Ellerman, David (2025) Born Again! The Born Rule as a Feature of Superposition. [Preprint]
![[img]](https://philsci-archive.pitt.edu/style/images/fileicons/text.png) |
Text
IJQF2025v11n2p2_corrected.pdf Download (348kB) |
Abstract
Where does the Born Rule come from? We ask: “What is the simplest extension of probability theory where the Born rule appears”? This is answered by introducing “superposition events” in addition to the usual discrete events. Two-dimensional matrices (e.g., incidence matrices and density matrices) are needed to mathematically represent the differences between the two types of events. Then it is shown that those incidence and density matrices for superposition events are the (outer) products of a vector and its transpose whose components foreshadow the “amplitudes” of quantum mechanics. The squares of the components of those “amplitude” vectors yield the probabilities of the outcomes. That is how probability amplitudes and the Born Rule arise in the minimal extension of probability theory to include superposition events. This naturally extends to the full Born Rule in the Hilbert spaces over the complex numbers of quantum mechanics. It would perhaps be satisfying if probability amplitudes and the Born Rule only arose as the result of deep results in quantum mechanics (e.g., Gleason’s Theorem). But both arise in a simple extension of probability theory to include “superposition events”–which should not be too surprising since superposition is the key non-classical concept in quantum mechanics.
| Export/Citation: | EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL |
| Social Networking: |
| Item Type: | Preprint | ||||||
|---|---|---|---|---|---|---|---|
| Creators: |
|
||||||
| Keywords: | Born Rule; superposition; quantum mechanics; superposition event | ||||||
| Subjects: | General Issues > Scientific Metaphysics Specific Sciences > Probability/Statistics Specific Sciences > Physics > Quantum Mechanics |
||||||
| Depositing User: | Dr. David Ellerman | ||||||
| Date Deposited: | 03 Apr 2025 13:18 | ||||||
| Last Modified: | 03 Apr 2025 13:18 | ||||||
| Item ID: | 24960 | ||||||
| Official URL: | https://ijqf.org/archives/7372 | ||||||
| Subjects: | General Issues > Scientific Metaphysics Specific Sciences > Probability/Statistics Specific Sciences > Physics > Quantum Mechanics |
||||||
| Date: | March 2025 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/24960 |
Monthly Views for the past 3 years
Monthly Downloads for the past 3 years
Plum Analytics
Actions (login required)
 |
View Item |
![[feed]](http://philsci-archive.pitt.edu/style/images/feed-icon-32x32.png){kind=icon}