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Born rule: quantum probability as classical probability

Stoica, Ovidiu Cristinel (2022) Born rule: quantum probability as classical probability. [Preprint]

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Abstract

I provide a simple derivation of the Born rule as giving a classical probability, that is, the ratio of the measure of favorable states of the system to the measure of its total possible states.

In classical systems, the probability is due to the fact that the same macro state can be realized in different ways as a micro state. Despite the radical differences between quantum and classical systems, the same can be applied to quantum systems. More precisely, I show that in a continuous basis, the contributing basis vectors are present in a state vector with real and equal coefficients, but they are distributed with variable density among the eigenspaces of the observable. The measure of the contributing basis vectors gives the Born rule without making other assumptions.

This works only if the basis is continuous, but all known physically realistic measurements involve a continuous basis, because they involve the positions of the particles.

The continuous basis is not unique, and for subsystems it depends on the observable.

But for the entire universe, there are continuous bases that give the Born rule for all measurements, because all measurements reduce to distinguishing macroscopic pointer states, and macroscopic observations commute. This allows for the possibility of an ontic basis for the entire universe.

In the wavefunctional formulation, the basis can be chosen to consist of classical field configurations, and the coefficients Ψ[ϕ] can be made real by absorbing them into a global U(1) gauge.

This suggests an interpretation of the wavefunction as a nonuniform distribution of classical states. For the many-worlds interpretation, this result gives the Born rule from micro-branch counting.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Stoica, Ovidiu Cristinelholotronix@gmail.com0000-0002-2765-1562
Keywords: Born rule; state counting; Everett's interpretation; many-worlds interpretation; branch counting.
Subjects: Specific Sciences > Physics > Quantum Mechanics
Depositing User: Ovidiu Cristinel Stoica
Date Deposited: 02 Nov 2022 21:21
Last Modified: 02 Nov 2022 21:21
Item ID: 21349
Subjects: Specific Sciences > Physics > Quantum Mechanics
Date: 18 September 2022
URI: http://philsci-archive.pitt.edu/id/eprint/21349

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