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Source Charge, Van Flandern Waterfall, and Leyton Geometry

T. E. Bearden  (Dec. 2, 2003)


In 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 {[1]}, refining it in 2002 {[2],[3]} 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 Problem

Electrodynamicists 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 contradicting most of present physics.


Sen {[4]} 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 {[5]} 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 {[6]} also pointed out that:

" is not usually acknowledged that electrodynamics, both classical and quantal, are in a sad state."  

Kosyakov ([7]) 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 Fields

First, 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 Analogy

We 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 {[8]} 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 Flows

We 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 {[9]} 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 {[10],[11],[12]} showed in 1903 that any static potential decomposes into a harmonic set of bidirectional EM longitudinal wavepairs. In 1904, he also showed {[13]} 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 {[14]}. 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 Symmetry

Fortunately, Lee and Yang {[15]} strongly predicted broken symmetry in 1956-57, and Wu and her colleagues {[16]} 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 {[17]} 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 {[18]}. He also strongly pointed out that science has simply sidestepped the internal structuring of electrodynamics, including of the vacuum potential itself. He stated {[19]}:

"…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 Vacuum

As Nobelist Weinberg {[20]} 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 Thermodynamics

We 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 {[21]} 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. ([22]) 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 {[23]} now demonstrated in more than 600 experiments worldwide {[24]}. That is another related matter we have separately dealt with elsewhere {23}.

Evans and Rondoni {[25]} 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 Mechanism

Thermodynamically, 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 Results

We 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 {[26]}. 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 ≥ 0.

To include the negative entropy changes required in an expanded second law, we restate the second law as follows:

"First a negative entropy interaction occurs to produce some controlled order (available controlled energy). Then that initial available controlled order will either remain the same or be progressively disordered and decontrolled by subsequent entropic interactions over time, unless additional negative entropy interactions occur and intervene."

Or, simply put, - dS/dt ≤ +∞.

It only takes one white crow to prove that not all crows are black. The source charge with its input virtual EM energy and its associated output EM fields and potentials are an experimental example of a physical system totally violating the old second law, to any size level desired and for any time interval desired. The violation of the old second law is complete, thus falsifying its formerly assumed absoluteness.

Leyton’s Work Solves the Problem of the Klein Geometry

A final problem can still be raised: The standard Klein geometry {[27]} will not support the finding.

In Klein's geometry and with his group symmetric methods, broken symmetry at a given level results in the loss of symmetry information at that level, and hence reduces the overall symmetry. Klein's approach applies successive restrictions from the general case to the special case, e.g., from projective geometry down to Euclidean geometry. In Leyton’s approach, one builds up from the special case to the general case, e.g., from Euclidean geometry up to projective geometry. This reversal of fundamental methodology allows the creation of a higher order group as a result of symmetry-breaking. That situation is impossible in the Klein approach, which fundamentally opposes the building up process.

As shown by the source charge, just such a different geometry is required with new, more advanced group symmetric methods such that, when symmetry is broken at a given level, the symmetry information for that level is retained and a new symmetry is generated at the next higher level—thus increasing the overall symmetry.

In short, one cannot model an observed negative entropy process by assuming a foundational approach that only permits positive entropy. This is precisely why the conventional form of the second law excludes half the thermodynamics—specifically, it excludes the negative entropy processes of nature.

But fortunately, the required geometry and methods do already exist as rigorously shown by Leyton {[28]}. From Leyton's work, a hierarchy of symmetries effect emerges, and the old Klein geometry and methods are replaced (and reversed in approach) by Leyton's more advanced object-oriented geometry and group symmetric methods.

Leyton’s hierarchies of symmetry effect implicitly includes a universal law and mechanism of negative entropy production—and, in our view, it heralds a dramatic revolution in physics, chemistry, electrodynamics, and electrical engineering.

Solving the Central Problem of Thermodynamics

The epochal work by Leyton {28} also solves the tremendous central time asymmetry problem of thermodynamics.

Price {[29]} states the problem this way:

"A century or so ago, Ludwig Boltzmann and other physicists attempted to explain the temporal asymmetry of the second law of thermodynamics.  …the hard-won lesson of that endeavor—a lesson still commonly misunderstood—was that the real puzzle of thermodynamics is not why entropy increases with time, but why it was ever so low in the first place."

Many thermodynamicists add: “Or how could it still be so low now?” Indeed, Price himself states {[30]}:

"…the major task of an account of thermodynamic asymmetry is to explain why the universe as we find it is so far from thermodynamic equilibrium, and was even more so in the past."

Thermodynamicists have debated and fought, and sought the answer for a century, to little avail. The problem cannot be solved within the Klein geometry model and approach. The answer is given by Leyton's geometry and methodology, and specifically by his hierarchies of symmetry principle. The temporal asymmetry is and was possible because there do exist negative entropy processes in nature and in physics after all, due to Leyton hierarchies of symmetry. The old second law and Klein geometry only addressed the entropic half of thermodynamics and ignored the excluded negentropic half.

A rather astounding fallout of Leyton’s approach is the potential for developing negentropic engineering rather than the present exclusively entropic engineering taught and practiced worldwide. If one considers many or most operating system entropic losses as potentially harmful byproducts affecting the environment negatively, then the coming age of negentropic engineering will eventually allow reprocessing and “recovery” of entropic byproducts into negative entropy resources once again. As the new engineering is developed together with extracting energy directly from the vacuum, the two will provide the real and final solution for the ever-increasing biospheric pollution and contributions to global warming by present energy and power processes.

Correcting the First Law of Thermodynamics

In passing, we also found and corrected a minor error in the present statement of the first law of thermodynamics. The first law presently equates the change of magnitude of an external parameter—such as the potential and the field—of the system as work. If true, that would exclude gauge freedom, widely used in electrodynamics and physics.

Even in the Lorentz-symmetrically regauged Maxwell-Heaviside equations, the potential energy of a system can be freely changed at will, by the gauge freedom principle. Put into concrete terms, changing the voltage (and hence the potential energy collected in the system) of an EM system—and changing nothing else—is not work, nor does it require work. It merely requires work-free flowing of excess potential onto the circuit or system.

Correcting a Misunderstanding of the First Law of Thermodynamics

We also corrected the long-prevailing but erroneous scientific perception that the first law prohibits perpetual motion. If that were true, then it would falsify Newton’s first law of motion.

Newton’s first law simply states that an object, once placed into a state of motion, will perpetually remain in that state of motion unless and until acted upon by an external force to change it. An isolated object not affected by net external forces thus really does exhibit perpetual motion, requiring no input of extra energy and doing no work. So either one accepts perpetual motion or one gives up Newton’s first law. In that case, without any restraints, the motion of an object would be totally random from moment to moment, thereby destroying any organized universe such as we observe and live in.

Inexplicably, for a hundred years a great part of the scientific community has made a simple error in logic, so that the phrase “perpetual motion” has become a dogma evoking a knee-jerk reaction. We explain it by examining Max Planck’s statement as an example. Planck stated {[31]}:

"It is in no way possible, either by mechanical, thermal, chemical, or other devices, to obtain perpetual motion, i.e., it is impossible to construct an engine which will work in a cycle and produce continuous work, or kinetic energy, from nothing."

The statement contains two assertions and an assumption. Paraphrasing, the two assertions are: (i) “It is impossible to obtain perpetual motion,” and (ii) “It is impossible for an engine to perform continuous work or energy, from nothing.” The assumption (contained in the use of the “i.e.”), is that the two assertions are identical.

The first assertion is false, since it contradicts Newton’s first law of motion and common observation of the organized universe.

The second assertion is true. No source-free system can perform work or output energy, without the appropriate input of the energy.

However, the second assertion has nothing at all to do with Newton’s first law of motion, or with the first assertion. The assumption that the first and second assertions are identical is false.  They are not even related, since an object in Newton’s first law state of perpetual motion requires no extra energy input and does no work. That is not the same as a hypothetical system doing work without energy input.

Hence Planck’s statement asserts that a false assumption is identical to a true assumption, thereby proving the false assumption to be true. That, of course, is a logical non sequitur.

So Planck’s statement is falsified completely, as is the prevailing scientific attitude that perpetual motion automatically means a continuously working system without any energy input at all, and thereby creating energy from nothing.

The only scientists who unwittingly accept the creation of energy out of nothing at all, are those who accept that all EM fields and potentials as well as every joule of EM energy in the universe, is and has been freely created out of nothing at all by their associated source charges, without any energy being input to the charges.

Negative Resonance Absorption of the Medium

For an interesting experimental phenomenon showing lack of accountability for an unsuspected but massive EM energy component actually available in every EM system, one turns to the established field of negative resonance absorption of the medium. E.g., the Bohren-type experiment {[32]} results in a resonant particle medium absorbing oscillating energy furnished by the operator and then re-emitting some 18 times as much oscillating energy from the medium! The charged particles of the medium are in particle resonance at the frequency of the input energy (IR in the case of insulating particles, and UV in the case of conducting metal particles). In each case, far more energy is re-emitted from the medium than the energy one inputs by conventional Poynting flow calculation.

Thus, either the experiments falsify the conservation of energy law, or else there is another previously unaccounted energy input from the environment itself.

Scientists in that area have not recognized the source of the excess energy input. They carefully refrain from speaking of excess emission, and from discussing the thermodynamic coefficient of performance—which of course is COP = 18 in this case. Instead, they carefully speak innocuously of the change in reaction cross section. They do not recognize that the foundations definition of the field intensity is being altered, and that in electrodynamics the E-field or the B-field (intensity) is defined only insofar as its own “point intensity” of E or B at each spatial point. The geometric regional E or B field is not defined at all in electrodynamics.

Even then, the “intensity” of the field is considered to be measured by what is diverged from the energy flow (comprising the actual geometrical field passing through a given point), by a reacting unit point static charge placed at that point. So it is not the “field intensity in mass-free space” that is being dealt with at all, but the field intensity in a specific kind of charged matter consisting of totally static charges. It is in fact what is being diverged from the actual intensity of the energy flows comprising the geometrical field {10,13} by a static unit point charge at a point. And of course, that divergence is by a specific divergence reaction, and the amount of that divergence is therefore determined by the nature of that specific reaction as expressed in terms of its “reaction cross section” (output divided by input, for that reaction only).

The practitioners feed oscillating field energy into the particulate medium wherein the medium’s particles are self-resonant at the input energy frequency. In that case, the reaction cross section of course dramatically increases (in this case, by a factor of 18) {[33]}. But that is also an increase in calculated or measured output divided by calculated or measured operator input. It therefore represents a change in the thermodynamic COP of the process itself (which includes both absorption and re-emission).

For its output to exceed the operator’s energy input, any physical EM system exhibiting COP>1.0 thermodynamically must have an extra or second energy input furnished freely by the active environment itself (e.g., as in the case of a common heat pump). The efficiency x of a thermodynamic system (system output divided by total system input) can never exceed 100%, else the conservation of energy law is violated. The COP (system output divided by operator’s input only) can of course be COP>1.0, even for a system with efficiency x << 100%, if the environment furnishes the excess energy. The common heat pump in nominal conditions may have x = 50%, but a COP = 3.0 to 4.0 because of the extra energy input by the atmosphere and extracted and used by the heat pump process.

In the case of negative resonance absorption of the medium, the resonant particles are also able to diverge and absorb some of the huge but long-neglected Heaviside energy flow component {[34],[35]}, arbitrarily discarded by Lorentz {[36]}. Specifically, the resonant particles do diverge some of that normally nondivergent Heaviside energy flow, thus increasing the absorbed EM energy available to be re-emitted. The resonant particles thereby increase their reaction cross section, and also the COP of the system, because now the particular system has a second source of input energy: a little of the long-ignored Heaviside component of energy flow that accompanies every Poynting energy flow but is usually not diverged. The ordinary vector divergence of the curl is zero in a flat spacetime, but it is not necessarily zero in a curved spacetime. The self-oscillating particles of the medium do provide sufficient spacetime curvature to allow some of the normal divergence-free Heaviside component to be diverged anyway, thus furnishing an extra Poynting energy flow input (diverged) component. This is an extra environmental energy input to the resonant charged particles, though unaccounted in the present electrical engineering theory and therefore unaccounted by the researchers in the field of negative resonance absorption of the medium.

Since the resonant particles absorb more energy than the operator himself inputs in his Poynting energy flow input component, the particles are then free to re-radiate all the energy they absorbed, in Poynting divergent form, thereby providing COP = 18, while rigorously obeying x £ 100%.

We have previously pointed out the advantage that could be gained by developing and incorporating such a heat amplifying processor between the boiler and the heat furnished by the hydrocarbon combustion flames (or the heat radiated from a nuclear reactor). Even a “staging” amplification of 4 to 10 would enormously reduce the fuel burned, its cost, and the pollution of the atmosphere.

Rotary Motion from Static Fields

According to Whittaker’s work {10,13}, a “static” EM field is actually comprised of a multitude of internal EM longitudinal wave energy flows. What we calculate and call the “static field” is only the observed point intensity of the sum of those flows at a point. That intensity is a fixed value only for a given type of intercepting unit charged particle and its given type of reaction. Since so-called static fields actually are steady state dynamic flow systems, it follows that rotary motion can be obtained by asymmetries produced by sets of receiving circuits, objects, or particles in a static field.

This is experimentally verified by the important Coulomb motor work of Khachatourian and Wistrom {[37]}. Three conducting spheres are suspended by torsion wires, with a fixed potential applied to one sphere and the other two spheres at different distances from the potentialized sphere. Angular rotation of the two spheres is observed, and continues until stopped by the reaction back-torquing force produced by their supporting wires. Thus, a net torque or motor effect is observed on the two spheres. When the potential is removed from the first sphere, the other two spheres are returned back to initial position by the back torque from the wires.

Obviously one could switch the potential on sphere 1 back and forth from positive to negative, with timing precisely synchronized to the spherical excursion of the two torquing spheres, and the two spheres would turn back and forth. But now the torquing excursion would be even further, since in each excursion the back torque of the wire is assisting the forward torque from the asymmetrical potential forces on each torquing sphere. In short, a motor that will do useful back-and-forth reciprocating work on a load can be constructed, where the only energy required is the switching energy. In such a system, the motor will continually perform useful to and fro work, proving that the static potential does furnish flowing input energy.

Conservation of energy is not violated, since—other than a tiny switching cost—the energy is furnished work-free by free asymmetrical regauging {[38]}.

Some Energy Ramifications

The flow of potential (or the transfer of Poynting energy flow) is mere energy transfer, which is work-free. What does require work is when the input of excess energy has to be changed in form to change the magnitude of the external parameter (the potential). Thus, inputting mechanical shaft energy to a generator does require work to be done, in order to form the magnetic field energy that is "regauged" or produced inside the generator. The work is required because the mechanical shaft energy must be changed in form. Work is rigorously involved in the change of form of energy, not necessarily in the change of magnitude of energy. When a change of magnitude of an external parameter requires work to change the form of the input energy, then work is required. When it does not require a change of form of the input energy, no work is required because that is simply free regauging.

By asymmetrically regauging the potential energy of a circuit from the static potential V of an external source dipole, any amount of EM energy W can be freely collected on charges q and utilized, by the simple but well-known equation W = Vq. Similarly, any amount of emf F can be furnished by any EM field E, according to the equation F = Eq.

How one then dissipates the freely collected potential energy W and emf F to power external loads without destroying the primary source of potential V and electric field E, is a matter of proper engineering and developing the circuitry mechanisms. It requires that the dipolar source of potential be used to only furnish potential energy flow to the external circuit, in the absence of electron current flow, and nothing else.

In short, here is the “free energy from the vacuum” principle: First potentialize the circuit statically (without current flow) with the source dipole connected and the circuit electrons “pinned”. Then switch and dissipate the collected static energy dynamically (with accompanying current flow) in the loads, but with the original source of potential disconnected.

If one uses the dipole only to furnish work-free flows of EM energy extracted from the local vacuum, the dipole will last indefinitely. From the static potential V between the ends of any nonzero dipole, as much EM energy W can be collected on charges q as is desired and cleverly arranged, by W = Vq. Simply adjust the available amount of charge q, and apply the free energy principle. There is no energy crisis after all, and never has been. Instead, there is a crisis of scientific understanding and inadequate modeling in electrical power engineering.

The great advantage of the new approach is that it now gives us the ability to use the direct mechanism by which source charges already extract energy from the vacuum. Every EM field, potential, and joule of EM energy in the universe has been and is freely extracted from the vacuum by the associated source charge(s) and their dipolarities.

The developed source charge mechanism is consistent with experiment, with quantum field theory, with particle physics, and with a corrected and extended thermodynamics. But it is inconsistent with any model—such as the classical EM model—that arbitrarily and erroneously assumes an inert vacuum and flat local spacetime.

The mechanism advances a ubiquitous and valid mechanism for extracting EM energy freely from the seething local vacuum. It proves that such extraction of useful EM energy from the vacuum is not only possible but practical and easily developed. Simply pay to make a source dipolarity once, and use it thereafter as a continuous source of energy flow and a means of furnishing static potential energy flow only, to the receiving external circuit. During potentialization of the receiving external circuit, do not permit any current to be run backward through the back emf of the dipolarity, from the ground return line to the potentialization line, since that current performs detrimental work upon the dipole charges to scatter and disperse them, destroying the dipole and cutting off the free flow of EM energy from the vacuum.

This hopefully spurs us to examine why our present circuits and power systems do not take advantage of this fundamental mechanism that is ongoing in all of them. The basic problem in electrical power systems is the ubiquitous use of the closed current loop circuit, which self-enforces Lorentz symmetrical regauging and violates the asymmetrical regauging principle required for free extraction of EM energy from the vacuum and using it to freely power external circuits. The closed current loop circuit containing the main source of potential energy also destroys that source dipolarity faster than it powers its loads.

The solution(s) to that power system problem, of course, is (are) the solution(s) to the problem of constructing and operating a circuit or EM system that does indeed comply with the principle of free energy from the vacuum (free asymmetrical regauging). That, however, is a different discussion we have already addressed at length elsewhere {[39],[40]}.



[1].  T. E. Bearden, "Giant Negentropy from the Common Dipole," Proc. Congress 2000, St. Petersburg, Russia, Vol. 1, July 2000, p. 86-98. Also published in J. New Energy 5(1), Summer 2000, p. 11-23. Also carried on and on DoE restricted website

[2].  T. E. Bearden, Energy from the Vacuum: Concepts and Principles, Cheniere Press, 2002, “Chapter 3: Giant Negentropy, Dark Energy, Spiral Galaxies and Acceleration of the Expanding Universe.” Available from

[3].  M. W. Evans, T. E. Bearden, and A. Labounsky, "The Most General Form of the Vector Potential in Electrodynamics," Found. Phys. Lett., 15(3), June 2002, p. 245-261.

[4]D. K. Sen, Fields and/or Particles, Academic Press, London and New York, 1968, p. viii.

[5]Mario Bunge, Foundations of Physics, Springer-Verlag, New York, 1967, p. 173.

[6]Bunge, ibid., p. 176.

[7]B. P. Kosyakov,  "Radiation in electrodynamics and in Yang-Mills theory," Sov. Phys. Usp. 35(2), Feb. 1992, p. 135, 141.

[8]Tom Van Flandern, “The speed of gravity – What the experiments say,” Phys. Lett. A, Vol. 250, Dec. 21, 1998, p. 8-9.

[9]Jed Z. Buchwald, From Maxwell to Microphysics, University of Chicago Press, Chicago and London, 1985, p. 44.

[10].  E. T. Whittaker, “On the Partial Differential Equations of Mathematical Physics,” Math. Ann., Vol. 57, 1903, p. 333-355. This paper has largely been ignored.

[11].  However, see Richard W. Ziolkowski, “Exact Solutions of the Wave Equation with Complex Source Locations,” J. Math. Phys., 26(4), April 1985, p. 861-863; I.M. Besieris, A.M. Shaarawi, and R.W. Ziolkowski, "A bidirectional travelling plane wave representation of exact solutions of the scalar wave equation," J. Math. Phys., 30(6), 1989, p. 806; Rod Donnelly and Richard Ziolkowski, “A Method for constructing solutions of homogeneous partial differential equation: localized waves,” Proc. Roy. Soc. Lond. A, Vol. 437, 1992, p. 673-692.

[12].  For a practical weapon application utilizing the “inner” electrodynamics, see Richard W. Ziolkowski, "Electromagnetic or Other Directed Energy Pulse Launcher," U.S. Patent No. 4,959,559, Sep. 25, 1990, assigned to the U.S. Government; — "Electromagnetic or Other Directed Energy Pulse Launcher," U.S. Patent No. 4,959,559, Feb. 23, 1993. The latter was a re-examination of the earlier 1990 patent, and it verified the first 20 claims.

[13].  E. T. Whittaker, “On an Expression of the Electromagnetic Field Due to Electrons by Means of Two Scalar Potential Functions,” Proc. Lond. Math. Soc., Series 2, Vol. 1, 1904, p. 367-372. The latter paper was orally delivered in 1903.

[14].  For an excellent overview discussion of superpotentials and related things, see Melba Phillips, “Classical Electrodynamics,” in Principles of Electrodynamics and Relativity, Vol. IV of Encyclopedia of Physics, edited by S. Flugge, Springer-Verlag, 1962.

[15]T. D. Lee, "Question of Parity Conservation in Weak Interactions," Phys. Rev., 104(1), Oct. 1, 1956, p. 254-259; T. D. Lee, Reinhard Oehme, and C. N. Yang, "Remarks on Possible Noninvariance under Time Reversal and Charge Conjugation," Phys. Rev., 106(2), 1957, p. 340-345.

[16]C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes and R. P. Hudson, "Experimental Test of Parity Conservation in Beta Decay," Phys. Rev., Vol. 105, 1957, p. 1413.

[17].  T. D. Lee, Particle Physics and Introduction to Field Theory, Harwood, New York, 1981, p. 184.

[18].  Lee, ibid., p. 826-828.

[19].  Lee, ibid., p. 826.

[20]Steven Weinberg, Dreams of a Final Theory, Vintage Books, Random House, 1993, p. 111-112.

[21]D. J. Evans and D. J. Searles, "Equilibrium microstates which generate second law violating steady states," Phys. Rev. E, Vol. 50, 1994, p. 1645-1648.

[22]G. M. Wang, E. M. Sevick, Emil Mittag, Debra J. Searles, and Denis J. Evans, "Experimental Demonstration of Violations of the Second Law of Thermodynamics for Small Systems and Short Time Scales," Phys. Rev. Lett., 89(5), 29 July 2002, 050601.

[23].  See T. E. Bearden, Energy from the Vacuum, 2002, Chapter 10: “Cold Fusion: Low Spatial-Energy Nuclear Reactions at High Time-Energy.”

[24].  Hal Fox and Mitchell Swartz, “Progress in Cold Nuclear Fusion—Meta Analysis Using an Augmented Database,” presented at ICCF-5, 1995. This paper reviewed over 3,000 papers on cold fusion and found over 600 papers from over 200 laboratories in 30 countries that had replicated or found cold fusion.

[25]D. J. Evans and Lamberto Rondoni, "Comments on the Entropy of Nonequilibrium Steady States," J. Stat. Phys., 109(3-4), Nov. 2002, p. 895-920.

[26].  Kurt Gödel, "Über formal unentscheidbare Sätze der Principa Mathematica und verwandter Systeme" ("On Formally Indeterminable Propositions of the Principia Mathematica and Related Systems”), in Monatshefte fur Mathematik und Physik, Vol. 38, 1931.  This is the publication in which Gödel's Proof first appeared, of his theorem which states that within any logical mathematical system there are propositions or questions that cannot be proved or disproved on the basis of the axioms within that system. In short, no mathematical system is complete, so neither is any theoretical mathematical model.

[27]Felix Klein, "Vergleichende Betrachtungen über neuere geometrische Forschungen," 1872. Klein's Erlanger program was initiated in 1872 to describe geometric structures in terms of their automorphism groups. It has driven much of the physics development in the twentieth century. Also see I. M. Yaglom, Felix Klein and Sophus Lie: Evolution of the Idea of Symmetry in the Nineteenth Century, Birkhäuser, Boston, MA, 1988.

[28]Michael Leyton, A Generative Theory of Shape, Springer-Verlag, Berlin, 2001.

[29]Huw Price, Time's Arrow and Archimedes' Point, Oxford University Press, 1996, paperback 1997, p. 78.

[30].  Price, ibid., p. 36.

[31].  As quoted by Dilip Kondepudi and Ilya Prigogine, Modern Thermodynamics: From Heat Engines to Dissipating Structures, Wiley, Chichester, 1998, reprinted with corrections in 1999, p. 39.

[32].  Craig F. Bohren, "How can a particle absorb more than the light incident on it?" Am. J. Phys., 51(4), Apr. 1983, p. 323-327. For confirmation, see H. Paul and R. Fischer, {Comment on “How can a particle absorb more than the light incident on it?’},” Am. J. Phys., 51(4), Apr. 1983, p. 327.

[33].  Imagine a fixed “standard” rock in a river’s flow. That “static” rock will divert a certain amount of water in streamlines around it. Now suppose the rock is moved violently back and forth at right angles to the river’s flow. Obviously it will divert more water from the same river’s flow. Similarly, greater divergence occurs around the resonant standard unit point charge than occurs when the charge is not resonant but static.

[34].  See E. R. Laithwaite, “Oliver Heaviside – establishment shaker,” Electrical Review, 211(16), Nov. 12, 1982, p. 44-45. Quoting: “Heaviside had originally written the energy flow as S = (E´H) + G, where G is a circuital flux.  Poynting had only written
S = (E´H).”

[35].  In our own work, we estimated that the extra curled or circuital energy flow component discovered by Heaviside is nominally on the order of a trillion or more times the diverged Poynting component. But in a flat or nearly flat spacetime situation, the divergence of that Heaviside circuital component is zero, so that it does not usually react with anything at all. Hence the Lorentz argument that it “has no physical significance”—which is false if the local spacetime has non-negligible curvature.

[36].  H. A. Lorentz, Vorlesungen über Theoretische Physik an der Universität Leiden, Vol. V, Die Maxwellsche Theorie (1900-1902), Akademische Verlagsgesellschaft M.B.H., Leipzig, 1931, "Die Energie im elektromagnetischen Feld," p. 179-186. Figure 25 on p. 185 shows the Lorentz concept of integrating the Poynting vector around a closed cylindrical surface surrounding a volumetric element. This is the procedure which arbitrarily selects only a small component of the energy flow associated with a circuit—specifically, the small Poynting component being diverged into the circuit to power it—and then treats that tiny component as the "entire" energy flow. Thereby Lorentz arbitrarily discarded all the extra Heaviside circuital energy transport component which is usually not diverged into the circuit conductors at all, does not interact with anything locally, and is just wasted.

[37].  Armik V. M. Khachatourian and Anders O. Wistrom, “Coulomb motor by rotation of spherical conductors via the electrostatic force,” Appl. Phys. Lett., 80(15), April 15, 2002, p. 2800-2801; — “Coulomb torque—a general theory for electrostatic forces in many-body systems,” J. Phys. A: Math. Gen., Vol. 36, 2003, p. 6495-6508. For the latter paper, a Corrigendum is published in J. Phys. A: Math. Gen., Vol. 36, 2003, p. 8359-8360.

[38].  In theory, with very efficient optically coupled switching the system could produce COP > 1.0, much like a heat pump. With a little high efficiency generator as part of the load, in theory the system could also produce a self-powering (nonequilibrium steady state) system, with a COP = ¥, powering a small load as well. We strongly stress that energy would still be conserved in all cases, and the overall efficiency x would always be
x £ 100%.

[39].  Bearden, Energy from the Vacuum, ibid., 2002. In this book we addressed some 40 different COP > 1.0 “energy from the vacuum” systems produced by scientists and inventors, and the initial theory of such systems. See also T. E. Bearden, "Extracting and Using Electromagnetic Energy from the Active Vacuum," in Modern Nonlinear Optics, Second Edition, Edited by M. W. Evans, Part 2, Wiley, New York, 2001, p. 639-698; — "Energy from the Active Vacuum: The Motionless Electromagnetic Generator," in Modern Nonlinear Optics, Second Edition, Edited by M. W. Evans, Part 2, Wiley, New York, 2001, p. 699-776; — "On Extracting Electromagnetic Energy from the Vacuum," Proc. Congress 2000, July 2000, St. Petersburg, Russia; — "Bedini's Method For Forming Negative Resistors In Batteries," Proc. Congress 2000, St. Petersburg, Russia, Vol. 1, July 2000, p. 24-38; Floyd Sweet and T. E. Bearden, "Utilizing Scalar Electromagnetics to Tap Vacuum Energy," Proc. 26th Intersoc. Energy Conversion Engineering Conf. (IECEC '91), Boston, Massachusetts, 1991, p. 370-375.

[40].  M.W. Evans, P.K. Anastasovski, T. E. Bearden et al., "The Aharonov-Bohm Effect as the Basis of Electromagnetic Energy Inherent in the Vacuum," Found. Phys. Lett., 15(6), Dec. 2002, p. 561-568; — "Runaway Solutions of the Lehnert Equations: The Possibility of Extracting Energy from the Vacuum," Optik, 111(9), 2000, p. 407-409; — "Classical Electrodynamics without the Lorentz Condition: Extracting Energy from the Vacuum," Physica Scripta, 61(5), May 2000, p. 513-517; — "Explanation of the Motionless Electromagnetic Generator by Sachs's Theory of Electrodynamics," Found. Phys. Lett., 14(4), Aug. 2001, p. 387-393; — "Explanation of the Motionless Electromagnetic Generator with O(3) Electrodynamics," Found. Phys. Lett., 14(1), Feb. 2001, p. 87-94. See also M.W. Evans, T. E. Bearden, and A. Labounsky, "The Most General Form of the Vector Potential in Electrodynamics," Found. Phys. Lett., 15(3), June 2002, p. 245-261.