Courtesy of Sean Carroll at Cosmic Variance (and many other sources, but this is the one I happen to like linking to), the ICARUS experiment has performed a direct measurement of the speed of neutrinos coming out of CERN, and they’ve found it to be exactly consistent with the speed of light. This is hot off the physics presses, so to speak; the paper was posted on arXiv just yesterday. CERN has updated their press release with the latest information.

The neat thing about the ICARUS result is that they use the same neutrino beam as the OPERA experiment. The same neutrinos can’t be traveling at two different speeds, so clearly one or the other of these results is wrong. Given that the OPERA team has already identified a couple of construction errors in their detector, and their result was the wacky one anyway, this pretty much settles the problem with the apparent faster-than-light neutrinos: they don’t exist. It was just a detector malfunction, not any sort of strange physics.

Of course, most physicists were pretty confident that this was the case all along, but you can never be sure that something is wrong with your experiment …

There’s been a lot of big news from the experimental physics community over the past week or so, but unfortunately I’ve been busy with spring cleaning and making arrangements for a trip to DIS 2012 so I haven’t been able to keep on top of it. Funny how I have less free time when I’m on vacation…

Anyway, here’s a recap of some of the major recent events in the physics world:

Higgs boson search update

Tevatron combined Higgs signal

At the Moriond conference on electroweak physics, CDF and D0, the two major experiments from the (now closed) Tevatron, reported an excess of collision events between about \(\SI{115}{GeV}\) and \(\SI{140}{GeV}\), peaking at \(2.2\sigma\). This could be a very weak signal of the Higgs boson, but it wouldn’t have been much to get excited about if ATLAS and CMS hadn’t already detected similar (but stronger) signals in the same energy range.

It’s worth keeping in mind that the Tevatron has been shut down, so these latest results aren’t based on new data (like the LHC results); they’re based on a new analysis of the same …

One of the most important principles of thermodynamics is the equipartition theorem:

A system in thermodynamic equilibrium will have an internal thermal energy of \(\frac{1}{2}k_BT\) in each degree of freedom.

But there’s a subtlety here: what exactly are degrees of freedom? There are (at least) two slightly different kinds:

• A mechanical degree of freedom is any way in which a system can freely change its spatial configuration
• A thermodynamic degree of freedom is any way in which a system can freely increase its stored energy

The degrees of freedom the equipartition theorem mentions are the thermodynamic variety. It’s important to know this because the equipartition theorem predicts the heat capacity for many substances in the high-temperature limit, and if if you count the wrong kind of degrees of freedom, you’ll get the wrong answer.

Diatomic molecules

One simple example of this is a diatomic molecule. If you want to figure out how many mechanical degrees of freedom this molecule has, you just count up all the various distances that you need to completely specify the molecule’s spatial configuration. They break down like this:

• Three positions \(x\), \(y\), \(z\) to specify the center of …

Here’s one for the fellow Star Trek fans out there. At the end of Star Trek: Nemesis (SPOILER ALERT), the Enterprise-E and Shinzon’s Romulan warbird, the Scimitar, get involved in a battle in which the Scimitar latches on to the Enterprise using grips. One of the community members at Science Fiction and Fantasy Stack Exchange thought to ask, when the Scimitar fired its engines in reverse, why did it detach from the Enterprise rather than dragging both ships along?

At the question on SFFSE, there are two proposed explanations, the inertia of the Enterprise and the failure point of the grips. Both of them are relevant, but inertia doesn’t explain what happens all by itself. After all, if it were just inertia, what’s to say that the Scimitar detaches from the Enterprise instead of the engines detaching from both ships? As we’ll see, inertia does play a role in determining how much force is exerted on each part of each of the two ships’ structures. But once that force distribution is determined, it really comes down to whether the amount of force on the grips is enough to break them.

In the grand tradition of …

Since the big news in the physics world is this morning’s presentation of the Higgs search results from the LHC, it’s only appropriate that I comment on it here, even though every physics blog in the world will be doing the exact same thing so there will be no shortage of Higgs information out there ;-) In summary: no, they haven’t really found it, but there is a bump around \(\SI{126}{GeV}\) that could represent detection of a Higgs boson. It will take another year’s worth of data to be confident either way.

Here are the plots that were released this morning by ATLAS and CMS, respectively:

The quantity being plotted here is the cross section for candidate Higgs events, which is denoted \(\sigma\), relative to a theoretical prediction, \(\sigma_{SM}\). In other words, the thing on the vertical axis is related to the fraction of collisions in which something that looks like a sign of a Higgs boson comes out. (I’ll perhaps post on this in more detail later; for now see Matt Strassler’s post on Higgs production for a good explanation.) But not everything that looks like a sign of a Higgs …

Some time ago I posted about the theoretical justification for exponential decay. In that post, I showed that you can quantify exponential decay with this equation:

where \(N(t)\) is the number of undecayed atoms at time \(t\) and \(\lambda\) is a constant representing the decay rate. If you plug in \(N(t) = \frac{1}{2}N(0)\), the condition for the half-life, you can find that

But physicists usually write the formula like this,

where \(\tau\) is called the time constant. We prefer this to using the decay rate because, as I wrote in Calculating Terminal Speed, it’s often best to write a physics question in terms of dimensionless ratios like \(\frac{t}{T}\), where \(T\) is some time characteristic of the physical system you’re studying. We could use the half-life for \(T\), but the time constant \(\tau\) is more appealing for a couple of reasons: it keeps that ugly factor of \(\ln 2\) out of the formula, and more importantly, \(\tau\) is physically meaningful because it’s the average lifetime of an individual atom …

Among this week’s big news in physics is that the OPERA experiment, which reported a detection of faster-than-light neutrinos back in September, has repeated their experiment and is still finding the same results. What they have changed this time is the width of the neutrino pulses, down to \(\SI{50}{ns}\).

In the original measurement, neutrinos were generated in bunches more than \(\SI{3}{km}\) long, so that it took \(\SI{10.5}{\micro\second}\) for each bunch of neutrinos to pass through a detector. This spread is much larger than the \(\SI{60}{ns}\) or \(\SI{18}{m}\) discrepancy that the original OPERA paper reported. Some scientists were concerned that the neutrino bunches were getting distorted in flight, which could skew the apparent average time that it took for the neutrinos to travel the distance they did. I’m not sure how valid of a criticism this was, since if you look at the picture at the left, you can actually identify peaks and valleys of the experimentally detected shape of the neutrino bunch (the black dots, representing the rate at which neutrinos are detected as a function of time), which match up pretty well with corresponding features …