A problem with probabilites in many worlds

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SUMMARY

The discussion centers on the interpretation of probabilities within the Many Worlds Interpretation (MWI) of quantum mechanics, particularly addressing the challenges posed by low-probability events. Participants highlight that while flipping a coin 100 times yields a probability of (1/2)100, this does not equate to a probability of zero. The conversation references the Everett III solution and the ongoing debate regarding the derivation of the Born rule, emphasizing the ignorance interpretation post-measurement. The lack of consensus on how classical probability aligns with MWI remains a significant issue in the field.

PREREQUISITES
  • Understanding of Many Worlds Interpretation (MWI) of quantum mechanics
  • Familiarity with the Born rule in quantum mechanics
  • Knowledge of Shannon entropy and its application in probability
  • Basic concepts of quantum measurement and state collapse
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  • Research the implications of the Everett III solution on quantum mechanics
  • Study the derivation and significance of the Born rule in quantum theory
  • Explore the ignorance interpretation of measurement outcomes in MWI
  • Investigate alternative interpretations such as Many Minds and their postulated structures
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Quantum physicists, philosophers of science, and students exploring the implications of Many Worlds Interpretation and quantum probability theory.

StarsRuler
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In many worlds, all the results with probability>0 happens. But the predictive power of a theory is based in that events with very low probabilities no matter ( the possible ocurrence is `[but a constant]) around the averaged valued by the exponential of shannon entropy, that in the case of gaussians distributions, it is the typical standard deviation) Without this limitation, we could flip a coin 100 times and obtain 100 faces, probability is not 0 is 1/2^(100). What is the Everet III solve of this problem? I read his thesis but not mention to it. HOw is this trouble solved??
 
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StarsRuler said:
Without this limitation, we could flip a coin 100 times and obtain 100 faces, probability is not 0 is 1/2^(100). What is the Everet III solve of this problem?

That can happen in classically too. The probability of flipping 100 heads is always ##(1/2)^{100}##, it doesn't become 0 in classical probability.

In any case, there is currently no agreement on how our familiar understanding of probability is recovered from MWI, which has lead to some of the variants of MWI. Probably the simplest proposal, which doesn't add any additional major assumptions, is the ignorance after measurement interpretation. It still is not agreed if you can derive the Born rule, or if it must be postulated that the Born probability of a world constitutes its 'measure of existence'. Whichever it is, the reality of every day life is that you are not aware of the outcome of a measurement instantaneously when it is performed. By the time you become aware of the measurement outcome (if you ever become aware of it), the worlds have split and you are ignorant of which world you are in. Hence, if I do 100 quantum mechanical coin flips (e.g. Stern-Gerlach trials) while you are in the next room, and then walk over and ask you, "Which world are you in?" the Born rule-motivated ignorance-based probabilistic answer is, "Very likely not the world corresponding to 100 'spin ups' in a row."

There are other proposals under various names like Many Minds and so on, but in addition to the Born rule, additional structure has to be postulated.
 
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