"When you change the way you look at things, the things you look at change."   —Max Planck

CONTENTS

Analysis Of Miley Data
Consequences Of Partitioning The Photon Into Its Electrical And Magnetic Vectors Upon Absorption By An Electron
Nickel Transmutation and Excess Heat Model Using Reversible Thermodynamics - The Least Action Nuclear Process (LANP) Model
Re-thinking Cold Fusion Physics: An Essay
Cold Fusion and the First Law of Thermodynamics: An Essay
Can We Explain Excess Heat Uncertainty With a Law of Physics: An Essay
The Atom's Temperature
Cold Fusion and the Three Laws of Thermodynamics
Review Of Temperature Issue And My Calculations 12/8/15
Theory of Heat I - Non-equilibrium, Non-quantum, Blackbody Radiation Equation Reveals a Second Temperature Scale
Theory of Heat II - A Model of Cell Structure and Function
Theory of Heat III - Nickel Transmutation and Excess Heat Model Using Reversible Thermodynamics

Cold Fusion and the Three
Laws of Thermodynamics

Submitted to Infinite Energy Magazine, 1/2/16
Daniel S. Szumski1
1Independent Scholar, 513 F Street, Davis, CA 95616, USA, danszumski@gmail.com

A. Introduction

The three Laws of Thermodynamics are universal. There is no process in nature, either known or unknown, that violates these sacred principles of physics, nor will there ever be one. They apply everywhere, and always; and I sincerely doubt that we will find an exception as we continue our scientific exploration of cold fusion, or its misnomer, LENR.

There is one cold fusion fact that we must be absolutely clear about. Nuclear transmutations require thermonuclear energies and temperatures. Low energy nuclear reactions cannot, and do not exist. For this reason alone, it is incumbant upon theoriticans to focus their creativity on finding the means by which nature allows these energies and temperatures to be present in a way that they remain hidden from our observation. It is my carefully considered opinion, that the coulomb barrier and all of the other anomolous behavoirs in our experiments will fall into place if we just keep our attention focused on this one fact about the cold fusion process.

There have been numerous attempts by cold fusion theorists to show how the fusion energy might occur. But in all of those cases, whether it be phonon coherance(1), massive electrons(2), or deep Dirac level electrons(3), the problem is always the same: Where does the process energy come from? And then: How is it stored in a manner that we cannot detect? We are always in this same quandry: the theories seem to require a magic step. This essay evokes the three Laws of Thermodynamics to find the way out of this dilema.

So, how do the Laws of Thermodynamics produce such uncharacteristic physics? I have endevored to put this issue into perspective in three other essays published in Infinite Energy Magazine(4,5,6). This is the final essay in that series. It addresses the question: How is the fusion energy required for nuclear transmutations accumulated in a room temperature cold fusion apparatus?

B. Modes of Energy Storage in the Cold Fusion Electrode

We will begin with the Energy Principle: Energy can neither be created or distroyed, it can only change forms. A thoughtful review finds that there are four types of energy in the cold fusion reactor: 1) Electrical energy in the electrolysis circuit, 2) Chemical free energy between chemical constituents, 3) Blackbody heat radiation, and 4) The kinetic energy of molecular motion. There is in addition, the mass constituents and their implied Einstinian energy equivelance, E = mc2.

These energy components then become initial candidates for the undefined energy storage mechanism. But it is not immediately obvious that any of them is suitable. An increase in the electrical circuit energy would be seen as higher amperage, increasing electrical resistance, and the consequent losses as waste heat to molecular motion. Increased chemical free energy would cause chemical phase redistribution, with endo- or exo-thermal heat energy shifts. Blackbody storage would raise the temperature of our device. Similarly, kinetic energy storage would be obvious as it approached thermonuclear conditions, and melts our electrodes. So, with the one exception of chemical equilibria shifts where heat storage effect is ambigous, all of the apparent energy storage modes, produce heat of kinetic motion, which if it approached thermonucear conditions, would result in something that we do not observe, a melt down.

So there must be some other way of achieving thermonuclear energy storage in a room temperature device. Let's begin our inquiry by looking more carefully at those ambigous chemical equilibria shifts. Clearly, the exo-thermal reactions are not a favorable way to store energy. But the endo-thermal process holds some promise.

Heat energy exists in two forms, each of which is described by its own equilibrium modeling framework. The first is a theory of molecular motion in a gas which bears the revered names of Maxwell and Boltzman. It relates the heat energy of molecular motion to the system's thermodynamic temperature. Then, in an entirely independent theory, Planck relates the energy of radiant heat, again, to the temperature. However, there is no connection between these two modeling frameworks even though we know that they continually exchange heat, always moving a thermodynamic system to a mutual temperature equilibrium, and a lowest entropy state.

When chemical equilibria shifts occur, a system's chemical constituents and its free energy (radiation domain heat energy) become redistributed into a new lowest entropy state in accordance with the Second Law, and in all irreversible thermodynamic displacements, some of the systems free energy is lost to heat of motion. That lost heat resides in the more primitive of the two heat forms, and it can never be reintroduced so as to reconstruct the previous energy/entropy state.

Nevertheless, it is possible to reverse the direction of an irreversible process by introducing some sort of thermodynamic work. But, when the work is stopped, the process will reverse direction again, and return to its lowest entropy state.

Ilya Prigogine(7) studied these out-of-equilibrium processes, and coined the term 'dissipative structure' to describe a displacement of state, to a non-equilibrium condition, from which there is no return to the previous state. Such a process decreases the system's entropy, and might serve as a basis for models of neg-entropic or far-from-equilibrium transitions similar to those that we see in F&P experiments. In fact, there is already a precedent in cold fusion science for dissipative structures. Hydrogen uptake by a metal hydride lattice is a reversible thermodynamic process exhibiting the disipative structure's characteristics. Hydrogen nucleii are absorbed into the metal lattice structure, and stored there in a stable, far-from-equilibrium manner. Let's see how this might further our understandng of the cold fusion process.

So what is it that locks hydrogen nucleii in the metal lattice, preventing their return to the aqueous phase? The hydrogen nucleus posessed kinetic energy that is no longer apparent once it is absorbed into the metal lattice. Let's for argument's sake, assume that the metal lattice is so large that it has no measurable kinetic energy relative to the tiny proton or deuteron. Let's also assume, that in accordance with the First Law, the proton's initial kinetic energy is completely transferred to the metal lattice. Remember, this is heat energy of molecular motion that is being transferred. Finally, we will assume that the coordinated electrons in the lattice's metal bonds are able to absorbe this energy and store it in accordance with the QED definition of a covalent bond; as electromagnetic energy that is continually exchanged between covalent electrons. The reversible process framework allows this kind of transference to a different type of energy. At the same time, each new deuteron that is ‘quieted', adds to the radiation domain energy stored as covalent bond energy, thereby moving the radiation domain energy storage one more step away from equilibrium. Later in the loading process, resonant sharing of gamma photons between covalent nucleii facilitates energy storage( ).

Do you see the working of a disipative structure in this process? The initial kinetic energy is absorbed into the covalent bond structure of the metal lattice where it is stored as radiation domain energy between electrons. This traps it in a stable far-from-equilibrium state, a chemical bond. Furthermore, this is an endo-thermol process, absorbing heat energy of molecular motion from the electrodes surroundings. At the same time, the proton is prevented from moving back into the aqueous phase because, in doing so, it would have to re-aquire its temperature dependent thermal energy, which we might generalize as kBT.

C. A New, Non-equilibrium Theory of Heat

I have proposed elsewhere (8) a non-equilibrium theory of heat that allows us to follow heat exchange between the radiation and molecular motion domains. But more important for our purposes here, it allows us to quantify their far-from-equilibrium separation. This theory contains two temperatures; one for the mass domain (Tm) and another for the radiation domain (TR). These can be separated in a very far-from-equilibrium way as shown in Figure 1. For example, mass domain heating alone, by friction for example, causes the black body spectral curve to move vertically, while radiation domain heating alone moves the spectral curve to the right, but at the same thermodynamic (mass domain) temperature. A normal irreversible heat process causes the curve to move in both directions. A discussion of this theory is contained in (8).

So there are three types of heating that can take place in nature: power accumulation in the mass and radiation domains simultaneously, the normal case, and two far-from-equilibrium heat storage cases. We are now poised to return to the cold fusion question that brought us to this point: How can the cold fusion process accumulate thermonuclear energies in a laboratory temperature device?

I would like to propose that the answer can be found by contrasting the efficiencies of these modes of heating, but with particular reference to the efficiency of radiation domain heating alone. This is most easily seen in Figure 1, which shows the log-log spectral distribution of power emittance for two thermal equilibrium conditions: 300°K and 105 °K, and two very far-from-equilibrium conditions. I want to draw your attention to the two curves at the right hand side of the figure where an equilibrium blackbody at 105 °K is compared to the non-equilibrium case where the thermodynamic temperature remains at a laboratory temperature of 300°K, while the radiation temperature rises to 105 °K. In both cases the effective temperature is 105 °K, but the upper curve's equilibrium representation requires a total power (area beneath the curves) more than two orders of magnitude greater that the far-from-equilibrium condition. In other words, more than 99% of the irreversible process' energy storage is tied up in molecular motion. And yet, the effective free energy available in both cases, the radiation domain energy, is the same. Do you see how radiation domain energy storage is an incredibly efficient way to store free energy?

But there is a more important point to be made here that will be the subject of this paper's next section. In particular, this condition where energy is stored exclusively as radiation domain power, describes the operating conditions for processes that take place at the very limit of the Second Law, where entropy production ceases and the operative thermodynamics are exclusively those of reversible processes.

This is the place where a chemical process in state A, can proceed to state B, but with no loss of process energy to heat of motion. In fact kinetic motion is foreign to the reversible thermodynamic processes, unless, and this is important, it occurs in amounts that are so small that they do not impact the reversble process state in any way. We will revisit this constraint later, when we consider the Third Law of Thermodynamics.

If we now continue along this same line of thought, we find that the reversible process domain is the one place in physical theory where the reservoirs of radiant heat energy and heat of molecular motion have no interaction. Kinetic movement is always an entropic process, and therefore foreign to the reversible process domain. This means that the reversible chemical process describing the transition from State A to State B proceeds without any loss of energy to heat of motion, and at least in theory, the chemical equilibria can shift from state B, back to State A, again, without energy loss or entropy increase, and, this forward and backward chemical shift can recurr indefinitely. Do you see the fundamentals of a covalent chemical bond in this description?

This is the domain of the reversible themodynamic process. It is a 'neverland' that we are taught does not exist, and yet it is the only path out of the cold fusion theory dilema. Furthermore, there is nothing in the laws of physics that precludes this adventure. Indeed, if you carefully critique this presentation, there is no place where it conflicts with experimental evidence or the laws of physics. It is merely an extension of our understanding beyond the current paradygms.

D. The Reversible Thermodynamic Process in Nature

Let's begin at the beginning. Metal hydrides load at standard conditions in what is known to be a reversible thermodynamic process. These are processes that operate at the very limit of the Second Law of thermodynamics, where there is no energy loss, and the process produces no entropy increase. Another way of viewing the reversible thermodynamic process is that as a result of its operation, there remains no outstanding change in nature.

In fact, it is not possible to view the fundamentals of a reversible thermodynamic process because there is quite simply nothing to look at. There is no energy or matter coming off the process, not even light. These 'visuals' or 'detectables' would be losses from the process, and by definition it would no longer be a reversible process. Thus, the reversible thermodynamic process is essentially hidden from our observation by its very fundamentals.

These processes are generally understood to be only an idealized curiosity in physics, that does not exist in the real world. But if we think about it, our experience can recall several common processes that appear to meet our criteria for thermodynamically reversible.

For instance, an atom exhibits all of the reversible thermodynamic characteristics. Its nucleus and electron configuration can remain intact without energy losses or entropy increase for billions of years. The work that the atomic process accomplishes is the stable atomic form. There is one fundamentally important observation that I want you to be clear about in this and all other reversible processes that we will be referencing. It is the absence of any kinetic energy or mass domain events in the reversible thermodynamic process itself. So while the atom may exhibit kinetic behavior, the reversible process that holds it together lies entirely in the radiation domain without recourse to any form of internal thermal motion.

A second example is found in the chemical bond of two or more atoms in a stable molecular form, for example, H2. The covalent bond structure of the molecule is a reversible thermodynamic process that can remain fixed for billions of years with no energy loss or entropy increase. There may be thermal motion of the atomic costituents relative to one another, or kinetic movement of the molecule as a whole, but the internal mechanism, the operative reversible thermodynamic process, exists entirely within the radiation domain. For our purposes, we will view the dynamics of the chemical bond in accordance with QED as the continual exchange of a single photon between two electrons, without energy loss or entropy increase.

Now, I know that this definition of a chemical bond is not exactly that of QED, quantum mechanics, density function models, or emperical models of how chemical bonding works. But, this way of looking at new physics: that it should conform to only what is known (the current paradygm), is counter productive, particularly in cold fusion theory development. We have simply run out of traditional theoretical frameworks to address the anomolous physics seen in our experiments. If we are to advance our understanding of physics, we need to instead ask: Is this new or different concept inconsistent with the physics and experimental results that we are aware of? If the answer is no, some sort of tentative or provisional acceptance should be possible, at least untill we see where this nuance takes our understanding of physical principles.

A third example is a photon traveling through the vaccum of space. It exhibits no energy loss or entropy increase. And although it may possess kinetic energy, the photon itself conserves its internal electrical and magnetic energies in accordance with Maxwell's equations, and therefore without internal kinetic energy.

Our fourth example is the reversible process known as Mossbauer resonance(9). Mossbauer found that gamma photons could under certain conditions be absorbed by atomic nucelii that are bound in a metal lattice, and then be re-emitted without loss of energy or entropy increase. The absorbtion and emission processes were thus, thermodynamically reversible. Similar behavior had previously been observed for x-rays in gasses. Now, I understand that Mossbauer never considered the dynamic state wherein a single gamma photon is continually exchanged between two nucleii. But this behavior is not inconsistent with known physical principles, and lends itself to an understanding of energy storage that will prove usefull to our hypothesis of energy accumulation and storage in the cold fusion process.

The last example that I want to bring to your attention was referenced earlier: the loading of a metal hydride lattice with hydrogen or deiterium. It occurs without energy change or entropy increase. But I want you to see how this process is different than the other reversible thermodynamic processes cited above. It includes a kinetic energy component, the deuteron motion, which is followed by a step that is more like the reversible processes above: the transformation of that kinetic energy to radiation domain energy. So let's take a more careful look at the partitioning of the deuteron absorption process.

E. The Thermodynamics of Energy Accumulation

So what energy does the deuteron possess. There are two kinds. It certainly has kinetic energy, 12, and it also has its mass/energy equivelant, E = mc2. At laboratory temperature, only the first of these is accessible. We can then contrast the deuteron's kinetic energy with that of the massive metal hydride lattice where there is virtually no kinetic enegy present. At the instant when absorption takes place, the kinetic energy of the deuteron becomes identically zero, but as a consequence of the First Law, the energy is not lost. It is absorbed into the metal lattice structure. And because this process is thermodynamically reversible, the second law requires that the entropy change in the deuteron/lattice complex be zero.

We will begin by recognizing that we are dealing with two thermodynamic systems, not one. One of these exists entirely within the mass domain, where we will be looking at thermodynamic variations resulting from a change in free energy. The free energy/entropy relatonship in the mass domain is given by:

(1a)     Fm = Em – TmSm
(1b)     dFm = dEm – d(TmSm)
(1c)     dFm – dEm =  –TmdSm – SmdTm

and it is characterized by: Tm the thermodynamic temperature,
Fm its Helmholtz free energy,
Sm its entropy, and
Em its total energy.

We use the Helmholt free energy because the process that we hope to analyse is thermodynamically reversible, and the Gibbs free energy form is inappropriate to that case.

A second thermodynamic system is wholly contained within what I have refered to as the radiation domain. It is characterized by the same four quantities.

(2)     dFR – dER =  –TRdSR – SRdTR
The deuteron absorption process captures the deuteron's kinetic energy from within the mass domain, and absorbs it into the metal hydride lattice where it will be stored as radiation domain energy, and more specifically we will assume that it is stored as electromagnetic bond energy (10).

There are only six unknown differentials in this system of equations. This is so, because the change in both Helmholtz free energy quantities is identically zero. Our process is thermodynamically reversible.

Deuteron absorption into the metal lattice results in a decrease in the mass system's total energy by , the deuteron's kinetic energy, while the radiation domain acquires that energy equivalent.

Moving on to the temperature changes in the mass and radiation domains, we recall that the mass domain's temperature is defined entirely by the kinetic energy of the mass system. So when the deuteron's kinetic energy goes to zero there is an infinitesimal decrease in the mass domain temperature. At that same instant in time, the radiation domain's temperature increases because a single quantum is added to the electrodes internal spectral emittance. We can now calculate the entropy changes.

The molecular motion that specifies the mass domain's temperature is more accurately described as the rate of kinetic energy exchange between molecular quantities. And because temperature is a derivative, it is the rate at which kinetic energy is increased and simultaneously decreased within the F&P cell's deuterium phase. At equilibrium, the total amount of kinetic energy being lost to collisions equals the amount being gained in those same collisions, and there exists an equilibrium between the mass and radiation domain's energy content.

This equilibrium is upset by deuteron absorption into the metal hydride lattice. In particular, as the deuteron is 'quieted,' there is an infinitesimal decrease in the rate at which kinetic energy is being restored to the mass domain, and the deuteron phase takes a negative kinetic energy step. Some of the mass domain's heat has been lost, Qm is negative, and the entropy of the mass domain increases.

(3)     eq 3
When this same energy appears in the radiation domain as a positive change in the rate of radiation emittance and absorption, the radiation domain entropy decreases by that same infinitesimal amount. Nota bene: the non-differential temperature and entropy quantities in both the mass and radiation domains are always positive numbers.

eqs

So, the radiation domain is slightly more organized, taking one small step away from equilibrium. Do you see how the net effect of deuterium absorption into the metal hydride lattice, is in essence, harvesting energy and neg-entropy(10) from the domain of random molecular motion where the entropy increases, and converting it to an entropy decrease, and radiation domain storage of useful free energy that will ultimately be used for thermo-nuclear transmutations.

In reference (10), I go through the calculations that show the deuteron's initial kinetic energy to be about 7.x10-22 ergs, and that absorption of enough deuterons to fill the surface sites on Fleischmann and Ponn's original experimental electrode would require about deuterons, or enough energy transferred to the electrode (1.35MeV) for ignition of deuterium-deuterium fusion. In effect, the reversible process responsible for electrode loading (say 30 days) has harvested heat of molecular motion from about a billion (3.8x108) deuterons per second to achieve the fusion ignition temperature.

I want you to note that this might explain the very long loading times in Fleischmann-Ponns experiments. The ignition requirement is satisfied in 1015 deuteron absorption steps having extremely small energy increments (in the radio frequency range), and infinitesmal but discrete temporal increments (reversible process steps are sequential).

F. The Third Law's Relevance

Our quest has now brought us to the Third Law of Thermodynamics: The entropy change associated with any condensed system undergoing a reversible isothermal process approaches zero as the temperature at which it is performed approaches 0 °K. This Law appears to be telling us that the thermodynamic temperature, Tm, must go to zero degrees Kelvin for a reversible thermodynamic process to occur. But this is not true. The Third Law acually provides a reference point for the determination of entropy at any other temperature. "The entropy of a system, determined relative to this zero point, is then the absolute entropy of that system (11)."

(4)     eq 4

Where: S and S0 are the system entropy and the reference entropy respectively,
kb is Boltzmann's constant, and
alpha is the number of accessible micro-states that the process can advance to.

Do you see how it is not necessary that the temperature, and with it the entropy go to zero, but rather, it is a sufficient condition that the entropy difference, relative to the reference entropy, goes to zero. This is, by definition, a reversible thermodynamic process. "Hence the initial entropy, S0, can be any selected value so long as all other calculations (of the action) include that as the initial entropy(11)."

I want to now complete our earlier discussion of the Second Law with one final point that becomes relevant here. In all reversible thermodynamic processes, every next step is exactly and unambigously determined by the Principle of Least Action. Thus, the number of accessible micro-states, alpha, at any time is identically 1, and the identity in equation (4) is always true for the reversible process. Thus, we say that the reversible thermodynamic process is absolutely deterministic, with no reference to the kinds of probalistic outcomes that characterize the Second Law's irreversible thermodynamic processes.

Now, let's go back to Figure 1 to see what the Third Law is telling us about the cold fusion process. We will recall that heat is made up of two different processes each existing within its own thermodynamic domain.

The first process is that occuring in the material world, or the mass domain. It contains a certain amount of kinetic energy by virtue of the sensible temperature of the cold fusion device, Tm. This is the thermodynamic temperature. It defines the reference state, S0, the absolute entropy state of the cold fusion electrode as that prior to every next step in the reversible process. It is the entropy of the mass domain system, Sm, that must remain constant, ensuring that the difference, Sm – S0, remains null during that step. But, because there is no increase in the system's entropy, Sm, there can be no decrease in the thermodynamic temperature, Tm, of the overall cold fusion process. And this conflicts with the thermodynamic analysis in Section E above, where at the micro-scale, the thermodynamic temperature decreased an infinitesmal amount. However, if we are clever we will see the way out of this conflict.

What does Sm – S0 = 0 really mean? The earlier thermodynamic analysis indicated an infinitesmal decrease in the mass domain's temperature as a deuteron is absorbed. But, we now find that there can be no decrease in Tm. So, if Sm – S0 is to remain null, there appears to be an allowable departure from the mass domain's absolute entropy state, a very small entropy quantity:

(5)     eq 5

that must be restored continually to satisfy the reversible process constraint that (Sm – S0 = 0) remains essentially zero. I don't know what this limit is, but I do know that it sets the maximum energy increment that can be absorbed in a single deuteron absorption step, thereby limiting energy harvesting to small kinetic energy increments that are, at least according to this theory, in the RF range. It is, I believe this small increment that will help define operating conditions for commercial cold fusion devices such as the elevated temperature and pressure device that Brillouin Energy is developing.

Furthermore, this observation also shows how the cold fusion process fails the test for a perpetual motion machine. In particular, the decrement in kinetic energy must be restored after every process step. This heat can be derived from the electrical current in the electrode, and even by recycling heat from the nuclear process. Its speed is the speed of light.

I have identified a second place where a similarly small energy quantity needs to be computed. In particular, there is a limit to the velocity at which hydrogen nucleii can move from their absorption site into deeper lattice locations. This energy too, needs to be below a permissible threashhold. I don't know what this threashhold is, or if it might impact design criteria for a cold fusion prototype.

Finally, regarding the second thermodynamic system, denoted by the temperature, TR. The radiation and mass domains normally exchange heat energy, always seeking an equilibrium state where TR = Tm. However, because the mass and radiation thermodynamic systems are separate within the context of the reversible thermodynamic process, it becomes possible to increase the radiation domain's free energy storage while holding the mass domains energy constant. In this way the two can be separated in both their energy content, and their entropy state in a very far-from-equilibrium way. More importantly for our purposes, if we store the radiation domain energy as chemical bonds, it becomes possible to make this separation stable even as the two thermodynamic systems move to a very far-from-equilibrium separation. Thermonuclear energies and temperatures become possible when photon energy storage between covalent electrons makes a transition to resonant, gamma photon, storage between Mossbauer resonant nucleii, and ultimately, the ignition energy for nuclear transmutations. This far-from-equilibrium state was the subject of my paper at ICCF-19(12), where I discuss the atom's temperature, and its consequences to a theory for overcoming the coulomb barrier.

G. References

  1. Hagelstein, P. L., "Bird's Eye View of Phonon Models for Excess Heat in the Fleischmann-Pons Experiment", J. Condensed Matter Nucl. Sci. 6, (2012) 169-180.
  2. Widom, A, Larsen, L, "Ultra Low Momentum Neutron Catalyzed Nuclear Reactions on Metallic Hydride Surfaces", European Physical Journal C - Particles and Fields, Vol. 46(1) (2006), 107-110.
  3. Muelenberg, A., Sinha, K.P., "Deep-electron Orbits in Cold Fusion", J. Condensed Matter Nucl. Sci. 13 (2014) 368-377
  4. Szumski, D. S., "Rethinking Cold Fusion Physics", Infinite Energy, 20, 120, 2015.
  5. Szumski, D. S., "Cold Fusion and the First Law of Thermodynamics", Infinite Energy, 20,122, 2015.
  6. Szumski, D. S., "Can We Explain Excess Heat Uncertainty with a Law of Physics - An Essay", Accepted by Infinite Energy, 21,128, 2015. (available at ww.leastactionnuclearprocess.com)
  7. Prigogine, I., Self-Organization in Non-Equilibrium Systems, Wiley, 1977.
  8. Szumski, D.S., "Consequences of Partitioning the Photon into its Electrical and Magnetic Vectors upon Absorption by an Electron", In the Nature of Light: What are Photons? V. Chandrasekhar Roychoudhuri; Al F. Kracklauer; Hans De Raedt, editors, Proceedings of SPIE Vol 8832 (SPIE, Bellingham, WA), 883201, 2013.
  9. Mossbauer, R. L., Recoilless Nuclear Resonance Absorption of Gamma Radiation", Nobel Lecture, December 11, 1961.
  10. Szumski, D.S., "Nickel Transmutation and Excess Heat Model Using Reversible Thermodynamics", J. Condensed Matter Nucl. Sci. 13, 554-564, 2014.
  11. 'Third law of thermodynamics' in Wikipedia, Retrieved 11/15 from http://en.wikipedia.org.
  12. Szumski, D.S., "The Atom's Temperature", submitted to J. Condensed Matter Nucl. Sci.