From: svetlich@math.rutgers.edu (George Svetlichny)
Newsgroups: sci.physics,alt.sci.physics.new-theories
Subject: No FTL signal proofs still good.
Summary: Sarfatti's objections to no FTL signal proofs do not stand.
Keywords: superluminal, signal, quantum, correlation, Heisenberg, uncertainty
Date: 5 Nov 92 17:47:41 GMT
Followup-To: sci.physics
Organization: Rutgers Univ., New Brunswick, N.J.

Sarfatti's argument against the validity of the contention that standard
quantum mechanics (SQM) forbids superluminal quantum-correlation signals
is apparently based on two allegations:

1. Besides dynamical equations there are boundary conditions and
Sarfatti uses novel boundary conditions.

2. Commuting observables are nevertheless incompatible due to state
entanglement as was shown by Schroedinger in 1930 and by de la Torre in
the past two years.

Neither of these allegations stand up as an argument for SQM implying
superluminal signals.

In relation to the first one should call attention to the fact that SQM
_does_ impose restrictions on boundary conditions, usually through
precise domain requirements on unbounded operators in hilbert space.
Such requirements are usually to the effect that any putative operator
(generally differential) that is to represent an observable should be
essentially self adjoint, and this translates itself into boundary
conditions on the vectors in its domain. Imposing any other "novel"
boundary conditions is as much a deviation from SQM as is using
non-unitary evolution (and in particular cases can amount to the same
thing).

More to the point though is that considerations of evolution for the
no-signal theorem is secondary. The theorem is basically a consequence
of two main assumptions:

   a) The mean value of any observable is given as a matrix element
   (F,AF) of a self-adjoint operator A in the state F.

   b) Operators corresponding to observations carried out at space-like
   separation commute.

Now an observation can be carried out by a complex arrangement of
physical object which may interact among themselves and with the system
being observed. The functioning of such an arrangement can then be
described by appropriate dynamical laws, evolution equations, boundary
conditions, etc. If these do not follow SQM rules one may end up with an
arrangement that doesn't satisfy a) above. But then such an arrangement
by definition does not realize a SQM observable. The role of evolution
in the no-signal theorem is thus indirect and the argument does not
essentially depend on it. One just has to ask if the arrangements on
both sides of Sarfatti's experiment satisfy a) above or not. If not, SQM
has been abandoned, if yes, all arguments concerning evolution and
boundary conditions are irrelevant.

If Sarfatti admits that his arrangements satisfy a) he must now face b).
Since he apparently doesn't deny this, the no-signal theorem follows and
his device can't work.

Well, what about Schroedinger and de la Torre? Sarfatti doesn't supply us
with references and I've not located Schroedinger's argument, but for
de la Torre (where one finds some mention of Schroedinger's expression)
he probably means:

        A. C. del la Torre, P. Catuogno and S. Ferrando

        "Uncertainty and nonseparability"
        Found. Phys. Lett. 2, 235 (89)

        and

        "Nonseparability and noncommutativity in quantum systems"
        Found. Phys. Lett. 4, 49 (1991)

Now these papers are certainly within the realm of SQM and though the
authors seem to derive some of their motivation from philosophical
considerations usually found in hidden-variable arguments, their
calculations are within SQM. Their calculation is nothing more than to
derive what appears to be a Heisenberg-type uncertainty relation for
commuting observables in a given state, that is if A, B are quantum
mechanical observables (commuting or not) then in a state F one can
derive that

        Delta A Delta B >= |T(A,B,F)|

where Delta A  is the root mean square of the observed values of A in F
and similarly for B. (Delta A)^2 = (F, A^2F) - (F, AF)^2, and T(A,B,F)
= (F, ABF)-(F, AF)(F, BF).

This is nothing more than the Cauchy Schwartz inequality. Similarly if X
and Y are two  _classical_ random variables then

        s(X)s(Y) >= |C(X,Y)|

where s(X) is the standard deviation of X, likewise for Y. and C(X, Y)
is the covariance. Thus _classical_ random variables satisfy (shall we
say it?) a Heisenberg-type inequality.

De la Torre et al. have a curious phrase in their second paper:

"In the last section we have shown that there are physical states where
commuting observables are incompatible due to the nonseparability or
non-PI."

(non-PI translates to T(A, B, F) not vanishing). This is a very strange
idea of incompatibility. They seem to feel a Heisenberg-type inequality
implies incompatibility. They missed a few essential points about
Heisenberg uncertainty relations (like being able to give a
state-independent lower bound to the right hand side). One cannot derive
from their inequality for commuting observables the same type of
conclusions that one derives from the Heisenberg uncertainty relations.
If one could, all statisticians would have to study quantum mechanics
as classical random variable would then behave like quantum
observables.. For instance, knowing that incidence of lung cancer and
smoking are correlated one deduces an a-priori inequality relating the
standard deviations of the number of cigarettes smoked and of the
severity of lung lesions, making their product bounded below by the
modulus of the covariance. Does does this means these two variables are
incompatible? Does it mean reducing the one number (holding smoking to
zero, hence zero standard deviation) will make the other standard
deviation (severity of lung lesions) go infinite? Do people with perfect
lungs invariably smoke a widely varying number of cigarettes a day?

The cited results (and probably Schroedinger's as well) have nothing to
do with superluminal signals as the same reasoning would apply to states
and experimental arrangements conforming to Bell's inequalities for
which a common cause explanation for the correlations can be given, and
no one believes that common-cause correlations can be used for
superluminal signals. Otherwise one could build a superluminal telegraph
utilizing a "source" that randomly picks matched pairs of socks and
sends each one in opposite directions. There would be an observer
catching one of the socks, and by analyzing it, would determine if the
space-like separated observer was looking at the color or at the
weave-pattern of the other mate. If a state-dependent seemingly
Heisenberg-like inequality was all that was needed to send signals, this
would work.

-- 
George Svetlichny                    /\      On leave from:
Department of Mathematics          /***|     Departamento de Matematica
Hill Center, Rutgers University   /****|     Pontificia Universidade Catolica
New Brunswick, 08903 NJ          /*****|     Rio de Janeiro, Brazil