The Born rule -- 100 years ago and today

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SUMMARY

The discussion centers on A. Neumaier's paper titled "The Born rule -- 100 years ago and today," which explores the evolution of the Born rule from its original formulation by Max Born in 1926 to contemporary applications in quantum optics and information theory. The paper references significant works, including 'Coherent Quantum Physics' and 'Algebraic Quantum Physics, Vol. 1,' both authored by Neumaier and D. Westra, and discusses the generalization of the Born rule to Positive Operator-Valued Measures (POVMs). It emphasizes the importance of observations in defining the fundamental state of the universe and addresses the limitations of the Born rule's applicability outside its intended domain.

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  • Understanding of the Born rule in quantum mechanics
  • Familiarity with Positive Operator-Valued Measures (POVMs)
  • Knowledge of quantum optics principles
  • Basic grasp of quantum information theory
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Researchers, physicists, and students in quantum mechanics, particularly those interested in the historical development and modern applications of the Born rule, quantum optics, and quantum information theory.

A. Neumaier
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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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