There's an interesting text on Many Worlds,(adsbygoogle = window.adsbygoogle || []).push({});

http://www.anthropic-principle.com/preprints/manyworlds.html

and I'd like to discuss it.

There are 2 aspects with many worlds that I do not fully grasp. The first one, the more technical one, is how the correct probabilities emerge in MW. But it is related to the second, more philosophical one. However, let me concentrate on the first one, because I think it is a technical misunderstanding on my part.

Let me first state what I understand of MW. It is in fact "normal" quantum mechanics, with the extra discovery that "macroscopic" or "irreversible" interactions give rise to decoherence, in the following way:

Consider a (microscopic) system s, in t's lab, which is in a quantum superposition, and t is going to perform a measurement on s. R is the rest of the world.

Before, we have:

( a |s1> + b|s2> + c|s3>) x (|t0>) x |R> (1)

and after that subsystems s and t have irreversibly interacted, we obtain a state like:

a |s1>x|t1>x|R> + b|s2>x|t2>x|R> + c|s3>x|t3>x|R> (2)

and the 3 terms are called "different worlds".

This is nice, no problem, a priori. It is now assumed that each of these individual terms will never notice anything anymore from its neighbours, so let us concentrate on the term:

b|s2> x |t2>x|R> = |u0>

Imagine now that the state |u0> can be written as (d |k1>+ e|k2>)x|v>x|S>.

It is clear what happened: in another lab, a microscopic system k was prepared in a superposition, and v, the scientist in that lab, is also going to perform a measurement. S represents the rest of the world, including the first laboratory, s and t.

After measurement in the second lab, we'll have that:

|u0> = d |k1>x|v1>x|S> + e |k2>x|v2>x|S> (3)

Let us call the first term |uu0>, it is a new "world" just as the second term.

In the other "u" states, maybe this experiment didn't take place.

Anyway, ALL vectors in hilbert space representing different worlds are constantly getting shorter and shorter (for instance, u0 had norm b, while uu0 has norm bxd). This is also understandable, because their sum is the "universal state" which keeps length 1, and there are more and more "decohered" worlds as time evolves.

If I understand well, my mind is being cloned all the time, but there seems, each time, to be one copy that is "me". Now, my difficulty is, how can that "me" experience the right probabilities if it is not postulated that the "true me" follows a random choice path between worlds that is dictated by the amplitudes squared of the individual worlds ? If I can only talk about the "true me" with hindsight, because all "me"'s are equivalent, then I have a problem.

Let me explain: there's a copy of "me" in each of the terms of (2). I do this experiment several times and I can label each of the individual terms by the successive measurement results that lead to that term. Take the term 121112312, for instance, which means that the result of the first experiment was 1, the result of the second was 2, the result of the third was 1 etc...

There will be exactly one final state corresponding to each possible sequence.

If at each "split", my mind splits equally in 3 clones (1,2,and 3), the big majority of minds ending up after many measurements (the big majority of sequences given above) will find roughly equal times a measurement 1, a measurement 2 and a measurement 3, with probabilities, 1/3, 1/3 and 1/3 for each. But we shouldn't find that ! We should find a^2, b^2 and c^2 !! How do these numbers get into the history of most minds ? True, the length of the vector in which they are is longer, but as they are decohering all the time, the individual lengths don't matter, they are independently evolving.

So where is my mistake ? This is something that has been bothering me with the way I see many worlds for a long time, and nobody seems to be able to answer the question.

cheers,

Patrick.

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# Many Worlds, a discussion.

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