Axiomatization of quantum mechanics and physics in general ?

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SUMMARY

The discussion centers on the axiomatization of quantum mechanics and its relationship with mathematical formulations. Key points include the necessity of establishing rules to map physical concepts into mathematical objects, as well as the distinction between formal proofs and their interpretations in mathematical physics. The conversation highlights the work of Constantin Piron, who proposed a three-axiom formulation of quantum mechanics, and references various mathematical models and theorems such as Noether's theorem. The challenges of interpreting mathematical symbols in relation to physical experiments are also emphasized, showcasing the complexity of bridging formal systems with practical applications.

PREREQUISITES
  • Understanding of formal proofs and well-formed formulas in mathematical logic.
  • Familiarity with model theory and its application in mathematical structures.
  • Knowledge of quantum mechanics axioms and their implications.
  • Basic concepts of mathematical modeling in physics.
NEXT STEPS
  • Research Constantin Piron's three axioms of quantum mechanics.
  • Explore the implications of Noether's theorem in mathematical physics.
  • Study the geometric approach to quantum mechanics as presented in Varadarajan's "Geometry of Quantum Theory."
  • Investigate the differences between frequentist and Bayesian interpretations of probability in quantum mechanics.
USEFUL FOR

This discussion is beneficial for physicists, mathematicians, and researchers interested in the foundational aspects of quantum mechanics, mathematical modeling, and the interplay between formal systems and physical theories.

  • #211
atyy said:
Where did you learn to derive CHSH?

Originally a combination of an introduction to Bell's theorem by Travis Norsen [arXiv:0707.0401 [quant-ph]], one of Bell's explanations ["The theory of local Beables"], and just sitting down and working it out. I'd read both Bell's original 1964 article the 1969 CHSH article before that but didn't find the reasoning quite as clear.

Deriving the local bound on a given linear Bell correlator isn't really an issue though. Like you pointed out earlier in post #192, it's sufficient to consider deterministic models. You can always work out the local bound on a linear Bell correlator just by maximising it over the set of local deterministic strategies (i.e., deterministic ways of mapping inputs ##x## and ##y## to outputs ##a_{x}## and ##b_{y}##), and there are a finite number of these (e.g., there are sixteen in the situation that the CHSH correlator applies to).
 
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