TITLE: Applying the principle of Occam's Razor to Quantum Mechanics
QUESTION [15 upvotes]: Wolfgang Demtröder writes this in his book on Experimental Physics, 

The future destiny of a microparticle is no longer completely determined by its past. First of all, we only know its initial state (location and momentum) within limits set by the uncertainty relations. Furthermore, the final state of the system shows (even for accurate initial conditions) a probability distribution around a value predicted by classical physics.

If the quantum probabilistic distribution always lie near the classical prediction, why do we need quantum mechanics in the first place? According to the Feynman interpretation, if an electron has to go from A to B, it can take all the paths but the weight is more on the path predicted by classical mechanics. We know that it is unlikely that the electron travel through the mars to go from A to B on earth. Then, is not that path through mars is unnecessary? Should not in the spirit of Occam's razor, we exclude such thing in a theory?

REPLY [0 votes]: Feynman thought his path integral formulation might be conceptually useful, but it is a matter of opinion whether it actually is (personally I don't find it helpful). If you want to apply Occam's razor, then at least do it to the mathematical structure defined by Dirac and von Neumann. This is expressed in Wikipedia with only three axioms. You could hardly get simpler than that, so (for what it is worth) Occam's razor clearly supports quantum mechanics. If you are talking of interpretations, then again von Neumann's approach could hardly be simpler as I have explained in The Hilbert space of conditional clauses.
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