On 8/14/2013 6:41 PM, smi...@zonnet.nl wrote:
I guess I don't understand that. You seem to be considering a simple case of amnesia
- all purely classical - so I don't see how MWI enters at all. The probabilities are
just ignorance uncertainty. You're still in the same branch of the MWI, you just don't
remember why your memory was erased (although you may read about it in your diary).
No, you can't say that you are in the same branch. Just because you are in the clasical
regime doesn't mean that the MWI is irrelevant and we can just pretend that the world is
described by classical physics. It is only that classical physics will give the same
answer as QM when computing probabilities.
Including the probability that I'm in the same world as before?
If what you are aware of is only described by your memory state which can be encoded by
a finite number of bits, then after a memory resetting, the state of your memory and the
environment (which contains also the rest of your brain and body), is of the form:
"The rest of my brain"?? Why do you suppose that some part of my brain is involved in my
memories and not other parts? What about a scar or a tattoo. I don't see that "memory"
is separable from the environment. In fact isn't that exactly what makes memory classical
and makes the superposition you write below impossible to achieve? Your brain is a
classical computer because it's not isolated from the environment.
|memory_1>|environment_1> + |memory_2>|environment_2>+...
where |environment_i> is not (necessarily) normalized.
It then follows that a process that can lead to the same memory state via different
paths (routine resetting or resetting in case of bad news) will lead to a state |psi>,
such that projecting out a definite memory state gives:
|memory> sum over different |environments>
where the different environments contain different information about the paths that led
to the memory.
So, from the point of view of a memory state that has undergone a resetting, the
environment will be in a superposition of different states, the reason why the reseting
has been done is thus undetermined prior to a measurement.
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