Science

This year we give thanks for a concept that has been particularly useful in recent times: the error bar. (We’ve previously given thanks for the Standard Model Lagrangian, Hubble’s Law, the Spin-Statistics Theorem, conservation of momentum, and effective field theory.)

Error bars are a simple and convenient way to characterize the expected uncertainty in a measurement, or for that matter the expected accuracy of a prediction. In a wide variety of circumstances (though certainly not always), we can characterize uncertainties by a normal distribution — the bell curve made famous by Gauss. Sometimes the measurements are a little bigger than the true value, sometimes they’re a little smaller. The nice thing about a normal distribution is that it is fully specified by just two numbers — the central value, which tells you where it peaks, and the standard deviation, which tells you how wide it is. The simplest way of thinking about an error bar is as our best guess at the standard deviation of what the underlying distribution of our measurement would be if everything were going right. Things might go wrong, of course, and your neutrinos might arrive early; but that’s not the error bar’s fault.

Now, there’s much more going on beneath the hood, as any scientist (or statistician!) worth their salt would be happy to explain. Sometimes the underlying distribution is not expected to be normal. Sometimes there are systematic errors. Are you sure you want the standard deviation, or perhaps the standard error? What are the error bars on your error bars?

While these are important issues, we’re in a holiday mood and aren’t trying to be so picky. What we’re celebrating is not the concept of statistical uncertainty, but the elegant shortcut provided by the concept of the error bar. Sure, many things can be going on, and ultimately we want to be more careful; nevertheless, there’s no question that the ability to sum up our rough degree of precision in a single number is enormously useful. That’s the genius of the error bar: it lets you decide at a glance whether a result is possibly worth believing or not. The power spectrum of the cosmic microwave background is a pretty plot, but it only becomes convincing when we see the error bars. Then you have a right to go, “Aha, I see three peaks there!”

And the error bar isn’t just pretty, it provides some quantitative oomph. An error bar is basically the standard deviation — “sigma,” as the scientists like to call it. So if your distribution really is normal you know that an individual measurement should be within one sigma of the expected value about 68% of the time; within two sigma 95% of the time, and within three sigma 99.7% of the time. So if you’re not within three sigma, you begin to think your expectation was wrong — something fishy is going on. (Like maybe a Nobel-prize-worthy discovery?) Once you’re out at five sigma, you’re outside the 99.9999% range — in normal human experience, that’s pretty unlikely.

Error bars aren’t the last word on statistical significance, they’re the first word. But we can all be thankful that so much meaning can be compressed into one little quantity.

Here in the Era of 3-Sigma Results, we tend to get excited about hints of new physics that eventually end up going away. That’s okay — excitement is cheap, and eventually one of these results is going to stick and end up changing physics in a dramatic way. Remember that “3 sigma” is the minimum standard required for physicists to take a new result at all seriously; if you want to get really excited, you should wait for 5 sigma significance. What we have here is a 3.5 sigma result, indicating CP violation in the decay of D mesons. Not quite as exciting as superluminal neutrinos, but if it holds up it’s big stuff. You can read about it at Résonaances or Quantum Diaries, or look at the talk recently given at the Hadronic Collider Physics Symposium 2011 in Paris. Here’s my attempt an an explanation.

The latest hint of a new result comes from the Large Hadron Collider, in particular the LHCb experiment. Unlike the general-purpose CMS and ATLAS experiments, LHCb is specialized: it looks at the decays of heavy mesons (particles consisting of one quark and one antiquark) to search for CP violation. “C” is for “charge” and “P” is for “parity”; so “CP violation” means you measure something happening with some particles, and then you measure the analogous thing happening when you switch particles with antiparticles and take the mirror image. (Parity reverses directions in space.) We know that CP is a pretty good symmetry in nature, but not a perfect one — Cronin and Fitch won the Nobel Prize in 1980 for discovering CP violation experimentally.

While the existence of CP violation is long established, it remains a target of experimental particle physicists because it’s a great window onto new physics. What we’re generally looking for in these big accelerators are new particles that are just to heavy and short-lived to be easily noticed in our everyday low-energy world. One way to do that is to just make the new particles directly and see them decaying into something. But another way is more indirect — measure the tiny effect of heavy virtual particles on the interactions of known particles. That’s what’s going on here.

More specifically, we’re looking at the decay of D mesons in two different ways, into kaons and pions. If you like thinking in terms of quarks, here are the dramatis personae:

• D0 meson: charm quark + anti-up quark
• anti-D0: anti-charm quark + up quark
• K-: strange quark + anti-up quark
• K+: anti-strange quark + up quark
• π-: down quark + anti-up quark
• π+: anti-down quark + up quark

Let’s look at the D0 meson. What happens is the charm quark (much heavier than the anti-up) decays into three lighter quarks: either up + strange + anti-strange, or up + down + anti-down. …

New Physics at LHC? An Anomaly in CP ViolationRead More »

While my first column for Discover was on the multiverse, the second one is more down to Earth (as these things go): searching for new forces. Of course we are searching for new short-range forces at the Large Hadron Collider and in other particle-physics experiments, but here I’m talking about long-range “fifth forces.” While there are plausible motivations for searching for such forces, and the experimentalists have done an heroic job in constraining them, I argue that the most impressive thing is how we can say what forces are not out there — in particular, anything that would have any important effect on everyday life. There probably are more forces than we know about, but they’re only going to be of direct interest to physicists, I’m afraid. No tractor beams.