Stoica, Ovidiu Cristinel (2022) Born rule from counting states. [Preprint]

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Abstract

I give a very simple derivation of the Born rule by counting states from a continuous basis.

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. Counting the contributing basis vectors while taking their density into account 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 $\Psi[\phi]$ can be made real by absorbing them into a global U(1) gauge.

For the many-worlds interpretation, this result gives the Born rule from micro-branch counting.

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Item Type:	Preprint
Creators:	Creators Email ORCID Stoica, Ovidiu Cristinel holotronix@gmail.com 0000-0002-2765-1562
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:	07 Oct 2022 13:46
Last Modified:	07 Oct 2022 13:46
Item ID:	21244
Subjects:	Specific Sciences > Physics > Quantum Mechanics
Date:	18 September 2022
URI:	https://philsci-archive.pitt.edu/id/eprint/21244

Available Versions of this Item

• Born rule from counting states. (deposited 18 Sep 2022 19:42)
  • Born rule from counting states. (deposited 07 Oct 2022 13:46) [Currently Displayed]
    • Born rule from counting states. (deposited 08 Oct 2022 15:24)
      • Born rule: quantum probability as classical probability. (deposited 02 Nov 2022 21:21)
        • Born rule: quantum probability as classical probability. (deposited 13 Jan 2023 14:03)

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