Are World Counts the Key to Understanding the Born Rule?

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Discussion Overview

The discussion revolves around the coherence of world counting in the context of the Born rule within the Everett interpretation of quantum mechanics. Participants explore whether assigning probabilities based on the number of distinguishable branches or worlds is valid, particularly in relation to measurement statistics that appear to align with the Born rule.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants reference Wallace and Greaves' claim that world counting is incoherent, questioning whether this incoherence applies universally or only in specific contexts.
  • Wallace argues that realistic models of macroscopic systems are infinite-dimensional, complicating the notion of counting branches and suggesting that decoherence is an ongoing process rather than discrete events.
  • Another participant draws an analogy with entropy, suggesting that while the exact number of states can be sensitive to model details, the concept of entropy remains useful for making predictions about system behavior.
  • Concerns are raised about the assignment of equal probabilities to worlds, with one participant noting the lack of ergodicity in world counting, which complicates the justification for uniform probability distributions across worlds.
  • Some participants express skepticism about the claim that ambiguities in defining worlds render the concept incoherent, arguing that these ambiguities may not significantly affect the observation of Born rule frequencies in measurements.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the coherence of world counting or the implications for the Born rule. Multiple competing views are presented, with ongoing debate about the validity of world counting and its relationship to probability assignments.

Contextual Notes

Participants highlight limitations in defining the number of descendants and the sensitivity of such definitions to model specifics, suggesting that the discussion is constrained by the complexities of quantum systems and the nature of decoherence.

  • #31
Ontoplankton said:
Still, there is something that bothers me. The extra branching process could happen later than the coinflip, right? In that case, you're letting probabilities be influenced by events that happen later in time. Does that make sense?

I don't see a problem with it.
 
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  • #32
straycat said:
according to the APP/outcome counting, if the extra branching process happens later than the coinflip, then the extra process does not influence the probability that the coinflip comes up heads or tails

If post-experiment branching doesn't matter, then isn't that already enough to complete the erasure proof in section 8?
 
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  • #33
Quantum Arson: You can win the lottery by resolving to burn a lot of stuff if you win, because that will generate a lot of entropy, so it will have happened in more worlds.
 
  • #34
RobinHanson said:
FYI, in the latest issue of the British Journal of the Philosophy of Science, Hillay Putnam has an article http://bjps.oxfordjournals.org/cgi/reprint/56/4/615" , wherein he rejects the many worlds view because of the conflict between world counting and the Born rule.

Unfortunately, Wash U does not have an online subscription to BJPS :mad: .

D
 
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  • #35
Ontoplankton said:
Quantum Arson: You can win the lottery by resolving to burn a lot of stuff if you win, because that will generate a lot of entropy, so it will have happened in more worlds.

No, this wouldn't work, because the APP, as I understand it, is transitive.

David
 
  • #36
I've started a new thread on a different but (obviously) closely related topic to this one.

"Attempts to make the Born rule "emerge" explicitly from outcome counting"

https://www.physicsforums.com/showthread.php?t=101982

If the Born rule can be made to emerge explicitly from world counts, then that would be an "existence proof" to the claim that the title-question of this thread is: no!

:smile:

David
 

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