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


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

Consequences Of Partitioning The Photon
Into Its Electrical And Magnetic Vectors
Upon Absorption By An Electron

Published 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.
Daniel S. Szumski*
*Independent Scholar, 513 F Street, Davis, CA 95616, USA, DanSzumski@sbcglobal.net Phone: 510-418-7155


This research uses classical arguments to develop a blackbody spectral equation that provides useful insights into heat processes. The theory unites in a single equation, the heat radiation theory of Planck and the heat of molecular motion theory of Maxwell and Boltzmann.

Light absorption is considered a two-step process. The first is an adiabatic reversible step, wherein one-dimensional light energy is absorbed in a quantum amount, , by an electron. The absorbed quanta is still 1-dimensional(1-D), and remains within the domain of reversible thermodynamics. There is no recourse to the Second Law during this first step.

The absorption process' second step is a dimensional restructuring wherein the electrical and magnetic vectors evolve separately. The 1-D electrical quanta transforms into its 3-D equivalent, electrical charge density. The resulting displacement of the generalized coordinates translates to 3-D motion, the evolution of Joule heat, and irreversible thermodynamics. The magnetic vector has no 3-D equivalent, and can only transform to 1-D paramagnetic spin. Accordingly, photon decoupling distorts time's fabric, giving rise to the characteristic blackbody spectral emittance.

This study's spectral equation introduces a new quantity to physics, the radiation temperature. Where it is identical to the classical thermodynamic temperature, the blackbody spectral curves are consistent with Planck's. However, by separating these two temperatures in a stable far-from-equilibrium manner, new energy storage modes become possible at the atomic level, something that could have profound implications in understanding matter's living state. Keywords: Blackbody equation, far-from-equilibrium, temperature, heat radiation, covalent bonds


Planck's blackbody emittance equation(1) is the universally accepted model for heat radiation's equilibrium, spectral distribution. It has been found superior to any other contemporary form(2,3,4,5,6). However, this acceptance is only justified for equilibrium, and leaves two important issues unresolved. First, Planck's solution provides no insight into non-equilibrium or far-from-equilibrium states, or the mechanisms of redistribution between equilibrium states(7). Only Ehrenfest (8) has explored redistribution mechanisms, and Forte(9) describes a non-equilibrium Wein Displacement Law. Secondly, Planck's energy quanta violated the continuity requirements of Maxwell's equations. Einstein first enunciated this discrepancy, and Planck spent the next 2 decades, unsuccessfully trying to resolve it. Meanwhile, the experiments of Stark(10), and Einstein's light particle theory(11) demonstrated the dual nature of light, galvanizing the discontinuity's place in physics. More recent studies of non-quantum blackbody theory(12,13,14,15,16,17) have not reconciled this conflict.

This paper explores one possible avenue to a non-equilibrium blackbody equation. The goal here, is understanding free energy partitioning between the domains of heat radiation, and molecular motion.


Planck(18) viewed the separation of all physical phenomena into reversible and irreversible processes as the most elemental, and most important, because all irreversible processes share a common similarity that makes them unlike any reversible process. This distinguishing characteristic is the transformation of heat energy to motion, which can in no way be referred back to the process from which it came. This research considers Maxwell's electromagnetic wave traveling undiminished in time, its information content preserved, until it encounters a material particle.

Light absorption is considered a two-step process as illustrated in Figure 1. The first is an adiabatic reversible step, wherein one-dimensional light energy is absorbed in a quantum amount, hv, by an electron, and is wholly contained within it. The absorbed quanta is still 1-dimensional(1-D), remains within the domain of reversible thermodynamics, and does not emit Joule heat. There is no recourse to the Second Law during this first step.


Figure 1: Evolution of electrical vector during light absorption. (A) Pre-encounter - Maxwell's equations valid, discontinuity does not yet exist; (B) First absorption step - complete 1-D, adiabatic absorption of quantum; (C) Non-adiabatic conversion of quantum to 3-D charge. Dielectric loss is operative.

The absorption process' second step is a dimensional restructuring that the 1-D electrical quanta undergoes in evolving into its 3-D equivalent, electrical charge density. This occurs in accordance with the Equi-partition Theorum, along the axes of the electron's three spatial coordinates. The resulting displacement of the generalized coordinates translates to 3-D motion, the evolution of Joule heat, and irreversibility. The magnetic vector has no 3-D equivalent, and can only transform to 1-D paramagnetic spin. Accordingly, photon de-coupling distorts time's fabric, giving rise to the characteristic spectral emittance.

This second absorption step is represented by a Dirac delta over the 3-D transformation's time interval


with variance distribution:


The probability distribution's re-structuring from a 1-D quanta, hv, to three dimensions requires taking the next two moments of the variance function relative to the Wein frequency, vm Thus:


The results are summarized as:



The third moment represents all of the possible interconnections between any arbitrary frequency and the Wien frequency. vm is the most probable frequency at the prevailing temperature. v1 is the damped frequency continuum of the blackbody spectra.

Assuming the radiation absorption function to be exponentially distributed,


and substituting this absorption and the Raliegh-Jeans emittance into Kirchhoff's Law:



This spectral distribution: 1) is derived entirely from classical theory; 2) contains the discontinuity indirectly, vm(h); 3) incorporates the consequences of electro-magnetic theory (Rayleigh-Jeans Law); and 4) suggests a mechanism for exchange of energy between frequencies. Sears[19] gives Wien's Displacement Law as:


Figure 2: Comparison of Equation (7) with Planck's Equation (9). The curves terminate at a single quanta per frequency


Figure 2 displays features of the blackbody radiation spectra described in this way. The figure also displays calculations using Planck's Equation:


(9) The agreement is close, but not exact, differing by less than 2% at vm, and in the 5%-8% range to the left, where Eq.(7) better represents Raliegh-Jeans. The curves terminate at the point where the calculations yield partial quanta. The number of quanta is obtained by dividing the spectral emittance by the conversion factor vm and then dividing by vm.


Both the two slit experiment and the photo-electric effect are consistent with this theory. The wave properties of light are unaltered. The theory eliminates discontinuity as a property of light, placing it instead in the electron, more precisely, in the electrons absorption of light in quantum amounts. This reassignment isn't contrary to, nor does it change, existing theory.

Eq.(7) offers two significant advances over Planck's which are instructive in furthering our understanding of heat processes. The first is Eq.(7)'s explicit statement for energy transference between frequencies. This was identified at the outset as the distinguishing characteristic of the required non-equilibrium blackbody form. Eq.(5) suggests that the common channel for energy re-distribution is the Wien frequency, since each spectral frequency is explicitly related to it. Planck's equation can also be shown to contain the same ratio(21).

Second, Eq.(7) contains two distinct thermodynamic scales (Figure 3), representing the entire range of non-equilibrium heat conditions. The concept of two temperature scales is not new(22,23,24,25,26,27). The first of these scales is the classical thermodynamic temperature, of the Rayliegh-Jeans Law, Tm. It is common to both equations, and expresses the temperature of thermal motion alone.

temp scale

Figure 3: Far-from-equilibrium blackbody spectral equation showing the two temperature scales: Tm, the classical thermodynamic temperature, and TR, a new temperature, the radiation temperature.

The second temperature, that contained in the Wien Displacement Law, is identical to the first where the system is in equilibrium. However, it is fundamentally different from Tm in ways that could give profound meaning to Eq.(7). This is the radiation temperature, TR. That it can be expressed in the same units as the classical thermodynamic temperature, is seen in the equilibrium case. However, changes in TR, independent of the thermodynamic temperature, shift the spectral distribution in plausible non-equilibrium ways that may provide insight into both non-equilibrium and far-fromequilibrium heat processes.


Figure 4: Illustration of non-equilibrium changes in the heat radiation spectra (Equation 7). Case A represents instantaneous mass domain heating (i.e. friction) at constant radiation temperature. Case B represents adiabatic energy accumulation at a constant thermodynamic temperature. Such displacements can be unstable as in the case of sono-luminesence, or stable in accordance with the authors hypothesis, as in living cells.

Consider Figure 4 where TR, and consequently the Wien frequency remain constant while Tm increases from 300 °K to 105 °K (Case A). This represents a sudden frictional input of heat to a material body that is initially at thermal equilibrium. Similarly, TR can be increased without a increase in the thermodynamic temperature (Case B). The radiation density within the blackbody is increased without a corresponding increase in the Rayliegh-Jeans emittance. The new region delineated by this spectral distribution consists primarily of higher energy radiation, but the process from which it arises appears to an observer to be adiabatic, and might therefore, be viewed as completely reversible. From this theory's standpoint, the energy content within this new region (Case B) consists entirely of radiation transfers that are undergoing the first stage of radiation absorption, alone. That is, radiation is fully absorbed in its onedimensional form and immediately re-emitted. There is no de-coupling of light's electro-magnetic structure, and therefore no entropy increase. This is the initial condition when high energy radiation strikes a body initially at equilibrium.

Taking this result further, one might ask: Are there states in nature that exploit the energy/entropy relationship suggested by these calculations? There might be. Living systems are constructed of high energy covalent bonds that both, represent very far-from-equilibrium conditions, and store larger amounts of electro-magnetic energy than would normally exist at the Tm. It is possible that Case B shows how far-from-equilibrium energy storage might be masked from ambient thermodynamic conditions in matters living state. Each covalent electron pair shares the wave function, trident2, alternately absorbing and re-emitting light energy, but only in a manner consistent with this theory's first absorption step. This portion of the heat radiation spectra is localized (masked) between electron pairs, and does not contribute to either the measurable heat spectra or to dielectric losses. Thus, the thermodynamic temperature of the cell (Tm) is unaffected, and a stable far-from-equilibrium condition with lower localized entropy, is possible. The degree of entropy decrease is defined by the separation between Tm and TR. The permanence of that change appears to depend on irreversible storage of neg-entropy outside mechanistic pathways back to equilibrium(28). Covalent bonds in living systems could satisfy this condition. Eq.(5) suggests enormous capacity for far-from-equilibrium entropy absorption and the information storage this implies. The thermodynamically reversible character of the covalent bond is illustrated in Figure 5.


Figure 5: (A) The covalent bond stores heat energy between two covalent electrons by maintaining the photon storage continuously in the the first step of photon absorbtion, and in this way maintains a stable adiabatic reversible state. (B) Different portions of the far-from-equilibrium covalent energy storage might be apportioned by function, mitotic state, or structural elements.

As the energy storage requirements begin to exceed the capacity of the covalent bond system, other mechanisms for storing this biological energy in a stable far-from-equilibrium state might be found in elevated electronic states, and probably even excited nuclear states, where the energy storage would take the form of Mossbauer Resonance.

A second example of far-from-equilibrium spectral energy storage might be found in sonoluminesence, wherein mechanical energy is converted to electro-magnetic energy. In this case, mechanical energy increases Tm instantaneously without a corresponding increase in TR (Mass domain heating in Figure 4). Lacking any mechanism to maintain this far-from-equilibrium condition, the system spontaneously moves toward equilibrium by channeling the stored mechanical energy through the Wein frequency channel, and thence, into the radiation domain. If the energy flux is high enough, visible light is observed.


Figure 6: Illustration of the the hypothesized far-from-equilibrium spectral distribution in a cold fusion reactor that is at 'room temperature.' The temperature at the right side of the far-from-equilibrium energy spectrum approaches solar core temperature by taking an energy shortcut around the enormous energy of thermal motion required to achieve the same solar core temperaature in the Tokamak.

A final example of where this type of heat theory may prove important to scientific understanding is found in what has been called cold fusion. Energy storage in a palladium or nickel electrode might occur in the radiation domain (Case B in Figure 3), first as excited electronic states and a corresponding increase in the redox state, and later in excited nuclear states. Is it possible that such a system could exhibit radiation temperatures approaching 107°K while the ambient temperature of the electrolysis apparatus is around 373 °K? Stranger paradigms have occurred in the history of science.


  1. M. Planck, Verhandlunger der Deutschen Physikalischen Gesellschaft, 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 (1972).
  2. H. Rubens and F. Kurlbaum, Ann. Physik, 4, 649 (1901).
  3. F. Paschen, Ann. Physik,4, 277 (1901).
  4. E. Warburg, Ann. Physik, 48, 410 (1915).
  5. W. Nernst and T. Wulf, Ber. deut. phys. Ges., 21, 294(1919).
  6. W.W. Coblenz, Dict. Appl. Phys., Vol. IV, "Radiation".
  7. T.S. Kuhn, Black-Body Theory and the Quantum Discontinuity 1894-1912, Oxford University Press, New York (1978).
  8. Kuhn found references to non-equilibrium transitions only in Ehrenfest's notes.
  9. J. Fort, J.A. Gonzalez, J. E. Llebot, Physical Letters A, 236,193-200 (1997).
  10. J. Stark, Phys.ZS.,8(1907), 913-919, received 2 December 1907.
  11. A. Einstein, Ann. d. Phys.,17(190), 132-148, 1905.
  12. H. Dingle, Phil Mag, XXXVII,246, 47 (1946).
  13. T.H. Boyer, Phys. Rev. 182, 1374 (1969).
  14. T.H. Boyer, Phys. Rev. 186, 1304 (1969).
  15. T.H. Boyer, Phys. Rev. D, 11, 790 (1975).
  16. T.H. Boyer, Phys. Rev. D, 29, 1089 (1984).
  17. D.C. Cole, Phys. Rev. A, 45, 8471 (1992).
  18. M. Planck, Eight Lectures in Theoretical Physics-1909, translated by A.P. Wills, Columbia U Press, NY (1915).
  19. F.W. Sears and M.W. Zemansky, University Physics, 3rd ed., Addison-Wiley, Reading, MA (1964).
  20. see T. Preston, Theory of Heat, Macmillan and Co, London (1929) for a description of their methods and results.
  21. If we rearrange Equation (8) and substitute for T in Planck's Equation(9), the exponential term becomes e282.
  22. B.C. Eu, L.S. Garcia-Colin, Phys. Rev. E, 54, 2501 (1996).
  23. D, Jou, J. Casas-Vazquez, Phys. Rev. A, 45, 8371 (1992).
  24. K. Henjes, Phys. Rev. A, 48, 3194 (1993).
  25. W.G. Hoover, B.L. Holian, and H.A. Posch, Phys. Rev. A, 48, 3191 (1993).
  26. D. Jou, J. Casas-Vazquez, Phys. Rev. A, 48, 3201 (1993).
  27. J. Fort, D. Jou, and J.E. Lleobot, Physica A, 269, 439(1999).
  28. G. Nicolis, I. Prigogine, Self-Organization in Non-Equilibrium Systems, John Wiley and Sons, NY, 1977