Re: all of me or one of me

From: Gilles HENRI <Gilles.Henri.domain.name.hidden>
Date: Mon, 12 Apr 1999 09:31:51 +0200

>GH:
>>It is not against these theories. The many-worlds hypothesis + a
>>mathematical constraint such as analyticity of fields could lead to an
>>"everything possible" hypothesis that would imply that all possible worlds
>>are also different everywhere, so "clone free"...
>
>BM:
>This would make the "many-worlds hypothesis" empty. If the worlds
>are so different, how will interference be possible ?

In fact there is no precise definition of what is a macroscopic world in
MWI. This is one of the major difficulties of the theory; however it is
logical to consider that two different macroscopic worlds have by
definition negligible interference terms, which makes the conventional
interpretation of QM work (reduction of the wave packet). Interference
terms are important only at the microscopic level.
 Note also that the fact that fields are different over any neighborhood of
any point doesn't imply that the interaction vanishes!(Ex: cos x and
 cos (x+a) if a<>0 [Pi/2])

>
>GH:
>> ... it relies on the hypothesis that you think you will
>>really be , or "identify yourself to", one of your copy, which is
>>contestable, especially if you consider that no copy can be exact.
>
>BM:
>Remember that with comp we are by definition informatical (in the
>classical sense) entity, and we are (from a third person point of view)
>100% exactly duplicable. (In the same sense that you can make *in
>principle* a perfect copy of the 10E100 first decimal of PI).

but not of PI in a finite time. Of course as we already discussed the
universe could be discrete. But you cannot make an exact copy of it at its
finest level (ie Planck scale) with a machine embedded in it.
The point is that when you say "we are informatical", you probably mean
that, like a computer, our computational structure can be described with
much less information than our physical one. That's why we can built
perfectly reproducible computers, and we can duplicate them with very
different physical structures.
But it can well be (and it is very probable) that the brain is not like our
simple computers. For example the response of neural cell can be some
continuous function of the concentration of hormons. Of course you can hope
to modelize it with a discrete approximation at any level of accuracy. But
by doing that, you start another stuff. The reproduction is not exact
anymore, and you are facing the problem of how deep you must go to
reproduce EXACTLY its behaviour. And in fact the brain is no more
informatical in the first sense, because it may well be that you need the
complete description of its physical state. So unlike our artificial
computers, its evolution is NOT simpler than the evolution of any physical
system. And if you have to go to the quantum level ,(even worse, to the
Planck scale!) you are facing a practical impossibility: it is (even in
principle) impossible to measure the complete quantum state of a single
system, and a fortiori to reproduce it (just because the complex value
Psi(x,t) can not be an observable). And as we already discussed you will be
lead to simulate the whole environment (ie visible Universe) at this level,
which is also impossible...

>Exercice (I am joking) :
>
>If a mad scientist decides to put you
>into the following quantum "cat" state: Psi =
>
> (1/sqrt(|a_1|^2 + |a_2|^2))*
> [a_1*|you in-hell> + a_2*|you in-paradise>]
>
>and give you the opportunity to choose between
>
>A) Psi with a_1 >>>>>>>>> a_2 (a_2 negligeable compare to a_1) and
>B) Psi with a_2 >>>>>>>>> a_1 (a_1 negligeable compare to a_2)
>
>Will you care about that opportunity ? and if you care,
>what will you choose: A or B ?

As you well know, it is impossible to prepare a macroscopic system in any
coherent superposition because of the environment induced decoherence. So
your joke experiment is really impossible (the scientist is either mad or a
lier!).
What is possible of course, and very simple, is to prepare you in some
state like
 (1/sqrt(|a_1|^2 + |a_2|^2)*
 [a_1*|you in-hell>|world with you in-hell> + a_2*|you in-paradise>|world
with you in-paradise>]

simply by measuring the spin of a polarized electron on a conveniently
chosen axis (with relative probability a1/a2) and decide to send you in
hell or paradize following the result. Of course as your states are
incoherent you are back to simple probability calculus and the choice is
obvious.


>
>GH:
>>You
>>could also think that you will die whatever, and choose B just by
>>compassion with other copies.
>
>BM:
>Indeed, but it is better, if only for the sake of the argument,
>to presuppose a minimal amount of selfishness.

What I meant is that if you think you die, your selfishness is useless. You
only need a minimal amount of altruism to choose B. If you are a pure
selfish man, you won't care about your choice.

>
>GH:
>>For example, just
>>modify a little bit your experiments: you won't be destroyed, but you will
>>be put in the unique "paradise" box in A and in the unique "hell" box in B.
>>The other 999999 copies will be placed in the hell or paradise boxes,
>>respectively. Unless you are a saint, and without misprint, won't you
>>choose "A"? It would mean that you care less about your copies than about
>>yourself...
>
>BM:
>I will not choose A, because with comp, a teleportation without
>annihilation of the original is equivalent with a duplication where the
>original is destroyed. So, with comp, your experiment is equivalent to
>mine!
>I have no doubt that this is rather counter-intuitive. But comp, if true,
>is necessarily *unbelievable*.

Ok, Bruno may be you would choose B. What about if, despite my promises,
you are not completely confident in my capability of creating the other
999999 copies? (I assume of course that once in the box, you are totally
unaware of what happens really in the other boxes. As is well known, we
will forget everything in paradise!)
May be this thought experiment is a proof that COMP (understood as the
possibility of creating an EXACT copy of yourself) is false?

Cheers

Gilles
Received on Mon Apr 12 1999 - 00:33:24 PDT

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