The Atom's Temperature
Presented at ICCF-19, submitted to J. Cond Matter Nuclear Sci.
Daniel S. Szumski1
1Independent Scholar, 513 F Street, Davis, CA 95616, USA, firstname.lastname@example.org
Temperature is a derivative. By convention(1) it is the rate of radiation emittance from any material body
expressed either as J/t, or more practically, J/m2-t. It is uniquely defined by a temperature-specific, equilibrium
blackbody spectrum, which is identical in the interior of all material bodies at the same temperature, regardless
of their composition, and as we will see, regardless of their size. Max Planck's theory(1) of the blackbody's
equilibrium spectra, introduced the quantum into physics.
Temperature also has foundations in molecular motion. It was Helmholtz's great contribution to physics that
heat reduces to motion. Planck(2) places this understanding on an equal footing with James Clerk Maxwell's treatment
of light as electromagnetic waves. The Maxwell-Boltzmann equation (3,4) for an ideal gas's molecular velocity
distribution expresses this theory's fundamentals.
While there has been theoretical consideration of the relationship between these heat theories(see (5)), the only
theoretical framework relating the two in a quantitative way, is a model containing two temperatures(5), one for the
radiation domain, and another for the domain of molecular motion, or what I will call the mass domain. This
non-equilibrium heat theory recognizes heat transfer between the mass and radiation domains, and is elegant in the
way that the two temperatures can be separated in a far-from-equilibrium manner. The theory's principle shortcoming
is a small, but real departure from Planck's theory when the two temperatures are at equilibrium. It is possible that
this difference might itself be a fundamental element of heat theory.
The foundations of temperature as a measure of heat content lie in the probabilistic domain of statistical
mechanics. In Planck's radiation form, the equilibrium state's statistics are derived from the energy distribution
of harmonic oscillators; while in the mass domain, it is the statistical distribution of molecular velocity in an
ideal gas which is distributed according to the Maxwell distribution(3). Because these laws are statistical, there
should be limits to their validity as the number of participating energy units decreases. Here we will consider the
limiting case where the statistical foundations of the Second Law transition from probabilistic to wholly
deterministic. It is in this limit, that we will enter the domain of the thermodynamically reversible process.
B. The Photon's Irreversible and Reversible States
Our quest for the atom's temperature begins with an understanding of the photon, and in particular, the two
mechanistic pathways accessible for its evolution in the presence of an electron(5). This theory of photon
absorption is the first of two elements of new science required by the Least Action Nuclear Process model of cold
Photon absorption is considered to be a two step process. In the first step, the photon is wholly absorbed into
the electron but retains its identity as a reversible process. In the second absorption step, the photon evolves
into the electron's three dimensions. The electrical and magnetic components decouple, and the electrical vector
evolves to three-dimensional charge (with its dielectric loss), and as a consequence, enters the domain of
irreversible thermodynamics. The magnetic vector on the other hand has no three-dimensional equivalent, remains
one-dimensional, and contributes to the electrons one-dimensional para-magnetic spin. This asymmetrical evolution
from one dimension to three, distorts the space/time fabric, giving rise to the characteristic blackbody emittance
However, there is nothing requiring that the absorbed photon evolves into three dimensions. Consider the
possibility that it is immediately re-emitted in precisely the state that had only undergone that first step of
photon absorption. The emitted photon is still 1-D, and remains in its reversible thermodynamic state. But let's
go one step further and allow this emitted photon to undergo first step absorption by a second electron…and then be
re-emitted still as 1-D, and re-absorbed by the first electron, and so on. We have just arrived at the quantum
electro-dynamic description of a covalent bond(6). Its photon energy is locked between two electrons, and remains
unchanged indefinitely. This view of the covalent bond allows us to assign it a definite energy, while allowing
for a broad range of energy conditions where either of these atoms is covalently paired with a different atom, or
in a different molecular structure.
First, note how this resonant bond is a wholly reversible thermodynamic quantity, existing without any losses,
and with no change in its entropy condition. The effective distance between these covalent electrons is the shared
photon's wave length. Secondly, this model describes the permanence of the bond. It is this stability of the
covalent bond that gives it the very special place in the energy structure of biological and chemical molecular
C. Temperature of the Irreversible Thermodynamic Process
The area beneath any of the temperature curves described by Planck's blackbody
radiation spectra (Figure 2) uniquely defines a specific temperature:
where K(v) is the blackbody spectral emittance; the factor
is the conversion factor: per
m2; and the statistical representation in Equation (1) includes both
radiation domain heat energy, and heat of molecular motion. The temperature measurement is independent
of the material's composition, and as it turns out, it is also independent of its size.
Figure 1- Planck's equilibrium blackbody spectral curves, illustrating the types of photonic
interaction required of harmonic oscillators across the spectrum.
Before going further in our understanding of how this irreversible process definition of temperature might
differ from that of the reversible thermodynamic state, I need to divert your attention to a conundrum that arises
in the contemporary interpretation of Planck's equilibrium blackbody theory, and which is central to what is to
follow. In particular, the range of Planck oscillator energies in Figure 1 is far beyond the normal range for
electron absorption and emission. It extends into the X-ray and gamma portions of the spectrum where the oscillator
energies can no longer be emitted by, or transferred between, electrons. Muelenberg( 7) has pointed out that this
spectral continuum has to include intermediate energy exchanges that can only occur between higher energy electrons,
probably extending to Deep Dirac Level (DDL) s-shell electrons. Szumski(8) has proposed a further extension of this
continuum to Mossbauer resonant nuclear bonds, extending into the gamma range shown in Figure 1, and possibly into
the far-gamma range. In these Mossbauer resonant bonds, gamma energy photons are emitted by lattice nuclei, and
absorbed by its 'covalent' nuclei, then emitted by that nuclei, and absorbed by the original nuclei, and so on. As
in the covalent bond case, this process is thermodynamically reversible, conserves energy, and functions without
entropy change. What resonant electron and resonant nuclear bonding might look like over the blackbody spectrum's
frequency range is shown at the top of Figure 1.
Do you see how these spectra necessitate an energy continuum from very low energy electron transitions, through
what can only be described as nuclear energy transitions, or in this theory's terminology, nuclear resonant bonding.
The validity of these curves is well established over this temperature range.
One final point in this regard. My calculations of Widom-Larsen's(9) 'heavy electrons' finds electron masses more
than double those of 'standard model' electrons. These turn out to be equivalent to the mass-plus-energy of
Muelenberg's(10) DDL electrons, which is a much more satisfying way of looking at the Widom-Larsen model's
D. Temperature of the Reversible Thermodynamic Process
My purpose here is to discuss the temperature sub-model of the Least Action Nuclear Process theory of cold fusion.
The discussion begins by noting that nuclear transmutations are routinely observed in cold fusion experiments. This
implies that the cold fusion process probably includes thermonuclear temperatures, and the associated thermal energy.
But we see neither temperatures in this range, nor fusion energies in our experiments. This doesn't make sense.
These are thermodynamic processes that are temperature and energy dependent. As such, it is essential that we
understand how the required thermonuclear temperatures are masked from our observation in these room temperature
So, how is temperature measured in a reversible thermodynamic process? It has to be fundamentally different than
the temperature of an irreversible thermodynamic process, wherein heat energy storage is partitioned between the mass
and radiation domains, and the process is of a statistical nature. In the reversible process, there is no kinetic
energy, and therefore, no mass domain energy storage. In fact, heat energy, or at least that portion that is
accessible from the reversible process reaction space, is limited exclusively to the radiation domain. The motion of
material particles, and the statistical uncertainty that it introduces, is foreign to reversible thermodynamics.
We will begin our inquiry by affirming that our focus on a reversible thermodynamic
process does not change our definition of temperature. It is still the derivative expressing the total radiant
emittance from a mass particle per unit time. Either of the covalent electron's discussed above, exhibit a
temperature that is proportional to its emittance, K(v) measured as the photon energy, hv, times
the frequency, v, of the individual emissions, but with the emittance of either electron occupying only one
half of the process time. Therefore:
And, for nuclei in Mossbauer resonance:
Equations (2) and (3) are infinitesimal subsets of Equation (1). This treatment of nuclei in Mossbauer resonance
is the second element of new science in the Least Action Nuclear Process modeling framework.
There are several important observations in this result. First, while Equations (2) and (3) are precise
definitions, they can be misleading. The energy quanta involved in these temperature definitions cannot exist
without a very structured antecedent spectral distribution that has to be filled before these quanta can exist [see
Figure 2]. In this Theory of Heat the distribution of reversible process energy accumulates sequentially as
TR increases, while Tm remains constant. In the illustration,
Tm equals 300 °K as TR increases in quantum increments from
300 °K to 107 °K. There is nothing in this theory's fundamentals which
precludes solar core, and even stellar nucleosynthesis temperatures between Mossbauer resonant nuclei. This is
indeed, a requirement if the transmutation measurements of Mizuno (11) and Miley (12) are to be believed.
Figure 2- Far-from-equilibrium blackbody spectral distribution for the reversible thermodynamic
process in a Fleischmann-Pons cell, wherein all of the energy storage is in the radiation domain. Note the five order
of magnitude difference between the cold fusion process and the Tokamak.
Secondly, the energy difference required to affect equivalent temperatures in a reversible and irreversible
process is almost unbelievable. Consider the solar core temperatures for these processes shown in Figure 3. The
irreversible thermodynamic process requires five orders of magnitude more energy than the reversible process.
Coincidentally, this is the observed difference in energy requirements for fusion in the Tokomak, and in our cold
Third, we note that this efficiency in the reversible process arises only because it by-passes the enormous
kinetic energy requirements of the irreversible process. In other words, there is a dynamic equilibrium existing in
all irreversible processes, between radiation and mass domain energy storage. In effect, the irreversible process
drags around a lot of kinetic energy in order to produce an equivalent free energy (i.e. radiation domain) condition.
Cold fusion exploits this advantage.
And finally, the improbable nature of this energy accumulation is dramatically demonstrated when we consider how
the radiation domain energy in the metal lattice is accumulated(8). It is the waste heat of random deuterium motion
that is harvested (in radio frequency quantum amounts) into the metal hydride lattice, and stored there as resonant
bond energy. This flux of chemical (and nuclear) free energy into the lattice creates resonant photons having
ever-increasing energy storage. This is the LANP model's forcing function. In effect, the continuous influx of
these low energy quanta adds to the far-from-equilibrium energy storage until energies sufficient for nuclear
ignition occur. Then energy accumulation continues, establishing ever increasing process energy, that causes a
sequence of stepwise nuclear transmutations, always occurring in an order exactly specified by the Principle
of Least Action(5).
E. Consequences of Thermonuclear Temperatures
It now becomes informative to inquire: what consequence results from this theory of the atom's temperature?
Remember how we placed our covalent electrons close enough that they shared a single photon. When we do the same
with two nuclei in Mossbauer resonance two things happen. First, the electromagnetic force increases in proportion
to the increase in , thereby decreasing , and drawing the nuclei closer together. Do you see, in Figure 8, how the
electro-magnetic force increases to energy levels that could become operative in overcoming the coulomb barrier in
the cold fusion process?
Simultaneously, the inter-nuclei temperature rises in proportion to v2, achieving thermonuclear temperatures in a
stable far-from-equilibrium manner. As these two conditions converge on impending fusion/fission, this dissipative
structure "exploits an instability in the normal thermodynamics (an extraordinarily high reservoir of free energy),
causing a branch to what would otherwise be an inaccessible thermodynamic state." (nuclear fusion/ fission) .
These temperatures must rise to extraordinary levels, if the nuclear products in Miley's and Mizuno's data are to
Finally, I want you to clearly see how both the energy storage for nuclear transmutations, and the lattice
temperatures, are localized between sub-atomic particles, and in this way, hidden from our observation. This is
consistent with what we see in our experiments. More importantly, it is consistent with the fundamental tenant of
physics: nuclear transmutations require both thermonuclear temperatures and thermonuclear energies. Low Energy
Nuclear Reactions and similar representations of the cold fusion process are a misnomer. Cold fusion is indeed very
Finally, this model element appears to offer explanations for certain mechanical properties observed in cold
fusion experiments. For instance, we might expect that the tightening at the surface of the metal hydride lattice
would increase its surface hardness and tensile strength. This appears to be born out by measurement. Furthermore,
the surface cracking in electrodes could now be explained as the result of competition between dramatically
increased surface tension due to decreasing lattice distances in near surface layers, and the uneffected bulk of
F. Covalent Bonds, and a Lesson from the History of Science
All covalent bonds possess a very specific energy, and according to the theory developed in this paper, exhibit
a specific temperature. It is proposed that the same energy relationships could also hold for Mossbauer resonant
bonds between nuclei. In both cases, the bond is characterized as a shared photon operating as a reversible
thermodynamic process, and at an effective distance of one wavelength. The force that facilitates these bonds is
the electro-magnetic force, one of two forces in nature that holds up under careful scrutiny. The other is
The presence of extraordinary temperatures in these bonds is more speculative. The only evidence lies in the
transmutation products measured in post-electrolysis cathodes. That these products could only have formed at
nucleosynthesis temperatures is a compelling argument. And, perhaps equally impressive is the compact theoretical
package that describes this temperature in relationship to the fusion energy's source, and a plausible solution to
the coulomb barrier problem.
This type of speculation, based on theory, is one half of the research process. The other half is experimental
inquiry to see if key elements of the theory can be verified by observation. The question then becomes: How can we
measure these temperatures and energy quanta? This may be difficult. There is nothing in the literature that I am
aware of, where covalent bond strength has been measured directly. The covalent force in biological systems is
normally calculated from free energy considerations. Lattice bonding in metals might be calculated as well,
possibly from considerations of tensile strength, and the yield properties of the metal. However, direct
measurements are preferred. I don't know how this might be done. This is a call to the experimentalists'
We have to also ask ourselves, is it possible that extreme thermodynamic conditions like this might occur
elsewhere in nature? Bockris (14) summarized what is generally seen as nuclear transmutation 'fringe literature',
including biological transmutation research. More recently, Biberian(15) prepared an exhaustive review of the
biological transmutation literature. I believe that it is not a coincidence that biological transmutation research
is frequently reported at ICCF conferences. Both cold fusion and the living cell are very far-from-equilibrium
processes that continue to confounded scientific inquiry.
Our understanding of biological fundamentals really began in the post-WWII era where experimental discovery
seemed to be working hand-in-hand with theoretical advances, and a 'solution' to the living state question seemed
at hand. The ensuing 65 years have seen extraordinary advances in our understanding of biomolecules and their
systematic place in life. But on the theoretical side, the great promise of a theory of the living state dwindled
to the point, where today, only a few individuals pursue Big Picture biology in any serious way. Those few
theorists are humbled by the vast chasm between the experimental evidence and our understanding of the living
system's fundamental processes. Of particular import is the high degree of variability in biological systems in
spite of our intuitive sense that the highly organized and very exact cell structure should be highly deterministic
in its function. And yet, it is not apparent that this is the case. There are, undoubtedly, deterministic trends,
but these are obscured by a high degree of what is seen as randomness.
The same pattern is emerging in cold fusion research. Here again the variability is large relative to the heat
response that we measure. At one end of the experimental response spectrum there is no excess heat evolution. At
the other end, there is extraordinarily high excess heat production. At this point in theory development,
experimental findings have outstripped theoretical understanding. Like the theoretical biologists before us, we are
rapidly exhausting the understanding that contemporary science allows, and theory is floundering.
It is only with the greatest respect for the cold fusion theory community that I suggest, there is one poorly
understood area of scientific inquiry that I believe could offer profound insights into both processes. It is
reversible thermodynamics; where theory operates at the very limit of the Second Law of Thermodynamics.
Consider the facts. The cold fusion process and the scientific principles underlying the living state, are both
very, very far-from-equilibrium events. Both seem to defy the Second Law; in the one case by producing large amounts
of anomalous heat energy, and in the other, by producing a highly ordered state from light energy and a mostly random
landscape of minor molecular forms. Both appear to be operating at the very limits of the Second Law, which is
precisely the domain of the reversible process. Is it possible that the fundamentals of both processes might have
roots in reversible thermodynamics? Is it possible that the common notion that reversible thermodynamic processes do
not exist in nature impedes our ability to understand the fundamentals of both?
- Planck, M., Eight Lectures in Theoretical Physics, 1909, translated by A.P. Wills, Columbia U. Press, NY 1915.
- Planck, M., "Verhandlunger der Deutschen Physikalischen Gesellschaft" vol. 2, 237, 1900, or in English translation:
Planck's Original Papers in Quantum Physics, Volume 1 of Classic Papers in Physics, H. Kangro ed., Wiley, New York,
- a: Maxwell, J.C. "Illustrations of the Dynamical Theory of Gases. Part I. On the Motion and Collision of
Perfectly Elastic Spheres.". Phil. Mag., 4th Series, 19:19-32. 1860.
b: Maxwell, J.C. "Illustrations of the Dynamical Theory of Gases. Part II. On the Process of Diffusion of
Two or More Kinds of Moving Particles Among One Another". Phil. Mag., 4th Series, 20:21-37. 1860.
- Boltzmann, L., Lectures on Gas Theory, Translated by Stephen G Brush, University of California Press, Berkeley, 1964.
- 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.
- Serway, R.A., Vuille, C., College Physics, 4th Ed., Charles Hartford (pub.), 2012
- Muelenberg, A., Personal communication.
- Szumski, D.S. "Nickel Transmutation and Excess Heat Model Using Reversible Thermodynamics", J. Condensed Matter Nucl.
Sci. 13 (2014) 554-564.
- 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.
- Muelenberg, A., Sinha, K.P., "Deep-electron Orbits in Cold Fusion", J. Condensed Matter Nucl. Sci. 13 (2014)
- Miley, G., J Patterson, "Nuclear Transmutations in thin-Film Nickel Coatings Undergoing Electrolysis", J. New Energy,
vol. 1, no. 3, pp. 5-38, 1996.
- Mizuno, T., T. Ohmori, and M. Enyo, "Anomalous Isotopic Distribution in Palladium Cathode After Electrolysis", J. New
Energy, 1996. 1(2): p. 37.
- Prigogine, I., Self-Organization in Non-Equilibrium Systems, Wiley, 1977.
- Bockris, J.O.M., Mallove, E.F., "Is the Occurrence of Cold Nuclear Reactions Widespread Throughout Nature?, Infinite
Energy, 27, 29-38.
- Biberian, J.P., "Biological Transmutations: Historical Perspective", J Condensed Matter Nucl. Sci. 7 (2012) 11–25.