From: Stathis Papaioannou (stathisp@gmail.com)
Date: Fri Mar 06 2009 - 06:50:59 MST
2009/3/6 Matt Mahoney <matmahoney@yahoo.com>:
> Remember that probability is a model of belief, not of reality. In quantum mechanics, the square of the modulus of the wave function fits our model of probability only in the absence of other knowledge. For example, if constraints such as conservation of mass-energy, electric charge, momentum, and angular momentum restrict the possible combinations of observations we could make, we call that entanglement. As another example, the probability of observing a radioactive decay over one half-life interval is 1/2 only if that interval is in the future. But if you knew the quantum state of the universe, you would know everything about the future and probability would be a meaningless concept.
If you knew the quantum state of the universe you would know
everything that happens from the point of view of an observer outside
the multiverse. However, as an observer inside the multiverse you
would not know whether you would end up experiencing the atom decay or
not decay. To give another example, a computer program with an
observer that branches into two processes, one where the observer sees
heads and the other where he sees tails, will be completely
deterministic viewed from outside, but it will seem to the internal
observer that he has a 1/2 chance of seeing heads or tails, even if he
has full access to the source code and the data.
> The reason we expect a coin to come up heads with probability 1/2 is because of the way our brains compute probabilities based on past experience.
Yes, and the same psychopathology applies in the equivalent situation
where there are multiple copies, half of which see heads and the other
half tails.
-- Stathis Papaioannou
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