Archive for Dirac equation

The Effect of Gravity on the Muon Magnetic Moment

Posted in The Universe and Stuff with tags , , , , , on February 3, 2018 by telescoper

Only time for a short post today, but I think this may turn out to be an important result. There’s a paper by Morishima et al. on the arXiv with the rather dry title Post-Newtonian effects of Dirac particle in curved spacetime – III : the muon g-2 in the Earth’s gravity, which suggests that the anomalous magnetic dipole moment of the muon.

Here is the abstract of the paper. You can click on it to make it bigger.

In a nutshell the anomaly is that according to basic relativistic quantum theory in the form of the Dirac equation, the muon (and any other charged spin-1/2 fermion) should have a magnetic dipole moment μ of magnitude (given in terms of its mass m and fundamental constants) by μ=geħ/4m with the g-factor g=2 for Dirac fermions. The anomaly is that this can be measured and it appears that g differs from zero by a small but significant amount, i.e. (g-2) is not zero. It has been widely suggested that this discrepancy suggests the existence of physics beyond the Standard Model of Partlce Physics. Well, gravity is not included in the Standard Model so I suppose this could still be right, but the it this calculation may well disappoint those who were hoping that (g-2) might provide evidence for, e.g., supersymmetry when it looks like it might be something rather more mundane, ie the Earth’s gravity!

UPDATE: It appears there is an error in the paper; see here. You may stand down.

UPDATE: Well, that was pretty fast. There’s now a paper on the arXiv by Matt Visser that gives a detailed refutation of the above claim. Here is the abstract:

In three very recent papers, (an initial paper by Morishima and Futamase, and two subsequent papers by Morishima, Futamase, and Shimizu), it has been argued that the observed experimental anomaly in the anomalous magnetic moment of the muon might be explained using general relativity. It is my melancholy duty to report that these articles are fundamentally flawed in that they fail to correctly implement the Einstein equivalence principle of general relativity. Insofar as one accepts the underlying logic behind these calculations (and so rejects general relativity) the claimed effect due to the Earth’s gravity will be swamped by the effect due to Sun (by a factor of fifteen), and by the effect due to the Galaxy (by a factor of two thousand). In contrast, insofar as one accepts general relativity, then the claimed effect will be suppressed by an extra factor of [(size of laboratory)/(radius of Earth)]^2. Either way, the claimed effect is not compatible with explaining the observed experimental anomaly in the anomalous magnetic moment of the muon.

That’s how science goes!

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The Cake Equation

Posted in The Universe and Stuff with tags , , , on May 31, 2014 by telescoper

Yesterday being the last Friday of the month of May it was time for another tea-and-cake event in the School of Mathematical and Physical Sciences. These provide an opportunity for staff to get together and chat while demolishing a specially-themed cake. The cakes themselves are organized by the inestimable Miss Lemon and I never know what the theme is before the goods arrive, so I have to ad lib a short introduction (for just a minute, without repetition, hesitation, deviation or repetition) before cutting the cake.

As you will observe, this time the (Lemon Drizzle) cake was decorated with the Dirac Equation (which I consider to be the most beautiful equation in physics)..

The most beautiful equation?

Posted in The Universe and Stuff with tags , , , , on February 13, 2014 by telescoper

There’s an interesting article on the BBC website today that discusses the way mathematicians’ brains appear to perceive “beauty”. A (slightly) more technical version of the story can be found here. According to functional magnetic resonance imaging studies, it seems that beautiful equations excite the same sort of brain activity as beautiful music or art.

The question of why we think equations are beautiful is one that has come up a number of times on this blog. I suspect the answer is a slightly different one for theoretical physicists compared with pure mathematicians. Anyway, I thought it might be fun to invite people offer suggestions through the comments box as to the most beautiful equation along with a brief description of why.

I should set the ball rolling myself, and I will do so with this, the Dirac Equation:

dirac_equation

This equation is certainly the most beautiful thing I’ve ever come across in theoretical physics, though I don’t find it easy to articulate precisely why. I think it’s partly because it is such a wonderfully compact fusion of two historic achievements in physics – special relativity and quantum mechanics – but also partly because of the great leaps of the imagination that were needed along the journey to derive it and my consequent admiration for the intellectual struggle involved. I feel it is therefore as much an emotional response to the achievement of another human being – such as one feels when hearing great music or looking at great art – as it is a rational response to the mathematical structure involved. But it’s not just that, of course. The Dirac Equation paved the way to many further developments in particle physics. It seems to encapsulate so much about the behaviour of elementary particles in so few symbols. Some of its beauty also derives from its compactness.

Anyway, feel free to suggest formulae or equations through the comments box, preferably with a brief explanation of why you think they’re so beautiful.