Re: philosophical collapse question

Posted by DickT on May 19, 2003 at 11:09:29:

In Reply to: Re: philosophical collapse question posted by yanniru on May 19, 2003 at 08:30:27:

yanniru,

How do the philosophers of physics explain the magic of collapsing wave functions

They don't! They call it "the measurement problem" and write long books about it.

Here's what happens formally. A quantum state is representd by a set of elements in a vector space called Hilbert space. Actually all the elements that can be obtained from each other by multiplying by a complex number are called a "ray" and each physical state is represented by such a ray. Comes now along an operator (like a matrix) and acts on the ray, producing a set of states called eigenstates and a set of real numbers called eigenvalues. The eigenvalues give the probability for the physical system to be in the correspending eigenstate.

You may have noted there's no wave function in all of this. But historically Schrodinger's wave equation gave the state in terms of a wave. And the operator/eigenvalue thing was what they called the collapse of the wave function. Many physicists reified the wave - thought of it as a real thing - and so they were troubled by the unphysical properties it had. Collapse was just one. Other physicists abandoned the wave for a completely Hilbert space approach. This is pretty abstract, but it allows calculations without unphysical interpolations.

Regards,
Dick

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