The Axiomatization of Physics?

"pi"mp

So I have read that Hilbert and his student, Hermann Weyl both attempted to "axiomatize" physics. What exactly does this mean? I'm sort of naively assuming it means they should like to have a small set of axioms from which all of physics follows. Is that kind of the idea?

But isn't that sort of what physics is already? Like in classical mechanics, can't you make a leap of faith as to the relation between force and acceleration and everything follows very nicely?

Sorry if I'm way off base; just a curious undergrad...also does anyone know of any good books on this topic? or in regard to philosophy of math/physics in general?

atyy

Perhaps he meant a complete axiomatization. In his day, they didn't have quantum mechanics, so many Newtonian forces like friction would just be "effective", not fundamental. Of course today, we believe that even the standard model of particle physics is effective (ie. wrong at high energies). And I'd be surprised if anyone can calculate friction from the standard model.

Travis_King

They wanted to build a proof of physics based on "axioms" or self-evidentially true statements. By creating a physics which was bourne out of a priori arguments, it could be accepted universally as valid. Axiomatization rarely works for anything, though.

A. Neumaier

The 1932 book by von Neumann may be considered the answer to Hilbert's quest. See http://en.wikipedia.org/wiki/Von_Neu...ntum_mechanics

PatrickPowers

Right, the idea was to have a small set of axioms from which all physics follows.

However general relativity is not built this way. The definitions are circular, which axiomatics does not allow.

A. Neumaier

It is easy to remove circularity from any set of postulates, just be rephrasing things properly.
Otherwise, Euclid's axioms for elementary geometry (_the_ paradigm fior an axiom system) would have to be regarded as circular, too.

andrebourbaki

Dear Student and Prof. Neumaier:

In my opiniion, and I am convinced this was Wigner's opinion too,
the Dirac--von Neumann axiomatisation of QM suffers from one (fatal) flaw that
means it is not 'Hilbertian'. Wigner called this 'The Problem of Quantum Duality'
and he did not mean wave-particle duality, which he believed was no big deal
and should not even have been called a duality. See his classic papers on
this reprinted in his collection *Symmetries and Reflections*. Wigner was
much influenced by Hilbert, and on this question of Quantum Measurement,
von Neumann learned from Wigner (they were good friends).

Briefly, this 'duality' is that different axioms can be applied to the
exact same physical situation and one gets different answers. This is a fatal
ambiguity or duality. This is the same flaw John Bell pointed to. See Bell's
classic articles reprinted in *Speakable and Unspeakable in Quantum Mechanics*
where he is always careful to distinguish his logical complaints from his
realism and intuition complaints.

I agree with Prof. Neumaier that Hilbert's problem would be
(essentially) solved if Dirac--von Neumann were acceptable, I think QFT
is derivable from QM in principle so introduces no foundational difficulties,
only the usual difficulties of finding practical working approximations that
will calculate answers. And I anticipate no problems unifying GenRel with
QM except that the lack of data means we are going to be unable to distinguish
which unification is correct....not an axiomatic problem.

Try googling on Wigner Quantum Duality to see what I mean.

Oddly enough, *I* am the problem of Wigner's friend since I am
a friend of (his son, David) Wigner and I am certainly a problem... jajajaja....
just ask him....