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COMMUNICATION ON THE QUANTUM CONNECTION
Jack Sarfatti

ABSTRACT
Objections that my gedankenexperiment violates unitarity are shown to be
false
as are the claims of Eberhard, Stapp et-al that communication on the quantum
connection is impossible.

#1 I claim that the following demonstration of faster-than-light (FTL)
communication on the spin quantum connection is unitary for all possible
input
states.

#2 The usual argument against faster-than-light communication in standard
relativistic quantum field theory is false because the criterion used to
prohibit it
(namely, that the expectation value of the commutator of space-like
separated
local observables vanish ) is not sufficient in presence of entanglement (de
la
Torre et-al, Fdn Phys. Lett 4, 49-59 1991)

#3 Photon pair source from atomic cascade used by John Clauser of Alain
Aspect producing a pure photon pair state at source emission event S

|1(S),2(S)> = [ |v1>|v2> + |h1>|h2>]/sqrt2      (1)

#4 This state is cylindrically symmetric about line of flight of
back-to-back
photon pair.  This means if both single photon base states are rotated by
the
same angle one gets the same form in the new base states.

#5 If both single photon base states are rotated by different angles one
gets the
actually observed correlations.  For example if two counters are placed
behind
each calcite in the extraordinary and ordinary paths, the joint probability
to find
both photons in the extraordinary path of their respective calcite rhombs is
p(v1,V2) = [cos^2theta]/2                (2)

where theta is the misalignment v.V of the two calcites. This violates
Bell's
locality inequality.

#6 Without loss of generality we can write

|1(S),2(S)> = [ |E(T)1>|E(T)2> + |O(T)1>|O(T)2>]/sqrt2    (3)

where E(T) is the extraordinary path for transmitter doubly refracting
calcite
rhomb and O(T) is the ordinary path.  This E(T) O(T) basis will be
determined
by the actual future orientation of the transmitter calcite at the
space-time event
T in which photon 1 locally interacts with the transmitter calcite.

#7 The quantum magic of action at a distance is in the fact that both
photons 1
(transmitter) and 2 (receiver) are in the same basis - whatever it may be.

#8 The transmitter (to the right photon 1) is a calcite rhomb.
The extraordinary E(T) path passes through a variable phase platePHI
(translational phase shift phi(T)) which will encode the superluminal, and
possibly "delayed choice" (backwards-in-time or BIT), message by phase
modulation.  The E(T) path is reflected by a nonabsorbing mirror M
(reflection
phase shift m) to a half-silvered nonabsorbing beam recombiner B (reflection
phase shift b). The ordinary O(T) path passes through a half-wave plate
before
it reaches B. Therefore, the linear polarization of photon 1 is the same
from
either path before it is incident on B.  Two interferogram outputs from B
each
each fed to a separate photon counter.  Therefore, the two paths for photon
1
exiting B are distinguishable noninterfering alternatives in Feynman's path
quantum mechanical sense.

#9 The receiver is simply an identical calcite rhomb whose orientation at
the
receive space-time event R for the twin photon 2 has local basis e(R) and
o(R).
Each output is fed into a separate counter. The angle between the receiver
basis
and the transmitter basis is a nonlocal parameter

theta(T,R) = theta(T) - theta(R)        (4)

#10 In interferogram I if photon 1 takes the E(T) path it picks up a phase
shift
phi(T) from the phase plate, a phase shift m from M, a phase shift b from B,
and a 1/sqrrt2 from B before going to photon counter I.  This Feynman path
is
described by the local unitary (phenomenological) evolution

|E(T)1>   -> exp{i[phi(T)+m+b]}|E(T)1> /sqrt2    (5)

#11 If photon 1 takes the O(T) path instead, its local unitary evolution is

|O(T)1>  -> |E(T)1>/sqrt2      (6)

#12 Equations (5) and (6) follow from the superposition principle and the
well
known optical effects of mirrors, phase plates and half-wave plates. For
example, how can one deny (6)?

Substitute equations (5) and (6) into equation (3)

|1(S),2(S)> ->

[ exp{i[phi(T)+m+b]} |E(T)2> +|O(T)2>] |E(T)1>/2    (7)

Similarly for interferogram II, along the E(T) path there is a reflection at
M
and a transmission at B so that

|E(T)1>   -> exp{i[phi(T)+m]}|E(T)1> /sqrt2    (8)

and along O(T) path there is a reflection at B so that

|O(T)1>  -> |E(T)1>exp{ib}/sqrt2      (9)

Substitute (8) & (9) into (3) to get

|1(S),2(S)> ->

[ exp{i[phi(T)+m]} |E(T)2> +exp{ib}|O(T)2>] |E(T)1>/2    (10)

since

<E(T)2|O(T)2> = 0           (11)

#13 These interferograms at the transmitter counters I and II will be
uninteresting.  Each transmitter counter will click at equal rates
independent of
any of the phase shifts. Note that

p(I) = p(I,E(T)2) + p(I,O(T)2) = 1/4 + 1/4 = 1/2       (12)

p(II) = p(II,E(T)2) + p(II,O(T)2) = 1/4 + 1/4 = 1/2     (13)

p(I) + p(II) = 1   (14)

hence probability is locally conserved on the transmitter side.

#14 Equations (7) and (10) show that the initial pure pair state of equation
(3)
has been collapsed to a statistical mixture by the distinguishable
irreversible
measurements of photon 1 by counters I and II at the transmitter.

#15 It is important to realize that I am using the Feynman path
interpretation of
quantum mechanics in which the photon pair amplitudes are nonlocal functions
of the three space-time events S,T,and R (approximated as points).

#16 Now let's compute what happens at the receiver. We must resolve the kets
for (spin 1 massless real) photon 2 into the kets for the receiver calcite.

|E(T)2> = |e(R)2> cos{theta(T,R)} + |o(R)2> sin{theta(T,R)}   (15)

|O(T)2> = - |e(R)2> sin{theta(T,R)} + |o(R)2> cos{theta(T,R)}   (16)

For interferogram I (eq. 7)

[ exp{i[phi(T)+m+b]} [ |e(R)2> cos{theta(T,R)}

+ |o(R)2>sin{theta(T,R)}]

+[- |e(R)2>sin{theta(T,R)}+ |o(R)2> cos{theta(T,R)}]] |E(T)1>/2

=  [exp{i[phi(T)+m+b]} cos{theta(T,R)}-sin{theta(T,R)}]|e(R)2> |E(T)1>/2

+ [exp{i[phi(T)+m+b] sin{theta(T,R)}+cos{theta(T,R)}] |o(R)2> |E(T)1>/2
(17)

Therefore, we have the joint nonlocal probabilities

p[e(R),E(T),I] = [1 -sin{2theta(T,R)} cos{phi(T)+m+b}]/4        (18)

p[o(R),E(T),I] = [1 +sin{2theta(T,R)} cos{phi(T)+m+b}]/4       (19)

Similarly for interferogram II (eq. 10)

[ exp{i[phi(T)+m]}[ |e(R)2> cos{theta(T,R)} + |o(R)2> sin{theta(T,R)} >]

+exp{ib}[- |e(R)2> sin{theta(T,R)} + |o(R)2> cos{theta(T,R)} ] |E(T)1>/2

= [exp{i[phi(T)+m]}cos{theta(T,R)} -exp{ib}sin{theta(T,R)]|e(R)2>|E(T)1>/2

+[exp{i[phi(T)+m]}sin{theta(T,R)}+exp{ib}cos{theta(T,R)}]|o(R)2>|E(T)1>/2
(20)

p[e(R),E(T),II] = [1 -sin{2theta(T,R)} cos{phi(T)+m-b}]/4        (21)

p[o(R),E(T),II] = [1 +sin{2theta(T,R)} cos{phi(T)+m-b}]/4       (22)

From the Feynman rule to add probabilities of distinguishable alternatives

p[e(R),E(T),I]+p[e(R),E(T),II] = [1-sin{2theta(T,R)}cos{phi(T)+m}cos{b}]/2

= p[e(R),E(T)]   (23)

p[o(R),E(T),I]+p[o(R),E(T),II] = [1+sin{2theta(T,R)}cos{phi(T)+m}cos{b}]/2

= p[o(R),E(T)   (24)

 p[e(R),E(T)] + p[o(R),E(T)  = 1    (25)

#17 So that probability is locally conserved on the receiver side. Any claim
that
this model violates unitarity is false. It is in accord with Feynmans rules
to add
amplitudes before squaring for indistinguishable histories and to square
before
adding for distinguishable ones.

#18  The FTL/BIT signal on the spin quantum connection is then

p[e(R),E(T),I] - p[e(R),E(T),II] = -sin{2theta(T,R)}cos{phi(T)+m}cos{b}
(26)

So that the nonlocally encoded message is locally decoded.

#19. This demonstration illustrates the general conclusion of Schrodinger
(Berliner Berichte 296 1930) that measurements of spacelike separated
commuting local operators can still disturb each other because of the
reality of
the nonlocal quantum connection which is a communication channel.

#20  It is also easily shown that the transmitter apparatus is unitary for
an
arbitrary input state including the one given by Carlton Caves

[|v> - |h>]/sqrt2   (27)

I have shown this elsewhere.