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nshepperd comments on Probability is in the Mind - Less Wrong

60 Post author: Eliezer_Yudkowsky 12 March 2008 04:08AM

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Comment author: nshepperd 23 May 2013 06:22:02AM 0 points [-]

Specifically, if you measure the spin of the particle along any axis, both maps predict that you will measure the spin to be in one direction with 50% probability and in the other direction with 50% probability.

On the other hand, if the particle is spin up, the probability of observing "up" in an up-down measurement is 1, while the probability is 0 if the particle is down. So in the case of an up-down prior, observing "up" changes your probabilities, while in the case of a left-right prior, it does not.

Comment author: TobyBartels 26 May 2013 07:35:20PM 0 points [-]

That's a good point. It seems to me another problem with the MWI (or specifically, with Bayesian classical probability on top of quantum MWI) that making an observation could leave your map entirely unchanged.

However, in practice, followers of MWI have another piece of information: which world we are in. If your prior is 50% left and 50% right, then either way you believe that the universe is a superposition of an up world and a down world. Measuring up tells you that we are in the up world. For purposes of future predictions, you remember this fact, and so effectively you believe in 100% up now, the same as the person with the 50% up and 50% down prior. Those two half-Bayesians disagree about how many worlds there are, but not about what the up world —the world that we're in— is like.

Comment author: nshepperd 27 May 2013 04:53:56AM 0 points [-]

To be precise, if your prior is 50% left and 50% right, then you generally believe that the world you are in is either a left world or a right world, and you don't know which. A left or right world itself factorises into a tensor product of (rest of the world) × (superposition of up particle and down particle). Measuring the particle along the up/down axis causes the rest of the world to be become entangled with the particle along that axis, splitting it into two worlds, of which you observe yourself to be in the 'up' one.

Of course, observing the particle along the up/down axis tells you nothing about whether its original spin was left or right, and leaves you incapable of finding out, since the two new worlds are very far apart, and it's the phase difference between those two worlds that stores that information.