“….Negative resistance or negative differential resistance is a property of electrical circuit elements composed of certain materials in which, over certain voltage ranges, current is a decreasing function of voltage. This range of voltages is known as a negative resistance region.
Some writers prefer to reserve the term negative resistance for situations in which the negatively-sloping portion of the load line passes through the origin, so that a positive absolute value of voltage is associated with a negative absolute value of current. Such a circuit must contain an energy source, and can be used as a form of amplifier. However, the use of the term negative resistance to encompass negative differential resistance is more common.
Absolute negative resistances without an external energy source cannot exist as they would violate the law of conservation of energy.”

"I assert... that for the general theory of relativity, i.e., in the case of general invariance of the Hamiltonian function, energy equations... corresponding to the energy equations in orthogonally invariant theories do not exist at all. I could even take this circumstance as the characteristic feature of the general theory of relativity." [D. Hilbert, Gottingen Nachrichten, Vol. 4, 1917, p. 21.].

"In formulating the equivalence principle, Einstein actually abandoned the idea of the gravitational field as a Faraday-Maxwell field, and this is reflected in the pseudotensorial characterization of the gravitational field that he introduced. Hilbert was the first to draw attention to the consequences of this. … Unfortunately, … Hilbert was evidently not understood by his contemporaries, since neither Einstein himself nor other physicists recognized the fact that in general relativity conservation laws for energy, momentum, and angular momentum are in principle impossible." [Logunov and Loskutov, "Nonuniqueness of the predictions of the general theory of relativity," Sov. J. Part. Nucl., 18(3), May-June 1987, p. 179.].

Penrose gives a good discussion on the situation vis a vis general relativity versus the conservation of energy law. Quoting Penrose:

“We seem to have lost those most crucial conservation laws of physics, the laws of conservation of energy and momentum!” [Penrose then adds the Killing symmetry arbitrarily, to get conservation again, whenever the Killing vector applies and gravity is separated.]. “These conservation laws hold only in a spacetime for which there is the appropriate symmetry, given by the Killing vector ĸ…. [These considerations] do not really help us in understanding what the fate of the conservation laws will be when gravity itself becomes an active player. We still have not regained our missing conservation laws of energy and momentum, when gravity enters the picture. ... This awkward-seeming fact has, since the early days of general relativity, evoked some of the strongest objections to that theory, and reasons for unease with it, as expressed by numerous physicists over the years. … in fact Einstein’s theory takes account of energy-momentum conservation in a rather sophisticated way – at least in those circumstances where such a conservation law is most needed. …Whatever energy there is in the gravitational field itself is to be excluded from having any representation…” [Roger Penrose, The Road to Reality, Alfred A. Knopf, New York, 2005, p. 457-458.]

So as can be seen, the “solution” accepted by many general relativists is to just arbitrarily toss out the gravity and gravitational energy density of spacetime in a given troublesome case, and the problem of nonconservation of energy and momentum then vanishes. In short, one must separate the spacetime itself from the fields, and then the problem is avoided! However, simply avoiding the problem itself is not solving the problem! Further, considering the neglected and unaccounted giant Heaviside energy flow always accompanying every Poynting EM energy flow, and dramatically increasing the local energy density because of that flow, the gravity effect is always at least of importance. So in general the Killing vector “solution” is nearly always untenable, and thus is unsatisfactory.

"[The total energy of the atom] depends on the bare mass and bare charge of the electron, the mass and charge that appear in the equations of the theory before we start worrying about photon emissions and reabsorptions. But free electrons as well as electrons in atoms are always emitting and reabsorbing 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 … that is infinite because it receives contributions from virtual photons of unlimited energy." [Steven Weinberg, Dreams of a Final Theory, Vintage Books, Random House, 1993, p. 109-110.].

Suddenly we see there are serious problems (flaws) in some of the basic assumptions and definitions of thermodynamics. In thermodynamics, a “closed” system is defined as a system wherein mass flow does not cross its boundaries. But energy flow across its boundaries is permitted. Well, today we know that energy and mass are the same thing. If mass is prohibited from crossing the system boundary, that is a form of energy that is not restricted from crossing the boundary. Also, an “isolated” system is defined as one in which neither energy nor mass crosses the system boundaries. Well, there exists no such system in the entire universe. Every electric charge and magnetic pole in every system is in a continual seething exchange of virtual energy and virtual mass with its local and surrounding vacuum. So suddenly that “definition” bites the dust.

"All we ever know is our models, but never the reality that may or may not exist behind the models and casts its shadow upon us who are embedded inside it. We imagine and intuit, then point the finger and wait to see which suspect for truth turns and runs. Our models may get closer and closer, but we will never reach direct perception of reality's thing-in-itself." [As given by George Zebrowski, "The holdouts," Nature, Vol. 408, 14 Dec 2000, p. 775,]

Or as put very bluntly by Silverman for charge itself:

"The theory of quantum electrodynamics provides a comprehensive and (as far as experiment has been able to confirm) correct description of the interaction of charged matter with electromagnetic fields. And yet, curiously enough, we do not know exactly what charge is, only what it does. Or, equally significantly, what it does not do." [M. P. Silverman, And Yet It Moves: Strange Systems and Subtle Questions in Physics, Cambridge University Press, Cambridge, 1993. p. 127].

This is also true of energy. E.g., quoting Nobelist Feynman:

"It is important to realize that in physics today, we have no knowledge of what energy is." [Richard P. Feynman, Robert B. Leighton, and Matthew Sands, The Feynman Lectures on Physics, Addison-Wesley, Reading, MA, Vol. 1, 1964, p. 4-2].

And the “EM force fields in space” that we study in classical electromagnetics and electrical engineering, also do not exist. There are no forces or force-free fields in space, but only in matter. So there are no electromagnetic force fields in space, but only in charged matter. Nobelist Feynman pointed this out in his three volumes of sophomore physics in 1964. Quoting Feynman:

"…the existence of the positive charge, in some sense, distorts, or creates a "condition" in space, so that when we put the negative charge in, it feels a force. This potentiality for producing a force is called an electric field." [Richard P. Feynman, Robert B. Leighton, and Matthew Sands, The Feynman Lectures on Physics, Addison-Wesley, Reading, MA, Vol. 1, 1964, p. 2-4].

"We may think of E(x, y, z, t) and B(x, y, z, t) as giving the forces that would be experienced at the time t by a charge located at (x, y, z), with the condition that placing the charge there did not disturb the positions or motion of all the other charges responsible for the fields." [ibid, vol. II, p. 1-3.]

Further, Lorentz’s symmetrization of Heaviside’s severely truncated version of Maxwell’s theory also simply tossed out all asymmetrical Maxwellian systems, and retained only symmetrical systems. This includes all systems that receive and use virtual state energy from the vacuum, and it includes the source charge, the electrical dipole, and magnetic dipole. All exhibit broken symmetry, as predicted by Lee and Yang and proved by Wu et al. in 1957.

“…the violation of symmetry arises whenever what was thought to be a non-observable turns out to be actually an observable.” [T. D. Lee, Particle Physics and Introduction to Field Theory, Harwood Academy Publishers, Chur, New York, and London, 1981, p. 181.].

In particle physics, of course the virtual state vacuum/spacetime is already considered extremely energetic and active, and of course there are interactions ongoing between any circuit (particularly its charges) and the local active vacuum/spacetime. E.g., for a few quotations:

"…curved empty space is a dynamic entity, as competent to store and carry energy as are ordinary elastic materials and electromagnetic waves." [John A. Wheeler and Seymour Tilson, "The Dynamics of Space-Time," International Science and Technology, Dec. 1963, p. 62.]

"The electromagnetic field distorts space by creating regions of greater density of energy and stress … where lines of force are more closely spaced. But energy implies mass; and mass is the source of a gravitational field which, in relativity, is identical with a curvature of space. So, in essence, the curvature in space created by the electromagnetic field is the electromagnetic field; and this curvature can in principle be detected by purely geometric measurements." [John A. Wheeler and Seymour Tilson, "The Dynamics of Space-Time," International Science and Technology, Dec. 1963, p. 72.].

"...the concept of a 'single particle' actually breaks down in relativistic quantum field theory with interactions, because the interactions between 'the particle' and the vacuum fluctuations (or virtual quanta) cannot be ignored." [I. J. R. Aitchison, "Nothing's Plenty: The Vacuum in Modern Quantum Field Theory," Contemporary Physics, 26(4), 1985, p. 357.].

In the modern thermodynamics of nonequilibrium steady state (NESS) systems there are already known areas recognized to allow violation of the old second law of equilibrium thermodynamics (the older stuff that contains also some errors). To see a list of some of these areas, see Dilip Kondepudi and Ilya Prigogine, Modern Thermodynamics: From Heat Engines to Dissipative Structures, Wiley, New York, 1998, reprinted with corrections 1999. Areas known to violate the old second law of equilibrium thermodynamics are given on p. 459. One area is strong gradients (as used in the MEG and many other systems such as Bedini’s battery-charging processes) and another is memory of materials (as used in the MEG in the nanocrystalline core materials and layered crystalline structures to invoke the Aharonov-Bohm effect). We strongly comment that these known, recognized mechanisms allow macroscopic and significant violations of the Second Law that are directly usable in real systems and circuits.

"A source of electric energy does not increase the number of free electrons in a circuit; it merely produces a concerted pressure on any aimlessly moving electrons." [Robert L. Shrader, Electronic Communication, Sixth Edn., MacMillan/McGraw-Hill, New York, NY, 1991, 1993 Imprint, p. 6.].

In other words, lowering the entropy of a system (a negative entropy operation of/on the system) is marked by an increase of the pressure or force on the Drude electron gas, and increasing the entropy of a system (a positive entropy operation of/on the system) is marked by a decrease of the pressure of force on the Drude electron gas. In the negative entropy operation, usable potential energy flows into the local vacuum, and increases the energetic exchange between charge and vacuum. In the positive entropy operation, potential energy flows away from the local vacuum, lowering the local vacuum’s energetic exchange between charge and vacuum.

Once the local vacuum is potentialized (excited), it will freely alter its ongoing interaction with the local charges to give them extra energy and power (extra “pressure”), and it will continue to do so indefinitely – including freely giving energy to additional charges brought into the exchange region – unless a depotentializing operation is subsequently done to reduce the excess potential energy of that local vacuum back to its quiescent state. But that is the operation of an asymmetrical Maxwellian system a priori. Unfortunately, in 1892 Lorentz arbitrarily symmetrized the Heaviside equations and arbitrarily discarded all asymmetrical Maxwellian systems, just to get simpler equations easier to solve. Hence he arbitrarily discarded from the model any ability to accurately describe all those Maxwellian systems where the (1) local interacting vacuum is potentialized, (2) the altered local vacuum is freely furnishing or creating excess energy (or “pressure”) to and on the circuit charges, and (3) the circuit is then using some of that excess free energy-from-the-vacuum interaction to power its loads, at least partly “for free” with excess energy that the operator did not have to pay for. Instead, the Lorentz-symmetrized equations now allow or prescribe only a “symmetrical” circuit with equal and opposite forward and back emf (electrical circuit) or with equal and opposite forward and back mmf (magnetic circuit).

(a) First, there is the source charge problem – how an ordinary charge just sits there and continuously pours out real, observable, measurable, and usable EM energy in all directions – while there is no observable energy input detectable by any known instrument. Either the outpouring of usable EM energy has to be obtained from the virtual vacuum, or else the charge freely creates all its output energy, and its associated EM fields and their energy, from nothing at all. In the latter case, that would destroy the energy conservation law and all of physics and thermodynamics along with it. So the source charge problem has been expunged from all the texts and EE curricula.

(b) Another grave anomaly is the fact that simply laying a charged capacitor on a permanent magnet, so that the E-field of the capacitor and the H-field of the magnet are at an angle – produces a true, certified “free energy machine” that steadily and continuously pours out real EM Poynting energy, without any further energy input by the operator. Again, either the energy steadily flowing is extracted from the local vacuum via the source dipolarities and their broken symmetry, or else the contraption is freely creating energy out of nothing at all. Again, this would destroy the conservation of energy law, and physics and thermodynamics along with it. E X H = S is a standard formula for S, the Poynting energy flow, and E and H may indeed be “static” fields.

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

For the reader’s clarity, we point out that a magnetic “pole” is actually a magnetic charge.

“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. …So are … fields for a rigid, stationary source frozen, or are they continually regenerated? Causality seems to require the latter.” [Tom Van Flandern, “The speed of gravity – What the experiments say,” Physics Letters A, Vol. 250, Dec. 21, 1998, p. 8-9].

Indeed, a permanent magnet in one’s hand, or a charged capacitor or electret in one’s hand, constitutes a working, operational “free energy from the seething vacuum” device, but one which only produces a rock-steady outflow of photons, continually establishing and replenishing their “static” field(s). All “static” EM fields and potentials are thus “static” in the sense of being composed of smaller parts in continual motion and replacement – like an unfrozen waterfall in the analogy advanced by Van Flandern.

"…the acceptance of a structured vacuum described by an O(3) gauge group leads directly to the existence of novel charges and currents in the vacuum. These are conserved, or Noether, currents and charges and are clearly topological in origin. They spring from the fact that the vacuum is a topological space. Four such entities emerge: [1] A topological vacuum electric charge, also proposed empirically by Lehnert et al. [2] A topological vacuum electric current, also proposed empirically by Lehnert et al. [3] A topological vacuum magnetic charge, proposed also by Barrett and Harmuth. [4] A vacuum topological magnetic current, proposed also by Barrett and Harmuth.

Each of these four objects can provide energy, which can be loosely termed 'vacuum energy': energy coming from the topology of the vacuum." [Myron W. Evans, "O(3) Electrodynamics," in Modern Nonlinear Optics, Second Edition, 3 Vols., edited by M.W. Evans, Wiley, New York, 2001, Part 1, p. 84].

We note Bo Lehnert is an important scientist in the Swiss Academy, while Harmuth and Barrett are pioneers of modern ultrawideband radar, which was considered impossible and viciously opposed when first proposed.

We nominated the source charge and dipole as concrete examples of real physical systems that do exhibit such violation.

"The truth of the second law is … a statistical, not a mathematical, truth, for it depends on the fact that the bodies we deal with consist of millions of molecules… Hence the second law of thermodynamics is continually being violated, and that to a considerable extent, in any sufficiently small group of molecules belonging to a real body." [J. C. Maxwell, “Tait's Thermodynamics II,” Nature 17, 278–280 (7 February 1878)].

See also 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.

This paper experimentally demonstrated the operation of the integrated transient fluctuation theorem, which predicts appreciable and measurable violations of the second law of thermodynamics for small systems over short time scales. Entropy consumption (production of negative entropy) is experimentally shown to occur over colloidal length and time scales, for up to two seconds and at micron size scales.