From: sarfatti@well.sf.ca.us (Jack Sarfatti)
Subject: Not so Hidden Variables!
Organization: Whole Earth 'Lectronic Link
Date: Fri, 11 Sep 1992 02:06:24 GMT


From Physics Conference Internet (Aug 24,1992, world-wide distribution)

THE QUANTUM SPIN CONNECTION IS A COMMUNICATION CHANNEL

by Jack Sarfatti

ABSTRACT

Based upon a referee's report from Physical Review Letters, I present a
new gedankenexperiment in which the transmitter design is changed in such
a way that the reflection phase shift of 90 degrees at the beam
recombiner does not destroy communication on the quantum connection in
the mean. The difference in the receiver count rates is sin(2misalignment
of transmitter & receiver calcites) cos(transmitter phase). The
transformation at the transmitter beam recombiner is unitary. The trick
is not to have two distinguishable measurements at the transmitter but
only one. Thus, feed the two output interferograms from the beam
recombiner into the same specially designed clamped photon counter. The
clamping, as in the Bohr-Einstein double-slit gedankenexperiment, assures
the indistinguishablity of the interferograms in the transmitter
measurement. This is a counter-example to the published proofs that
unitarity prevents communication on the nonlocal quantum spin connection.
The published proofs only apply if there is no quantum erasure of
distinguishability of alternative Feynman histories of the transmitter
photon in the connected photon pair. The design given here allows the
cause to be in the future of the effect which may be the basic mechanism
for the creation and purposeful evolution of what Fred Hoyle calls "the
Intelligent Universe."
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The back-to-back photon pair state used in real experiments is

|1,2> = [|1E>|2E> + |1O>|2O>]/sqrt2   (1)

in the bases (E,O) defined by the actual orientation of the transmitter
calcite rhomb (which spatially splits the 2E path from the 2O path) when
transmitter photon 2 locally interacts with it. The 2E path passes a
variable phase plate which sends |2E> -> e^iphi(2)|2E> (phi(2) is the
modulation variable for encoding the message). External reflection from a
non-absorbing mirror gives an additional pi phase shift for a TE wave.
The 2E path is then the I+ input to the transmitter beam recombiner. The
2O path passes a half-wave plate set at 45 degrees to the plane of
polarization of O so that |2O> -> |2E> which is the I- input to the
transmitter beam recombiner. It is physically obvious and elementary
physics that the half-wave plate properly oriented rotates the plane of
polarization by 90 degrees. This is "spin disentanglement" in which the
half-wave plate quantum erases the polarization distinguishability for
the alternative Feynman histories of the transmitter photon. The O+(O-)
outputs of the recombiner are:

|O+> = [- re^iphi(2)|1E> + t|1O>]|2E>/sqrt2    (2a)

|O-> = [- te^iphi(2)|1E> + r|1O>]|2E>/sqrt2    (2b)

The transmitter beam recombiner quantum erases the spatial
distinguishability for the alternative Feynman histories of the
transmitter photon.

It is important to notice that the net nonlocal transformation in the
spin space of the receiver photon 1 is unitary provided that the complex
reflection r and transmission t transfer functions for the twin
transmitter photon obey

r*r + t*t = 1        (3a)

r*t + rt* = 0        (3b)

This last equation implies that b = phi(r) - phi(t) = pi/2 as pointed out
by Aephraim Steinberg and referee A of Physical Review Letters.

The transmitter geometry is such that we superpose |O+> and |O->
coherently and constructively to get

|O+> + |O-> = {-[re^iphi(2)+te^iphi(2)]|1E> + [r+t]|1O>}|2E>/sqrt2

            = [r+t]{-e^iphi(2)|1E> + |1O>}|2E>/sqrt2    (4)

This superposition is automatically normalized to unity by the unitarity
of equations (3a,b).


The important observation is the [r+t] factor that has slipped out in
front! Now project the receiver photon kets onto the actual base states
(e,o) of the receiver crystal at the event of local detection of receiver
photon 1 (where misalignment x is a nonlocal parameter x(1,2) i.e.,the
angle between (E,O) and (e,o) at the two events in which each photon
interacts with its crystal).

|1E> =  cos(x)|1e> + sin(x)|1o>   (5a)

|1O> = -sin(x)|1e> + cos(x)|1o>   (5b)

|O+> + |O-> = [r+t]{-e^iphi(2)(cos(x)|1e>+sin(x)|1o>)

            + (-sin(x)|1e> + cos(x)|1o>)}|2E>/sqrt2

= {[-e^iphi(2)cos(x)-sin(x)]|1e>

+ [-e^iphi(2)sin(x)+cos(x)]|1o>}[r+t]|2E>/sqrt2  (6)

As already noted, unitarity of the lossless beam recombiner
transformation

[r*+t*][r+t] = 1  (7)

So we can forget it.  It plays no further role. Together with
orthogonality of the spin states <1E|1O> = 0,equation 7 implies that the
probability to detect the single  transmitter counter is 1 (i.e., ideal
case 100% efficiency). This is the big improvement of the new design over
my earlier one. This design change was stimulated primarily by the
remarks of Aephraim Steinberg a grad student in Ray Chiao's group at UCB,
and also by Brian Josephson, Mike Gallis, Carlton Caves, and John Baez.

Therefore, the receiver count rates are:

p(1e) = {|[-e^iphi(2)cos(x)-sin(x)]|^2}/2

      = [1 + sin(2x(1,2))cos(phi(2))]/2   (8a)

p(1o) = {|[-e^iphi(2)sin(x)+cos(x)]|^2}/2 (8b)

      = [1 - sin(2x(1,2))cos(phi(2))]/2

p(1e) + p(1o) = 1  (9)

So probability is conserved locally on both sides of the device. The
quantum connection signal is:

p(1e) - p(1o) = sin(2x(1,2))cos(phi(2))   (10)

In physical terms I am predicting that the receiver light will be
polarized and that this polarization can be controlled by quantum action
at-a-distance from the transmitter by changing the setting of the phase
plate in the transmitter or by rotating the transmitter crystal. In the
old experiments by Clauser and Aspect the receiver light is always
unpolarized because there is no quantum erasure of both spin and space
information for the transmitter photon.

The published proofs forbidding communication on the quantum spin
connection are wrong. QED!