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 macrostate can be realized in different ways as a microstate. Despite the radical differences between quantum and classical systems, I show that the same can be applied to quantum systems, and the result is the Born rule.
This works only if the basis is continuous, but all known physically realistic measurements involve a continuous basis, because they are based eventually on distinguishing positions.
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.
For the manyworlds interpretation, this result gives the Born rule from microbranch counting.
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Item Type:  Preprint  

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Keywords:  Born rule; state counting; Everett's interpretation; manyworlds interpretation; branch counting.  
Subjects:  Specific Sciences > Physics > Quantum Mechanics  
Depositing User:  Ovidiu Cristinel Stoica  
Date Deposited:  13 Jan 2023 14:03  
Last Modified:  13 Jan 2023 14:03  
Item ID:  21654  
Subjects:  Specific Sciences > Physics > Quantum Mechanics  
Date:  18 September 2022  
URI:  https://philsciarchive.pitt.edu/id/eprint/21654 
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)

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) [Currently Displayed]

Born rule: quantum probability as classical probability. (deposited 02 Nov 2022 21:21)

Born rule from counting states. (deposited 08 Oct 2022 15:24)

Born rule from counting states. (deposited 07 Oct 2022 13:46)
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