NetNews Usenet Archive 1993 #3/NN_1993_3.iso/spool/sci/physics/23430

Internet Message Format | 1993-01-25 | 2.3 KB

Path: sparky!uunet!mtnmath!paul
From: [e-mail] (Paul Budnik)
Newsgroups: sci.physics
Subject: Re: hidden variables
Message-ID: <[e-mail]>
Date: 25 Jan 93 17:52:49 GMT
References: <[e-mail]> <[e-mail]>
Organization: Mountain Math Software, P. O. Box 2124, Saratoga. CA 95070
Lines: 39

In article <[e-mail]>, [e-mail] (Dale Atems) writes:
][...]
] Well, here is a rather half-baked proposal based on what I said
] earlier. Let the left and right kets in the singlet state vector
] be in the internal spaces of *distant* wavefronts. I have in mind
] wavefronts corresponding to distinct photons; thus they are emitted
] simultaneously in opposite directions. As each wavefront encounters
] a polarizer, expand its kets in a basis aligned with that polarizer.
] The encounters need not be simultaneous, but the result is that the
] relative angle @ in the formula
]
]       |psi> = 2^(-1/2) (cos@ |x>|x'> + sin@ |x>|y'>
]                        -sin@ |y>|x'> + cos@ |y>|y'>)
]
] is the angle between the polarizers at the time the two encounters
] occur in a reference frame in which they are simultaneous.

This is an explicitly nonlocal wave function that cannot be
derived within QM. The amplitude of `psi' is a function of `@' which
is the angle between two spatially separated polarizers. Changing either
polarizer instantaneously changes the amplitude of a distant wave function.
Such a wave function cannot be Lorentz invariant and cannot be derived
from the relativistic Shrodinger equation.

][...]
] I have no idea if this can be made mathematically rigorous in
] the wave equation formalism. I think it is in the spirit of the
] QM description and shows that, at least on the conceptual level,
] one need not invoke collapse or nonlocal interactions to obtain
] the expected probabilities and timing.

On the contrary I think it helps to illustrate why you have to invoke
collapse. A non Lorentz invariant wave function cannot be derived within
QM. The only mechanism QM provides for deriving violations of locality
involve collapsing the wave function to be consistent with an observation
at one site and then using this collapsed function to compute the
probability of detection at the other site.

Paul Budnik