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 …

Here’s an interesting, and perhaps occasionally useful, identity: suppose you have a function defined on a two-dimensional space, \(f(\vec{r})\). And suppose that this function is independent of the angle of \(\vec{r}\) but rather is only a function of the magnitude \(r = \norm{\vec{r}}\). Then

(where \(\ln r\) is shorthand for \(\ln\frac{r}{r_0}\) where \(r_0\) is some constant) In other words, the radial term of the polar Laplacian is equal to the second logarithmic derivative divided by \(r^2\) for rotationally invariant functions.

At this point you might be wondering, why the heck is this interesting? Well, for me, it’s because my current research project happens to involve logarithmic derivatives of rotationally invariant functions in 2D space. But for (almost) everyone else, this is related to the way electric potential drops off with distance in 2D space.

Consider, for example, a wire that carries a charge density \(\lambda\) (but no current). Since this system is translationally symmetric (nothing changes if you …

Yesterday’s big news in the physics world: the LHCb experiment has observed a \(3.5\sigma\) asymmetry between the decays of \(D^0\) and \(\bar{D}^0\) mesons. This has already been described in detail elsewhere on the web: Sean Carroll has a nice explanation accessible to non-experts, or you can look at the presentation of the results from the HCP conference (which itself is reasonably clear and informative, if you have some experience looking at particle physics presentations).

For those who are not inclined to click on links, here’s a quick summary of the story. CP symmetry violation is a difference between the behaviors of a particle and the mirror image of its antiparticle. The probability of a CP-violating process to occur is controlled by a complex phase parameter in the quark mixing matrix. There are two kinds of CP-violating processes that we can detect:

• Some particles (kaons, D and B mesons) transform into their antiparticles and back as they propagate. CP violation means that the oscillation probability for going from the particle to the antiparticle is different from the probability to go from the antiparticle to the particle. Intuitively, you could imagine that the meson spends …

Ever since the story of the sex abuse scandal and coverup in Penn State’s football program broke last Saturday, there has been a lot of attention focused on Joe Paterno’s role in it, specifically regarding whether he deserved to be punished for failing to report the incident to the police.

There have also been a lot of people saying that it’s wrong to be devoting so much attention to the coach when we should be focusing on the victims and using this as an opportunity to increase awareness of child abuse prevention. They are right, of course. To their credit, many Penn State students are doing just that, between holding a candlelight vigil tonight and encouraging everyone to wear blue at this weekend’s football game.

But there is a sense in which I think it’s worth talking about Paterno’s role. Not because of his celebrity, but because he is the “everyman” in this incident. Many of us could imagine ourselves being in much the same situation that he was when Mike McQueary told him what he saw. The question of Paterno’s guilt is a question of ethics that, in the quest to stop …

Many of this blog’s readers will know by now about the sex abuse allegations involving a former football coach at Penn State (where I’m a student). If you haven’t heard about it, take a look at this excellent summary of the allegations. You can also read the grand jury report, which first made this whole thing public, at that page, or via the New York Times.

What I find most, um, “interesting” about this is how many of the reactions to the scandal don’t tell you to do just that.

I don’t often talk about ethical issues because they’re messy business, and this story, in particular the role that Joe Paterno plays in it, is a perfect example of why. Paterno is the heart and soul of Penn State. He’s been working at the school for 61 years, helping it grow academically and athletically every step of the way. You can’t argue with the fact that he has done a tremendous amount of good for the university, and the students and alumni are definitely justified in loving him for it. Heck, even though I’m not a football fan in the slightest …