Packing

Just a note to explain the lighter than usual posting over the last couple of weeks.  I'm packing stuff up to ship for when I leave for Australia in a few weeks, and this has taken up a lot of time.  I should have that finished soon, which will hopefully let me finish off a couple of posts I'm working on.

While this is necessary, my apartment is looking increasingly empty, which does make me feel a bit sad.  I've enjoyed my time in Vancouver, and will definitely miss it.

Armstrong in Hospital

Neil Armstrong has just had heart surgery.  The reports suggest that he's recovering well, and cutting into your heart is almost routine these days.  But I couldn't help but be reminded of this old XKCD comic.

Shiny Dark Matter

A couple of months ago, I discussed a recent paper by Christoph Weniger that claimed strong evidence for dark matter from the Fermi Satellite Large Area Telescope.  In short, the Fermi LAT detects gamma rays, light of very short wavelength/very high energy.  Looking at gamma rays from the centre of the galaxy, Weniger claimed to see a feature in the spectrum:

Weniger's main result: black points are data with error bars; the green line is a featureless background; and the red line the combination of that and the proposed signal, shown in blue at the bottom.

Such a feature is difficult to produce by conventional astrophysics (stars, pulsars, etc).  It can be easily produced from dark matter.  For example if two dark matter particles annihilate into two photons, then conservation of energy and momentum forces those two photons to have the same energy, equal to the mass-energy of the dark matter.  Throw in the effect of experimental resolution and we get something that looks like the above, a small peak in the spectrum.

Since Weniger's original paper there has been a lot of work done.  In summary, this feature stands up to reanalysis but is not statistically strong enough to claim a true discovery.  Non-dark matter explanations have been offered, but are not compelling.  However, the dark matter explanation has problems of its own; the signal seems to be too big.

Feynman Diagrams

In an earlier post, I talked about perturbation series, one of the most important tools in physics calculations.  In brief, there are very few problems in science that we can solve exactly.  Instead, we approximate the problem we have as a simple one that we can solve, plus terms that are "small".  The real solutions are the solutions of the simpler problem, plus an infinite set of corrections.

In that earlier post, I was pretty general.  In a sense this made things harder for me than necessary.  In particle physics, or relativistic quantum mechanics, there is a nice intuitive split between things we can solve exactly and things we can't.  The only problems we can solve exactly are non-interacting.¹  We could only describe an electron exactly, if we turned of electromagnetism.²  The small numbers that we make our expansions in are the coupling constants.  For example, the natural definition of the charge of the electron is the through the fine structure constant,
$\alpha \equiv \frac{e^2}{4\pi\hbar c} \approx \frac{1}{137}.$
Here, e is the electron charge; h is Planck's constant; and c is the speed of light.

While the idea of a perturbation series is relatively simple, actually constructing one can be a bit tricky. The main problem is to ensure that you get all the relevant terms with the right factors.  This is where Feynman diagrams come in.  They are a concise way to construct perturbation series from a simple set of rules.  They can be easily coded into software programs, and a number of options exist.  And they have a really nice intuitive interpretation.