The lore on complex probabilities

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    Quantum mechanics
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Discussion Overview

The discussion revolves around the origins and interpretations of complex probabilities in quantum mechanics, particularly in relation to Feynman's path integral formulation and its connections to Dirac's work. Participants explore historical references and the evolution of these concepts within the framework of quantum theory.

Discussion Character

  • Exploratory, Historical, Debate/contested

Main Points Raised

  • One participant suggests that the concept of complex probabilities in quantum mechanics may originate from Feynman's interpretation of space-time paths, which involves a complex exponential related to a Dirac delta function.
  • Another participant mentions that Dirac discussed this topic in his 1932 work, "The Principles of Quantum Mechanics."
  • A participant notes that Feynman claimed to have derived insights from Dirac, particularly regarding contact transformations, but also indicates that there were disagreements between them on the significance of these ideas.
  • There is a clarification about the editions of Dirac's work, with a participant correcting the year of the first edition to 1930 and providing details about subsequent editions.
  • One participant expresses difficulty in accessing earlier editions of Dirac's work, noting their rarity in libraries.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the exact origins of complex probabilities, and there are multiple viewpoints regarding the historical context and significance of the contributions from Feynman and Dirac.

Contextual Notes

Participants reference specific editions of Dirac's work, but there are limitations in accessing earlier texts, which may affect the completeness of the discussion.

arivero
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I think that the lore on the need of having probability interference in quantum mechanics and then a complex probability originates in Feynman interpretation of space-time paths, whose probability is weighed with a complex exponential that approaches a dirac delta.

But I can not pinpoint a concrete source of this lore; perhaps it even predated the path integral. Any guesses?
 
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AFAIK Dirac mentioned it in 32. The Action Principle, The Principles of Quantum Mechanics.
 
Going to check, thanks. It makes sense because Feynman claims to have got is insight from Dirac, I think from some work on contact transformations. But also [I believe to remember that he told...] that he was unable to agree with Dirac on the significance.
 
I see, this is the third edition, that already uses Dirac notation:

1707148447124.png


Is it the same in the 1932 edition?
 
1930 you mean. It was the 1st edition, second came in 1935, third in 1947, and fourth and final in 1958. I don't have access to any of thr first two editions. Very rare in libraries.
 

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