Born rule: quantum probability as classical probability
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912347456536576 |
|---|---|
| author | Stoica, Ovidiu Cristinel |
| author_facet | Stoica, Ovidiu Cristinel |
| contents | 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 (an eigenbasis of observables with continuous spectra), but all known physically realistic measurements involve a continuous basis (the position basis).
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 a unique 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 many-worlds interpretation, this result gives the Born rule from micro-branch counting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_08621 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Born rule: quantum probability as classical probability Stoica, Ovidiu Cristinel Quantum Physics Mathematical Physics History and Philosophy of Physics 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 (an eigenbasis of observables with continuous spectra), but all known physically realistic measurements involve a continuous basis (the position basis). 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 a unique 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 many-worlds interpretation, this result gives the Born rule from micro-branch counting. |
| title | Born rule: quantum probability as classical probability |
| topic | Quantum Physics Mathematical Physics History and Philosophy of Physics |
| url | https://arxiv.org/abs/2209.08621 |