From: scerir (scerir@libero.it)
Date: Wed Sep 18 2002 - 07:01:23 MDT
Lee Corbin
One would say (in MWI) that we're talking about the state of
the entire universe (or a part of it, anyway). Perhaps you
regard "locality" to mean something different; I think of it
as not requiring spooky influences at a distance (which is
incredibly uncomfortable to those to whom special relativity
has become second nature).
Very interesting point.
Pauli wrote (in a letter to Heisenberg) about the EPR question: "Quite
independently of Einstein, it appears to me that, in providing a systematic
foundation for quantum mechanics, one should start more from the
composition and separation of systems than has until now (with Dirac, e.g.)
been the case. - This is indeed - as Einstein has correctly felt - a very
fundamental point in quantum mechanics ......". Pauli's hint had no
followers.
At the Solvay 1927 'Conseil de Physique' Pauli also suggested a sort
of MWI, a 'polydimensionel' interpretation, that is to say a QM without
the 'collapse'.
Following Jarrett, Shimony, Howard, Cushing, Suppes, van Fraassen,
the original John Bell's 'realist' condition (*) is equivalent to the
conjunction of two independent conditions: a 'locality' condition (**)
and a 'separability' condition (***).
Now the violation of the 'locality' condition would imply superluminal
comunication. Actually Jarrett proved that, when the locality condition
is violated, one can send FTL signals from wing A to wing B of the EPR
apparatus (or viceversa), provided that the variables, which specify
completely the state of the system, are known.
But Eberhard, Page, Ghirardi (et al.) showed that standard QM implies
just the violation of the 'separability' condition and 'not' the violation of
the 'locality' condition. So standard QM does not allow us to send FTL
messages or informations (are FTL 'influences', FTL 'random'
informations', or FTL 'exchanges' of informations possible?).
Notice that a 'deterministic' QM (****) which would be able to
reproduce all predictions of standard QM, implies the violation
of the 'locality' condition. Which means: superluminal signals!
(Actually Bohm's quantum theory allows such effects).
Hence determinism and non-locality (actions-at-a-distance) are
linked. Indeterminism and non-separability (passions-at-a-distance)
are linked. In general SR and QM are linked, in the sense that there
is a 'peaceful coexistence' (Abner Shimony) or a 'conspiracy'
between these two theories.
Now, as all of us know very well, the MWI is, exactly, a
'deterministic' quantum theory. Does it mean that MWI allows
FTL messages? (*****).
[I'll stop this endless, and perhaps also boring 'filastrocca',
with the next post :-)]
s.
--------------------------------------------------------------
(*) For a composite system, in a joint state, the joint probability
of outcomes, for measurements of observables, is equal to the
product of the separate probabilities.
(**) Def. of locality = Given two systems A and B, space-like
separated, the state of A cannot be influenced by events (measurements)
on B, and viceversa.
(***) Def. of separability = Two separated systems possess their own
separate states, regardless of their previous history, and the joint state
is completely determined by their own separate states.
(****) One in which the range of any probability distribution of
outcomes is the set [0,1].
(*****) I do not think that Lev Vaidman discusses this topic in
his beautiful http://plato.stanford.edu/entries/qm-manyworlds/
In http://www.hedweb.com/manworld.htm Price writes:
"So where did Bell and Eberhard go wrong? They thought that all
theories that reproduced the standard predictions must be non-local.
It has been pointed out by both Albert and Cramer (who both support
different interpretations of QM) that Bell and Eberhard had implicity
assumed that every possible measurement - even if not performed -
would have yielded a 'single' definite result. This assumption is called
contra-factual definiteness or CFD. What Bell and Eberhard really
proved was that every quantum theory must either violate locality
or CFD. Many-worlds with its multiplicity of results in different worlds
violates CFD, of course, and thus can be local."
[But many Everettistas do not agree with this, and say that the MWI
is a non-local theory, because the very basic concept of 'worlds' is
non-local.]
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