I The Born rule -- 100 years ago and today

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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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Thread 'Violation of Bell Inequality with unentangled photons'

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I understand that the world of interpretations of quantum mechanics is very complex, as experimental data hasn't completely falsified the main deterministic interpretations (such as Everett), vs non-deterministc ones, however, I read in online sources that Objective Collapse theories are being increasingly challenged. Does this mean that deterministic interpretations are more likely to be true? I always understood that the "collapse" or "measurement problem" was how we phrased the fact that...
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Thread 'Modern View of Quantum Phenomena'

This is not, strictly speaking, a discussion of interpretations per se. We often see discussions based on QM as it was understood during the early days and the famous Einstein-Bohr debates. The problem with this is that things in QM have advanced tremendously since then, and the 'weirdness' that puzzles those attempting to understand QM has changed. I recently came across a synopsis of these advances, allowing those interested in interpretational issues to understand the modern view...
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