Quantum Interactions on Null Surfaces
What is the meaning of physical locality in Minkowski spacetime, given
that for any two events A and B there exist other points C such that
the spacetime intervals CA and CB are both zero. This leads to the
question of whether physical effects can operate "in both directions"
along a null interval ("is locality transitive?"). The space-time
separation between the transmission and absorption of a photon is
zero, so does a photon already 'know' how it will be absorbed when
it is emitted? This is closely related to the Wheeler-Feynman
"absorber theory" of advanced and retarded electromagnetic waves,
although the Minkowski metric has similar implications for massive
particles as well, noting that Schrodinger's wave equations, like
Maxwell's equations, work equally well forwards and backwards in
time. Of course, on a macroscopic level we seem to only observe
outward "retarded" waves, not inward "advanced" waves.
Several people have suggested interpretations along these lines, but
it seems to me that the actual content of this kind of interpretation
hasn't yet been fully and clearly articulated. The existing
descriptions remind me somewhat of the old Lorentz theory of the
electron around the turn of the century, in which they had the length
and time contractions, etc., but hadn't quite figured out that they
were dealing with a fundamental aspect of space and time that could
be explained (and even deduced) very simply from a sound set of
fundamental principles.
Surprising as it seems, nearly a century after special relativity
was first put forward, physicists have yet to fully grasp the
physical significance of the Minkowski structure of spacetime,
particularly the singularities in the pseudo-metric that represent
null surfaces. For any two spacetime points A,B the intersection of
the corresponding nullcones is a quadratic surface: a hyperboloid if
the interval AB is spacelike, an elipsoid if AB is timelike, and a
paraboloid if AB is lightlike. Notice that of these three surfaces
only the elipsoid (corresponding to the intersection of time-like
separated nullcones) is finite.
In conventional terms, suppose an electron is emitted from System
X at point A and absorbed by System Y at point B, with no intermediate
interactions. The interval AB is necessarily timelike, and the
intersection between >A < and >B < is a closed elipsoidal surface
in spacetime. Relative to the frame of the interval AB this surface
is simply a sphere of radius r = cT/2 (where T is the time interval
between A and B) at the instant half-way between A and B.
The interaction between Systems X and Y is symmetrical in time,
and can be considered to originate on the surface of intersection
between >A < and >B <. This surface consists of precisely all
the points in spacetime that are null-separated from both A and B.
Two equal and opposite electron waves "emanate" from this surface.
The positive wave converges along the nullcone >B < to point B,
and the negative wave converges along the nullcone >A < to point
A. The net effect is to deduct an electron from System X at point A
and add an electron to System Y at point B.
This basic model can be used to represent all physical interactions,
and gives results entirely consistent with observation. However,
this view has the distinct advantage that, because interactions occur
along null absolute separations, all the familiar "quantum paradoxes"
of locality vanish. To illustrate, consider the traditional EPR
experiment in which two initially coupled particles are discharged
from emitter A in opposite directions and are absorbed by spin-
detecting sensors at locations B and C. If w denotes the difference
between the spin-orientation test angles at sensors B and C, we
expect the probabilities of the four possible outcomes to be as
shown below
spin at C
up down
spin up (1+cos(w))/2 (1-cos(w))/2
at B down (1-cos(w))/2 (1+cos(w))/2
The time-symmetric interpretation has no difficulty describing how
such a correlation can be realized, because the discharge emanates
from the surfaces of intersection >A<|>B< and >A<|>C<, both
of which are on the nullcone of A. The coupled discharge at A takes
place only if/when two suitably correlated negative electron waves
reach it simultaneously. These electron waves are correlated with
the absorptions of the corresponding positive electron waves at
sensors B and C because the two emanating surfaces are null-
separated from points B and C.
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