The Born rule -- 100 years ago and today

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Discussion Overview

The discussion centers around the evolution and implications of the Born rule in quantum mechanics, tracing its historical development from its introduction by Max Born in 1926 to contemporary interpretations and applications. The scope includes theoretical aspects, historical context, and recent advancements in understanding the Born rule, particularly in relation to quantum optics and information theory.

Discussion Character

  • Exploratory
  • Technical explanation
  • Historical

Main Points Raised

  • A. Neumaier presents a new paper discussing the historical and modern formulations of the Born rule, emphasizing its generalization to positive operator-valued measures (POVMs) and its relevance in current quantum theories.
  • Neumaier argues that the various forms of the Born rule have restricted domains of validity, which can lead to issues when applied outside these domains.
  • There is a discussion regarding the nature of observations in quantum mechanics, referencing Dyson's views on the reality of observations and their role in defining the fundamental state of the universe.
  • Neumaier suggests that what is observable experimentally contributes to our understanding of reality in physics, raising questions about the relationship between quantum states and the fundamental state of the universe.
  • Neumaier has uploaded a revised version of his paper, incorporating improvements on derivations of the Born rule.
  • An extended version of the paper has been published, which includes translations of German quotes for broader accessibility.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints regarding the interpretation and implications of the Born rule, with no consensus reached on the nature of observations or the extent of the rule's applicability.

Contextual Notes

Participants express varying interpretations of the foundational aspects of quantum mechanics, particularly concerning the relationship between observations and the underlying reality, which may depend on differing philosophical perspectives.

A. Neumaier
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TL;DR
announces my newest paper, and relates it to a recent discussion on reality and quantum physics
I have written a new paper:
  • A. Neumaier, The Born rule -- 100 years ago and today, Manuscript (2025). arXiv:2502.08545
Abstract. Details of the contents, and formulations of the Born rule changed considerably from its inception by Born in 1926 to the present day. Based to a large extent on little known results from the recent books 'Coherent Quantum Physics' by A. Neumaier and 'Algebraic Quantum Physics, Vol. 1' by A. Neumaier and D.Westra, this paper traces the early history of the Born rule 100 years ago, its generalization (essential for today's quantum optics and quantum information theory) to POVMs 50 years ago, and a modern derivation from an intuitive definition of the notion of a quantum detector. Also discussed is the extent to which the various forms of the Born rule have, like any other statement in physics, a restricted domain of validity, which leads to problems when applied outside this domain.

A. Neumaier said:
Observations are physical in Dyson's text quoted in #1, since they are taken as objective pieces of evidence. Since they do not appear in the wave function, they are additional input to reality.
martinbn said:
Not sure what you mean by this and how it relates to my post! Are you saying that Dyson takes observations for lambda?
A. Neumaier said:
I am saying that Dyson takes certain things for real. These must be described by real physics, and play the role of what Demystifier calles lambda.
See Subsection 3.5: What is missing in the foundations? of my new paper.

What is observable experimentally is part of what is real (if there is anything real in physics). The totality of what is real defines (by definition) the fundamental state of the universe. Thus each observation (and in particular each measurement) encodes a certain tiny part of this fundamental state.

The question is what quantum mechanical states have to do with this fundamental state of the universe, to which we have partial experimental access.
 
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Greg Bernhardt said:
Congrats Arnold!
You are welcome.
In the mean time, I uploaded v2, with some improvements on various attempted derivations of the Born rule.
 
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