is completed, engineers are putting the LHC magnets through a strenuous training program. Like Rocky Balboa prepping for a big fight, the magnets must be pushed repeatedly to the limits of their operation. This will prime them for the strenuous running conditions of the LHC.

The LHC magnets are superconducting, which means that when they are cooled down, current passes through them with zero electrical resistance. During powering, current is gradually increased in the magnetic coils, which sometimes generates tiny movements in the superconductor. These movements create friction, which in turn locally heats up the superconductor and makes it quench—or suddenly return to a non-superconducting state. When this occurs, the circuit is switched off and its energy is absorbed by huge resistors.

“By purposefully making the magnets quench, we can literally ‘shake out’ any unresolved tension in the coils and prep the magnets to hold a high current without losing their superconducting superpowers,” says Matteo Solfaroli, an LHC engineer-in-charge and co-leader of the commissioning team. “This is a necessary part of prepping the accelerator for the restart so that the magnets don’t quench while we are running the beam.”

The magnets in all the other sectors will undergo similar training before being ready for operation. Many other tests will follow before beams can circulate in the LHC once more, next spring.

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arXiv blog

How to Measure Planck’s Constant Using Lego

If you’re searching for the perfect present for the physicist who has everything, how about a Lego kit for measuring one of the universe’s fundamental constants?

Planck’s constant is one of the most important numbers in science. It describes the relationship between the energy and frequency of an electromagnetic wave in an equation known as the Planck-Einstein relation: E = hv (where E is energy, v is frequency and h is Planck’s constant).

December 09, 2014

Clifford V. Johnson - Asymptotia

Grabbing Fun Shapes
A quick sketch of a building in Culver City, done while waiting for a meeting to finish (I was in my occasional role as chauffeur). A very classic and pleasing combination of shapes for Southern California. (I splashed on ink and colour later on, once home). In other news, I'm all ready for the last teaching event of 2014. I've written, typeset, and checked (multiple times) the final exam for the graduate electromagnetism class. There are some interesting things on there. I hope they like it! -cvj Click to continue reading this post

Symmetrybreaking - Fermilab/SLAC

New books for the physics fan

These recently published popular science books will help you catch up on particle physics news, knowledge and history.

Looking to stay current on your particle physics knowledge? Here are 10 recent popular science books you might want to check out.

1. Faraday, Maxwell and the Electromagnetic Field: How Two Men Revolutionized Physics

Nancy Forbes, Basil Mahon

Classical unified field theory came from the realization that electricity, magnetism and light all can be explained with a single electromagnetic field.

There is no modern physics without classical unified field theory—heck, there are no electronics without classical unified field theory—and there is no classical unified field theory without Michael Faraday (1791-1867) and James Clerk Maxwell (1831-1879).

The unlikely partners, born four decades apart, shared the achievement of upending a view of the world that had prevailed since Isaac Newton.

“The extraordinary idea put forward by Faraday and Maxwell was that space itself acted as a repository of energy and a transmitter of forces,” write Nancy Forbes and Basil Mahon in Faraday, Maxwell and the Electromagnetic Field: How Two Men Revolutionized Physics.

Faraday was largely self-taught and made important realizations without the benefit of a formal education in mathematics, while Maxwell was regarded as among the most brilliant mathematical physicists of his time. This double biography examines their differing lives and explains how their combined work paved the way for modern physics.

2. The Cosmic Cocktail: Three Parts Dark Matter

Katherine Freese

In The Cosmic Cocktail: Three Parts Dark Matter, physicist Katherine Freese explores the critical place dark matter occupies in our understanding of the cosmos.

It has yet to be observed directly. But, she tells us, dark matter’s day of reckoning might not be far off.

“Some new particles, unlike any from our daily experience, might be tearing through the galaxy,” she writes. “Scientists have already found hints of detection in their experiments… The nature of dark matter is one of the greatest puzzles of modern science, and it is a puzzle we are on the verge of solving.”

Freese, now the new director of the Nordic Institute for Theoretical Physics in Stockholm, admits to spending a disproportionate amount of time on the dance floor of nearby Studio 54 when she should have been focused on her doctoral studies at Columbia University. But she also tells a compelling history of the search for dark matter, from the cantankerous Fritz Zwicky’s early predictions in the 1930s to hopes for an appearance when the Large Hadron Collider fires up again in 2015.

3. The Large Hadron Collider: The Extraordinary Story of the Higgs Boson and Other Stuff that will Blow Your Mind

Don Lincoln

“My goal was to give readers an inside account of the hunt and discovery,” says Fermilab scientist Don Lincoln, a member of CERN’s CMS experiment, of his latest book, The Large Hadron Collider: The Extraordinary Story of the Higgs Boson and Other Stuff that will Blow Your Mind. “Almost all of the similar books have been written by non-physicists and theorists. I went to all the meetings, so I have a unique perspective.”

In the book, Lincoln describes the process of the discovery of the Higgs boson—and explains that it is not the end of the story.

Even though the widely celebrated appearance of the Higgs particle confirmed theorists’ predictions, Lincoln maintains that the relatively light mass of the Higgs raises enough questions to keep physicists awake at night.

“The measurement is quite inconsistent with the Standard Model and the quantum corrections,” he says. “This absolutely screams that there is something still to be found and this could be supersymmetry, extra dimensions, composite Higgs bosons or some other kind of new physics. In short, we know there is something big we’re missing.”

4. The Most Wanted Particle: The Inside Story of the Hunt for the Higgs, the Heart of the Future of Physics

Jon Butterworth

“I wanted it to give readers a sense of what it really feels like to work in a big experiment at such an amazing time and what it meant,” says University College London physicist Jon Butterworth of his book The Most Wanted Particle: The Inside Story of the Hunt for the Higgs, the Heart of the Future of Physics. “This meant occasionally the physics had to go a bit deeper than the common analogies, but also there is a lot of non-physics story which hopefully captures the real-time excitement.”

Butterworth, who works on the ATLAS experiment at CERN, uses a personalized approach to convey a sense of scene. In one chapter, he describes explaining the Higgs discovery to British TV reporter Tom Clarke while the two shoot pool.

He also uses his current hometown in England to describe his workplace at CERN, comparing the size of the Large Hadron Collider tunnel to the size of the London Underground.

The book, released in the UK in May under the title Smashing Physics: Inside the World’s Biggest Experiment, will be released in the US in January 2015.

5. The Perfect Wave: With Neutrinos at the Boundary of Space and Time

Heinrich Pas

Heinrich Pas, a theorist at the Technical University of Dortmund in Germany, studies neutrinos, particles that seem to defy the rules but may hold answers to the deepest questions of the universe.

In The Perfect Wave: With Neutrinos at the Boundary of Space and Time, Pas explains how powerful processes in the cosmos—from the fusion that lights the sun to the magnificent explosions of supernovae—are bound up in the workings of the mysterious particles.

“It is a story of an elementary particle that, just like the Silver Surfer in the superhero cartoons, surfs to the boundaries of knowledge, of the universe and of time itself,” Pas writes. “A story that captivates you as it sucks you into a maelstrom like an oversized wonderland. Jump on your board and hold tight.”

6. The Science of Interstellar

Kip Thorne

Kip S. Thorne, the Feynman Professor of Theoretical Physics Emeritus at Caltech, served as the executive producer for scientific credibility (and flexibility) on the space epic Interstellar. He explains that work in the book The Science of Interstellar.

In the film, astronaut Cooper (Matthew McConaughey) takes leaps and bounds over, under, around and through black holes and wormholes on his quest to find a refugee planet for the population of Earth, whose food supply is devastated by global blight.

Thorne writes that “[s]ome of the science is known to be true, some of it is an educated guess, and some is speculation.”

But he takes all of it seriously; Thorne and his colleagues even wrote a scientific paper based on their computer simulations of the movie’s black hole.

7. The Singular Universe and the Reality of Time

Roberto Mangabeira Unger, Lee Smolin

Physicist Lee Smolin of Canada’s Perimeter Institute for Theoretical Physics, author of the controversial book The Trouble With Physics, collaborated with philosopher and politician Roberto Mangabeira Unger on the new book The Singular Universe and the Reality of Time.

In it, Smolin and Unger argue against the idea of the multiverse and declare that it is time to view the cosmos as being governed by laws that are evolving rather than laws that are immutable. They contend that, “everything changes sooner or later, including change itself. The laws of nature are not exempt from this impermanence.”

8. Time in Powers of Ten: Natural Phenomena and their Timescales

Gerard ‘t Hooft, Stefan Vandoren

In Time in Powers of Ten: Natural Phenomena and their Timescales, Nobel Laureate Gerard ‘t Hooft and theorist Stefan Vandoren, both of Utrecht University in the Netherlands, step back and forth in time from the minutest fractions of a second to the age of the universe and beyond. Observations range from the orbits and rotations of planets and stars, down to the decay times of atoms and elementary particles and back to geological time scales.

“The smallest matter mankind has studied moves considerably faster than the quickest computing processes of the most expeditious machine; while on the other side of the timescale we see planets, stars and entire galaxies of unimaginably old age, some billions of years,” ‘t Hooft and Vandoren write. “Scientists believe they know almost exactly how old the universe is, but even its seemingly eternal lifetime does not constitute a limit for physicists’ research.”

9. Travelling to Infinity: The True Story Behind the Theory of Everything

Jane Hawking

In Travelling to Infinity: The True Story Behind the Theory of Everything, readers are introduced to a young, floppy-haired Stephen Hawking through the eyes of his first wife, Jane Hawking (née Wilde). Hawking published versions of this book in both 1999 and 2007, and the book was reissued this year to accompany the film adaptation, The Theory of Everything.

In the book, Jane describes an early impression of Stephen from a New Year's party in 1963: “Clearly here was someone, like me, who tended to stumble through life and managed to see the funny side of situations. Someone who, like me, was fairly shy, yet not averse to sharing his opinions, someone who unlike me had developed a sense of his own worth and had the effrontery to convey it.”

Here is a love story in which love is not enough. Hawking leaves and marries one of the nurses who tended him. Jane marries an old family friend. The two have reconciled and are on amicable terms—a good thing when the person writing your life story is your former spouse.

10. What If? Serious Scientific Answers to Absurd Hypothetical Questions

Randall Munroe

Randall Munroe’s stick-figure web comic strip, xkcd, comes with a warning: “This comic occasionally contains strong language (which may be unsuitable for children), unusual humor (which may be unsuitable for adults), and advanced mathematics (which may be unsuitable for liberal-arts majors).”

There are no dumb questions, only humorous and provocative answers from Munroe, a former NASA roboticist, in his book What If? Serious Scientific Answers to Absurd Hypothetical Questions. For example:

“Q – What would happen if the Earth and all terrestrial objects stopped spinning, but the atmosphere retained its velocity?

“A – Nearly everyone would die. THEN things would get interesting…”

In “What If?” what seems like the end is often just the beginning.

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December 08, 2014

Clifford V. Johnson - Asymptotia

LAIH Field Trip: The Clark Library!
One of the things I want the Los Angeles Institute for the Humanities (LAIH) to do more of is field trips - Exploring the city together! We're an LA resource (as I've said in earlier posts) and so we should visit with and strengthen our relationships with some of those other LA resources, whether they be physical places, or groups of people (like us), etc. Friday saw us take a wonderful field trip to the William A. Clark Memorial Library. It is another of those classic LA things - an amazing gem hidden away that you pass every day and don't see. It is not far from USC, and in fact a number of USC faculty I know have used it regularly for research, since it has several important collections of papers and rare books of various sorts (Oscar Wilde, Shakespeare, Edgar Allan Poe, etc). A lot of these were put out for us to see by Head Librarian (and LAIH Fellow) Victoria Steele and her staff, and they gave us a guided tour. During the tour [...] Click to continue reading this post

Marco Frasca - The Gauge Connection

Standard Model at the horizon

Hawking radiation is one of the most famous effects where quantum field theory combines successfully with general relativity. Since 1975 when Stephen Hawking uncovered it, this result has obtained a enormous consideration and has been derived in a lot of different ways. The idea is that, very near the horizon of a black hole, a pair of particles can be produced one of which falls into the hole and the other escapes to infinity and is seen as emitted radiation. The overall effect is to drain energy from the hole, as the pair is formed at its expenses, and its ultimate fate is to evaporate. The distribution of this radiation is practically thermal and a temperature and an entropy can be attached to the black hole. The entropy is proportional to the area of the black hole computed at the horizon, as also postulated by Jacob Bekenstein, and so, it can only increase. Thermodynamics applies to black holes as well. Since then, the quest to understand the microscopic origin of such an entropy has seen a huge literature production with the notable understanding coming from string theory and loop quantum gravity.

In all the derivations of this effect people generally assumes that the particles are free and there are very good reasons to do so. In this way the theory is easier to manage and quantum field theory on curved spaces yields definite results. The wave equation is separable and exactly solvable (see here and here). For a scalar field, if you had a self-interaction term you are immediately in trouble. Notwithstanding this, in  the ’80 Unruh and Leahy, considering the simplified case of two dimensions and Schwarzschild geometry, uncovered a peculiar effect: At the horizon of the black the interaction appears to be switched off (see here). This means that the original derivation by Hawking for free particles has indeed a general meaning but, the worst conclusion, all particles become non interacting and massless at the horizon when one considers the Standard Model! Cooper will have very bad times crossing Gargantua’s horizon.

Turning back from science fiction to reality, this problem stood forgotten for all this time and nobody studied this fact too much. The reason is that the vacuum in a curved space-time is not trivial, as firstly noted by Hawking, and mostly so when particles interact. Simply, people has increasing difficulties to manage the theory that is already complicated in its simplest form. Algebraic quantum field theory provides a rigorous approach to this (e.g. see here). These authors consider an interacting theory with a $\varphi^3$ term but do perturbation theory (small self-interaction) probably hiding in this way the Unruh-Leahy effect.

The situation can change radically if one has exact solutions. A $\varphi^4$ classical theory can be indeed solved exactly and one can make it manageable (see here). A full quantum field theory can be developed in the strong self-interaction limit (see here) and so, Unruh-Leahy effect can be accounted for. I did so and then, I have got the same conclusion for the Kerr black hole (the one of Interstellar) in four dimensions (see here). This can have devastating implications for the Standard Model of particle physics. The reason is that, if Higgs field is switched off at the horizon, all the particles will lose their masses and electroweak symmetry will be recovered. Besides, further analysis will be necessary also for Yang-Mills fields and I suspect that also in this case the same conclusion has to hold. So, the Unruh-Leahy effect seems to be on the same footing and importance of the Hawking radiation. A deep understanding of it would be needed starting from quantum gravity. It is a holy grail, the switch-off of all couplings, kind of.

Further analysis is needed to get a confirmation of it. But now, I am somewhat more scared to cross a horizon.

V. B. Bezerra, H. S. Vieira, & André A. Costa (2013). The Klein-Gordon equation in the spacetime of a charged and rotating black hole Class. Quantum Grav. 31 (2014) 045003 arXiv: 1312.4823v1

H. S. Vieira, V. B. Bezerra, & C. R. Muniz (2014). Exact solutions of the Klein-Gordon equation in the Kerr-Newman background and Hawking radiation Annals of Physics 350 (2014) 14-28 arXiv: 1401.5397v4

Leahy, D., & Unruh, W. (1983). Effects of a λΦ4 interaction on black-hole evaporation in two dimensions Physical Review D, 28 (4), 694-702 DOI: 10.1103/PhysRevD.28.694

Giovanni Collini, Valter Moretti, & Nicola Pinamonti (2013). Tunnelling black-hole radiation with $φ^3$ self-interaction: one-loop computation for Rindler Killing horizons Lett. Math. Phys. 104 (2014) 217-232 arXiv: 1302.5253v4

Marco Frasca (2009). Exact solutions of classical scalar field equations J.Nonlin.Math.Phys.18:291-297,2011 arXiv: 0907.4053v2

Marco Frasca (2013). Scalar field theory in the strong self-interaction limit Eur. Phys. J. C (2014) 74:2929 arXiv: 1306.6530v5

Marco Frasca (2014). Hawking radiation and interacting fields arXiv arXiv: 1412.1955v1

Filed under: Applied Mathematics, Astrophysics, General Relativity, Mathematical Physics, Particle Physics, Physics Tagged: Black hole, Hawking radiation, Higgs mechanism, Interstellar, Jacob Bekenstein, Kerr metric, Scalar Field Theory, Standard Model, William Unruh

December 07, 2014

Quantum Diaries

CERN appoints new Director-General

During November CERN’s Council chose Fabiola Gianotti to be the organisation’s 16th Director-General. She will take over from the current incumbent, Rolfe Heuer, on 1 January 2016 and will serve for five years.

A spokesperson for CERN’s Council stated:

“It was Dr Gianotti’s vision for CERN’s future as a world leading accelerator laboratory, coupled with her in-depth knowledge of both CERN and the field of experimental particle physics that led us to this outcome.”

CERN’s current Director General declared that:

“Fabiola Gianotti is an excellent choice to be my successor… [I] am confident that CERN will be in very good hands.”

And Gianotti herself proclaimed:

“It is a great honour and responsibility for me to be selected as the next CERN Director-General following 15 outstanding predecessors… I will fully engage myself to maintain CERN’s excellence in all its attributes, with the help of everybody, including CERN Council, staff and users from all over the world.”

Dr. Gianotti poses with the ATLAS experiment. (Image credit: Claudia Marcelloni)

Dr. Gianotti hails from Italy and holds a PhD in experimental particle physics from the University of Milan. She joined CERN in 1987 and worked on various experiments including the UA2 experiment and ALEPH, a detector for the Large Electron-Positron Collider (the LHC’s predecessor). She went on to join the ATLAS experiment, for which she was leader from March 2009 to February 2013. In July 2012 she, along with a spokesperson from the CMS experiment, announced that ATLAS and CMS had observed a ‘Higgs-like particle’. The discovery of the Higgs boson was subsequently confirmed and, as a result, Peter Higgs and Francois Englert were awarded the Nobel prize for physics in December 2013. (See here).

While she is no doubt a talented physicist, Gianotti has other strings to her bow. For example, she is an accomplished pianist who once considered a career in music. She also possesses a hint of mischief: having caused quite a stir for using the comic sans font in her slideshow presentation when announcing ATLAS’s observation of the Higgs (not serious enough apparently), she went on to announce this year that CERN would be adopting comic sans as its official font! – it was April 1st. (See this post from Rob Knoops for more.)

Being CERN’s big cheese is a tough gig but Gianotti seems qualified, experienced, able and passionate enough to be a great Director-General. It is also highly refreshing to see a female appointed to the highest profile physics office in the world.

From the Quantum Diarists, good luck Fabiola!

December 05, 2014

Quantum Diaries

Not all philosophy is useless.

In this, the epilogue to my philosophic musing, I locate my view of the scientific method within the landscape of various philosophical traditions and also tie it into my current interest of project management. As strange as it may seem, this triumvirate of the scientific method, philosophy and management meet in the philosophic tradition known as pragmatism and in the work of W. Edwards Deming (1900 – 1993), a scientist and management guru who was strongly influenced by the pragmatic philosopher C.I. Lewis (1883 – 1964), who in turn strongly influenced business practices. And I do mean strongly in both cases. The thesis of this essay is that Lewis, the pragmatic philosopher, has had influence in two directions: in business practice and in the philosophy of science. Surprisingly, my views on the scientific method are very much in this pragmatic tradition and not crackpot.

The pragmatic movement was started by Charles S. Peirce (1839 – 1914) and further developed by Williams James (1842 – 1910) and John Dewey (1859 – 1952). The basic idea of philosophic pragmatism is given by Peirce in his pragmatic maxim as: “To ascertain the meaning of an intellectual conception one should consider what practical consequences might result from the truth of that conception—and the sum of these consequences constitute the entire meaning of the conception.” Another aspect of the pragmatic approach to philosophic questions was that the scientific method was taken as given with no need for justification from the outside, i.e. the scientific method was used as the definition of knowledge.
How does this differ from the workaday approach to defining knowledge? Traditionally, going back at least to Plato (428/427 or 424/423 BCE – 348/347 BCE) knowledge has been defined as:
1) Knowledge – justified true belief
The leaves open the question of how belief is justified and since no justification is ever 100% certain, we can never be sure the belief is true. That is a definite problem. No wonder the philosophic community has spent two and a half millennia in fruitless efforts to make sense of it.

A second definition of knowledge predates this and is associated with Protagoras (c. 490 B.C. – c. 420 B.C.) and the sophists:
2) Knowledge – what you can convince people is true
Essentially, the argument is that since we cannot know that a belief is true with 100% certainty; what is important is what we can convince people of. This same basic idea shows up in the work of modern philosophers of science with the idea that scientific belief is basically a social phenomenon and what is important is what the community convinces itself is true. This was part of Thomas Kuhn’s (1922 – 1996) thesis.

While we cannot know what is true, we can know what is useful. Following the lead of scientists, the pragmatists effectively defined knowledge as:
3) Knowledge – information that helps you predict and modify the future
If we take predicting and modifying the future as the practical consequence of information, this definition of knowledge is consistent with the pragmatic maxim. The standard model of particle physics is not knowledge by the strict application of definition 1) since it is not completely true; however it is knowledge by definition 3 since it helps us predict and modify the future. The scientific method is built on definition 3). The modify clause is included in the definition since the pragmatists insisted on that aspect of knowledge. For example, C.I. Lewis said that without the ability to act there is no knowledge.

The third definition of knowledge given above does not correspond to what many people think of as knowledge so Dewy suggested using the term “warranted assertions” rather than knowledge: The validity of the standard model is a warranted assertion. Fortunately, this terminology never caught on. In contrast, James’s pragmatic idea of “truth’s cash value”, derided at the time, has caught on. In a recent book “How to Measure Anything,” on risk management, Douglas W. Hubbard spends a lot of space on what is essentially the cash value of information. In business, that is what is important. The pragmatists were, perhaps, just a bit ahead of their time. Hubbard, whether he knows it or not, is a pragmatist.
Dewey coined the term “instrumentalism” to describe the pragmatic approach. An idea or a belief is like a hand, an instrument for coping. A belief has no more metaphysical status than a fork. When your fork proves inadequate to the task of eating soup, it makes little sense to argue about whether there is something inherent in the nature of forks or something inherent in the nature of soup that accounts for the failure. You just reach for a spoon . However, most pragmatists did not consider themselves to be instrumentalists but rather used the pragmatic definition of knowledge to define what is meant by real.

Now I turn to C.I. Lewis. He is alternately regarded as the last of the classical pragmatists or the first of the neo-pragmatists. He was quite influential in his day as a professor at Harvard from 1920 to his retirement in 1953. In particular, his 1929 book “Mind and the World Order” had a big influence on epistemology and surprisingly on ISO management standards. One can see a lot of the ideas developed by Kuhn already present in the work of C.I. Lewis , for example, the role of theory in interpreting observation. Or as Deming, influenced by Lewis, expressed it: “There is no knowledge without theory.” As a theorist, I like that. At the time, this was quite radical. The logical positivists took the opposite tack and tried to eliminate theory from their epistemology. Lewis and Kuhn argued this was impossible. The idea that theory was necessary for knowledge was not new to Lewis but is also present in the works of Henri Poincaré (1854 – 1912) who was duly reference by Lewis.

Another person Lewis influenced was Willard V. O. Quine (1908 – 2000), although Quine and Lewis did not agree. Quine is perhaps best known outside the realm of pure philosophy for the Duhem-Quine thesis, namely that it is impossible to test a scientific hypothesis in isolation because an empirical test of the hypothesis requires one or more background assumptions. This was the death knell of any naïve interpretation of Sir Karl Popper’s (1902 –1994) idea that science is based on falsification. But Quine’s main opponents were the logical positivists. Popper was just collateral damage. Quine published a landmark paper in 1951: “Two Dogmas of Empiricism”. I would regard this paper as the high point in the discussion of the scientific method by a philosopher and it reasonably readable (unlike Lewis’s “The Mind and the World Order”). Beside the Duhem-Quine thesis, the other radical idea is that observation underdetermines scientific models and that simplicity and conservatism are necessary to fill the gap. This idea also goes back to Poincaré and his idea of conventionalism – much of what is regarded as fact is only convention.

To a large extent my ideas match well with the ideas in “Two Dogmas of Empiricism.” Quine summarizes it nicely as: “The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges.” and “The edge of the system must be kept squared with experience; the rest, with all its elaborate myths or fictions, has as its objective the simplicity of laws.” Amen.

Unfortunately, after the two dogmas of empiricism were brought to light, the philosophy of science regressed. In a recent discussion of simplicity in science I came across, there was neither a single mention of Quine’s work nor his correct identification of the role of simplicity – to relieve the under determination of models by observation. Philosophers found no use for his ideas and have gone back to definition 1) of knowledge. Sad

Where philosophers have dropped the ball it was picked by people in, of all places management. Two people influenced by Lewis were Walter A. Shewhart (1891 – 1967) and Edwards Deming. It is said that Shewhart read Lewis’s book fourteen times and Deming read it nine times. Considering how difficult that book is, it probably required that many readings just to comprehend it. Shewhart is regarded as the father of statistical process control, a key aspect of quality control. He also invented the control chart, a key component of statistical process control. Shewhart’s 1939 book “Statistical Method from the viewpoint of Quality Control” is a classic in the field but it devoted a large part to showing how his ideas are consistent with Lewis’s epistemology. In this book, Shewhart introduced the Shewhart cycle, which was modified by Deming (and sometimes called the Deming cycle). Under its current name Do-Plan-Check-Act (DPCA cycle) it forms the basis of the ISO management standards.

The original Shewhart cycle as given in Shewhart’s book.

What is this cycle? Here it is as captured from Shewhart’s book. This is the first place where production is seen as part of a cycle and in the included caption Shewhart explicitly relates it to the scientific method as given by Lewis. Deming added another step to the cycle, which strikes me as unnecessary; the act step. It can easily be incorporated in the specification or plan stage (as it is in Shewhart’s diagram). But Deming was influenced by Lewis who regarded knowledge without the possibility of acting as impossible, hence the act step. This idea has become ingrained in ISO management standards as the slogan “continual improvement” (Clause 10 in the standards). To see the extent Deming was guided by Lewis’s ideas just look at Deming’s 1993 book “The New Economics.” He summarizes his approach in what he calls a system of profound knowledge. This has four parts: knowledge of system, knowledge of variation, theory of knowledge and knowledge of physiology. The one that seems out of place is the third; why include theory of knowledge? Deming believed that this was necessary for running a company and he explicitly refers to Lewis’s 1929 book. Making the reading of Lewis’s book mandatory for business managers would certainly have the desirable effect of cutting down the number of managers. To be fair to Deming, he does suggest starting in about the middle of the book. We have two unbroken chain – 1) Peirce, Lewis, Shewhart, Deming, ISO management standards and 2) Pierce, Lewis, Quine, my philosophical musings . It reminds one of James Burke’s TV program “Connections”.

Popper may be the person many scientists think of to justify how they work but Quine would probably be better and Quine’s teacher, C.I. Lewis, through Deming, has provided the philosophic foundation for business management. Within the context of definition 3) for knowledge both science and business have been very successful. Your reading of this essay required both. In contradistinction, standard western philosophy based on definition 1) has largely failed; philosophers still do not know how to acquire knowledge. However, not all philosophy is useless, some of it is pragmatic.

Symmetrybreaking - Fermilab/SLAC

Vacuuming the ATLAS detector

One hundred scientists and engineers recently gave the ATLAS detector a deep cleaning in preparation for the Large Hadron Collider restart.

No, they’re not Ghost Busters looking for paranormal activity. Nor are they the last human survivors of a zombie apocalypse living in a complex underground society.

The people crawling around the ATLAS detector at the Large Hadron Collider with packs on their backs are particle physicists armed with vacuum cleaners and trash bags. They're moving through a more-than-7000-ton particle detector the size of the Notre Dame Cathedral, giving it a final scrub-down before testing its powerful toroid magnet.

It sounds almost as weird as ghosts and zombies, but vacuuming the detector is actually a standard procedure for physicists working on the ATLAS experiment based at CERN.

Before turning on the ATLAS toroid magnet—which is theoretically powerful enough to lift a car clear off the ground—students, professors, and other ATLAS experimental staff did a final sweep for loose bolts, cable ties and other foreign objects in the experimental cavern.

“We wanted to make our detector look nice and clean before operation,” says University of Michigan physicist Steve Goldfarb, who took two four-hour shifts vacuuming the detector. “Also, it’s not good to have loose metal lying around when you’re about to turn on a few-Tesla electromagnet.”

The ATLAS experiment is one of two general-purpose detectors located on the Large Hadron Collider at CERN. Unlike its sister experiment, the dense and compact CMS detector, the ATLAS detector has an air core between its eight-story high muon chambers. This allows ATLAS physicists to track the paths of muons over a great distance.

However, it also means that extraneous stuff sometimes winds up in the detector’s cracks and crevices. And after two years of upgrades and repairs, the hundred-person cleaning team had their work cut out for them tracking down rogue washers and other detritus.

But cleaning a particle detector the size of an office building is much more fun than cleaning, say, one’s apartment, according to Goldfarb.

“Crawling around inside the ATLAS detector, all I could think is that every single piece of this massive detector had to be built, shipped, tested and installed by someone,” Goldfarb says. “It made me marvel at just how complex this project really is—not just because of the science and engineering, but the huge collaboration between people and nations that had to happen just to bring these all these individual parts together.”

Symmetrybreaking - Fermilab/SLAC

Einstein papers go digital

More than 5000 documents collected by the Einstein Papers Project are now freely available online.

In a single year of his 20s, Albert Einstein published papers explaining the photoelectric effect, Brownian motion, special relativity and E=mc2. In his 30s, he lived through World War I and came up with the theory of general relativity. In his early 40s, he won a Nobel Prize.

Today a new window opened into this early period of Einstein’s life.

Princeton University Press, working with The Einstein Papers Project hosted at Caltech, has made freely available online more than 5000 documents from Einstein’s first 44 years.

The annotated documents are available in their original language and translated into English. They include his scientific papers but also professional letters to and from colleagues and personal notes to and from friends and family between the years 1879 to 1923.

“It’s one of the most exciting periods in modern science,” says Professor Diana Kormos-Buchwald, director of the Einstein Papers Project. “It was probably one of the most vibrant periods to be a scientist.”

The field of physics was different then, Kormos-Buchwald says. In 1900, there were only about 1000 physicists on the planet. Today that number makes up only about a third of a single experiment at the Large Hadron Collider.

Those physicists wrote to one another. But it’s not just the professional letters that allow one to follow Einstein’s thinking over the years, Kormos-Buchwald says.

“Einstein wrote a lot about his work in his private correspondence,” she says. “If you only look at his letters with Bohr and Schrodinger and Planck, you don’t get an idea of his day-to-day activities and his impressions of other people.”

Kormos-Buchwald is especially fond of the long-lasting correspondence between Einstein and fellow theoretical physicist Paul Ehrenfest, who made contributions to the field of statistical mechanics and its relationship to quantum mechanics.

“The two would switch easily between important scientific topics and personal ones, within one paragraph,” she says. “Very few people wrote this way to Einstein.”

In one May 1912 letter, Ehrenfest wrote to Einstein of a decision to take a position in Munich after hoping to find one in Zurich: “I must confess that I had lost myself very deeply in the dream of being able to work near you, and that it has by no means been easy for me to cut myself loose from this thought.”

He begins the very next sentence, “Regarding your remark about the Ritz-Doppler effect, I have the following to say…”

Similarly, Einstein ends a letter inviting Ehrenfest to visit with the unrelated post-script: “P.S. Abraham’s theory of gravitation is totally untenable.”

The papers give insight into Einstein’s scientific ideas but also other details of his life.

In 1895, his father Hermann Einstein wrote in a letter to Jost Winteler, family friend and the head of the special high school Einstein attended in Zurich: “I am taking the liberty of returning the enclosed school report; to be sure, not all of its parts fulfill my wishes and expectations, but with Albert I got used a long time ago to finding not-so-good grades along with very good ones, and I am therefore not disconsolate about them.”

Other documents of interest include a high school French essay Einstein wrote about his future plans (“young people especially like to contemplate bold projects”); a letter to his eventual first wife Mileva Maric celebrating the birth of their daughter Lieserl; Einstein’s first job offer; a telegram informing him he had won the Nobel Prize; and a letter to physicist Max Planck about receiving death threats from an increasingly hostile Berlin.

Also available are Einstein’s paper on the photoelectric effect (for which he won the Nobel Prize); his paper on special relativity; his paper on general relativity; and four lectures on relativity Einstein famously delivered at Princeton on his first trip to the United States.

This is only the first installment. Princeton University Press and the Einstein Papers Project plan to continue the project, adding new documents from their collection of about 30,000.

Like what you see? Sign up for a free subscription to symmetry!

Sean Carroll - Preposterous Universe

Einstein’s Papers Online

If any scientist in recent memory deserves to have every one of their words captured and distributed widely, it’s Albert Einstein. Surprisingly, many of his writings have been hard to get a hold of, especially in English; he wrote an awful lot, and mostly in German. The Einstein Papers Project has been working heroically to correct that, and today marks a major step forward: the release of the Digital Einstein Papers, an open resource that puts the master’s words just a click away.

As Dennis Overbye reports in the NYT, the Einstein Papers Project has so far released 14 of a projected 30 volumes of thick, leather-bound collections of Einstein’s works, as well as companion English translations in paperback. That’s less than half, but it does cover the years 1903-1917 when Einstein was turning physics on its head. You can read On the Electrodynamics of Moving Bodies, where special relativity was introduced in full, or the very short (3 pages!) follow-up Does the Inertia of a Body Depend on Its Energy Content?, where he derived the relation that we would now write as E = mc2. Interestingly, most of Einstein’s earliest papers were on statistical mechanics and the foundations of thermodynamics.

Ten years later he is putting the final touches on general relativity, whose centennial we will be celebrating next year. This masterwork took longer to develop, and Einstein crept up on its final formulation gradually, so you see the development spread out over a number of papers, achieving its ultimate form in The Field Equations of Gravitation in 1915.

What a compelling writer Einstein was! (Not all great scientists are.) Here is the opening of one foundational paper from 1914, The Formal Foundation of the General Theory of Relativity:

In recent years I have worked, in part together with my friend Grossman, on a generalization of the theory of relativity. During these investigations, a kaleidoscopic mixture of postulates from physics and mathematics has been introduced and used as heuristical tools; as a consequence it is not easy to see through and characterize the theory from a formal mathematical point of view, that is, only based on these papers. The primary objective of the present paper is to close this gap. In particular, it has been possible to obtain the equations of the gravitational field in a purely covariance-theoretical manner (section D). I also tried to give simple derivations of the basic laws of absolute differential calculus — in part, they are probably new ones (section B) — in order to allow the reader to get a complete grasp of the theory without having to read other, purely mathematical tracts. As an illustration of the mathematical methods, I derived the (Eulerian) equations of hydrodynamics and the field equations of the electrodynamics of moving bodies (section C). Section E shows that Newton’s theory of gravitation follows from the general theory as an approximation. The most elementary features of the present theory are also derived inasfar as they are characteristic of a Newtonian (static) gravitational field (curvature of light rays, shift of spectral lines).

While Einstein certainly did have help from Grossman and others, to a large extent the theory of general relativity was all his own. It stands in stark contrast to quantum mechanics or almost all modern theories, which have grown up through the collaborative effort of many smart people. We may never again in physics see a paragraph of such sweep and majesty — “Here is my revolutionary theory of the dynamics of space and time, along with a helpful introduction to its mathematical underpinnings, as well as derivations of all the previous laws of physics within this powerful new framework.”

Thanks to everyone at the Einstein Papers project for undertaking this enormous task.

Axel Maas - Looking Inside the Standard Model

Support, structure, and students
This time it will again be a behind-the-scenes entry. The reason is that we got just our graduate school prolonged. This is a great success. 'We' are in this case the professors doing particle physics here at the University of Graz, in total five. With this, we are now able to support nine new PhD students, i.e. give them a job during the time they are doing their PhD work, and giving them the opportunity to travel to conferences, or to invite people for them to talk to.

You may wonder what I mean by 'giving a job'. PhD students in physics are not only students. They are beginning researchers. Each and every PhD thesis contributes to our knowledge, and opens up new frontiers. In the course of doing this, the PhD students are guided and supported by us, their supervisors. The goal is, of course, that at the end of their thesis they have matured into equal partners in research. A goal, which is satisfyingly often achieved. And hence, they are not only studying but indeed contributing, and thus they also do a job, and should get paid for the work they are doing. And hence having PhD positions is not only nice - it is required already out of fairness. And therefore this success means that we can now accompany nine more young people on their way to become researchers.

But this is not everything a graduate school provides. A graduate school is also providing the infrastructure too provide advanced lectures by world-leading experts to the students. But here one has to walk a thin line. What we do not want is that they just soak up knowledge, and then reproduce it. This can never be how a PhD education should be. The aim of the PhD studies must always be that the students learn how to create, how to be creative, and how to think in directions nobody else did before. Especially not their supervisors. Providing a too much formalized education would quell much or all of this.

On the other hand, it cannot work without some formal education. While creativity is important, (particle) physics has become a vast field. As a consequence, almost every simple idea has already been found decades ago by someone else. Knowing what is known is therefore already important to avoid repeating the same things (and often the same mistakes) others did. At the same time, knowledge of general principles and structures is important such that one's own ideas can be embedded into the big picture. And in the course, checked for technical consistency. Without knowing about technical details, this would be hard to achieve. One could then easily loose oneself in pursuing a chain of technical points, leading one far astray. It is especially here where it shows that theoretical particle physics is nowadays an enormous collaborative and worldwide effort. None of the problems we are dealing with can be solved by one person alone. It requires the combined knowledge of many people to make progress.

Knowing what other people did - and do - is therefore of paramount importance. Here, the graduate school helps also in another way. It provides the PhD students with the possibility to travel themselves, meet people, and go to conferences. We also can make it possible for them to stay abroad for up to half a year at a different institution to work with different people on a different project. They can thereby substantially broaden their horizon, and learn how to cooperate with different people.

So, are there any downsides? Well, not for the students. Except that they may at times have to go a lecture or talk, which they otherwise would not go to. Most of the downsides are hitting us supervisors, because there is a lot of additional administrative work involved. However, this is easily outweighed by the possibility to have more PhD students to work with, and with their ambition achieve something new.

December 04, 2014

Matt Strassler - Of Particular Significance

How a Trigger Can Potentially Make or Break an LHC Discovery

Triggering is an essential part of the Large Hadron Collider [LHC]; there are so many collisions happening each second at the LHC, compared to the number that the experiments can afford to store for later study, that the data about most of the collisions (99.999%) have to be thrown away immediately, completely and permanently within a second after the collisions occur.  The automated filter, partly hardware and partly software, that is programmed to make the decision as to what to keep and what to discard is called “the trigger”.  This all sounds crazy, but it’s necessary, and it works.   Usually.

Let me give you one very simple example of how things can go wrong, and how the ATLAS and CMS experiments [the two general purpose experiments at the LHC] attempted to address the problem.  Before you read this, you may want to read my last post, which gives an overview of what I’ll be talking about in this one.

Filed under: Higgs, LHC Background Info, Particle Physics Tagged: atlas, cms, Higgs, LHC, long-lived particles, trigger

December 03, 2014

Jester - Resonaances

Weekend Plot: Stealth stops exposed
This weekend we admire the new ATLAS limits on stops - hypothetical supersymmetric partners of the top quark:

For a stop promptly decaying to a top quark and an invisible neutralino, the new search excludes the mass range between m_top and 191 GeV. These numbers do not seem impressive at first sight, but let me explain why it's interesting.

No sign of SUSY at the LHC could mean that she is dead, or that she is resting hiding. Indeed, the current experimental coverage has several blind spots where supersymmetric particles, in spite of being produced in large numbers, induce too subtle signals in a detector to be easily spotted. For example, based on the observed distribution of events with a top-antitop quark pair accompanied by large missing momentum, ATLAS and CMS put the lower limit on the stop mass at around 750 GeV. However, these searches are inefficient if the stop mass is close to that of the top quark, 175-200 GeV (more generally, for m_top+m_neutralino ≈ m_stop). In this so-called stealth stop region,  the momentum carried away by the neutralino is too small to distinguish stop production from the standard model process of top quark production. We need another trick to smoke out light stops. The ATLAS collaboration followed theorist's suggestion to use spin correlations. In the standard model, gluons couple  either to 2 left-handed or to 2 right-handed quarks. This leads to a certain amount of correlation between  the spins of the top and the antitop quark, which can be seen by looking at angular distributions of the decay products of  the top quarks. If, on the other hand, a pair of top quarks originates from a decay of spin-0 stops, the spins of the pair are not correlated. ATLAS measured spin correlation in top pair production; in practice, they measured the distribution of the azimuthal angle between the two charged leptons in the events where both top quarks decay leptonically. As usual, they found it in a good agreement with the standard model prediction. This allows them to deduce that there cannot be too many stops polluting the top quark sample, and place the limit of 20 picobarns on the stop production cross section at the LHC, see the black line on the plot. Given the theoretical uncertainties, that cross section corresponds to the stop mass somewhere between 191 GeV and 202 GeV.

So, the stealth stop window is not completely closed yet, but we're getting there.

Lubos Motl - string vacua and pheno

SUSY and extra dimensions together are more compatible with LHC data
In the morning, I read the daily papers on the arXiv and exactly one paper stayed open in my browser:
Auto-Concealment of Supersymmetry in Extra Dimensions (Stanford-Oxford-Airforce Collaboration)
Eminent physicist Savas Dimopoulos along with his pals (Howe, March-Russell, Scoville) argue that the LHC data don't imply that the superpartners – new elementary particles implied by supersymmetry – have to be as heavy as usually assumed. Instead, they may be rather light and such a theory yields predictions that are compatible with the LHC data – so far compatible with the Standard Model – anyway.

A possible reason why it may be hard for the collider to see SUSY is known as "compressed spectra". What does it mean? There are always some superparticles that are predicted to be produced rather often (if they're light enough). Why aren't they seen? Because they decay into products (including the lightest superpartner, the LSP, at the end) which have nearly equal masses (approximate degeneracy) which is why little energy is left for the "missing transverse energy".

And Savas et al. are proposing a clever microscopic explanation why the spectra might be compressed. Extra dimensions. They mean pretty large dimensions – much larger than the usual Planck length but much smaller than a millimeter, extra dimensions comparable to the size of a nucleus (or larger than at least 10% of a fermi, the nuclear length scale).

With such large dimensions, the momentum in the extra dimensions is "nearly continuous" which is why from the four-dimensional viewpoint, the spectrum of the new particles' masses is a discretuum, i.e. a very dense spectrum that almost resembles the continuum. With such a discretuum, pretty much any new superparticle X is rather likely to decay to a momentum mode of the LSP whose mass is just a little bit smaller than the mass of X. And the missing-energy signatures will therefore be missing. I mean suppressed or hard-to-see. Missing missing-energy signatures may sound too complex to some readers.

Generic SUSY spectra with a stop that decays to a simple LSP now require $$m_{\tilde t}\gt 700\GeV$$ or so, a pretty heavy stop squark (with some other loopholes I don't want to discuss). However, with the new large extra dimensions (yes, Savas is a co-father of the the ADD large extra dimensions models), the data only imply that the stop is heavier than $$350$$ or $$400\GeV$$. With these extra dimensions, the LHC data don't constraint the sleptons at all.

The fundamental gravitational scale $$M_*$$ is meant to be comparable to $$10$$ or $$100\TeV$$ – a rather natural scale "right above" the LHC, you might say, but a scale that has never been looked for in the usual searches for the extra dimensions. For example, you may be sure that the sub-millimeter gravitational experiments can't get to the nuclear distance scale. However, $$M_*$$ could be as high as an intermediate scale $$M_*\sim 10^9\GeV$$.

This general scenario might agree with some of the braneworlds in string theory where SUSY is broken on the non-MSSM brane(s).

Tommaso Dorigo's disrespect towards modern physics

I decided to publish this blog post when I saw Tommaso Dorigo's 11. Hide It In The Bulk. He says that according to a T-shirt, physicists who face problems because all of their other methods fail have to do one of the 10 things below:
1. Manipulate the data
2. Wave hands a lot, speak with a strong accent
3. Invoke the Anthropic Principle
4. Recall the success of the SM
5. Blame it on the Planck scale
6. Throw it on the lattice
7. Invent another symmetry
8. Set all fermion masses to zero
10. Subtract Infinity
And as you may have understood, Dorigo proposes to add a new line to the T-shirt, "11. Hide it in the bulk". He tries to mock the paper – and apparently all papers on new physics – and calls it "science-fiction" that contradicts Occam's razor.

Well, the difficulty with Dorigo's mocking efforts is that some or many of these qualitative proposals may be right and some of them are supported by rather nontrivial evidence that they may be right. Many insights that are established by today used to be new sometime in the past – and mocked by some of the older clones of a Dorigo. Some of the models are supported by stronger evidence, some of them are supported by weaker evidence.

The T-shirt with the 10 solutions above may be funny because it combines random confused states of physicists. But if you want to interpret it seriously, it is a damn stupid mixed bag of situations that have nothing to do with each other. The manipulation with the data is usually fraud – well, in some cases, one may correct errors in the data in this way, but one must have some good luck plus other good conditions.

Waving hands and accents are just funny but they don't really carry any physics idea.

On the other hand, the anthropic principle is an idea that has been proposed to be relevant for physics and it needs to be argued about and evaluated using physical arguments that the likes of Dorigo don't even want to consider. The status of the anthropic principle is "open" at the sociological level – although I will of course tell you why all of its existing versions are wrong.

On the other hand, the success of the Standard Model and the fact that at least some differences and surprises are caused by the existence of the Planck scale – i.e. by the existence of gravity – are indisputable facts. Lattices are clearly useful and legitimate methods in physics. Well, sometimes they are useful, sometimes they are less useful; the devil is in the details. And symmetries are important principles – and every symmetry we use today was new at some moment in the past which also suggests that every symmetry that is new now has a chance to be established in the future.

Both heavy fermions and the massless limit of the fermions are important limiting situations to consider and physics can derive important qualitative implications of both assumptions. Some of these derived claims are right, some of them are wrong. Infinities have been subtracted on a daily basis for 70 or 80 years and the process works great – unless one does it incorrectly. We've known why it works so great for over 40 years, too.

Finally, things may demonstrably hide in the bulk. It is an elementary fact of any physical model that contains the "bulk" that the "bulk" has some different properties than the branes or the boundaries. Certain things are more visible in the bulk, others are less visible, and so on.

The fact that all of these eleven diverse ideas and circumstances (each of which includes hundreds of inequivalent particular claims whose truth value may differ from the rest, too!) appear on the same meant-to-be-funny shirt doesn't mean that their status is the same. It certainly doesn't mean that an intelligent person may mock all of them. Everyone who just mindlessly mocks them is a low-energy, low-brow, low-status idiot resembling Tommaso Dorigo.

Everyone who is at least 20 IQ points smarter than Tommaso Dorigo knows that there are lots of very intriguing and potentially powerful arguments in this paper – or at least many other phenomenological papers on new physics that have been written. An honest physicist simply can't ignore them. An intelligent physicist can't consider all ideas about new physics to be science-fiction.

It's bizarre when such attitudes are displayed by someone who is employed as an experimental physicist. The very purpose of the occupation is to decide which of the new ideas are right and which of them are wrong, to direct the search. It is necessary to emphasize that the experiments are not the only considerations that direct the progress. There are lots of top-down arguments that help to determine how much time competent model builders spend on one class of ideas vs another class of ideas. For example, there are lots of top-down rational reasons to think that supersymmetry gets unbroken at a high enough energy scale.

If the experimenters don't find anything new (e.g. for the next 20 years), well, we will survive. Null results also carry some information value. It's just less interesting information. I would find it surprising why people would become experimenters if they were convinced that they may discover nothing new. Maybe most students in Italy only become experimenters because they view the field as a nonsensical human activity that is actually a good welfare system where one doesn't have to do much and gets a lot.

But the people who are doing experimental physics for meritocratic reasons – who think that their work is meaningful – do share the "belief" or "world view" that some ideas will turn out to be right and they want to contribute to the separation of the right ideas from the wrong ones. To use the phrase science-fiction for all potentially good ideas is just stupidity – something utterly incompatible with the very purpose of science.

What Dorigo calls "science-fiction" is actually called "science". Papers like this new paper by Savas and pals are really science at its best. They connect some principles extracted from previous experiments and previously overlooked possibilities to find some new possibilities that were being overlooked as recently as yesterday, and extract completely well-defined (and general enough as well as particular enough) observable implications out of these assumptions. These papers map the space of possible theories and ideas and they compare this space with the real world we know from the empirical data.

There is nothing "obviously unnatural" about these ideas. Top-down arguments generally imply that "some extra dimensions" exist and their size is unknown. Near-Planckian extra dimensions may be preferred for some (mostly top-down) reasons, very large dimensions for other (mostly bottom-up) reasons, but the intermediate size isn't really ruled out and must be considered as a possibility. Such intermediate-size extra dimensions require the Standard Model on a brane and the rest of the conclusions by Savas et al. is almost guaranteed, a robust consequence of very mild assumptions.

So such papers don't really violate any "Occam's razor". They are only in conflict with the stupidity of aggressive morons such as Tommaso Dorigo who like to "cut" everything that transcends the capabilities of these marginal primates. They may use such razors every day to cut pieces of pork off their bodies. But unlike Dorigo, legitimate scientists are able to check and see that the text by Dorigo is a foul play, a stupid rant for stupid readers that doesn't contain any scientifically tolerable evidence in one way or another.

This "Occam's razor" may be good enough for Dorigos to cut many pounds of the pork off their bodies but it – mindless mocking of very serious and rather clever papers – isn't compatible with science. So: vaffanculo, Dorigo!

And that's the memo.

Symmetrybreaking - Fermilab/SLAC

Searching for a dark light

A new experiment at Jefferson Lab is on the hunt for dark photons, hypothetical messengers of an invisible universe.

The matter we know accounts for less than 5 percent of the universe; the rest is filled with invisible dark matter and dark energy. Scientists working on a new experiment to be conducted at Thomas Jefferson National Accelerator Facility in Virginia hope to shed light on some of those cosmic unknowns.

According to certain theories known as hidden-sector models, dark matter is thought to consist of particles that interact with regular matter through gravitation (which is why we know about it) but not through the electromagnetic, strong and weak fundamental forces (which is why it is hard to detect). Such dark matter would interact with regular matter and with itself through yet-to-be-discovered hidden-sector forces. Scientists believe that heavy photons—also called dark photons—might be mediators of such a dark force, just as regular photons are carriers of the electromagnetic force between normal charged particles.

The Heavy Photon Search at Jefferson Lab will hunt for these dark, more massive cousins of light.

“The heavy photon could be the key to a whole rich world with many new dark particles and forces,” says Rouven Essig, a Stony Brook University theoretical physicist who in recent years helped develop the theory for heavy-photon searches.

Although the idea of heavy photons has been around for almost 30 years, it gained new interest just a few years ago when theorists suggested that it could explain why several experiments detected more high-energy positrons—the antimatter partners of electrons—than scientists had expected in the cosmic radiation of space. Data from the PAMELA satellite experiment; the AMS instrument aboard the International Space Station; the LAT experiment of the Fermi Gamma-ray Space Telescope and others have all reported finding an excess of positrons.

“The positron excess could potentially stem from dark matter particles that annihilate each other,” Essig says. “However, the data suggest a new force between dark matter particles, with the heavy photon as its carrier.”

Creating particles of dark light

If heavy photons exist, researchers want to create them in the lab.

Theoretically, a heavy photon can transform into what is known as a virtual photon—a short-lived fluctuation of electromagnetic energy with mass—and vice versa. This should happen only very rarely and for a very short time, but it still means that experiments that produce virtual photons could in principle also generate heavy photons. Producing enormous numbers of virtual photons may create detectable amounts of heavy ones.

At Jefferson Lab’s Continuous Electron Beam Accelerator Facility, CEBAF, scientists will catapult electrons into a tungsten target, which will generate large numbers of virtual photons—and perhaps some heavy photons, too.

“CEBAF provides a very stable, highly intense electron beam that is almost continuous,” says Jefferson Lab’s Stepan Stepanyan, one of three spokespersons for the international HPS collaboration, which includes more than 70 scientists. “It is a unique place for performing this experiment.”

The virtual photons and potential heavy photons produced at CEBAF will go on to decay into pairs of electrons and positrons. A silicon detector placed right behind the target will then track the pairs’ flight paths, and an electromagnetic calorimeter will measure their energies. Researchers will use this information to reconstruct the exact location in which the electron-positron pair was produced and to determine the mass of the original photon that created the pair. Both are important data points for picking the heavy photons out of the bunch.

The photon mass measured in the experiment matters because a heavy photon has a unique mass, whereas virtual photons appear with a broad range of masses. “The heavy photon would reveal itself as a sharp bump on top of a smooth background from the virtual photon decays,” says SLAC National Accelerator Laboratory’s John Jaros, another HPS spokesperson.

The location in which the electron-positron pair was produced also matters because virtual photons decay almost instantaneously within the target, says Timothy Nelson, project lead for the silicon detector, which is being built at SLAC. Heavy photons could decay more slowly, after traveling beyond the target. So photons that decay outside the target can only be heavy ones. The HPS silicon detector’s unique ability to identify outside-of-target decays sets it apart from other experiments currently participating in a worldwide hunt for heavy photons.

The HPS calorimeter, whose construction was led by researchers from the French Institut de Physique Nucléaire, the Italian Istituto Nazionale di Fisica Nucleare and Jefferson Lab, is currently being tested at Jefferson Lab, while scientists at SLAC plan to ship their detector early next year. The experiment is scheduled to begin in the spring of 2015.

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