The Field Interchange Hypothesis Continued

By David S. Schroeder

The second interpretation for a chronetic monopole also leads to some strange results when considering the spatial aspect of such a field. Here it is assumed that the chronetic field can induce expansion or contraction of time (relative to our rate of temporal passage at the Earth's surface) to varying degrees, but in either the forward or reverse directions. Therefore, the ultimate or extreme case as our imaginary test sphere shrinks down on the monopole is for the equipotential field on the sphere's surface to rise to infinity as the sphere diminishes to a point. More precisely, as one approached a chronetic monopole of one polarity the rate of temporal passage would increase steadily until it attained an infinite value - time would flow infinitely fast into the future. Conversely, as one approached a chronetic monopole of the opposite polarity, the rate of temporal passage would rise until it attained an infinite value - time would flow infinitely fast into the past. To establish a convention, a north chronetic monopole will be considered a locus of infinite acceleration of time into the future, while the south chronetic monopole will be considered a locus of infinite acceleration of time into the past.

With this second definition for chronetic monopoles the corollary for spatial charges is quite bizarre. To appreciate the connection it's necessary to refer back to relativity. We have already proposed that time be can expanded (slowed) in this type of chronetic field just as in relativity. The expansion of time can proceed all the way down to zero, again just as in relativity where time can freeze, for example, at the event horizon of a black hole. But, unlike in relativity this null state occurs at the physical halfway point between opposite chronetic charges forming a null plane between the two charges. Also unlike relativity on the other side of the null plane time goes negative - that is it flows backwards - smoothly transitioning through zero into the reverse temporal direction.

In relativity when time slows drastically, as for example in a reference frame approaching the velocity of light, the metric of space also foreshortens - the Lorentz-Fitzgerald contraction - and approaches a zero value. A moving reference frame cannot attain the velocity of light since infinite energy would be required to accelerate an infinite mass. However, a black hole horizon does constitute a state where time stops flowing, and the distance scale in the radial direction shrinks to zero. Similarly, since time in the second definition of a chronetic field can smoothly transition from an infinite positive value through zero to an infinite negative value, we should expect the same behavior in the spatial component of the GC field.

The seemingly inescapable conclusion is that the metric of space in a bipolar spatial field of this type must be able to transition from an infinite positive value for a spatial charge of one polarity, to an infinite negative value for a spatial charge of the other polarity. At the transition boundary between the positive and negative spatial regions the metric of space would presumably drop to zero in the radial direction. In the negative region of such a bipolar field space must take on a negative value. But, this begs the question of how to interpret the meaning for a negative metric of space. While such a notion sounds bizarre, it is perhaps no stranger than the notion of reversed time.

A clue to the meaning for a negative metric of space in our universe might be gleaned from a proposal put forth by the astrophysicist Thomas Gold in the 1960's. Gold was struck by the fact that the basic process imprinting an arrow of time in our universe was the flow of heat away from hot objects like stars into the cold reaches of space. He noted that the youthfulness of the universe and the expansion of space prevents space from reaching an equilibrium temperature with the stars. However, at some point eons from now the stars will have dumped all their heat energy into the void, the universe will have reached its maximum extent, and begin the process of contraction towards the big crunch.

Gold proposed that when the heat flow in the universe reverses, going from hot space to cold, burned out stars and planets, that the arrow of time will also reverse. Furthermore he proposed that the transition boundary for temporal reversal occurs when the universe ceases expanding and begins its contraction phase. Perhaps here lies the key to the notion of 'negative' space. Since space and time are linked in relativity (and in the hypothetical GC field), it makes sense for some property of space to reverse with temporal reversal. We have a simple intuitive picture of an expanding and contracting universe that is akin to an inflating and deflating balloon. But, if Gold's cyclic universe is correct, and time undergoes reversal in its latter phase, then space must also reverse in some sense. If Gold is right, the expansion and contraction of space-time in our universe may be a more subtle and complex phenomena than our simple intuitive picture suggests.

In any case, Gold's idea provides us with a possible guide to the definition for 'negative' space associated with G-matter's spatial charges, for our second proposed definition of such charges. We conclude therefore, that a negative spatial field is characterized, in general, by the contraction of the metric of space. The ultimate, or extreme case, for such a field, would be a point of infinite spatial contraction, which would define a spatial charge of one polarity. The other polarity for this version of a spatial field would correspond to a point of infinite spatial expansion. To establish a convention, a positive spatial charge is to be considered a locus of infinite spatial expansion, while a negative charge will be considered a locus of infinite spatial contraction. Notable in these definitions is the use of the same terminology - expansion and contraction - for both the temporal and spatial components of the GC field for this second interpretation of the meanings of spatial and temporal charges. This is deliberate to underscore the similarities in the behavior of these two field components of the GC field. The same situation is evident in electromagnetic field theory where a basic symmetry prevails between the electric and magnetic components of that field.

In postulating the existence of spatial charges and chronetic monopoles in several configurations, it was assumed that they represented loci of infinite field strength. To be sure, the concept of infinity is anathema in modern physics. The same difficulty was encountered in assessing the mass and charge of the electron during the formulation of quantum electrodynamics in the 1940's. The solution to that problem was achieved by resorting to a procedure known as renormalization. Most likely, a similar procedure could be developed and utilized to tame the problem of infinities in hypothetical chronetic monopoles, and spatial charges. Intriguingly, there is something of a natural renormalization effect that applies to the second interpretation for positive spatial charges existent in our universe. The closer one comes to the central locus of a positive spatial charge, the less volume of space that exists according to Euclidean geometry. This has the effect of canceling the infinite spatial volume that would otherwise be encountered in a positive spatial charge, inasmuch as a point particle constitutes an infinitely small domain.

Rather than belabor the issue of which set of interpretations for spatial charges and chronetic monopoles is the more viable version, or consider further refinements and modifications, we will instead jump ahead, and address the implications these concepts have for some of the outstanding puzzles of modern physics. Fortunately, either version leads to essentially the same results. Of particular interest is the temporal aspect of a GC wave propagating in our universe. A GC wave arising from an accelerated spatial charge in our universe will have exactly half its energy propagating into the future, and half its energy propagating into the past. Of course, the reader may ask what relevance does this have for the physics of our universe since no spatial charges have ever been detected. Surprisingly, it turns out this concept may resolve one of the most outstanding puzzles of physics - the problem of Mach's Principle.

Recall that earlier we stipulated an exact symmetry between G-matter and ordinary matter. By this was meant that the Maxwell field in G-matter had the dimensions of space and time, while the Einstein space-time field associated with G-matter had electric and magnetic dimensions (from our perspective). In ordinary matter the exact converse is the case, so that a kind of perfect symmetry exists between the two types of matter. An important consequence of this symmetry transformation is that the Einstein field in a hypothetical G-universe constitutes an electric-magnetic continuum, which we will abbreviate as the emc. This emc would have identical properties to the space-time continuum in our universe to a G-person (a person made of G-matter). In short, it would constitute their space-time continuum. But, from our perspective it would have electrical and magnetic properties - albeit formulated as a 10 component tensor field exactly as Einstein formulated the properties of space-time in our universe.

Now suppose, for the sake of argument, that our universe is permeated by an emc as a component of the quantum background. This idea may not be as far fetched as it first sounds. Present cosmological models propose that the configuration of the basic forces of matter - electromagnetism, strong force, weak force, gravity - crystallized out in the early stages of the big-bang, when the universe was an exquisitely hot ball of energy, a fraction of its present size. It's theorized that other field or symmetry configurations could have emerged during this epoch resulting in a universe with entirely different characteristics than we know today. Indeed, it's postulated that matter and antimatter were equally abundant early on, but a very slight asymmetry built into the laws of nature favored matter over antimatter leading to a universe overwhelmingly made of matter. Extrapolating from this notion, it's conceivable that other built-in imbalances led to the eradication of other mirrored types of matter. These may have included G-matter, which early on underwent systematic annihilation via processes analogous to those which eliminated bulk antimatter.

If G-matter really was created in the earliest epoch of the universe there may be a small residual quantity of it still present in our universe. But it should be far less abundant than naturally occurring antimatter, since presumably much higher energies would be needed to synthesize it. Only in the most exotic high energy environments would it be undergoing synthesis today. Assuming trace quantities of G-matter are still extant in the universe, and continue to be synthesized in small amounts, there may also be a relic emc field dating from the earliest universe. This would constitute a quantum backdrop to our familiar space-time continuum, and provide an appropriate space-time continuum for the residual G-matter. As we shall shortly see, this relic emc field may, in fact, turn out to be the long sought Higgs' field postulated to give mass to the fundamental particles. Just as there is postulated to be a graviton - the quanta of our gravitational (space-time) field, there would also exist a quanta for the emc field, which would correspond to the Higgs' boson.

The assumption that an emc coexists with our space-time continuum leads to far reaching consequences. Why? Because in the context of this continuum ordinary electric charges in our universe - electrons, quarks - constitute spatial charges. From the perspective of the emc ordinary electromagnetic radiation is seen as gravitochronetic radiation whose dimensions are space and time. This means that whenever an atom in our universe radiates electromagnetic energy, half of that energy is transmitted into an earlier epoch of the universe, both temporily and spatially while the other half is transmitted into a future epoch of the universe both temporily and spatially, from the perspective of the background emc

This concept is a variation on an idea developed by Richard Feynman and John Wheeler over half a century ago in 1945, but differs subtly, and in a significant way from that original concept. They noted that Maxwell's equations are fully symmetric with respect to time. That is, when Maxwell's equations are solved for a propagating electromagnetic wave it leads to two solutions - one describing the EM wave traveling into the future, and one describing the EM wave traveling into the past. The former is called a retarded wave (because it arrives late), and the latter is known as an advanced wave (since it arrives early).

Their model, in its most basic outline, imagines a single pair of electrons alone in the universe. When the first electron is jiggled it radiates an electromagnetic wave half of whose energy flows into the past, and half of which flows into the future. When the retarded component of this wave is absorbed by the second electron it stimulates it to vibrate to and fro leading to a new set of retarded and advanced waves. The advanced wave from this second electron then travels backwards in time from the moment of absorption to the first electron. Since this advanced wave also possesses 'negative' energy, the combination of negative energy and negative time is equivalent to an ordinary retarded wave. The result is that the original retarded wave from the first electron, and the advanced wave from the second electron mesh together perfectly, and appear as a solitary retarded wave.

The beauty of this scheme, which is known as the absorber theory, is that it invokes a mechanism for instantaneous interaction between the two electrons. In effect, the radiation resistance experienced by the first electron, when it accelerates, arises from the instant coupling to the second electron, no matter how far away it may be in our universe. This is possible because the advanced wave, traveling back from the future, will interact with the first electron at virtually the instant that electron emits a retarded wave. Another way of seeing this is to realize that from the perspective of a photon - the quanta of the electromagnetic field - time does not pass at all. Thus from the photon's viewpoint every point in the universe can be instantly reached from any other point.

In the mid 1980's John G. Cramer of the University of Washington developed a modern quantitized version of the Wheeler-Feynman Absorber theory. A prime motivation was to make sense out of the multiple interpretations of quantum mechanics; from the original one dubbed the Copenhagen interpretation, to more recent ones developed in response to dissatisfaction with that standard interpretation. Each of these interpretations contained paradoxes and counterintuitive notions that eluded a rational understanding.

The essence of the puzzle is embodied in the classic two slit experiment. In this experiment individual photons are fired at a detection screen through an intervening barrier containing two slits. Astonishingly, the outcome of this experiment is apparently dependent upon the observer. If two observers are monitoring the slits (one for each slit), and therefore the individual photons passing through them, the pattern formed on the screen from a large number of impinging photons is precisely the pattern expected if the photons were individual particles, and randomly passed through one slit or the other. But if observers are absent, the pattern that emerges is that of an interference pattern, as if each supposedly discrete photon was passing through both slits, and interfering with itself.

The standard Copenhagen interpretation deals with this paradox by proposing that the wave function of the photons collapse from a potential (wave) state into a real (particle) state, by the act of observation. Extrapolating from this standard interpretation leads to the bizarre conclusion that the existence of the universe arises because conscious beings are observing it. But, this leads to serious philosophical problems. How, for example, could the universe have evolved prior to the development of intelligent life in it? Equally puzzling in the standard Copenhagen interpretation is the issue of the dividing line between quantum processes and macroscopic everyday events. This interface, where the wave function collapses between the microworld and our everyday reality, is ill defined, and impossible to pin down to a specific level.

These difficulties, as well as others, are resolved with John Cramer's remarkable 'transactional' interpretation of quantum mechanics. Cramer's seminal idea neatly ties together two major mysteries at the heart of quantum mechanics - the paradox of the so-called two slit experiment (including its modern variant form), and nonlocal coupling whereby distant particles are correlated instantaneously, seemingly violating the most sacred of all rules in contemporary physics - the velocity limit of the speed of light. In the process of linking these puzzles, both are effectively resolved, and by extension, virtually the whole gamut of paradoxes contained in the assorted interpretations of quantum mechanics are eliminated.

Taking his cue from the Wheeler-Feynman Absorber theory, Cramer recognized that the fully relativized version of Schrödinger's wave equation described the evolution of a quantum system not only into the future, but into the past as well. The implication was that the Absorber theory originally applied to light, might be extended to particles as well, since in quantum theory particles are treated as "wave packets". Schrödinger's wave equation represents the potential of a quantum system before it collapses into some unspecified future state. The equation is in the form of a complex function containing both real and imaginary parts, and has two sets of solutions. The first solution set is the one utilized by most physicists to calculate quantum processes, and describes the evolution of a quantum system into the future. The second set of equations known as the complex conjugate is a mirror image of the first, and describes the evolution of a quantum system into the past.

In Cramer's transactional interpretation every quantum event represents a "handshake" across space-time. In analogy with the Feynman-Wheeler Absorber theory an "offer" wave from an excited electron propagates outward in an ever expanding bubble, corresponding to the first Schrödinger wave equation. At some future time the energy of this expanding wavefront is randomly absorbed by a second electron (or other charged particle), which then transmits a "confirmation" wave back into the past towards the original excited electron, arriving at that electron at the exact instant that electron radiated its initial signal. This confirmation wave which travels into the past corresponds to the complex conjugate of the first wave equation. Additionally, the original excited electron also sends a confirmation wave into the past, while the absorber electron sends an offer wave into the future. These two cancel out, however, while the primary confirmation wave possessing negative energy reinforces the primary offer wave, and the transaction is complete.

These ideas when applied to the two slit experiment provide a convincing and logical explanation for the strange behavior of the photons traveling through the apparatus. The offer wave from the photon source passes through both slits initially. If a detection screen is in place without observers present the confirmation wave traveling backwards in time will return through both slits since no target will have been specified, or in the jargon of standard quantum mechanics the wavefunction will not have collapsed, and thus the photon will remain in the wave state. The result is self interference, despite the fact that only a single photon has traveled through the apparatus. However, if observers with telescopes trained on the individual slits are present the outgoing offer wave will have specific targets eliciting the production of a confirmation wave from one of the telescopes at random. This confirmation wave traveling from the future (in this case a matter of picoseconds for a tabletop laboratory experiment) retrace the path of the outgoing offer wave, completes the transaction when the source randomly selects one or the other, thus establishing the route for a real photon traversing one, and only one slit.

John Cramer is careful to emphasize that the transactional interpretation differs in no way from the predictions of the standard interpretation. This is a significant point inasmuch as it sets the boundaries of the theory to coincide essentially with those of traditional quantum mechanics. Quantum mechanics as originally formulated by the Copenhagen school never addressed or attempted to resolve one of the outstanding puzzles of physics - the origin of inertia. This is despite the fact that it predicted instantaneous action-at-a-distance (non-local coupling), that would be an essential ingredient of any theory purporting to explain inertia through Mach's Principle. The transactional interpretation while it clearly identifies a mechanism for non-local coupling (backwards in time signaling), may fall short of a full recipe to account for the phenomena of inertia.

What exactly would be the prescription for a more complete theory of inertia? To answer that question we need to go back to the beginning of this century. The key insight that led Albert Einstein after 1905 to develop general relativity was the recognition that inertial forces and gravitational forces are fully equivalent. Now we know from general relativity that gravity arises from the distortion of space-time. By the equivalence principle it then follows that inertia must also have these dimensions. That is, every time we experience inertia, for example taking a corner in our car, both space and time must undergo minute distortions in our reference frame. Therefore, we can assume that the underlying mechanism responsible for inertia in our universe entails the warping of both space and time. But there's a caveat, this spatial and temporal distortion must be communicated instantaneously between all masses in our universe to comply with Mach's principle.

Intriguingly, the proposal that an electric-magnetic continuum (emc) pervades our universe at the quantum level, and which is identified with the Higgs' field, could, in principle, provide that mechanism. As pointed out earlier every fundamental electric charge - electron, quark - in our universe, from the perspective of the emc, constitutes a spatial charge. Whenever such charges undergo inertial change, that is, are accelerated, they emit electromagnetic radiation from our point of view. But, from the viewpoint of the emc ordinary electromagnetic radiation is seen as gravitochronetic radiation whose dimensions are space and time. The result is that whenever any mass undergoes acceleration in our universe it sends out a wave of energy, half of which is transmitted into an earlier epoch of the universe, both temporally and spatially, while the other half is transmitted into a future epoch both temporally and spatially. This notion is quite analogous to the absorber and transactional theories, except that it takes the spatial aspect of instantaneous momentum feedback into account as well as the temporal aspect. In sum, it could be that quantum non-locality has its origin entirely with the transactional concept operating through electromagnetic effects in our space-time, while momentum originates from spatial and temporal influences operating through the underlying Higgs' field as formulated here.

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