## Saturday, 3 February 2018

### Update on muon g-2: story of a debacle

MathJax example So I had a chance on the train home yesterday to digest the muon anomalous magnetic moment papers, and it is an amusing story that I have to share. In short, it is an example of a lie goes halfway round the world while the truth is putting on its shoes. Well, it only took the truth a day or so to get its shoes on, let's see how much damage the lie did.

Firstly, I'll give a short summary for physicists why the result is bogus. Then I'll give a general discussion below about what we can learn.

Lubos gives a nice summary of the physics, with a disclaimer added afterwards that the result is obviously wrong. This is true, because the result depends only on the gravitational potential, whose absolute value has no physical meanining. But below I give a proof that I earlier summarised in a tweet.

In the paper, they use the metric $$ds^2 = (1- 2 \phi(r)) dt^2 - \left( 1 - 2 \phi(r) \right)^{-1} dr^2 - r^2 d\Omega^2$$ This is fine, but they ignore the fact that in the lab we don't know that our time runs differently than at infinity, nor that our rules are not the same length. So instead we could just do a constant rescaling of the time and space coordinates so that $$\phi(\mathrm{lab}) = 0.$$ In other words, we can always define local Minkowski coordinates at a point, which we choose to be where our experiment is. Then we use that as the starting point and proceed as in their papers. Now, in their calculation, in the result nothing depends on the derivative of $$\phi$$, and so it must reduce to the flat space result. QED (+hadronic corrections). In other words, their "gravitational correction" must be exactly zero!

On the other hand, just after I blogged yesterday, a collaborator emailed me to say that they had pointed out to the authors that even if you accept their results they had misinterpreted how the experiments worked, and the correction would therefore be $$10^{-3}$$ times smaller, and thus negligible! This seems to be the line taken by the muon $$g-2$$ experiment team, which has also been conveyed in tweets. But the situation is worse: I believe there is no correction in the papers.

So what can we learn?

Unfortunately this gives a very bad impression for people outside of the field. It has shown how confirmation bias exists in the physics commentariat: one particular naysayer that I mentioned yesterday assumed it was probably true and was rather cruel in mocking people for placing hope in this tentative sign of new physics. It also shows that people working in physics can write papers that are wrong, and it can take a lot of time to see that this is the case.

Another thing that it highlights is how many people work. Clearly (to me) the result has been reverse-engineered: I am speculating, but I would guess that the senior physicist saw that in $$g-2$$ the discrepancy was a factor of $$10^{-9}$$, and that this was the same order of magnitude as the gravitational potential on the surface of the Earth in dimensionless units (even if this would be shocking if it could have anything to do with $$g-2$$). They then did a calculation. And then when the result that they got wasn't what they wanted to explain the experiment, they misinterpreted (not fudged) their own equations to give what they were hoping to find -- presumably entirely innocently, but let us say enthusiasm got the better side of rigour.

The reason that I propose this timeline is because it is very familiar: when we want to learn something new, we often have to guess what the answer will be before the calculation, to even have the motivation to do it in the first place. Research is actually a hugely creative process, rather than a merely deductive one. This debacle just shows that we have to be very honest with ourselves!

But on a more positive note, it shows how well the arXiv system works. The papers have effectively been massively peer reviewed in detail -- an actual peer review may not have been thorough enough (which is another discussion). Of course, now in retrospect we can see that splitting the calculation (which is not overly long or unduly technical) into three papers released at the same time was rather hubristic on the part of the authors, designed to attract attention, and the peer review process will not be smooth.

So finally: the anomalous magnetic moment of the muon persists as a possible portent for new physics, and two new experiments will be able to shed more light on the story within the next couple of years!

Note: I edited this post to tone down the language.