From: sarfatti@well.sf.ca.us (Jack Sarfatti)
Subject: Feynman 27 "at any speed"
Organization: Whole Earth 'Lectronic Link
Date: Tue, 10 Nov 1992 05:23:51 GMT


Feynman 27 "at any speed"
Gleick's book GENIUS p.229:"It was still possible, barely, to understand
spin literally: to view the electron as a little moon.  But if the electron
was also an infinitesimal point, it could hardly rotate in the classical
fasion.  And if the electron was also a smear of probabilities and a wave
reverberating in a constraining chamber. how could these objects be said to
spin?  What sort of spin could come only in unit amounts or half-unit
amounts (as quantum mechanical spin did)? ... (Feynman) reduced the problem
to a skeleton, a universe with just one dimensions (or two: one space and
one time).  This universe was merely a line, and in it a particle could
take just one kind of path, back and forth [at the speed of light! JS],
reversing direction like a crazed insect.  Feynman's ... method .... the
summing of all possible paths a particle could take .... he could derive
... a one dimensional Dirac equation .... he added something new - a
diagram ... for keeping track of the zigs and zags.  The horizontal
dimensions represented his one spatial dimension, and the vertical
dimension represented time.... Phase was crucial to the mathematics of
summing the paths, because paths would either cancel or reinforce one
another, depending on how their phases overlapped." p.231

[In this 1D Feynman picture a massive particle is a massless particle
trapped in a string of length equal to the Compton wavelength h/mc. JS]

... p.246 "In mid-1947 friends of Feynman persuaded him - threats and
cajoling were required - to write for publication ... He said he had
developed an alternative formulation of quantum mechanics to add to the
pair of formulations produced two decades before by Schrodinger and
Heisenberg.  He defined the notion of a probability amplitude for a space-
time path.  In the classical world one could merely add probabilities ...
In the quantum world probabilities were expressed as complex numbers,
numbers with a quantity and a phase, and these so-called amplitudes were
squared to produce a probability."

[Sarfatti comments: The square is the "absolute square" or product of the
"retarded" complex number with its "advanced" complex conjugate number. The
conjugate corresponds to running the path backward in time. Therefore, if
two different paths are indistinguishable, the interference terms
correspond to "loops in time" going forward in time on one path and
returning backwards in time on the other path.  Thus, the purely quantum
distortions of the classical probabilities are due to loops in time that
span a finite spacetime area.  The reason for the i in quantum mechanics is
the time loop.  It's interesting the classical Wheeler-Feynman
electrodynamics also has advanced backward in time effects. Similar loops
of parallel transport (curvature) in the limit of shrinking area also
determine the Newtonian limit of general relativity.]

p.247 "Feynman described .... the canonical thought experiment of quantum
mechanics, the so-cqalled two-slit experiment.... A beam of electrons (for
example) passes through two slits in a screen,  A detector on the far side
records their arrival. If the detector is sensitive enough, it wil record
individual events, like bullets striking; it might be designed to click as
a Geiger counter clicks.  But a peculiar spatial pattern emerges: the
probabilities of electrons arriving at different places vary in the
distinct manner of diffraction, precisely as though waves were passing the
slit and interfering with one another.  Particles or waves?  Sealing the
paradox, quantum mechanically, ... each electron 'sees' or 'knows about,'
or somehow goes through both slits.  Classically a particle would have to
go through one slit or the other. .... If one tries to glimpse the particle
as it passes through one slit or the other.... again one finds that the
mere presence of the detector destroys the pattern."

[Sarfatti comments: Bohm has still a fourth interpretation, the nonlocal
quantum potential acts at a distance with a new kind of force on a real
particle.  In the Dirac ket notation, destruction of the interference
pattern on the screen is caused by tracing over orthogonal kets of the
measuring device that is 1-1 correlated (entangled) to the alternative
paths of the electron from the two slits to a region on the screen.

My quantum connection communicatio gedankenexperiment is a variation on
"the canonical thought experiment of quantum mechanics".  Instead of a
single photon we have an entangled photon pair.  Instead of the paths
through the two slits we have the ordinary and extraordinary paths of the
transmitter photon exiting the transmitter calcite crystal.  A half-wave
plate disentangles the photon pair in polarization space but not in
physical space so that both paths of the transmitter photon have the same
polarization.  There is no contradiction with unitarity here as some
critics falsely claim because the spatial distinction keeps the two
parallel polarization states of the transmitter photon in different vector
spaces until they collapse on the same photo-sensitive surface of a
counter.  The "screen" where "fringes" are observed corresponds to the two
receiver counters behind the receiver calcite which is misaligned to the
transmitter calcite by angle theta.  The two reciever counters see
complementary fringes.  For example if one is bright, the other is dark.
The fringe formula is essentially sin(2theta)cos(phi) where phi is the mean
phase difference of the two alternative transmitter photon paths.  There
are no unitarity-violating fringes at the transmitter counter.  The fringe
shift quantum leaps to the two receiver counters where they obey local
unitarity!  It's a very pretty picture that is globally self consistent.
The first nonlocal fringe shift was predicted by Bohm and Aharonov.

*The amazing prediction is that one can cause a fringe shift at the
receiver by making a "delayed choice" decision after the fringe shift has
already happened.  In this way useful "precognitive information" can be
transmitted backward in time.  It is posible to know the future and to act
on that knowledge within certain limits.  Your actions cannot prevent the
future events that caused your knowledge.  No wonder the orthodox scream
"Crackpot!" - Sarfatti]

"Probability amplitudes were normally associated with the liklihood of a
particle's arrving at a certain place at a certain time.  Feynman said he
would associate the probability amplitude 'with an entire motion of a
particle' - with a path.  He stated the central principle of his quantum
mechanics: The probability of an event which can happen in several
different [indistinguishable or un-entangled - JS] ways is the absolute
square of a sum of complex contributions, one from each alternative way.
These complex numbers, these amplitudes, were written in terms of the
classical action ..[ i.e., quantum amplitude for a single path = e^i2pi
classical action for that path/Planck's constant h  is the fundamental
Feynman formula as important as Einstein's formula E = mc^2 - JS]

p.249  His readers ... found no fancy mathematics, just this shift of
vision, a bit of physical intuition laid atop a foundation of clean,
classical mechanics.

Few immediately recognized the power of Feynman's vision.  One who did was
the Polish mathematician Mark Kac, who heard Feynman describe his path
integrals at Cornell and immediately recognized a kinship with ... the work
of Norbert Weiner on Brownian motion, the herky-jerky random motion in the
diffusion process  [I took a math physics course with Kac at Cornell. - JS]
... Feynman's summing of paths - path integrals seemed bizzarre.   They
conjured a universe where no potential goes uncounted; where nothing is
latent, everything alive; where every possibility makes itself felt in the
outcome. He had expressed his conception to Dyson:

'The electron does anything it likes.  It just goes in any direction at any
speed, forward or backward in time, however it likes, and then you add up
the amplitudes and it gives you the wave function.'

Dyson gleefully retorted that he was crazy." p.250
 to be continued - don't miss the next episode at your computer coming
soon!