Many-Worlds, Deriving the Born Rule?

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Discussion Overview

The discussion centers on the many-worlds interpretation (MWI) of quantum mechanics, specifically examining Wallace's derivation of the Born rule through game-theoretic arguments as presented in his book, "The Emergent Multiverse." Participants explore the implications of decoherence in this context and whether it assumes the Born rule, leading to debates about circularity and the nature of probabilities in quantum mechanics.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants express concern that Wallace's derivation may be circular, as it appears to rely on the Born rule to explain decoherence, which is used to derive the Born rule.
  • Others argue that Wallace's approach is not circular, citing that decoherence does not depend on the Born rule and that Gleason's theorem can be applied independently.
  • A participant mentions that Gleason's theorem implies there can be no other probability measure than the Born rule in Hilbert spaces of dimension three or greater.
  • Some participants question the necessity of introducing probabilities in the MWI, arguing that the deterministic nature of quantum mechanics does not inherently require a probabilistic framework.
  • There is a discussion about the role of irreversibility in decoherence and measurement processes, with some suggesting that it may require probabilistic arguments, while others challenge this assertion.
  • Participants debate the relevance of Gleason's theorem, with some asserting it does not explain why probabilities should exist at all in a deterministic framework.
  • Concerns are raised about the interpretation of amplitudes in quantum states and whether they should be viewed as probabilities, with references to Wallace's explanations in his book.

Areas of Agreement / Disagreement

Participants express differing views on the circularity of Wallace's argument, the necessity of probabilities in the MWI, and the implications of Gleason's theorem. The discussion remains unresolved with multiple competing perspectives on these issues.

Contextual Notes

Limitations include the dependence on interpretations of quantum mechanics, the assumptions underlying decoherence, and the unresolved nature of the relationship between probabilities and deterministic evolution in quantum systems.

  • #61
bhobba said:
You misunderstand. No interpretation is wrong since none can be proven or disproven by experiment. Until that is the case all are equally valid. The choice of one over the other is purely based on its appeal to you.
I agree completely, and this is a good place to close the discussion. Everyone has had a chance to plug their favorite interpretation, and there is no way to objectively do anything else.
 

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