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entropy1
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If we have a spin measurement with P(up)=0.5 en P(down)=0.5, this is equivalent to tossing a coin P(heads)=0.5 and P(tails)=0.5.
The probability of having five heads and five tails out of ten tosses is the binomial: ##\binom{10}{5}(0.5)^5(0.5)^5##. So the same would hold for the spin measurement as given.
If we consider MWI to this respect, the probability of getting into (experience) a "world" in which we measure n(up) times spin up out of N measurements, would be the binomial ##\binom{N}{n(up)}(0.5)^{n(up)}(0.5)^{N-n(up)}##.
So the distribution of the worlds with n(up) spin-ups out of N measurements would be the binomial distribution. All "worlds" are actually realized, and all have probability 1. For every "world" with spin-up, there is a "world" with spin-down and vice-versa. In world A, probability for up=1, in world B, probability for down=1; overall the probability is (A+B)/2. For other probabilities of the spin measurement, the reasoning is the same. In the case of two eigenvalues, like spin, the "worlds" with n(up) would always have the binomial probability distribution.
This contradicts the Born rule, because what happens in MWI is independent of probabilities of outcomes.
Would that be correct?
The probability of having five heads and five tails out of ten tosses is the binomial: ##\binom{10}{5}(0.5)^5(0.5)^5##. So the same would hold for the spin measurement as given.
If we consider MWI to this respect, the probability of getting into (experience) a "world" in which we measure n(up) times spin up out of N measurements, would be the binomial ##\binom{N}{n(up)}(0.5)^{n(up)}(0.5)^{N-n(up)}##.
So the distribution of the worlds with n(up) spin-ups out of N measurements would be the binomial distribution. All "worlds" are actually realized, and all have probability 1. For every "world" with spin-up, there is a "world" with spin-down and vice-versa. In world A, probability for up=1, in world B, probability for down=1; overall the probability is (A+B)/2. For other probabilities of the spin measurement, the reasoning is the same. In the case of two eigenvalues, like spin, the "worlds" with n(up) would always have the binomial probability distribution.
This contradicts the Born rule, because what happens in MWI is independent of probabilities of outcomes.
Would that be correct?
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