From: Dan Fabulich (dfabulich@warpmail.net)
Date: Fri Oct 25 2002 - 12:45:33 MDT
gts wrote:
> This interesting little gem from scerir seems to have passed by almost
> unnoticed in yesterday's flurry of messages to this thread. I am
> reposting scerir's words without comment:
>
> > In QM no information can be cloned (xoxed)if
> > the number of states is equal or greater than 3
> > [Wootters, Zurek, 1982].
> >
> > Or, in other terms, a cloning (xoxing) of 2 non
> > orthogonal states violates the unitarity of evolution
> > [D'Ariano, Yuen, 1996].
> >
> > Or, in other terms, the linearity in QM (linear
> > superposition of quantum states) forbids the
> > perfect xoxing. Fortunately! Leibniz principle!
The point of the arguments from quantum synchronization (which, as Eugene
pointed out, does not have to be done via "cloning" necessarily) is MERELY
to show that identity doesn't inhere in the atoms you happen to occupy at
this second.
The proof goes like this: IF the two xoxes A and B are synchronized in
their quantum properties (perhaps by chance!), then they could be
interchanged without changing the physical state *or the logical state* of
the system. There could be no logical way to distinguish the "switched
state" from the "unswitched state", *not even by reference to the history
of A and B.*
To answer Michael/Jef's objections, *even the history gets obscured in
this example*. If mere history was enough to distingush particles with
perfectly similar quantum properties, *even logically* [by name], a
variety of important proofs in physics would fall apart. (I recall Tipler
mentions the law of mass action as another example, aside from the
well-known argument for the Pauli Exclusion Principle.) They rely on the
assumption that the physical state is the *same* post switch; if it was
different, even logically, even with reference to its history, then the
arguments for these important physical principles would fail, and we'd
have no understanding of modern chemistry.
It's just a funny fact about our world that when you jigger things up in
just the right way, switched particles become formally indistinguishable
from unswitched particles, even by name or by history.
But all this shows, all it's even TRYING to show, is that identity doesn't
inhere in the atoms. (The more trivial proof of this is that we consider
ourselves to persist over many years, even though we cycle through all of
our atoms in that time. Atoms just aren't where it's at.)
------------------------------------------------------------------------
But if identity doesn't inhere in the atoms *or* in the history of those
atoms, then in what does it inhere? How can you tell whether something
counts as "you" or not? The answer, as I've argued, is "whatever we
decide is relevant."
Functionalists will be happy to announce "the same person" so long as they
have the same function. Mentalists might announce "the same person" only
as long as they have the same "mental states" (which had better supervene
on the physical states somehow, or else you're talking about souls).
But you'll need to give up on the idea that it's [the history of] your
atoms that keeps xoxes unique from each other. The atoms just aren't
where it's at.
-Dan
-unless you love someone-
-nothing else makes any sense-
e.e. cummings
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