Objective Collapse Equation Maintains Conservation Laws With No New
Constants
- URL: http://arxiv.org/abs/2209.01015v3
- Date: Wed, 30 Nov 2022 20:12:16 GMT
- Title: Objective Collapse Equation Maintains Conservation Laws With No New
Constants
- Authors: Edward J. Gillis
- Abstract summary: Two-particle interaction potential energies can be used as the basis for a collapse term added to the Schr"odinger equation.
Conservation is exact for momentum and orbital angular momentum.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Modified versions of the Schr\"{o}dinger equation have been proposed in order
to incorporate the description of measurement processes into the mathematical
structure of quantum theory. Typically, these proposals introduce new physical
constants, and imply small violations of momentum and energy conservation.
These problematic features can be eliminated by assuming that wave function
collapse is induced by the individual interactions that establish correlations
between systems. The generation of a sufficient number of small, random shifts
of amplitude between interacting and noninteracting branches of the wave
function can bring about collapse on a scale consistent with our macroscopic
experience. Two-particle interaction potential energies can be used as the
basis for a collapse term added to the Schr\"{o}dinger equation. The range of
the interactions sets the distance scale of the collapse effects; the ratio of
potential energies to the total relativistic energies of the particles
determines the magnitude of the amplitude shifts, and the rate at which the
interactions proceed fixes the timing parameters.
Consistency with conservation laws in individual experiments is maintained
because the collapse operator automatically takes into account the small,
residual entanglement between the measured system and systems with which it has
previously exchanged conserved quantities during interactions. Conservation is
exact for momentum and orbital angular momentum, and it holds for energy within
the accuracy allowed by the limited forms of energy describable in
nonrelativistic theory.
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