Ken G
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Yes, I think that's a good way to frame the question. So then the question becomes, what are we trying to do-- fit the data with the best polynomial we can, and just tolerate it if we can't do it very exactly (that's more or less what Ptolemy and Copernicus did, when they were stuck with using only circles), or do we generalize our thinking until we can fit it even better (that's more or less what Kepler did when he used ellipses instead of circles). It would have been quite a shock to Ptolemy to imagine ellipses in space, indeed it might have shook him to his core (the ancient Greeks firmly believed in the perfection of the cosmos, and the perfection of circles). Yet today, we teach about ellipses, without batting an eye! Consider this wonderful quote by Feynman:Ozgen Eren said:Say we have 1,2 and 3 as experimental result. Then we say most probable function that satisfies it is x=y (like classical physics until it failed). Then we get 1,2,3,7 disproving x=y (7 is like the experiments that disproved classical physics). We can still write infinite functions (theories in this case) to satisfy the experimental data we have. All those infinitely many possible explanations will have different metaphysical assumptions. And I just think quantum physics is like drawing a really weird but valid curve to explain the sequence, instead of trying to fit a smooth polynomial (a theory with our usual perception is a smooth polynomial in this case).
"We always have had … a great deal of difficulty in understanding the world view that quantum mechanics represents. At least I do, because I'm an old enough man that I haven't got to the point that this stuff is obvious to me. Okay, I still get nervous with it. And therefore, some of the younger students … you know how it always is, every new idea, it takes a generation or two until it becomes obvious that there's no real problem. It has not yet become obvious to me that there's no real problem. I cannot define the real problem, therefore I suspect there's no real problem, but I'm not sure there's no real problem."
In that quote, he seems to agree with you that it would be nice to "fit a polynomial" in your words, but by the same token, he suspects this is just a prejudice of his, that will likely vanish in future generations-- much as the desire for circles in space vanished when ellipses came along.