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Feynman 29  INTERFERING ALTERNATIVES
from Feynman and Hibbs, QUANTUM MECHANICS AND PATH INTEGRALS:
"These early inquiries were involved with the problem of the infinite self-
energy of the electron.  In working on that problem, a 'least-action'
principle using half advanced and half retarded potentials was discovered.
The principle could deal successfully with the infinity arising in the
application of classical electrodynamics." p.vii

Thus, even on classical level the advanced electromagnetic potential wave
propagating at the speed of light but backward in time is required along
with its retarded partner propagating forward in time.  This same theme
reappears at the level of quantum amplitudes for histories when we go from
amplitude to probability using the absolute square.  The non-classical
interference contributions to the probability are from loops in time for
information flow around two different spacetime paths that start and end at
the same two events.

The key idea behind my conception of how the nonlocal quantum connection is
a practical communication channel in standard quantum mechanics in spite of
the bogus mathematical arguments to the contrary is right here.  Feynman's
"sum over histories" Lagrangian multiple-time formulation may not be
equivalent to the Hamiltonian operator fixed-time formulation of quantum
mechanics. The latter emerges from the former as a special case just like
the Schrodinger fixed-time wave function emerges from the sum of path
amplitudes.  The commutativity of the hermitian observables is necessary
for compatibility (i.e., non-interference) of measurements but not
sufficent in the presence of both "entanglement" and "interfering
alternatives".  It is the last that is essential.  It is correct to say
that if there is commutativity and entanglement but no interference (the
situation in the actual experiments of Clauser, Aspect et-al) then there is
no quantum connection communication.  But, if the interference is
engineered correctly then such communication across spacelike intervals and
backward along timelike and lightlike intervals is possible.  Indeed, the
origin and evolution of the universe depend upon quantum connection
communication.

p.13 1-3 INTERFERING ALTERNATIVES
Two Kinds of Alternatives.
... p.14 In order to make definite the new rules for combining
probabilities, it will be convenient to define two meanings for the word
'alternative'.  The first of these meanings carries with it the concept of
exclusion.  Thus holes 1 and 2 are exclusive alternatives if one of them is
closed or if some apparatus that can unambiguously determine which hole is
used is operating.  The other meaning of the word 'alternative' carries
with it a concept of combination or interference. (The term 'interference'
has the same meaning here as it has in optics, i.e., either constructive or
destructive interference.)  Thus we shall say, holes 1 and 2 present
'interfering alternatives' to the electron when (1) both holes are open and
(2) no attempt is made to determine through which hole the electron passes.
When the alternatives are of this interfering type, the laws of probability
must be changed to the form

P = |A|^2         (1-1)

A = A(1) + A(2)   (1-2)

The concept of interfering alternatives is fundamental to all of quantum
mechanics.  In some situations we may have both kinds of alternatives
present.  Suppose we ask, in the two-hole experiment, for the probability
that the electron arrives at some point, say, within 1 cm of the center of
the screen.  We may mean by that the probability that if there were
counters arranged all over the screen (so one or another would go off when
the electron arrived), the counter which went off was within 1 cm of x = 0.
Here the various possibilities are that the electron arrives at some
counter via some hole.  The holes represent interfering alternatives, but
the counters are exclusive alternatives.  Thus we first add A(1) + A(2) for
a fixed x, square that, and then sum these resultant probabilities over x
from -1 to +1."

Now let's apply this Feynman lesson to my quantum connection communicator.
On the receiver side there are only two counters which catch all the light
to a good approximation. Therefore x' is not a continuous variable but a
discrete one x' = +1 or x' = -1, and they are exclusive alternatives.  On
the opposite transmitter side, there is only one counter that catches all
the light to a good approximation. So there is only on alternative, say, x
= 0.

What corresponds to the "holes" which "represent interfering alternatives"?
Because of the half-wave plate one of the narrow beams emerging from the
transmitter calcite, the "holes" correspond to the two small area regions
(i.e., e & o) on the back-face of the transmitter calcite rhomb from which
the extraordinary and ordinary collimated beams emerge.  Both of these
beams are brought together to the same transmitter counter whose photo-
sensitive surface is shaped like a little cube. Each beam impinges on one
of the faces of the cube, but it is impossible to tell if an ejected photo-
electron is caused by a photon hitting one face or the other.  There must
be no entanglement of the state of the photo-electron with orthogonal
localized "face" states of the cube for this device to work.

What are the indistinguishable Feynman histories (.i.e. interfering
alternatives) A(1) and A(2).  Thes probability amplitudes are nonlocal
representing the histories of both connected (i.e. entangled) photons in
the same pair. Let us focus attention on the the receiver photon being
detected at the x' = +1 receiver counter. Then A(+,e (o)) is the amplitude
in which the receiver photon is detected in the +1 counter and its twin
transmitter photon has taken the e (o)-path at the faraway transmitter
calcite before it is detected at the single cubical x = 0 counter.  The
space-time interval between these two detections is irrelevant!

The quantum connection signal at the x' = +1 receiver is simply

S = |A(+,e) + A(+,o)|^2 - |A(+,e)|^2 - |A(+,o)|^2

Since x = 0 is the only exclusive alternative on the transmitter side (i.e.
the the classical probability distribution over exclusive alternatives is
essentially a Dirac delta function) S is locally measureable without having
to get data from the tramsitter by ordinary light-speed limited signals.
That is we are tracing over a Dirac delta function.

Now the skeptics will say that the Delta function model is impossible in
principle. That the interference terms will always be zero in the sum over
exclusive alternatives on the transmitter side. But this is adhoc there is
nothing in quantum mechanics to demand that.  Some say that the Heisenberg
principle demands it, but I say it demands just the opposite. Let
experiment decide!