Mathematics and the Universe

[infidel666]

But ... but ... but ...

OK, "predictions" are made, but the predictions are not things like E=mC^2. People don't come up with a theory based on quantum mechanics and then go look for a way to verify it.

What? Yes, we do! I myself have used quantum mechanics to predict the tunnelling current through a Scanning Tunnelling Microscope at a given distance from a sample.

The "predictions" of quantum mechanics are about probability fields of particle position and momentum.

That, and everything predicted by classical mechanics (above atomic-scale physics, that is; quantum mechanics refines classical predictions at the atomic scale and below).

Not hard to tell I took my physics degree at a University that adheres to the tradition of the experimental school, as opposed to the theoretical school. The rivalry lives!

Fair enough. I should have said that quantum mechanics is used to predict values of measurements of characteristics of observable quanta. But I don't think predicting the current in a microscope is quite the same thing as coming up with a paradigm shifting relationship like E=mC^2.

Just the way I view it anyway. Plus, I know I'm right because a bunch of esteemed physics profs told me so and I paid them lots of money to do it. So there!

Please, God, don't let it have been all for nothing. Oooops. I think I just prayed.

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For fundamental physics, I'm talking about the theory of gravity, for example. The greeks initially thought and took as given that objects of different masses, dropped from the same height, would hit the ground at different times. They thought that the rate of falling was proportional to the mass of the object, so the heavier object would fall faster. Eventually, someone discovered it was not true, and the mass of the object is irrelevant.

The relevant point is that it was found to be a wrong hypothesis empirically. The actual testing of hypothesis was a very significant break with traditional thinking. By it Aristotelean intuïtion was proven wrong. Also it should be made clear that at the time of the falling body experiment (for the first time in 1544, the historian Benedetto Varchi referred to tests which refuted Aristotle's assertion) the empirical scientific approach was in it's infancy. There was no distinction between philosophy and science. Because of this it doesn't serve as an example that fundamental physics arose from theory instead of experimentation.

Eventually, the theory of gravity was developed. Later, that theory was found to be incomplete, and so on.

Again it was found to be incomplete empirically. Also Einstein's original paper on Special Relativity emphasizes the empirical basis of the postulates he used.

But the problem is that people have continuously attempted to theorize something elegant to reconcile a foregone conclusion with a contradiction.

Do you mean contradiction with empirical facts?

In contrast, quantum mechanics has developed from pure experimentation.

I think theoretical consideration may guide empirical investigation and vice versa. The emphasis may vary from theory to theory, but there is never a strict division between the two. In case of the Pauli Exclusion Principle (PEP) I think it is clear that empirical facts (certain spectroscopic phenomena) are generalized to a prescriptive rule. In January 1925 Pauli wrote:

In an atom there cannot be two or more equivalent electrons for which the values of all four quantum numbers coincide. If an electron exists in an atom for which all of these numebers have definite values, then this state is occupied.

As you can see, it's first application was confined to the atom. A year later in 1926 Fermi and Dirac independently from each other reformulated the rule in a mathematical form that suggested a more general domain of application outside the atom but still for electrons only. Later in 1940 it became clear that the rule could be extended to any half spin particle. Eventually it became a building block for QCD. In this case you clearly can see that empirical facts are formulated as rules triggering the theoretical investigation into a broader domain of validity than from the empirical facts at hand could be deduced, in turn triggering empirical reasearch. In the case of the PEP this bouncing from empirical investigation to theoretical investigation happened more then once. It's almost a case of stress testing a principle. Pauli had struck gold without knowing it's broad application. Empirical testing was guided by theorizing about the genericity of the principle. Imo this shows that in QM also theoretical argument and empirical results go hand in hand.

Attempts to make predictions based on it have largely failed. Attempts to reconcile general relataivity with quantum mechanics have failed. And it is because we keep trying to reconcile this beloved, elegant, foregone conclusion with inconvenient evidence that it is wrong. Past attempts were successful, but quantum mechanics is an insurmountable hurdle. You have to give up the elegant math. The elegant stuff is wrong.

The history of PEP, I think, tells another story.

Well, I didn't mean to imply that no theoretical consideration has guided the development of Quantum Mechanics, or that no empirical evidence has guided Relativity or Classical Physics. I don't think I said that. What I did say, I think, or what I meant to say, was that Classical Physics and Relativity started out as pure conjecture/philosophy and was then guided by empiral evidence, while Quantum Mechanics started out as empirical evidence (non-intuitive evidence at that) that has been developed into a theory. And sure, predictions have been made from quantum mechanics, such as Hawking radiation, and later found (exception proves rule?). And sure, it is possible to view Relativity and Quantum Mechanics as two bracnhes of science that developed from classical physics in response to new observable phenomenon. But there is a philosophical difference in the type of rigor that led to these two branches of science (experiment as starting point vs. conjecture), perhaps simply because quantum mechanics is so non-intuitive.