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Jan7-08, 04:03 PM
Sci Advisor
P: 892

There is no derivation of the Schrodinger E., nor of the 2nd Law of Newton
If the chosen set of axioms does not contain Schrodinger/ Newton equations, then the formalisim should provide ways for DERIVING them from the axioms. Any failure means that your axioms contain a piece of garbage.
....Indeed, to the uncritical, non-Humean eye, Noether's Thrm is a derivation of Conservation Laws -- but how could we even begin to examine all the assumptions that lurk behind Emily Noether, which must be done in order to give a sound evaluation of derivation vs. plausibility argument?
Noether's theorem is a THEOREM! "given A, then B"; where A is the invariance under some Lie group, and B is a statement about a conserved quantity that can be DERIVED SYSTEMATICALLY from the action integral. If this is not a derivation, can you tell us what is it that we do when we play with equations and produce B from A?

Who cares, if nothing can be derived?
I do, because I lose my job if I cann't derive anything!

Mathematicians use axioms; physicists use experiments.
I am a physicist and I only care about a self-consistent set of axioms, I leave experiments for the more able peopel who work on them!