vanhees71 said:
Interesting. So it's an example for the sociological "bandwagon phenomenon": Whenever there's "considerable theoretical adjustment to the raw data" necessary and there is a previous supposedly very accurate result the theoretical adjustment is tending to be iterated such to come close to this previous value. How can we be now sure that the same doesn't apply to the new measurement(s), i.e., that now the understanding is that the muon measurements are less "theory dependent" and thus give "a better value" so that now one tends to do the "theoretical adjustments" to the effect to come closer to the "muon value"?
It isn't purely a bandwagon phenomena. The whole point of the scientific method is to favor theories that conform to experimental results.
For example, it would have been easy in the development of QED to rule out amplitudes deriving from paths at which a photon travels at more than the speed of light or less so, which would have produced slightly different theoretical predictions. But, including those adjustments produces more accurate results so we include those virtual path amplitudes in making our predictions and that is pretty much now universally accepted as the right way to the QED calculations.
Also, it is worth recalling that almost no SM calculations are made to absolute exact analytical precision. We intentionally omit terms from infinite series and estimate the uncertainty introduced by doing so.
Mathematical physics is less rigorous than purely theoretical mathematics.
In that context, the possibility that initial results could have omitted a term that is theoretically well justified and has an impact only on the 0.03 fm scale in the final result that it turns out was material enough that it should have been factored into get a result closer to experiment (without disputing any of the adjustments that actually were made), isn't just sociology, or at least, isn't sociology that is likely to lead the establishment astray.
Honestly, in the face of different measurements and predictions that shouldn't theoretically be different, but are, like the charge radius of the proton on the ordinary hydrogen and muonic hydrogen cases, using the more precise measurement as a pointer towards the direction and magnitude of something that is likely to be wrong in the less precise measurement or prediction should usually be the first instinct, instead of looking for BSM explanations. A situation like this is a bit like the practical and common issue in accounting of trying to reconcile two discrepant results from the same source documents that are produced using different approaches to calculate them. It is a trouble shooting process.
And, keep in mind, as hilbert2 implies, this is not a super old problem. It took a while for people qualified to evaluate the issue closely enough look to properly evaluate it. Many of the other biggest unsolved problems in physics have been around for many decades long than this one, and the tensions involved in some of them have greater statistical significance. Likewise, solved problems also took longer from discovery of the problem to resolution. It took more than eight or nine years, for example, to solve the Pioneer 2 anomaly.
If anything, the sociological bandwagon has been the effort to throw BSM theories at the discrepancy prematurely before more prosaic explanations for the discrepancy were throughly vetted. These efforts are blowing back against that now well developed trend to look for a BSM theory to explain every anomaly that results from a scientific culture in which coming up with a theory first, before it is a sure thing, is the path to fame and full professorship.
I am far more concerned about the bandwagon thinking that keep scientists working on programs like supersymmetry and theories based upon WIMP cold dark matter particles even when experimental and observational evidence hasn't provided anything to favor supersymmetry, and has done nothing to favor WIMP CDM over alternatives to it, for many years.
