From: Matt Mahoney (matmahoney@yahoo.com)
Date: Thu Mar 05 2009 - 14:16:00 MST
--- On Thu, 3/5/09, Stathis Papaioannou <stathisp@gmail.com> wrote:
> > Many-worlds is indistinguishable from the case that
> there is one universe in a definite quantum state, but you
> don't know what that state is.
>
> That's the point: your subjective expectation of seeing heads when you
> are duplicated and the two copies see opposite sides of the coin
> should be the same as your subjective possibility of seeing heads when
> you toss a coin in ordinary life.
Not exactly. Under many-worlds, universes don't actually "split" because quantum mechanics and general relativity are symmetric with regard to time. The universes were different before the split, but not at the macroscopic level. However, the two universes still had different quantum states.
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.
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.
-- Matt Mahoney, matmahoney@yahoo.com
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