Links between Everett, Feynman, Kripke?

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SUMMARY

The discussion explores the connections between Richard Feynman's path integral formulation, Hugh Everett's Many-Worlds Interpretation (MWI), and Saul Kripke's contributions to mathematical logic. Feynman's approach maintains a single universe while calculating wave functions, whereas Everett posits independent universes for each possible outcome, addressing the measurement problem without wave-function collapse. The relationship between Feynman and Everett is superficial, as they tackle different issues in quantum mechanics. Additionally, the discussion touches on Kripke frames and their potential parallels to quantum states, suggesting that while quantum logic has been explored, C*-algebra may offer a more effective framework.

PREREQUISITES
  • Understanding of Feynman's path integral formulation in quantum mechanics
  • Familiarity with Everett's Many-Worlds Interpretation (MWI)
  • Basic knowledge of Kripke frames in mathematical logic
  • Awareness of quantum logic and C*-algebra concepts
NEXT STEPS
  • Research Feynman's path integral formulation in detail
  • Explore the implications of Everett's Many-Worlds Interpretation
  • Investigate Kripke-Joyal semantics and its relevance to intuitionistic logic
  • Study the applications of linear logic in quantum mechanics
USEFUL FOR

Physicists, mathematicians, and logicians interested in the intersections of quantum mechanics, mathematical logic, and interpretations of wave functions.

nomadreid
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As I state my questions, there are likely to be errors that I would appreciate being corrected. Beyond that, however, if the gist of the questions can be salvaged after correcting these errors, I would also like answers to your version of the questions.
Both Feynman's summation over histories and Everett's MWI start off from the collection of possible events at any given moment. From there Feynman keeps them all in one universe and performs path integrals, while Everett has each path lead an independent existence in its own universe. Nonetheless, there is the gut feeling that the two have probably been unified somewhere. If so, could someone outline how or give me a link (that doesn't lead to a to-be-paid-for article)?
Secondly, in mathematical logic, the theory of Kripke frames is sometimes called many worlds, and one can see a superficial resemblance to the states of quantum physics, but has this ever been pursued?
 
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The relation between Feynman and Everett is only superficial. They address completely different problems. While Feynman gives a mathematical method to calculate the wave function and this method is completely equivalent to the Schrödinger equation, Everett attempts to solve the measurement problem, i.e., to give a physical meaning to the wave function without introducing the wave-function collapse.
 
nomadreid said:
Secondly, in mathematical logic, the theory of Kripke frames is sometimes called many worlds, and one can see a superficial resemblance to the states of quantum physics, but has this ever been pursued?
People have looked at something called "quantum logic" -- but my vague not-a-physicist impression is that you can do the same thing better with C*-algebra.

John Baez briefly mentions "linear logic" being applied to quantum mechanics. I'm not sure if this application is really different than quantum logic.


I'm really only familiar with Kripke through Kripke-Joyal semantics which relates to intuitionistic logic -- I can't say if it bears any relevance to what I mentioned above. But Stanford's page on linear logic does mention Kripke models.
 

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