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Source Charge, Van Flandern Waterfall, and Leyton Geometry
T. E. Bearden (Dec. 2, 2003)
IntroductionIn electrodynamics, some scientists do recognize a grave foundations problem: That of the "source charge" and how it produces its associated fields. We published a first proposed solution to that problem in 2000 {}, refining it in 2002 {,} and later.
In 2003 we finally found the exact mechanism by which the source charge continuously consumes virtual state entropy of the vacuum and produces observable state negative entropy via its observable EM fields, potentials, and their energy. Van Flandern’s waterfall analogy is very appropriate as an analogy for the mechanism discovered.
The findings strongly impact thermodynamics, falsifying the present second law and correcting a minor error in the first law. The Leyton object-oriented geometry and advanced group theoretic methods furnish the dramatic difference required to Klein geometry and Klein’s methods. The results show that continuous processes producing negative entropy are not only possible but also ubiquitous.
Some implications for electrical power engineering are pointed out.
The Source Charge ProblemElectrodynamicists generally agree that the fields and potentials are created and established by their associated source charges. However, many assume that the static fields and their potentials just "suddenly are there", all at once, and that there is no motion or energy flow whatsoever, with respect to static fields.
Suppose we do a gedanken experiment. If one merely separates a charge anew, one can measure its fields and potentials being established outward at the speed of light. That is a flow of energy steadily outward, from the charge. So, experimentally an energy flow is outgoing in all directions. It is observable, real EM energy since it can be detected and measured. Further, once the forward edge of the energy flow reaches any distant radial point and passes beyond, the intensity of the fields and potentials that are measured there at that point continuously remain from then on. This proves that a "transient pulse" was not what was emitted, but a steady energy flow is continuously being emitted. In other words, the static field is a steady state outflow of energy from its associated source charge.
However, our instruments cannot measure any input of energy to the charge. Thus we are faced with a dilemma: Either the charge freely and continuously creates observable EM field energy and EM potential energy out of nothing at all, or else there must be a corresponding input of energy to the charge from its active environment, but in nonobservable (virtual state) form.
Either we must totally surrender the conservation of energy law itself—as being falsified by every EM charge, field, potential and joule of EM energy in the universe—or else we must find, model, and account for that nonobservable EM energy input to the charge from its active ambient environment. The problem has not been resolved in more than a century. It has, however, largely been scrubbed out of the textbooks and hidden from the students.
This problem is especially critical in electrical engineering. In the Maxwell-Heaviside classical EM model, there is no active vacuum interaction. In that model, there is no “input” to the charge from its ambient environment. So the model implicitly assumes all EM energy is freely created from nothing at all, completely violating conservation of energy and falsifying most of present physics.
BackgroundSen {} refers to the source charge problem in these words:
"The connection between the field and its source has always been and still is the most difficult problem in classical and quantum electrodynamics."
Bunge {} referred to it in this more subtle way:
"In order to keep Maxwell's second order equations and at the same time discard its advanced solutions in a consistent way one must add the hypothesis that the charged bodies are the sources of the e.m. field—a hypothesis that is taken so much for granted that it is hardly stated explicitly. ...fields and currents are conjoined but not causally associated: only field changes are causally associated with charged bodies in case there are any in the region considered."
One notes that Bunge actually refers to field changes as due to currents. There are no overall field changes due to static charges, but only the “static” fields themselves.
Bunge {} also pointed out that:
"...it is not usually acknowledged that electrodynamics, both classical and quantal, are in a sad state."
Kosyakov () states it very bluntly, pointing out that the theory of radiation is incomplete. He stated:
"A generally acceptable, rigorous definition of radiation has not as yet been formulated. …"The recurring question has been: Why is it that an electric charge radiates but does not absorb light waves despite the fact that the Maxwell equations are invariant under time reversal? "
If an observable photon is absorbed by a charged mass and the charge is thereby "excited", the charge usually does indeed decay and re-emit an observable charge. But in the absence of any bombardment by external observable radiation—i.e., in the ambient vacuum environment—the “isolated” charge itself is continuously emitting real, detectable, measurable EM field energy and EM potential energy.
Original Charges in the Universe and Their FieldsFirst, we address Bunge's point that changes to fields are involved with charge currents (i.e., as compared to the static field from a static charge): In the original formation of the universe (by whatever model one wishes), at some point each original charge appeared. That was indeed a "change" or special kind of initial momentary current. So the fields that appeared from that charge (and that now—for the original charges—still appear from it and reach across the universe) may be regarded as original "changes" to the zero field that existed before the formation of the charge.
Even so, the appearing "change" fields—subsequently known as the "static fields"—do not just instantly appear "everywhere in the universe at once". The static fields must appear (as "changes occurring" to the basic background zero field) at light speed, spreading radially outward in all directions. Else the conservation law, relativity, and communication theory are dead along with much of present physics.
These “appearing” radial EM fields are comprised of observable photons, because they can be detected. A free observable photon in space must be moving at light speed. So from the charge—from the moment of its appearance—there must be an outpouring of a continuous stream of observable photons in all directions, continuously establishing and replenishing the presence of the associated "static fields". Thermodynamically the fields are not actually static entities at all; they are nonequilibrium steady state (NESS) systems because they consist of photons and photon energy flowing outward in all directions.
Van Flandern’s Waterfall AnalogyWe have arrived at the need for Van Flandern's beautiful analogy. I originally used the notion of a perfect whirlpool in the water as an analogy, but his waterfall analogy is much more elegant and suitable! Van Flandern {} stated it this way:
“To retain causality, we must distinguish two distinct meanings of the term ‘static’. One meaning is unchanging in the sense of no moving parts. The other meaning is sameness from moment to moment by continual replacement of all moving parts. We can visualize this difference by thinking of a waterfall. A frozen waterfall is static in the first sense, and a flowing waterfall is static in the second sense. Both are essentially the same at every moment, yet the latter has moving parts capable of transferring momentum, and is made of entities that propagate.”
This gets us to the understanding that the "static" EM fields are static only in Van Flandern's second sense. This NESS system view of the static fields and potentials is now consistent with the formation of the original charges of the universe and the consequent formation of their static fields radially outward at light speed, and with the continuous replenishment of the established fields at every point in them. It is also consistent with replication of similar experiments wherein one merely separates some "classically unipolar" charge in fixed position, then watches and detects its associated fields and potentials, as they grow radially outward from it at light speed.
Static Fields: How is the Energy Conserved?What remains is the conservation of energy problem. The source charge continuously emits observable energy to establish and replenish its associated fields and potentials, without an observable energy input. Fortunately, the basis for answering that problem has been in physics since 1957, but it does not appear to have been noticed as enabling the solution to the long-ignored source charge problem. Let us examine this further.
In classical Maxwell-Heaviside electrodynamics, there is no modeling of the active vacuum or of curved spacetime. Instead, the vacuum (space) is assumed inert, and the local spacetime is assumed flat. The first assumption has been falsified for some time by quantum mechanics and particle physics, and the second assumption has been falsified since the advent of general relativity (almost a century now).
With these crippling assumptions, the classical EM theory does not and cannot model the known virtual particle interchange between the active vacuum and the source charge. It therefore cannot model the charge as a special kind of NESS system receiving nonobservable EM energy in virtual form, and outputting EM energy in observable form.
Therein hangs the problem. Experimentally we know that (i) the input energy to the source charge must be in virtual state form, and (ii) when we produce a charge suddenly, the fields and potentials are created at light speed outward in all directions. Once they reach a distant point and pass beyond, the fields and potentials and their intensities at that point are also continuously maintained thereafter, showing that a continuous emission of real energy from the source charge is occurring so that the static fields are continuously replenished in place—precisely like Van Flandern’s waterfall analogy {8}.
The “External” and “Internal” Energy FlowsWe also add another observation regarding energy flow: If one accepts Poynting energy flow theory, then any static charge and any static dipolarity a priori exhibits an external dynamic energy flow by simple S = E ´ H. Or as Buchwald {} states:
"[Poynting's result] implies that a charged capacitor in a constant magnetic field which is not parallel to the electric field is the seat of energy flows even though all macroscopic phenomena are static."
This shows that one can make a “free energy” generator that freely and continuously pours out real EM energy. One way is to lay an electret or charged capacitor on a permanent magnet, so that the E-field of the capacitor or electret is at right angles to the H field of the magnet. That simple arrangement will continuously pour out real EM energy flow at light speed, so long as it remains intact.
So there is no real energy crisis per se. Instead, there is an energy-interception, collection, and usage problem. Even the static magnetic field of a permanent magnet represents a steady outpouring of real EM energy. How to extract and use it freely is the problem.
Further, Whittaker {,,} showed in 1903 that any static potential decomposes into a harmonic set of bidirectional EM longitudinal wavepairs. In 1904, he also showed {} that any EM field or wave (or other pattern) decomposes into two scalar potentials with differential functions imposed. This latter paper initiated what today is known as superpotential theory {}. The combination of the two papers demonstrates that any EM field, potential, wave, or other pattern is comprised of a set of bidirectional longitudinal EM wavepairs, with impressed differential functions. Thus any field, potential, or wave does possess and is comprised of an internal set of energy flows of the Whittaker type, in good correspondence to Van Flandern’s analogy.
The static charge's electric field and its magnetic field meet those Poynting and Whittaker energy flow conditions. Hence, either the static charge really does emit real EM energy flow continuously, or else we have to discard the Poynting theory and superpotential theory. Since both are well tested, the external and internal energy flows are substantiated.
It seems we really must look to particle physics and find the charge's steady input of EM energy in the virtual state—unless of course we surrender the conservation of energy law entirely. If one accepts that energy must be conserved, then one concludes that there does exist a virtual state energy input. Accordingly, one must find it.
Importance of Broken SymmetryFortunately, Lee and Yang {} strongly predicted broken symmetry in 1956-57, and Wu and her colleagues {} experimentally proved it in early 1957. So revolutionary was this discovery that with unprecedented speed the Nobel Committee awarded the Nobel Prize to Lee and Yang in that same year, 1957.
Broken symmetry means that something virtual and nonobservable has become observable. Lee {} states it as follows:
"...the discoveries made in 1957 established not only right-left asymmetry, but also the asymmetry between the positive and negative signs of electric charge." …“Since non-observables imply symmetry, these discoveries of asymmetry must imply observables.”
Lee even predicted the possibility of directly engineering and structuring the vacuum itself {}. He also strongly pointed out that science has simply sidestepped the internal structuring of electrodynamics, including of the vacuum potential itself. He stated {}:
"…we have avoided the opportunity to study coherent phenomena which may be connected with the vacuum."
The clue for the missing energy input is that we must find a proper broken symmetry exhibited by that "classically isolated" source charge.
One of those proven asymmetries experimentally proven by Wu et al. is the asymmetry of opposite charges—i.e., of any dipolarity. It involves charge and will do the job nicely. So our quest reduces to finding a dipolarity associated directly with the source charge. However, we also must have a source for that virtual energy, and this source must be a continuous source of input energy in the virtual form.
For all that, we simply turn to quantum field theory, and there it is.
Energetic Charge and VacuumAs Nobelist Weinberg {} points out:
"… free electrons as well as electrons in atoms are always emitting and absorbing photons that affect the electron's mass and electric charge, and so the bare mass and charge are not the same as the measured electron mass and charge that are listed in tables of elementary particles. In fact, in order to account for the observed values (which of course are finite) of the mass and charge of the electron, the bare mass and charge must themselves be infinite. The total energy of the atom is thus the sum of two terms, both infinite: the bare energy that is infinite because it depends on the infinite bare mass and charge, and the energy shift calculated by Oppenheimer that is infinite because it receives contributions from virtual photons of unlimited energy."
The picture that results of the “isolated classical charge” in its active vacuum environment is this: The "isolated charge" is an infinite bare charge that has polarized the vacuum, and is thus surrounded by an infinite charge of the furious virtual charges of opposite sign in the vacuum, appearing and disappearing at an incredible rate. The ensemble of the bare charge and its associated virtual charges has a net finite charge of the sign of the bare charge inside. That net finite charge is in fact the classical "separated charge" that our instruments see of the infinite bare charge through the infinite external screen of opposite virtual charges.
The quantum field theory ensemble—classically known as an "isolated source charge"—is thus a very special kind of dipolarity when both charge and vacuum activity are considered. As such a dipolarity, it exhibits the proven asymmetry of opposite charges.
This broken symmetry means that some of the virtual photon energy continuously absorbed by the charge is not reradiated as virtual photon energy, but instead is reradiated as observable photons in all directions. There is no problem with how much input energy is required to pour out the energy indefinitely, even over a period of billions of years, since the energy of both the virtual polarization charge and the bare charge is infinite.
Impact upon ThermodynamicsWe have found the source of the charge’s missing input energy: The infinitely active polarized vacuum. We also have the mechanism that produces the outflow of organized photons (radially ordered as to average intensity of the fields at every radial point in
3-space). But we still have a remaining dilemma: The input virtual state EM energy of the seething vacuum is totally disordered (random), while the output observable energy is macroscopically ordered, even eventually across the entire universe. The charge’s transformation of the disordered energy into ordered energy represents continuous negative entropy production, totally violating the present form of the second law of thermodynamics. Hence, we must also find the exact mechanism by which such giant negentropy can occur, and we must restate the second law so that it permits negative entropy reactions.
Fortunately, the relevant recent work is in the literature. First, the present second law—which prohibits negative entropy—is known to be violated by transient fluctuations, since the second law is based on statistical mechanics and in normal statistical fluctuations the reactions can and do "run backwards".
To deal with this "fluctuation production of negative entropy", Evans and Searles {} formulated a most useful transient fluctuation theorem (there are others), that has been very usefully applied in forefront thermodynamics to a variety of fields. Wang et al. () also showed that, surprisingly, statistical fluctuation alone does produce negative entropy excursions in certain chemical fluids for up to 2 seconds, at the cubic micron level. A cubic micron of water contains something like 30 billion ions and molecules, so the effect of negentropic reversal of chemical reactions in a zone containing 30 billion ions is certainly nontrivial. Reversed reactions such as momentary attraction of two like charges (e.g., two H+ ions to give a quasi-nucleus of deuterium or two D+ ions to give a quasi alpha particle) is probably sufficient, e.g., to produce most of the reported cold fusion transmutation results {} now demonstrated in more than 600 experiments worldwide {}. That is another related matter we have separately dealt with elsewhere {23}.
Evans and Rondoni {} showed that, theoretically at least, nonequilibrium steady state (NESS) systems can produce negative entropy continuously, so that the entropy starts negatively and further decreases toward negative infinity as time passes. Startled at their own results, they felt that no real physical system could exhibit such results, but did point out that "the problem remains for deterministic systems". In other words, theoretically the "problem" of systems that continuously produce negative entropy does remain.
We have therefore nominated the source charge as the first such physical system known, continuously producing negative entropy (order from disorder) in the manner theoretically predicted by the results of Evans and Rondoni {25}. As we saw, the output energy is indeed deterministic as a function of radial distance.
Search for the Coherent Integration MechanismThermodynamically, the problem is therefore amenable. However, we still are lacking the exact mechanism by which the source charge coherently integrates the continually received disordered virtual energy into observable energy (observable photons). In other words, how does the charge consume the positive entropy in the virtual state and integrate it into negative entropy in the observable state?
After a year of searching some intricate things that did not work, the solution to the desired negative entropy (coherent integration of virtual state disorder into macroscopic observable state order) turned out to be surprising simple. First, the receipt of “virtual EM energy" by the source charge is primarily via its absorption of virtual photons. Mass m of the absorbing charge q is unitary, and its absorption of a virtual photon thereby constitutes the production of a differential dm of mass, yielding (m + dm). As successive virtual photons are absorbed, we have m(t) = m0 +dm1 + dm2 + ... + dmi + ... and so on. In short, the differential unitary mass of the charge is steadily and coherently increasing in its virtual state toward the observable state. This mass-energy change becomes increasingly unstable (excited), from the virtual state viewpoint, as it nears the quantum level and the observable state threshold.
When this increasing total dm reaches sufficient magnitude to constitute the energy DE of an observable photon (DEDt) via DE = c2dm, the zitterbewegung (constant fierce bombardment of the charge by virtual particles) simply triggers the abrupt decay of the excited state and release of the excitation energy. This results in the radial emission of an observable photon from the charge, at light speed outward into surrounding space.
The “virtual photon absorption and unitary differential mass integration and summation” is the long-sought coherent integration process. The zitterbewegung plays the role of forcing the abrupt decay and quantum change that produce the observable photon emission. The process repeats over and over at incredible speed, in all directions, and this finishes the complete mechanism by which the source charge continuously absorbs and coherently integrates virtual energy from its seething vacuum exchange, and re-emits the integrated energy as real, observable photons traveling outwards at light speed.
The result completes the full mechanism by which the source charge produces and continuously maintains (at light speed) its associated "static" EM fields and potentials. Also, it is a mechanism that conserves energy during the process.
Tidying up the ResultsWe add that classical EM does not have this solution even in its model, because it does not model the active vacuum interactions or the ongoing process we described.
As a result, the classical EM model is in serious and fundamental error, because—as it models things—it implicitly assumes that every EM field, EM potential, and joule of EM energy in the universe is and has been freely created from nothing at all, in total violation of the conservation of energy law.
Models are useful, of course, in that range of phenomenology to which they "fit" the experiments. However, no model is ever perfect, as proven by Gödel {}. Models are not useful—or even to be used—in those areas where they no longer fit the experiments, and therefore no longer adequately describe the phenomenology.
The old concept of "static fields" being instantly full grown, and just being "everywhere at once" for all time, is a notion that is seriously flawed and must be changed.
However, we still must correct the second law of thermodynamics. The present second law can be simply stated as:
“Given some available controlled order (available controlled energy), this initial controlled order will either remain the same or be progressively disordered and decontrolled over time by subsequent entropic interactions.”
Or, simply put, dS/dt ³ 0.
To include the negative entropy changes required in an expanded second law, we restate the second law as follows:
"First a negat...
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