Visualizing the quantum world...
From: Vic Stenger <vjs@uhheph.phys.hawaii.edu>
To: quantum-d@teleport.com
Subject: Visualizing the quantum world...
----------------------------------------------------------------
Editor's comments - in a thread on this list Vic Stenger suggested
that proofs of quantum nonlocality were exaggerated, and that the
quantum mysteries can be generally dispelled by realizing that at
an elementary level there is no preferred direction in time. Here
is a paper he is preparing for publication which goes into greater
detail...
What he is about is rescuing the concept of a point particle from
its usual difficulties by setting it loose in time, which Vic takes
as in any event a natural interpretation of quantum field theory.
"The familiar picture of particles following definite paths through
spacetime can be retained to visualize the behavior of fundamental
particles, as long as we allow their spacetime worldlines to wander
around at will within both forward and backward lightcones."
I will hazard a comment. While i find these images interesting
and meaningful, i see no reason to regard them as an exorcism or
minimization of "nonlocality." It seems to me that to the extent
that Vic's picture is true then macroscopic spacetime and the arrow
of time are emergent aspects. Out of the bidirectional level that
Vic points to emerge among other things many dynamically trans- or
non-local effects as are characteristic of coherent quantum systems.
I guess the satisfaction comes from having managed without drawing
any superluminal worldlines - nevertheless, one has not untangled
different parts of spacetime. "Nonlocal" seems not such a bad word,
all things considered...
Rhett
this document also available at:
http://www.teleport.com/~rhett/quantum-d/posts/vjs_11-8.html
--------------------------------------------------------------------
The following is a draft of an article I have written for
possible submission to the American Journal of Physics.
I would appreciate your comments, corrections, and suggestions.
If you would like a postscript file, with the figures, let me
know. The figure captions are at the end of this file.
Please do not distribute our quote without checking with
me, or until the final version is submitted.
Vic Stenger
vjs@uhheph.phys.hawaii.edu
###########
DRAFT VERSION 11/6/96 Please Do Not Distribute
Visualizing the quantum world from a time-reversible
perspective
Victor J. Stenger
University of Hawaii at Manoa, Honolulu, Hawaii 96822
Fundamental processes do not mandate a particular direction
of time. Time reversibility is implicit in elementary particle
calculations, where particles travelling backward in time are
interpreted as forward-time antiparticles. The intuitive
picture of particles following precise paths in spacetime, with
definite position and momentum at each point, can be retained
in visualizing quantum phenomena when time reversibility is
allowed. Effective nonlocality occurs without superluminality.
The claimed paradoxes of quantum mechanics disappear when
the requirement of forward-time causality is eliminated.
I. INTRODUCTION
Over six decades of scientific effort have failed to
uncover a single empirical or theoretical inconsistency in the
formal theory of quantum mechanics. Despite this
unchallenged success, philosophers and other commentators
continue to argue about what quantum mechanics really
<<means.>> The conflicting reports that appear in the popular
press cannot help but lead the uninitiated to think that
quantum mechanics is in some sort of trouble, and may even
turn out to be wrong. Compounding this confusion, quantum
phenomena remain mysterious to the popular mind because they
differ so profoundly from common experience. In the
meantime, most physicists simply shrug. Quantum mechanics
agrees with all the data, so what's the big deal?
Instead of closing the book, however, science
popularizers flap the pages, fanning the flames of quantum
fantasy. And since fantasy is more fun than hard reality,
quantum mechanics has become a popular grab-bag for every
paranormal delusion, from miracle cures to ESP and time
travel.[1] Quantum mechanics is mysterious, and so all
mysteries must be quantum mechanical.
The source of the imagined mysteries and mysticism
attached to quantum mechanics can be traced to the way
quantum physicists have conventionally verbalized quantum
phenomena, most particularly the apparent dual nature of
matter. Light and other phenomena are said to sometimes be
waves and sometime particles. Quantum orthodoxy teaches
that it all depends on what you decide to measure. Measure its
position, and an object is a particle. Measure its wavelength,
and an object is a wave.
By themselves, dual properties need not present any
inherent paradoxes, so long as they are compatible. A chair can
be both a rocker and made of wood. The properties associated
with waves and particles, however, are seemingly
incompatible. It is difficult to visualize an object being a
localized particle and a spread-out wave at the same time.
The Heisenberg uncertainty principle deltaxdeltap .ge. hbar/2
quantitatively describes how any attempt to more precisely
measure an object's position x results in an increased
uncertainty in the object's momentum p and its corresponding
de Broglie wavelength lambda = h/p, and vice versa.
Bohr expressed this as the principle of complementarity.
A system is complementary when it can be described in either
of two (or more) incompatible ways. Quantum mechanics is
complete, in Bohr's view, because either the wave or particle
picture can be used to successfully describe all the results of
measurements. The wave functions that describe quantum
states can be expressed equivalently as either functions of x
or k = 2¹/lambda = p/hbar that are unambiguously connected
by a Fourier transform.
Einstein always insisted that quantum mechanics is
incomplete because it does not simultaneously contain within
its formalism all those quantities that have can, in principle,
be measured. In the famous Einstein-Podolsky-Rosen (EPR)
paradox,[2] two particles are emitted from a source and the
momentum or the position of one is measured. Since in either
case the momentum or position of the other particle is
determined with complete certainty, each quantity must have
objective reality, in the EPR view. Einstein and his
collaborators argued that quantum mechanics must be
incomplete since it does not allow a particle to simultaneously
possess definite values of momentum and position. In other
words, the commonsense notion of particles following definite
paths though space is discarded.
Bohr countered that since quantum mechanics accurately
describes the results of all the experiments you can perform
on the two particles, it is as complete as you can expect it to
be.[3] For example, if you measure the momentum of the first
particle, the momentum of the second particle is predicted
with certainty (within experimental errors). True you cannot
predict the second particleÕs position, but that very fact still
accurately describes the results of experiment; measure the
position many times and you will get a flat statistical
distribution, with all values equally likely just as predicted by
quantum mechanics.
BohrÕs position won the day and came to be part of what
is known as the Copenhagen interpretation, the orthodox view
of quantum mechanics. It remains today consistent with all
observations. However, Copenhagen expresses an ontology that
has become the source of much metaphysical speculation in
which human consciousness is given a role that is
unprecedented in physical theory. In the Copenhagen ontology,
an object is in reality either a particle or a wave, depending on
what you decide to measure. Since this decision can be made
long after the object has left its source, it appears that human
consciousness itself determines the nature of reality.[4]
Sometimes BohrÕs views are labelled as positivist, or
instrumentalist. Obviously the nature of a measurement plays
a role in defining the quantity being measured. While
positivism no longer has the following it had in BohrÕs day, a
positivist stance on quantum mechanics remains
philosophically arguable.[5] However, the ontological
implication that consciousness determines reality is far more
bizarre than mere positivism. It is idealism pure and simple.
It says the world is all in our heads.
Bohr did not believe this; nor does any respectable
present-day physicist. Yet mysticism seems to flow from any
attempt to explain quantum mechanics in the words of the
Copenhagen interpretation. The attitude of most physicists is
to ignore the words, and the mysticism, so long as the
mathematics works. However, while mathematics is the
language of physics, words and pictures are the media that
must be used with the layperson. If physicists abrogate their
responsibility for explaining their work in language that the
average person understands, then that task will be assumed by
others who may be less committed to the search for objective
truth.
The purpose of this article is not to review the many
interpretations of quantum mechanics that exist as
alternatives to Copenhagen, all giving identical experimental
results. A huge literature already exists on this subject and
Copenhagen is gradually falling out of favor if for no other
reason than the sheer volume of alternatives. Unfortunately,
some of the more popular modern alternatives, such as BohmÕs
hidden variables[6] and Everett's many worlds[7] are, in their own
ways, as bizarre as Copenhagen. Other, newer interpretations
such as consistent histories are less fantastic, but are not as
easy to verbalize in simple language or visualize in terms of
commonsense images.[8] The more boring, highly mathematical
interpretations have not received the same press as the
dramatic, visual ones. This naturally leads the layperson to
the view that quantum mechanics is as mysterious as ever and
to listen sympathetically when promoters of the paranormal
claim a scientific basis for their fantasies.
The argument over interpretations will continue as long
as experiment does not adjudicate between them, although a
careful application of Occam's razor should excise those
models that require the most fantastic assumptions, when
neither data nor reason demand these assumptions.
Here I wish to propose a way to verbalize and visualize
quantum mechanics in terms of the familiar concepts of
particles moving along well-defined paths through space, with
definite speeds and directions, that the average person should
find comprehensible. Furthermore, I hope to show that the
mystical consequences associated with Copenhagen and several
other interpretations can be avoided with this picture. Note,
however, that I am not proposing yet another interpretation of
quantum mechanics, just suggesting a way to think about the
quantum mechanics that is actually practiced by physicists,
though perhaps not so explicitly.
Two fundamental notions, which are by no means widely
appreciated, are exploited. First, despite the common
perception of physicists and laypeople alike, the quantum
world is in fact simpler than the classical world of everyday
experience. It is not any inherent complexity that makes
quantum mechanics difficult to comprehend. Rather, it is its
unfamiliarity. The macroscopic world of human experience is
far more complex, and in many ways more mysterious than the
quantum world. As we are now beginning to appreciate, the
nonlinearities that characterize most macroscopic events are
responsible for the richness and complexity of the world of our
experience. Quantum mechanics remains linear, and quantum
events are surprisingly simple. While this may seem a
paradoxical statement because of the esoteric mathematics
used in quantum mechanics, we must remember that we have
no mathematics, common or esoteric, that can be used to make
comparable predictions for most macroscopic systems. We can
calculate the magnetic moment of the electron to many more
significant figures than we can calculate the magnetic moment
of the earth.
Second, one aspect of the simplicity of the quantum
world is time-reversibility. Fundamental processes do not
follow a preferred arrow of time. Without an arrow of time,
we have no causality or determinism. And without causality
and determinism, we have none of the paradoxes that have
become associated with quantum mechanics and which are used
to support mystical claims. Since everything from common
experience tells us that time flows one way, this represents
the most difficult conceptual leap that must be take in the
process. However, once this is done, the claimed paradoxes of
quantum mechanics that lead us down the road to mysticism
disappear and particles move through space and time just as
they always did--along definite paths and with definite
momenta.
II. TIME-REVERSIBILITY
Nowhere is the conflict between basic physical theory and
common sense more profound than in their differing
conceptions of time. While everything in our experience points
to time as continuous stream that never reverses its flow, the
fundamental principles of physics contain no basis for a
singular direction of time. The dynamical equations of both
classical and quantum physics (relativistic and non-
relativistic) are completely time-symmetric. Solutions of the
classical equations of motion allow either time direction. In
quantum mechanics, the time evolution of a system is governed
by the Schrdinger equation:
ihbar delpsi/delt = Ht(1)
While this appears to single out one time direction, psi(x,t) =
psi*(x,-t) is an indistinguishable solution.
In conventional quantum mechanics, time irreversibility
enters in the measurement process which is usually described
in terms of <<wave function collapse.>> However, the collapse
of the wave function is not predicted by the Schrdinger
equation, and indeed is inconsistent with it. Most alternate
interpretations do away with the notion, though most still
retain uni-directional time. Gell-Mann and Hartle have shown
that quantum mechanics always can be formulated in a time-
reversible fashion.[9]
Usually the time-reversed solutions in classical and
quantum mechanics are ignored, with no reason given. As I
will argue below, this is an arbitrary procedure that has no
justification other than agreement with preconceptions that
have been conditioned by our macroscopic experience.
The time asymmetry existing in the irreversible
processes of thermodynamics, and forming part of normal,
macroscopic experience, are codified in the second law of
thermodynamics. As Boltzmann showed a century ago, this
asymmetry is purely a statistical one. Given sufficient
opportunity, any <<irreversible>> thermodynamic process can
reverse itself. All the air can flow out of a room when the
door is opened, if the molecules happen to be moving in that
direction at that instant. People can get younger and the dead
rise. However, the likelihood for these <<miracles>> happening
at the level of common experience is vanishingly small,
because of the large number of molecules involved. So, we can
safely proceed on the assumption that these events will not
happen in the age of the universe, that everyone ages together
and the dead stay dead.
The statistical arrow of time does not apply for systems
of few particles, as are involved in most elementary
processes. The only place where an asymmetry in time
direction is even suggested in fundamental physics is in CP-
violating processes such as Ko-decay. The CPT theorem
implies that these reactions violate time-reversal symmetry.
But even in this rare situation, time reversal is not forbidden.
We simply have a situation in which reactions occur in both
time directions, but the probabilities are slightly different--
on the order of one part in a thousand. It is difficult to see
how this can be a fundamental source of a singular arrow of
time. Irreversibility is the extreme limit of time-reversal
asymmetry in which one direction is completely forbidden or,
as is the case for the macroscopic arrow of time, highly
unlikely.
Furthermore, in theories that go beyond the current
Standard Model, such as grand unification or supersymmetry,
CP-violation may be what is called a broken symmetry. That
is, the asymmetry does not exist in the underlying physics but
<<freezes out>> at low energies. Within the current big-bang
cosmological model, the early universe was initially CP-
symmetric, and T-symmetric, with equal numbers of particles
and antiparticles. As the universe cooled, the slight difference
between particle and antiparticle reaction rates led to the
current excess of matter over antimatter, giving the so-called
baryon asymmetry of the current universe.
Prigogine and his followers have proposed that the time
irreversibility of macroscopic, many-body phenomena feeds
down to the microscopic level to give an arrow of time to the
microworld.[10] While this idea strikes a responsive chord for
those who find a holistic perspective emotionally more
appealing than the traditional reductionism of physics, it will
remain little more than wishful thinking until some
microscopic effect is observed that confirms the notion. Not
only have none been observed, none have been specifically
predicted. In the immortal words of Pauli, PrigogineÕs theory
is <<not even wrong.>>
In their book The Arrow of Time, Coveney and Highfield
even go so far as to suggest that the macroscopic arrow of
time can explain the paradoxes of quantum mechanics, although
they do not say how.[11] My thesis is the exact opposite, that a
recognition that time has no arrow at the quantum level
actually eliminates the so-called paradoxes of quantum
mechanics. The paradoxes result only when we try to force our
macroscopic prejudices on quantum systems.
At another level, Penrose has strongly asserted that
quantum gravity is necessarily asymmetric in time, although
he admits this is <<not accepted wisdom.>>[12] Since quantum
gravity is not expected to have any effects at distances
greater than 10^-33 centimeter, and no theory yet exists, we
will have to wait and see whether it can produce an arrow of
time at the distances currently explored in quantum
phenomena.
Time reversibility, if not complete time-reversal
symmetry, is deeply built into the way physicists describe
elementary interactions. In Feynman diagrams, antiparticles
can be viewed as particles going backward in time, with their
electric charges, momenta, lepton numbers, and baryon
numbers reversed. When the probabilities for various
elementary particle reactions are calculated, all the possible
Feynman diagrams that can connect the initial and final states
are drawn and their probability amplitudes calculated,
summed, and squared to get the final result. Nowhere is any
particular time direction singled out except arbitrarily, as
determined by the application at hand.
A similar situation exists in the Feynman path integral
formulation of quantum mechanics.[13] There the amplitudes
for all the paths connecting two points are also summed and
squared to get a probability independent of time direction. The
classical principle of least action, in a which a unique path is
determined, is shown to follow in the limiting case where the
phases of the amplitudes are random, that is, they decohere.
In both classical and quantum mechanics at the non-
relativistic level, time seems to play a special role. Time is a
parameter, while the position coordinates are observables. In
relativistic quantum field theory, as is often said, time does
not get promoted to an observable; rather, spatial coordinates
are demoted to parameters.
Time is treated as a fourth dimension of spacetime {x} =
{ xo ,x1, x2, x3}. If one defines the three cartesian spatial
coordinates as x1, x2 and x3, and uses xo = ict as the fourth
coordinate, no distinction is made between space and time.
And just as a particle can move either way along a spatial
axis, nothing forbids it from moving in a negative t-direction.
Furthermore, what can be said for spacetime coordinates {x}
can also be said for their conjugate four-momenta {p}, where
po = iE/c and E is the energy.
The relativistic worldline picture of particle motion, in
which a particle moves along a path through four-dimensional
spacetime, has become very familiar to the science-reading
public and can be used as a pedagogical tool in quantum
mechanics as well. Worldlines are not generally utilized in
describing quantum mechanics to laypeople, since only non-
relativistic examples are normally discussed. However, the
quantum world is very much relativistic. Photons are extreme
relativistic, and you rarely talk about quantum mechanics
without talking about photons. I will utilize the worldline
image to hopefully make time-reversibility more palatable.
Within the framework of relativity, a worldline can turn
around and go backward with respect to a particular, arbitrary
time axis just as readily as it can turn around with respect to
a particular, arbitrary spatial axis. The proper time, as
measured on a clock in the rest frame of the particle, will
continue to change monotonically; a particle can move either
way along the worldline, its antiparticle the opposite.
I could attempt to continue this paper without any
further use of the word <<time,>> referring only to the
spacetime coordinates {x} and treat the proper time as simply
some parameter that specifies the position of a particle on its
worldline. However, this would perhaps be too abstract and
defeat my purpose, which is after all to connect quantum
mechanics to common experience. Similarly, I could avoid the
use of <<antiparticle,>> since the notion of a separate type of
matter is eliminated (with satisfying economy) in the time-
reversible scenario. Once again, however, I will need to show
the connection with our usual description of observations, if
not those of common experience, then those in made in an
accelerator laboratory.
III. EFFECTIVE NONLOCALITY
The terms local and nonlocal frequently appear in the quantum
literature. Basically they refer to whether two events in
spacetime have timelike or spacelike separations. If the
separation is timelike, inside the light cone, a reference frame
can be found in which the two events are in the same place, and
so are local. If the separation is spacelike, outside the light
cone, such a reference frame cannot be found without
superluminal motion. Then the events are nonlocal.
Relativity by itself does not deny nonlocality or
superluminal motion. It simply forbids the acceleration of
particles with non-zero rest mass to or beyond the speed of
light. Massless particles, such as the photon, travel at the
speed of light. A whole separate world of objects, called
tachyons that always move at speeds greater than light can
exist without violating the postulates of relativity. They are
generally ruled out by the added postulate of Einstein
causality, which prevents the labels <<cause>> and <<effect>>
from depending on reference frame.
Increasingly, this seems to be a weak argument. The
labels cause and effect may not have any meaning in the
quantum world. They are used in discourses about elementary
interactions because we are used to talking that way, not
because the processes themselves require such concepts. In
any case, tachyons have not been observed and no measurement
demands their hypothesis. Applying Occam's razor, I will say
nothing further about them and consider only particles that
move at the speed of light or less.
Quantum phenomena are widely thought to be nonlocal.
However, this need not imply superluminal motion. As I will
now demonstrate, effective nonlocality can happen without
motion faster than the speed of light, provided we allow that
motion to take place in both the forward and backward
lightcones.
In Fig. 1, the worldline of an electron is shown on a two-
dimensional spacetime diagram. At point B it turns around and
goes back in <<coordinate time,>> as defined by the time axis
shown, which refers to the frame of reference of an arbitrary
observer. The proper time of the electron continues to change
monotonically. Then, at point C the electron turns around once
more to go forward in time, continuing on so that it passes the
point D separated from B by the distance deltax = BD, at the
same coordinate time that it originally (in proper time)
passed B.
To the observer in the reference frame of the diagram,
the electron appears to have made an instantaneous shift over
a spacelike distance from B to D. However, the electron
always remains within its forward or backward light cones.
No superluminal motion has taken place.
Before we conclude that this <<zigzagging>> through
spacetime makes spacelike connections across the cosmos
possible, thereby confirming the mystical belief in a holistic
universe in which everything, including the human mind, is
simultaneously connected to everything else, we need to be
more quantitative. For the electron to turn around in
spacetime, its four-momentum must be reversed at B. Overall,
momentum and energy are conserved because the electron's
four-momentum is reversed once again at C. Still, unless an
interaction with another particle takes place, momentum
conservation is violated at both B and C by an amount deltap =
2p. This is allowed by the uncertainty principle, provided that
deltaxdeltap .ge. hbar/2, or deltax .ge. h/p = lambda, the de
Broglie wavelength of the particle. (A similar argument can be
made for energy and time, deltat .ge. h/E = 1/nu). Thus
zigzagging through space time is confined to microscopic
distances (except for radio photons).
We can view zigzagging though spacetime as a
manifestation of the uncertainty principle. Conventional
quantum mechanics says that a particle cannot simultaneously
have a definite position and momentum. The time-reversible
picture allows us to maintain the image of definite paths, with
the particles having simultaneous position and momentum at
any given point on the path, but possibly multiple positions and
momenta at any given coordinate time. The unpredictability of
particle motion, and indeed its wavelike behavior, is
interpreted as a kind of random walk through spacetime.
Is the zigzagging of electrons through spacetime
observed? Yes! Only we call it pair production and
annihilation. As seen in Fig. 2, we can view the process as one
in which a positron and electron are produced by two gamma-
ray photons at B. The positron meets another electron at B
where they annihilate into photons. Meanwhile, the electron
originating from the pair at B continues on pass C. Zigzagging
results without real photons, as long as the distance is of the
order of the de Broglie wavelength.
IV. THE DOUBLE SLIT EXPERIMENT
Nowhere is the difficulty of applying commonsense notions to
quantum mechanics more evident than in the familiar double
slit interference experiment. When both slits are open, and no
attempt is made to determine which slit the light passed
through, a fringe pattern is observed on a screen. Since the
early nineteenth century, this effect has been conventionally
explained in terms of the interference of coherent,
monochromatic light waves from the two slits. Today,
however, we know that light is composed of photons. If we
place an array of photon detectors on the screen, then
individual, localized photons will be registered whose
statistical distribution will still follow the fringe pattern.
Note how this experiment already directly contradicts
the conventional folklore that a physical object is either a
particle or a wave, depending on what you measure. In this
example, individual particle properties are measured, with
photodetectors, yet wave properties are exhibited in the
observed statistical distribution.
This presents no problem for formal quantum mechanics,
as it has been practiced for over sixty years. The wave
function, whose interference gives the fringe pattern, is only
defined in the quantum formalism for a statistical ensemble of
particles, by the Born postulate.
However, when you attempt to visualize the process in
terms of individual particles following definite paths in space,
you run into a conceptual difficulty. How can a single photon
pass through both slits simultaneously so that the emanations
from the two slits are correlated individual particle by
individual particle? Since simultaneous events are outside the
light cone, any correlation between the two slits seems to
require a superluminal signal, what Einstein called a <<spooky
action at a distance.>>
Let me now show how, with the simple inclusion of time
reversibility, we can retain the intuitively comfortable view
of a single particle following a definite path through
spacetime, with a simultaneous position and momentum,
without the need for spooky, superluminal connections.
As shown in Fig. 3, we can picture the photon as
travelling through the top slit to the detector and then turning
around and travelling backward in time through the bottom
detector to the source. There the process repeats, with the
photon again going through the top slit (or, possibly the bottom
slit) to the detector. Indeed, the process can be viewed as
repeating itself continuously, as viewed in proper time in the
reference frame of the photon. (Using electrons, rather than
photons, may perhaps make this discussion more
comprehensible, since it is difficult to imagine oneself in the
reference frame of a photon).
Note that at the instant that the photon is passing though
the top slit, the same photon is simultaneously passing back
through the bottom slit. Thus we have solved the conundrum of
having a particle pass simultaneously though two slits
separated in space without any signals moving faster than the
speed of light. As in the previous example, an effective
nonlocality occurs with all particles remaining on or within
the forward and backward light cones. That is, we have
nonlocality without superluminality. Of course, it only
happens when the distance between the slits is comparable to
the wavelength.
Now you might ask, what is the mechanism by which the
photon turns around at the detector and goes backward in
time? First we must rid ourselves of another unreasonable
Copenhagen notion, that the detection process is completely
classical and irreversible.
Let us look more closely at photodetection. The primary
process of producing an electron by the photoelectric effect is
clearly quantum mechanical and reversible. This experiment
was the very first that was explained in terms of photons, by
Einstein in 1905. If the photodetector is a photomultipler
tube, then as the number of electrons is multiplied, typically
by a factor of a million, and an electric current is collected at
the anode, the system rapidly becomes classical and
irreversible. Other photodetection techniques involve a
similar quantum-to-classical transition as single quantum
particles induce multiple particle effects that grow into a
classical, macroscopic signal that can be reported to a human
observer or recorded in computer memory. Classical
mechanics is the many-particle limit of quantum
mechanics when the coherence of the many-particle wave
function is not maintained. But the primary process,
photon -> electron, is time-reversible: positron -> photon.
As is the case when analyzing Feynman diagrams, we
must consider all the possible ways in which the state labelled
<<initial>> can result in the state labelled <<final.>> For the
double slit, the Feynman path integral formalism can be used.
We normally think of the paths of the photon through the two
slits as independent <<histories>> that must be added. But, as
we have seen, these leads us to introduce superluminal
connections. In the view I am proposing here, we have a single
history. The same photon passes simultaneously through both
slits and all connections are local.
Another question that might be asked is why we do not
observe positrons in the double slit experiment. A simple
answer is that we do, but they go backward in time and we call
them electrons! However, you might also wonder what happens
if we put some matter behind the lower slit in Fig. 3. Why do
we not observe positron annihilation?
Again, we must remember that the picture being proposed
involves a single electron circulating around, in either
direction, through the two slits. As is well known, placing
some matter behind one slit, or a detector, changes the
experiment in one that produces no interference fringes. This
is simply viewed as a single slit experiment, with an electron
going back and forth through the top slit.
V. THE BOHM-BELL-EPR EXPERIMENT
Perhaps the most important class of experiments that
have been performed in recent years to test the foundations of
quantum mechanics is the version of the EPR experiment first
suggested by Bohm.[14] The inequality known as BellÕs theorem[15]
has been accurately tested and shown to be violated in the
precise amount predicted by conventional quantum
mechanics.[16] While most physicists yawned at the
announcement, the implications are still being debated by
those of more philosophical bent, while these debates are
reported in the popular media.
One undebated conclusion is that any yet-to-be-
discovered, underlying , sub-quantum theory of deterministic
hidden variables, such a those suggested by de Broglie and
Bohm, necessarily imply nonlocal forces. However, the
implications for standard quantum mechanics remains
arguable.[17]
In a 1985 article in this journal, Stapp generalizes BellÕs
theorem and concludes that <<a locality property expressing
the idea that causal influences can propagate only forward in
time, from earlier cause to later effect, and no faster than the
speed of light is . . . mathematically incompatible with certain
predictions of quantum theory.>> His judgment is that quantum
mechanics, regardless of interpretation, must be nonlocal.[18]
But note that Stapp requires causal influences to propagate
<<forward in time.>> Relaxing that requirement, we can
eliminate the need for superluminality.
In another important contribution, Eberhardt and Ross
have proved that no superluminal signalling is possible in any
theory consistent with the axioms of quantum field theory.[19]
Since all the current interpretations of quantum mechanics
agree with all known data (any that do not are automatically
eliminated), and thus by default must be consistent with
quantum field theory, they cannot allow for signals moving
faster than light. Much verbal contortion, reminiscent of
theology, must then be relied on to explain how a theory can
have superluminal <<effects>> without superluminal signals.
As I demonstrated above, effective nonlocality, the
apparent instantaneous, nonlocal jump of a particle over a
spacelike distance, can happen in a time-reversible scenario
without the particle travelling faster than light. This
seemingly contradictory result is obtained by simply allowing
the particle to turn around and go backward in time, and then
forward again so it passes another place at the same original
time. Let me show specifically how time-reversibility easily
explains the correlations observed in the Bohm-Bell-EPR
experiment, without superluminal effects.
The experiment as viewed from our preconceived, uni-
directional flow of time is shown in Fig. 4(b). A singlet
source emits electrons that travel in opposite directions to
spin detectors whose orientations are variable, allowing the
spin components of the electrons to be measured along any axis
perpendicular to the beam line. ( In this example, electrons are
utilized, as originally proposed by Bohr and analyzed by Bell,
although the best implementations of the experiment have
actually involved photons; the conclusions are the same in
either case). Since the orientation of the spin detectors can
be set after the electrons have left the singlet source (and
indeed have been so set in an actual experiment[20]), the
observed correlation between the measured spin components
implies some kind of superluminal correlation, when viewed in
this way.
Let us now view the same experiment in a time-reversed
perspective. In Fig. 4 (a), polarized positrons are emitted from
the <<detectors>> to the <<source>> where they form singlet or
triplet states. Since only singlet sources are allowed in the
experiment, we can picture the process, in the time-reversed
view, as one in which triplet combinations are tossed out at
the <<source.>> Since this happens at one point in space, the
mechanism is completely local.
Analogous to our interpretation of the double slit, we can
think of a continuous process in which positrons leave the spin
detectors with random spin orientations, as in Fig. 4(a), travel
to the source where only the triplets are locally removed, and
then turn around in time, as in Fig. 4(b), to return to the
detectors as electrons in our normal perspective. The reason
this experiment seems so profound is that we insist on
viewing it only in our conventional time-direction. By
eliminating that prejudice, and thinking of the process as one
of positron emission, with the positrons turning back in time
to give the conventional electrons, we no longer have the need
for any spooky action at a distance.
VI. <<THEY ARE ALL THE SAME ELECTRON>>
In FeynmanÕs Nobel-Prize acceptance speech, he told a
story about how he got the idea of treating antiparticles as
particle going backward in time.[21] He quoted Wheeler as
saying, <<I know why all electrons have the same charge and
the same mass.>> Feynman asked <<Why?>> and Wheeler
replied: <<because they are all the same electron.>> That is,
the electron (and presumably other particles) zig and zag back
and forth in spacetime with its worldline passing many places
in space at the same time.
While this was not proposed to be taken seriously,
perhaps the idea can still serve as a useful pedagogical tool.
It cannot but puzzle the layperson why no two snowflakes are
alike while all electrons are completely indistinguishable.
Gardner has described WheelerÕs scenario, but commented
that <<there is an enormous catch to all of this>> since it
demands there be equal number of electrons and positrons in
the universe, which is apparently not the case.[22] However, we
can construct a spacetime path in which all the positrons
occur at small distances or early times, where current
theories in particle physics and cosmology predict particle-
antiparticle symmetry (see Fig. 5).
VII. MACROSCOPIC IMPLICATIONS
The time-reversible picture presented here should not be
interpreted as implying that macroscopic objects, such as
human beings, can travel back in time. The quantum
fluctuations that result in the zigzagging in spacetime
illustrated in Fig. 1 occur only over distances comparable to
the de Broglie wavelength of a particle and indeed account for
the wavelike behavior of particles. For particles like
electrons, wave effects are limited to small distances.
Only in the case of radio photons can the effects of
spacetime zigzagging be observed on macroscopic scales.
While we do not normally think of radio waves in terms of
photons, they are photons nonetheless, appearing
simultaneously at widely-spaced receivers. Deep inside the
nuclei of our atoms, elementary particles are zigging and
zagging in spacetime, but the net motion of the aggregate is in
the direction that chance chooses as the arrow of time.
Large-scale quantum correlations can exist, as in the EPR
experiment. However, we have seen that these do not require
superluminal connections in the time-reversible view.
Furthermore, quantum correlations have no obvious role in the
operation of human bodies and brains. Macroscopic systems
are composed of many particles, and behave classically
because of the decoherence that occurs as the phases of the
various probability amplitudes are scrambled by the random
interactions of the particles with each other and the particles
of the environment.[23] The states of most macroscopic
systems, including Schroedinger's cat, must be represented by
density matrices rather than wave functions; the off-diagonal
elements, wherein quantum effects reside, becoming negligible
as a result of decoherence.
As many particles interact and decohere to form a
complex, classical system, random processes lead to the
emergence of a new set of principles that do not exist at the
quantum level. These include the second law of
thermodynamics and causality, which codify our experience of
irreversible time. Many other macroscopic principles, such as
evolution and the causal mechanisms of biology and geology
can be seen in this light. They are not derivable from basic
physics which, at best, sets certain limitations such as those
imposed by the conservation principles.
Coherent, macroscopic, many particle systems, for
example, superconductors and bose condensates do exist.
Suggestions have been made that the human brain is such a
coherent system, and that consciousness is somehow related.[24]
However these remain highly speculative and controversial.[25]
No evidence currently exists that quantum effects play any
role in human thinking other than the role they play in the
structures of the brainÕs atoms. But then they play that same
role for the atoms of the big toe and no one suggests
consciousness resides there.
VIII. RANDOMNESS
Perhaps the most difficult quantum notion for most
people to accept is indeterminacy. Einstein objected to God
playing dice. Most people assume causal explanations exist for
everything that happens in the universe. But this is a prejudice
based on macroscopic experience. Things could just happen
The hidden variable interpretations attempt to put back
determinism by way of nonlocal, subquantum forces. The many
worlds interpretation retains determinism by saying that all
the paths that can taken are in fact taken as the universe
continually splits into parallel universes. Consciousness is
then brought in, as it is in some accounts of the Copenhagen
view, as the entity that decides (actualizes) which particular
path we each take, sort of like the way we choose which
channel to watch on television.[26]
However, determinism in quantum mechanics comes with
a big price tag, namely, the uneconomical introduction of
bizarre, mystical notions that have no empirical foundation.
Deterministic hidden variables theories are nonlocal,
<<holistic.>> Many worlds are, well, many worlds.
Consciousness, as the actualizing agent of reality, is
solipsism.
By contrast, a picture in which uncaused, undetermined,
random fluctuations in spacetime results in the wavelike
properties and other quantum effects we observe for particles
is economical and non-mystical. It does not require holistic
connections across atoms or the universe. It does not require a
multiplicity of worlds. And it does not require any special role
for human consciousness which is most likely the result of
complex but perfectly classical interactions of the many
particles in the brain.[27]
IX. SOME HISTORY
Advanced electromagnetic waves that travel backward
in time are allowed solutions of Maxwell's equations, which
are time-symmetric. In the 1940s, Wheeler and Feynman
unsuccessfully attempted to explain the self-energy of the
electron in terms of classical electrodynamics by including
advanced waves.[28] Following Stckelberg,[29] Feynman later
extended the idea to quantum field theory, associating
antiparticles with the advanced waves, that is, as particles
going backward in time.[30] The self-energy problem was
eventually solved quantum mechanically. In 1953, Costa de
Beauregard suggested that the EPR paradox could be resolved
by including the action of advanced waves, but he did not think
of them in terms of antiparticles.[31]
More recently, Cramer has introduced the transactional
interpretation of quantum mechanics in which advanced and
retarded waves, called <<offer>> and <<confirmation>> waves
engage in a handshake between source and detector.[32] Cramer
has worked out the model in some detail and showed how it
eliminates various quantum paradoxes. The actual physical
particle, in CramerÕs interpretation, moves forward in time as
the linear combination of the offer and confirmation waves.
The view I present here differs, but can be connected if we
take the offer and confirmation waves to represent the
particle going forward and backward in time, respectively. I
believe this is more economical, and more in the spirit of
FeynmanÕs association of retarded waves with particles and
advanced waves with antiparticles, that is, particles going
backward in time. With that proviso, all of CramerÕs results
can be applied here and, indeed, saves this author the trouble
of working them all out again.
X. CONCLUSION
While quantum mechanics continues unchallenged as a
formal, mathematical theory that describes matter at its most
fundamental level, it remains mysterious to philosophers and
laypeople alike when they seek to go beyond the mathematics
and attempt to understand quantum phenomena in familiar
terms. The orthodox Copenhagen interpretation serves only to
deepen the mystery since it forbids us from using the
intuitively compelling image of physical bodies moving along
well-defined paths in space. This is further compounded by
the absurd notion that the properties of bodies do not even
come into existence until those properties are measured.
We have seen how, by utilizing the almost trivial
expedient of allowing fundamental particles to turn around and
go backward in time we can maintain the intuitive image of
definite particle paths. This picture is already present in
relativity, where particles follow worldlines in spacetime.
Since time is simply another coordinate of spacetime,
worldlines can turn around and go backward with respect to
the time axis of some arbitrary reference frame just as
readily as they can turn and go backward with respect to a
coordinate axis. No superluminal motion need occur, with the
worldlines confined to the combination of forward and
backward lightcones. The universe is like an hour glass that
runs both ways.
Nonlocality in quantum mechanics is implied by many
observations, such as double slit interference, but is most
strongly suggested by the empirical violation of BellÕs
inequality. Although no superluminal signalling is possible in
any theory consistent with the hypotheses of quantum field
theory, some type of superluminal connection seems
compelling as long as one insists on forward-time causality.
However, nothing in fundamental physics demands that
time flow in one direction. TimeÕs arrow in our normal,
macroscopic experience can be construed as a statistical
convention, as suggested by Boltzmann a century ago. The
mysteries and claimed paradoxes of quantum mechanics,
including superluminal correlations, arise from our enforcing
the arbitrary, macroscopic arrow of time at the microscopic
level, simply to suit our prejudices.
The time-reversible perspective outlined here is not yet
another interpretation of quantum mechanics. It is implicit in
the way quantum mechanics is actually practiced at the level
of elementary interactions. With either Feynman diagrams, or
Feynman path integrals, the probabilities that connect two
states, arbitrarily labelled <<initial>> and <<final>> are
computed by adding the probability amplitudes of all possible
paths in spacetime, in both time directions. A fiction of a
single time direction is maintained by uneconomically
identifying backward-time paths with forward-time
antiparticles.
From its earliest days, quantum mechanics was
recognized to be contextual, That is, both final and initial
states must be specified and a given initial state does not
generally determine a specific final state. This disturbed
Einstein, who refused to believe that <<God plays dice.>> He
also objected to the <<spooky action at a distance,>> the
superluminal signalling that seemed to be implied by the
Copenhagen interpretation. But he could not have it both ways.
The empirical violation of BellÕs inequality demonstrates that
a deterministic universe, one with time-directed causation,
requires spooky superluminality. However, no superluminal
motion has even been detected, and indeterministic, time-
reversible quantum mechanics remains consistent with all
observations. As I have shown here, the familiar picture of
particles following definite paths through spacetime can be
retained to visualize the behavior of fundamental particles, as
long as we allow their spacetime worldlines to wander around
at will within both forward and backward lightcones.
REFERENCES
[1]Victor J. Stenger. The Unconscious Quantum: Metaphysics
in Modern Physics and Cosmology. (Prometheus Books, Amherst,
NY, 1995).
[2]A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47,
777 (1935).
[3]N. Bohr, Phys. Rev. 48, 696 (1935).
[4]E.P. Wigner in M. Polanyi,The Logic of Personal Knowledge
(Free Press, Glencoe,IL, 1961) p. 232.
[5]For a lucid explanation of the four current philosophical
schools of thought on the nature of science: relativism,
positivism, realism, and pragmatism, see L. Laudan,
Science and Relativism: Some Key Controversies in the Philosophy
of Science(University of Chicago Press, Chicago, 1990).
[6]D. Bohm, Phys. Rev. 85,166 (1952); D. Bohm and B. J. Hiley,
The Undivided Universe: An Ontological Interpretation of Quantum
Mechanics(Routledge,London, 1993).
[7]Hugh Everett III, Rev. Mod. Phys. 29, 454 (1957).
[8]R. J. Griffiths, J. Stat. Phys. 36, 219 (1984); R. J. Omnes,
The Interpretation of Quantum Mechanics (Princeton University Press,
Princeton,1994).
[9]M. Gell-Mann and J. P. Hartle, <<Time Symmetry and Asymmetry
in Quantum Mechanics and Quantum Cosmology>> in the Proceedings
of the 1st International A. D. Sakarov Conference on Physics,
Moscow, May27-31, 1991 and in the Proceedings of the Nato Workshop
on the Physical Origin of Time Asymmetry, Mazagon, Spain,
September 30-October 4, 1991, ed. by J. Haliwell, J. Perez-Mercader,
and W. Zurek (Cambridge University Press, Cambridge, 1992).
[10]I. Prigogine and I. Stengers, Order out of Chaos
(Bantam, New York, 1984).
[11]P. Coveney and R. Highfield, The Arrow of Time
(London, Flamingo, 1991), p. 288.
[12]R. Penrose, The EmperorÕs New Mind: Concerning Computers,
Minds, and the Laws of Physics. (Oxford University Pres, Oxford,
1989), p. 351.
[13]R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path
Integrals (McGraw-Hill, New York: 1965).
[14]D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs,
N.J., 1951).
[15]J. S. Bell, Physics 1, 195 (1964).
[16] A. Aspect, P. Grangier, and R. Gerard, Phys. Rev. Lett. 49,
91 (1982).
[17]J. Cushing, and E. McMullin, eds. Philosophical Consequences
of the Quantum Theory: Reflections on BellÕs Theorem (University
of Notre Dame Press, Notre Dame, Indiana, 1989).
[18]H. P. Stapp, Am. J. Phys. 54, 306 (1985).
[19]P. H. Eberhard, and R. R. Ross. Found. Phys. Lett. 2, 127
(1989).
[20]A. Aspect, P. Grangier, and R. Gerard, Phys. Rev. Lett. 49,
1804 (1982).
[21]R. P. Feynman, <<The development of the space-time view of
quantum electrodynamics.>> Nobel Lectures Physics 1963-1970.
(Elsevier, New York, 1992).
[22]M. Gardner, The Ambidextrous Universe (Charles Scribner's,
New York, 1979), p. 269.
[23]W. H. Zurek, Physics Today 36, 36 (1991).
[24]H. P. Stapp, Mind, Matter, and Quantum Mechanics (Springer
-Verlag , New York, 1993); R. Penrose, The Emperor's New Mind:
Concerning Computers, Minds, and the Laws of Physics (Oxford
University Press, Oxford, 1989); R. Penrose, Shadows of
the Mind: A Search for the Missing Science of Consciousness
(Oxford University Press, Oxford 1994).
[25]See reference 1 for a critical discussion of the proposed
connections between quantum and consciousness.
[26]E. Squires, Conscious Mind in the Physical World
(Adam Hilger, New York,1990).
[27]D. Dennett, Consciousness Explained (Little Brown. New York,
1991); F. Crick, The Astonishing Hypothesis: The Scientific
Search for the Soul (Charles Scribner's Sons, New York, 1994).
[28]J. A. Wheeler and R. P. Feynman, Rev. Mod. Phys. 21, 157
(1945); Rev. Mod. Phys. 17, 425 (1949).
[29]E. C. G. Stckelberg, Helv. Phys. Acta 14, 588 (1941).
[30]R. P. Feynman Rev. Mod. Phys. 20, 367 (1948).
[31]O. Costa de Beauregard, Comptes Rendus 236, 1632, (1953).
[32]J. Cramer, Rev. Mod. Phys. 58, 647 (1986).
FIGURE CAPTIONS
Fig. 1. How an apparent instantaneous jump in space can result
at the quantum level. An electron starts at A. At B it receives
an impulse from the vacuum that sends it backward in time to
C. At C it receives another impulse sending it again forward in
time. Thus it appears to jump instantaneously from B to D.
This is allowed by the uncertainty principle, provided the
distance BD is less than the de Broglie wavelength, that is,
Planck's constant divided by the impulse. Note that the proper
time of the electron changes monotonically along its path,
even as it goes backward in coordinate time.
Fig. 2. An alternate way to view Fig. 1. Here an electron-
positron pair are created by a vacuum fluctuation at C. The
positron annihilates the original electron at B. The other
electron from the pair created at C continues on, taking the
place of the original electron.
Fig. 3. The double slit experiment, as visualized in a time-
symmetric picture. An electron from the source goes through
the top slit to the detector. Then it travels backward in time
through the bottom slit to the source, and then back again
through the top slit. The path has been displaced for
illustration. The process is repeated indefinitely, with all
possible paths covered. The Feynman path integral formalism
can then be used to compute the observed interference pattern.
Fig. 4. Time-reversed EPR experiment. In (a), polarized
positrons e+ with arbitrary spin axes are emitted toward each
other from A and B. The collide in the center and form a two-
positron state that will in general be a singlet (total spin
zero) or triplet (total spin one). However only singlet states
are accepted (locally) by the singlet selector S. This results
in a correlation that is the same as calculated by quantum
mechanics in the normal EPR experiment in which electrons e-
are emitted at S and detected at A and B, as seen in (b). In the
time-reversible scenario (a) happens <<firstÓ in the proper
time of the positron, and then the positron turns around to give
what appears as an electron in our conventional time-
direction.
Fig. 5. Spacetime diagram showing how it is possible for a
single electron to appear in many places <<here and now>>
(only two are shown) without any in the vicinity going
backward in time and thus appearing as positrons. The
positrons all appear at either small distances or early times,
where particle-antiparticle symmetry is theoretically
envisioned.
This document published as part of the archive
of the mailinglist quantum-d
http://www.teleport.com/~rhett/quantum-d/posts/vjs_11-8.html