> If both the math constraints and the interpretation of an experiment are based on the same assumption, why are you taking the interpretation of the experiment any more seriously than the pure math.
Because math models the experiment, it does not define it's results.
Even math as fundamental as the laws of thermodynamics does not constrain what is permitted; they are axioms which describe the universe as best we are able to view it. If all competing theories of quantum gravity agree on a point, it would mean almost[1] nothing until that point is observed.
From the outside it feels like there is a fallacy common in at least some branches of physics (string theory...) where over-fitting math is equated with insight.
[1]I suppose you could break out Bayes' theorem and try to work out a prior for comparable theories being wrong, degree of independence between theories, etc...
Maybe a 100 years ago. With today's fundamental physics experiments (accelerators, non EM telescopes, and especially quantum foundations tests) the mathematical constructs are an inseparable part of the interpretation of the experiment.
And there it is hardly over fitting when the same results come from vastly different mathematical constructs.
Because math models the experiment, it does not define it's results.
Even math as fundamental as the laws of thermodynamics does not constrain what is permitted; they are axioms which describe the universe as best we are able to view it. If all competing theories of quantum gravity agree on a point, it would mean almost[1] nothing until that point is observed.
From the outside it feels like there is a fallacy common in at least some branches of physics (string theory...) where over-fitting math is equated with insight.
[1]I suppose you could break out Bayes' theorem and try to work out a prior for comparable theories being wrong, degree of independence between theories, etc...