From: ericf@central.co.nz (Eric Flesch)
Subject: Wave-Particle Duality -- Solution using SR, GR, and Time Quantization
Date: 1996/07/11
Message-ID: <31e4a4a7.38545880@news.nn.iconz.co.nz>
organization: Internet Company of New Zealand
newsgroups: sci.physics,sci.physics.electromag
This article ties together my recent postings on this topic.
Wave-Particle Duality (WPD) has been called the "Great Mystery of the
20th Century". Well, it's 1996 now and high time to solve this
problem so we can get on with 21st century issues. All the necessary
artifacts are in place, but today's Physics community has a blind spot
which is preventing it from seeing the solution. I will describe the
blind spot and show how it is addressed by Time Quantization (TQ).
The concept of wave-particle duality (WPD) has come about because
light (and electrons, etc) behaves like particles in some ways and
like waves in other ways. The problem is that *individual* photons
have this duality, so that a statistical explanation is ruled out.
QED has indeed shown that an individual photon appears to take a
summation of all possible paths to reach its destination.
It is fashionable nowadays amongst the Physics/Optics community to
account for this by positing that light travels as wave-packets, and
that this confers wave-like qualities which allow light its
I-am-everywhere-at-once behavior. The following account will show
that this perspective is unnecessary, and that, as Richard Feynman
said, light is simply made up of photon particles. SR and TQ together
solve the WPD mystery, and give a physical description of how the
photon's impingement pattern diffracts. This solution is shown to be
consistent with GR, but entails a re-interpretation in one area which
remains consistent with observation.
The blind spot causing our problem is the idea that if an object moves
from A to B, it must therefore perforce occupy all intermediate
positions in turn. This may seem a sensible view to hold. However,
this premise is directly addressed by Time Quantization, which holds
that time is reducable (in principle) to discrete time quanta (one
Planck time quantum = 5.9*10^-45 sec). We can use the word
"manifestation" to mean one such time quantum. Betwixt two contiguous
manifestations there is no in-between, but in principle there are
boundary conditions.
Of course, we cannot discern these time quanta, but it gets
interesting when we combine TQ with SR's time dilation. A particle
moving at relativistic speeds travels a calculable distance between
manifestations. What does it mean, to manifest at point A, and then
to manifest at point B, with no manifestation in between? And if the
particle is at point A, how does it know exactly where point B is to
be? It's a bit of a guess -- a probability game. Ah.
Let us return to the photon. The photon, travelling *at* the speed of
C, "exists" in a state of 100% time dilation. This means that no time
passes for the photon. As seen by itself, it is emitted, and
immediately absorbed. There is nothing between (i.e., there is no
time quantum in between the photon's emission and absorption).
Now. the standard model of light holds that the photon cruises the
cosmos whilst interacting gravitationally with its environment.
Such a scenario demands that the photon "do" things in its flight.
However, the above discussion of the photon's available-time
shows that no such interactions can happen in the photon's inertial
frame, as it has no time in which to do them. This contradicts a
fundamental principle of SR that an event which occurs in one inertial
frame must occur in all frames. Therefore, the photon CANNOT perform
these interactions.
The logical extension of this is that the photon does not even inhabit
its own flight path, as simple existence constitutes an event as
defined by SR. For us to say that the photon is e.g. 2 AU from the
sun is to say that a sun-photon configuration exists which does not
exist in the photon's frame. Again, this must be wrong. Only those
events which occur in the photon's frame can be ascribed to the
photon. And those events are only 1) its emission 2) its absorption.
There is nothing in between.
The premise that the photon moves from A to B without existing at the
intermediate points is immediately justifiable by using the photons
frame. Moving *at* the speed of C obviates time and space -- the
photon, to itself, is a simple instantaneous transfer of energy
between two coexisting bodies. There are no points-in-between for the
photon in its frame. The photon simply does not exist in our
4D-manifold, and indeed experiences a zero-dimensional universe.
Thus, what is physically sensible in the photon's frame is simply
mapped into our own space-time frame (which is defined by our maximum
speed C). This mapping is what we call the photon's path. It is this
path which follows the null geodesics which bend as per GR's
prescription. The photon itself is never present.
To summarize, light (the photon) experiences no time between its
emission and absorption. Thus it has no existence between its
emission and absorption. Thus, the photon's PATH follows null
geodesics, but there is no photon there -- the path is only a mapping
from the photon's 0-D metric into our 4-D metric. No photon = no
gravitation or momentum. Even in GR.
Note that this solution is falsifiable in a simple way: the photon is
held to experience no events between its emission and absorption.
Therefore the photon cannot be detected non-destructively. Indeed,
the only way which we have ever detected a photon is by absorbing it.
If someday a device is built which detects a photon while leaving it
intact, then this solution is false. But it will never happen. And
GR-textbook's visions of photons interacting gravitationally with
massive bodies are simply the fantasies of authors using invalid
examples to illustrate the valid tenets of GR. The examples are
mistaken, not GR, as GR is not a theory of the nature of light.
In GR, light paths follow null geodesics on the gravity-influenced 4-D
manifold. Standard analysis in GR is that momentum is conserved
between bodies using gravitation. Given the concept here is that the
photon path contains no actual photon, this means no momentum needs to
be exhanged. However, the final momentum of the impacting photon has
been affected, as the photon's vector points differently. Does this
violate conservation of momentum?
The answer is no, if we slightly modify our interpretation of GR. The
key is to fully understand how GR treats space-time and massive
bodies. The massive bodies warp space-time, causing the 4-D
space-time manifold to undulate according to the positions of the
massive bodies. As the photon's path crosses this terrain, its null
geodesic goes ever straight according to the terrain's contours --
even though it may look curved to our eyes. Current practice is to
enforce conservation-of-momentum in our own 3-D geometry, in other
words to un-GR the tensors back to our own geometry for the final
bottom-line reconciliation. If instead the *GR 4-D manifold* is used
for the momentum calculations so that conservation-of-momentum is
reconciled on that terrain, then the above scenario does not violate
this dictum. Timelike geodesics will also be recalculated, with
minute changes in results -- e.g. calculations of Mercury's precession
would yield an imperceptible increase. Perhaps Einstein thought about
doing the calculations this way but shrunk back, just as he shrunk
back from letting GR annoint the idea of an expanding universe (by
introducing the universal constant). Einstein had to sell the GR idea
to others, after all.
Thus, momentum direction is preserved *on the GR space-time map*,
although perhaps not according to our 3-D metric. As an aside, Bryan
Beatty came up with a beattiful thought experiment showing that, given
the above, an internally-powered craft can in theory be built if it
includes a mass great enough to bend light paths 180 degrees. I don't
think it would be a popular design, though. :-)
Let's shift our view to the electron, continuing to bear in mind the
principle of TQ that there is one "manifestation" per time quantum.
Again, the photon, being 100%-time-dilated, gets zero manifestations.
By comparison, a relativistically-moving electron might travel some
pathetically small distance between its manifestations, maybe 10^-20
m. Past a certain threshold speed (i.e. above a certain energy level)
its distance-travelled while in a non-manifested state will be long
enough that the positional uncertainty allows it to diffract.
Subsequent manifestations are oriented accordingly.
So, how has this solved the problem of wave-particle duality?
The solution is that if a particle uses a single time quantum to go
from point A to point B, with a measurable space in between
(preferably longer than the particle's radius), then the exact
location of B becomes unclear, and maps into a diffuse path. In the
case of the photon, it travels all the way from its source to its
destination in the space of a single time quantum. The photon's path
diffuses broadly and the end result is that we cannot say exactly
where it will hit, unless we cheat by pre-determining its position (a
la double-slit experiment). The final impact-point of the photon is
reduced to probabilities and interference patterns. But when the
photon hits -- splash, it's the particle which strikes, one
time-quantum after it was emitted.
And where does the photon hit? The mapped path decides, but it does
not follow Newtonian rules, as no physical object is involved. The
path diffuses and the precise point of impact becomes a probability
game. Diffraction et all. You know the rest.
Once we remove the idea of photons in flight, diffraction of the
impact pattern of the light particles is immediate. Wave-particle
duality is solved, with the simplest of solutions. Simple. As, of
course, it must be.
Eric Flesch
Nelson, New Zealand
7 July 1996
ADDENDUM:
On Quantum Field Theory:
This is 20th century Ptolemaic epicycles. An attempt to formulate
a complete mathematical description, but the underlying principle is
wrong.
On the idea that a travelling photon can be located in space-time:
The double-slit experiment (which shows that a single photon
goes thru both slits) can confidently be extrapolated to a double-slit
apparatus light-years across. The photon coming from a distant
source will still go through both slits, even though those slits are
light-years apart. Therefore the photon is spread over an unbounded
area. Therefore the photon is not discernable from the background
vacuum. Therefore the photon does not exist.
(Note that no time-analysis is needed in this identical conclusion)