End notes have been included in the text, with brackets.
The vacuum is capable of producing interactions between particles at effectively spacelike separations. This occurs when quantum fluctuations in the vacuum cause a particle to zigzag backward and forward through spacetime. Let me explain.
No doubt the idea of motion backward in time makes a grievous assault on common sense. The world just does not seem to operate that way, as our ever-aging bodies testify. However, to a particle physicist raised on a diet of Feynman diagrams, motion backward in time is not all that disturbing. All fundamental particle interactions work backward as well as forward and, with rare exceptions, do not distinguish between directions of time [The rare exceptions occur in so-called CP violating interactions involving short-lived particles called K0 and B mesons, which are thought to have different probabilities in time-reversed directions. These can be ignored in the current discussion since they play only a very indirect role in the structure of normal matter].
Feynman used the idea of motion backward in time when he invented his famous diagrams in the late 1940s. Dirac had developed his fully-relativistic quantum theory of the electron in 1928, and discovered that it contained negative energy solutions. These solutions were identified as anti-electrons or positrons. Positrons were observed as predicted in 1932. Following Stückelberg [Stückelberg 1942] and Wheeler, Feynman re-interpreted positrons as electrons moving backward in time [Feynman 1948, 1949a, 1949b, 1965b].
Feynman's idea grew out of his earlier work at Princeton as a graduate student of John Wheeler. Together they had developed a theory of electromagnetic waves involving solutions of Maxwell's equations that travel both ways in time, the so called retarded and advanced waves. The advanced waves travelled backward in time, that is, they arrived at the detector before they left their source. Despite their presence as valid solutions to Maxwell's equations, advanced waves had been previously ignored by less bold thinkers [For an amusing anecdote concerning Feynman's first talk on the subject, given before Einstein, Pauli, and other physics greats, see Feynman 1986, pp. 77-80]. Feynman later extended the idea to quantum field theory, in which waves are particles and vice versa, associating antiparticles with the advanced waves [Feynman 1948. See also Stückelberg 1942].
Feynman noted that whether you say you have a particle moving forward in time with negative energy, or its antiparticle moving backward in time with positive energy, is really quite arbitrary at the fundamental level. Energy conservation and the other laws of physics remain intact. By reversing the charges and momenta of the backward particles, charge and momentum conservation are unaffected.
The violation of causal precedence by tachyons, if they are ever found, will result not from their motion backward in time but from their superluminal motion. In the case of the known elementary particles, whether they move backward or forward in time they still remain within the light cone and retain causal precedence. That is, they do not exchange cause and effect from one reference frame to another. And, as I will now show, the apparent nonlocality proposed by Vigier is simply an artifact that can be understood without superluminal motion.
In Fig. 5.3, the Feynman diagram for the zigzag process is illustrated [Purists will object that the Feynman diagram is generally drawn in terms of four-momenta rather space and time. However, the space-time diagrams I show are an equivalent way of describing the same ideas. Even the purists must admit that one can go from a momentum space to a spacetime description by a canonical transformation]. As usual, the time axis is up and a single spatial axis is indicated to the right. An electron starts at point A and follows a path through spacetime at constant velocity, changing its position as time progresses. At point B, a fluctuation in the vacuum results in a momentum transfer to the electron, which turns it around so it goes backward in time. At point C, another vacuum fluctuation causes the electron to turn around again and resume its forward course in time, passing point D at the same time as the interaction B, but at a point separated by the distance BD. Thus it appears that the particle has made an instantaneous jump from B to D.
Actually, it is possible to view this nonlocal artifact without introducing motion backward in time, as illustrated in Fig. 5.4. Note that all the particles are moving in one time direction. At time C an electron positron pair is created by a vacuum fluctuation. The positron goes to the left and collides with the original electron at B where they annihilate each other, the annihilation energy disappearing into the fluctuating vacuum. In the meantime, the electron from the pair created at C continues on and is interpreted as the original electron from A transported instantaneously from B to D.
The net result, in either view, is an effectively instantaneous jump of the electron over the spacelike separation BD. At time B the electron disappears and reappears at D some distance away. A quantum jump, a "spooky action at a distance," has taken place. However, when the event is not just viewed at one instant, but over the progression of time, nothing unusual has taken place.
Note that conservation of momentum is maintained overalland no other laws of physics are violated. The impulse delta(p) at B is exactly balanced by the opposite impulse at C. The impulses at B and C individually violate momentum conservation, but this is allowed by the uncertainty principle, provided the spatial distance delta(x) between B and C is less than h/delta(p).
Zigzagging in spacetime has been around since Feynman first introduced his diagrams. Feynman diagrams with effective spacelike interactions have appeared in hundreds of physics papers, books, and on thousands of chalkboards for over forty years. They are as much a part of the language of particle physics today as the word particle itself. So Vigier tells us nothing new when he says that quantum field theory allows for effectively spacelike interactions.
A particle can undergo a spacelike quantum jump over a distance that is of the order of its de Broglie wavelength. This is simply another way of viewing a particle's wavelike properties that you may find very useful. It provides a picture of a particle travelling through spacetime with a well-defined position and momentum. But because of impulses received from random vacuum fluctuations, the particle randomly jumps around in space within a region whose size is of the order of the particle's wavelength, and so appears to the detection apparatus as a spread-out wave packet. I see no reason why nonlocality, within an indeterministic quantum mechanics that still contains particles of definite momenta and positions, cannot be formulated in this fashion.
An ensemble of similarly prepared electrons will have measured positions whose
distribution is given by |psi|^2. Could vacuum fluctuations be the hidden variables?
If so, they do not provide for nonlocal connections across the universe, or even
across the room, for the material bodies of normal experience whose de Broglie
wavelengths are infinitesimal.
Macroscopic objects do not produce measurable wavelike effects.
If a one kilogram object is moving at 10^-10 meters per second, surely very close to being at rest (nothing is ever exactly at rest), it will have a de Broglie wavelength of 7x10^-24 meter, far smaller than the size of a nucleus. Its zigging and zagging would never be noticed.
This illustrates why quantum effects are not observable in everyday life, at least for the familiar objects that we think of as material "bodies." And it demonstrates why Vigier's idea, while qualitatively correct, does not provide quantitatively for holistic connections over macroscopic distances - certainly not the whole universe.
Light and other electromagnetic waves, however, do exhibit quantum effects on the macroscopic scale. The wavelength of visible light is in the range 4-6x10^-7 meter. Though this is small by macroscopic standards, light diffraction effects are observable to the naked eye. Radio waves can be of macroscopic and even planetary dimensions. Long wavelength radio photons appear instantaneously at widely separated receivers. In the vacuum fluctuation picture being considered here, individual radio photons hit all receivers at once by zigzagging through spacetime - not by some superluminal transfer of energy.
The vacuum is thought to be alive with particles and antiparticles that are constantly being created and destroyed, or zigging and zagging through spacetime if you prefer. Measurable effects have been calculated by quantum field theorists and checked to great accuracy against experiment for decades, with no violations of fundamental laws of physics evident or implied. Zigzagging in spacetime can produce what appears to be superluminal motion, but only when the wavelengths of the particles are of comparable dimensions. And even this is the result of random quantum fluctuations, and so cannot be perceived as transmitting superluminal "signals."
The measurable effects referred to above are precisely those quantum effects that physicists infer from observations in the laboratory, almost exclusively involving atomic and subatomic phenomena. The objects emitting and absorbing these zigzagging particles have sizes that are comparable to the wavelengths involved. For particles to similarly zigzag across the universe, the wavelengths would have to be of extragalactic extent. Such waves could not be emitted or detected by anything of human dimensions, like a brain or scientific instrument, by any conceivable application of existing knowledge.
One cannot simply speculate about possibilities, but must check the numbers. Much of pseudoscience is qualitative hand-waving. Until a concept can be made quantitative, or at least put on a firm logical foundation, it is not science [Some people have proposed that nonlocal effects are occurring in the alleged cold fusion process, so that energy is transferred holistically to a lattice without the telltale gamma rays or neutrons expected from nuclear processes. But this is also impossible for the same quantitative reason described here. The interatomic spacings in a material lattice are far greater than the distances at which spacelike interactions involving nuclear energies can take place. The wavelengths of nuclear particles are comparable to nuclear dimensions]. Certainly spacelike correlations across the universe, making the universe one "interconnected whole" are not possible unless you imagine particles of infinite wavelength. In short, the vacuum aether does not provide a quantitatively feasible metaphor for the holistic universe.
And what about the paradoxes of superluminal motion discussed earlier? Do they not exist for the effective superluminal motion produced by zigzagging in spacetime? No, since, as we have seen, no distinction between cause and effect is made at the elementary level. Only with complex systems, such as macroscopic bodies, do causal paradoxes present interpretational problems.
Local EPR in Reverse Time
As long as superluminal effects are not observed in experiments, any interpretation
of quantum mechanics that requires nonlocal effects is not parsimonious. If, as
many seem to think, conventional quantum mechanics is nonlocal, then proper
scientific method demands that we seek alternative, local interpretations.
Now I would like to show how the EPR "paradox" can in fact be almost trivially resolved by interpreting the experiment in reverse time. As far back as 1953, French physicist Olivier Costa de Beauregard had argued that the EPR paradox could be resolved by including the action of advanced waves [Costa de Beauregard 1953]. He pointed out that the exclusion of advanced waves is a classical prejudice that has no a priori justification. If they are present as solutions of Maxwell's equations, we make an added hypothesis in ruling them out, namely the hypothesis that I have called causal precedence. (Note that this is the same hypothesis used by Einstein to rule out superluminal motion.) The following explanation of the EPR experiment goes along similar lines, but uses Feynman's association of antiparticles with the advanced waves.
Let us again consider the Bohm/EPR experiment in which a singlet (total spin zero)
system decays into two electrons that go off down opposite beam lines A and B. At
the ends of the beam lines are the usual spin meters that can be oriented in any
direction perpendicular to the beams. Nonlocality is implied when the decision on
what orientation to use at A is made just before the detection, so no time is left for a
signal to reach B without travelling faster than light.
Now view the EPR experiment from the frame of reference that is time-reversed from the normal, familiar one, as illustrated in Fig. 5.5. The detectors at A and B then become polarized positron emitters. Suppose emitter A is set so that it gives a positron with its spin aligned along an axis x perpendicular to the beam line. Emitter B generally can emit a positron of any arbitrary spin axis orientation.
Let us first examine the special case in which the axis of emitter B happens to be the same as A and emits a positron whose spin is opposite to that of A. Then the total spin of the system of two positrons will be zero. When the two positrons moving backward in normal time along the beam lines come together they will form a two positron state that, from angular momentum conservation, will have total spin zero. That is, a singlet state will be locally produced.
If instead the spin of B were in the same direction as A, then a triplet state would be formed. However, the experiment, when viewed in the normal time sequence, was designed to include only singlet states as the electron source. Viewing this in reverse time, the triplet states that are formed are discarded (locally) from the sample. [Actually, a triplet state can also be formed from oppositely-spinning electrons, but this will also be discarded from the sample].
It is precisely this selection that produces the correlation that is observed in the experiment. Putting it another way, no correlations will be observed in a Bohm/EPR experiment if triplet states are included in the (normal time sequence) source. By using only singlets, we force a correlation.
If emitter B emits a positron with a spin along some other arbitrary axis, say the y axis, then it is a matter of chance (with calculable probabilities) whether a singlet or triplet is formed when the positrons collide. But once again a correlation is enforced by locally tossing out the triplet states. The equations for all this are the same as in standard quantum mechanics, and do not fundamentally distinguish between the two directions of time. Thus the quantitative correlation will be the same as that calculated assuming the macroscopic time direction.
This way of viewing the EPR experiment may also shed some light on why a deterministic theory is necessarily nonlocal. (Logicians note that I am not saying determinism is the only means for nonlocality). If you insist on producing a specific state, then you must know the orientation of one positron emitter relative to the other at the moment of emission. But this is unnecessary when you are willing to take your chances on what state is produced when the two positrons collide.
In short, the Bell's theorem correlation occurs because of a local selection of singlet
positron pairs at the point where the positrons come together. Since the elementary
processes involved can be viewed in either time direction, and since the process is
local in the time-reversed reference frame, we may conclude that the EPR
experiment is fundamentally local. An apparent paradox occurs only when we
insist on viewing the experiment in our prejudiced time direction. As Costa de
Beauregard has put it, "retarded causality looks trivial and advanced causality looks
paradoxical" [Costa de Beauregard 1987, p. 263]. Actually, I would have said it the
Costa de Beauregard does not conclude, however, that the consequences of time symmetry are trivial. On the contrary, he takes the directionlessness of time and causality at the elementary level to be so profound as to imply "the existence of subtle phenomena termed 'psychic' in a broad sense, inside the human, the animal, and possibly the vegetal kingdoms" [Costa de Beauregard 1987, p. 284].
I could not disagree more. The behavior of the microworld appears paradoxical only when we insist on applying to it concepts from the macroworld that have no meaning at the elementary level. [It might be argued that the EPR experiment, being conducted in a normal-sized laboratory, is part of the "macroworld." However, as I have noted in several places, the distinction between quantum and non-quantum effects is not one of scale. Quantum effects, including anything to do with photons, can appear on any scale. The EPR experiment, whether performed with electrons or photons, involves elementary interactions and so must be viewed in those terms]. The fact that our commonsense prejudices do no apply cannot be taken to mean that the microworld possesses mysterious properties. On the contrary, we have found that the microworld is far simpler than the macroworld and can be understood with a minimum set of physical ideas that do not have to be supplemented by emergent qualities such as a direction of time and causal precedence.
My view agrees with what I sense is the developing interdisciplinary consensus: Two sets of natural laws exist, one at the elementary level of fundamental particles that possesses a high degree of symmetry, and another that emerges at the levels of many particles where the elementary symmetries are accidentally broken and new laws appear to describe the structures that thereby evolve.
In the usual application of classical physics, the equations that govern the evolution of a physical system must be solved subject to certain boundary conditions. Because of our normal conception of time flow, these boundary conditions are usually taken to be initial conditions - that state of the system at some time t = 0 when we arbitrarily start our clock. Then the equations predict the future motion of the system, which is usually what we want to know. Prediction is the most common application of science, and its greatest power.
However, the equations computed with final conditions can also be used to postdict the past. We can use celestial mechanics to precisely date the past appearances of solar eclipses and comets, verifying certain historical events. For example, an eclipse occurred on March 28, 585 BCE that may have been the one reported to have been predicted by Thales of Miletus that perhaps triggered the development of Greek science and philosophy.
Nothing forces us to chose either initial or final boundary conditions. And in fact, the most general methods of classical mechanics make no distinction between initial and final conditions.
In quantum mechanics, the situation appears at first glance to be fundamentally different. Conventional quantum mechanical formulations incorporate a distinction between past and future. This is despite the fact that the Schrödinger equation and all relativistic formulations of quantum mechanics are time symmetric. [While the non-relativistic Schrödinger equation does not appear, at first glance, to be time-symmetric, it becomes so if you change ÿ to its complex conjugate ÿ*. See the later discussion on the transactional interpretation].
In the Copenhagen description of the measurement process, the act of measurement selects the state of a system from among all its possible states. This is a non reversible process, performed in the reference system in which the arrow of time is selected by the prejudice of everyday experience.
However, an important subtlety should be noted. The arrow of time, we have seen, is determined by the direction in which entropy increases. If we imagine a local system being organized by outside energy, it will have a decreasing entropy with reference to the arrow of time of the outside system. Should we not define its local time arrow in the opposite direction, and describe measurements in this system with reference to this time direction?
Issues of this sort have led quantum cosmologists to investigate ways in which time asymmetry can be built into cosmology, notably Penrose [Penrose 1979], Page [Page 1985], and Hawking [Hawking 1985]. However, Gell-Mann and Hartle have shown that a time-symmetric quantum cosmology can be developed using a time-neutral, generalized quantum mechanics of closed systems in which initial and final boundary conditions are related by time reflection symmetry [Gell-Mann 1991]. Thus even the quantum universe appears to be time-symmetric (except for a few rare processes), despite our psychological perception of a unique direction of time.
In an electronically disseminated paper [Sommers 1994], Paul Sommers has shown how time-symmetric quantum mechanics provides the natural way to view the contextuality of quantum mechanics. In classical physics, as I have noted, the normal procedure is to predict the future paths of particles using a set of initial conditions and solving the appropriate equations of motion. However, in quantum mechanics initial conditions alone do not suffice to determine the future. Each possible outcome is not pre-determined, but occurs with some probability. Furthermore, the set of possible outcomes differs for different arrangements of the detectors.
Sommers suggests instead that quantum probabilities must be calculated using final conditions as well as initial conditions. The universe is presumed to be subject to a final boundary condition which limits the set of possible final states, just as the possible final states for a laboratory experiment are limited by a particular arrangement of detectors. He further explores how particular types of final boundary conditions might account for the classical nature of the universe.
A quantum system can thus be viewed as being influenced by its future as well as its past. The final condition defines all the possible outcomes, with a quantum mechanical probability calculated for each. One of these outcomes happens in accordance with these probabilities. As long as the dice are being tossed to determine the outcome, that is, we do not have deterministic hidden variables, then the macroworld can develop with a future that is not already written in the stars.
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