On Wavefunction Collapse, the Einstein-Poldolsky-Rosen Paradox and Measurement in Quantum Mechanics and Field Theory

TL;DR

This paper argues that wavefunction collapse is unnecessary to explain quantum measurement and resolves the EPR paradox by emphasizing unitarity in quantum mechanics and field theory, leading to new insights on measurement processes.

Contribution

It demonstrates that wavefunction collapse is incompatible with fundamental principles in first-quantized QM and extends the analysis to quantum field theory, providing a consistent interpretation of entanglement and Bell experiments.

Findings

Wavefunction collapse violates conservation laws and uncertainty principles.

Unitarity alone suffices to resolve the EPR paradox in first-quantized QM.

In quantum field theory, collapse cannot be fully ruled out, but unitarity and complete degrees of freedom support a consistent interpretation.

Abstract

We first consider the Einstein-Podolsky-Rosen (EPR) paradox for the system of two particles with spin 1/2 with entangled spins in first-quantized quantum mechanics (QM). If measurement is governed by wavefunction collapse, then gedanken experiments show that a number of fundamental principles including conservation of angular momentum and the Heisenberg uncertainty principle can be violated. We conclude that the collapse of the spin part of the wavefunction cannot happen and therefore an EPR paradox does not arise for this system. QM unitarity alone is sufficient to rule out "spooky" action at a distance. The absence of spin wavefunction collapse leads to several interesting conclusions about how measurement works in QM: When wavefunction collapse does not happen, (i) a signal from a macroscopic measuring device indicating that a system is in a state S does not necessarily mean that it is or was in S and (ii) the uncertainty in QM at the microscopic level is transmitted to uncertainty in signals for the macroscopic measuring device. We derive two general results on how quantum measurement works and illustrate them in a spin-1/2 measurement. In contrast to first-quantized QM, in quantum field theory we are unable to fully rule out the possibility of wavefunction collapse. However, when we insist on unitarity (thereby excluding the possibility of wavefunction collapse) and additionally take into account in the wavefunction all degrees of freedom involved in the measurement (including those of the equipment, experimentalists, etc.), a consistant acceptable understanding of the Bell-inequality-type experiments involving entangled photon polarizations emerges including the absence of an EPR paradox. The ability of an experimentalist to be aware of his perceptions but unable to be conscious of other components of a generalized Schrodinger Cat plays a role in resolving the Measurement Problem.