Materials At The Nanoscale Have Zero Specific Heat

Specific heat is thought to be an intensive thermophysical property independent of the amount of the substance. Given the amount of the substance in a body is proportional to its volume, specific heat should therefore be independent of whether the body dimensions are macroscopic or nanoscopic. In contrast, specific heat that depends on the amount of the substance is an extensive property dependent on the dimensions of the body.  See

 Classical Specific Heat at the Nanoscale  Currently, specific heat at the nanoscale is considered an intensive property having the same value as for macroscopic bodies. The Debye and Einstein macroscopic theories of specific heat including modifications thereof by Raman are generally assumed in simulating heat transfer in nanostructures. See Thumbnail of “Macroscopic Specific Heat at the Nanoscale?”. What this means is the classical oscillators of statistical mechanics from macroscopic bodies all having the same kT energy are used to model specific heat at the nanoscale. See Ibid.

Specific Heat by Quantum Mechanics Contrarily, quantum mechanics (QM) embodied in the Einstein-Hopf relation for the harmonic oscillator shows the QM states do not have the same kT energy at the nanoscale. At ambient temperature, the average Planck energy of QM states is kT only at thermal wavelengths greater than about 50 microns while at shorter wavelengths is less than kT and vanishes for nanostructures at submicron wavelengths.  See Paper and Presentation at “Zero Specific Heat”, , 2010.

Since the Planck energy at a given wavelength is the amount of thermal energy that can be stored in the QM oscillator, and since the only thermal wavelengths that can fit into nanostructures are submicron, QM requires zero specific heat capacity at the nanoscale, the consequence of which is absorbed heat cannot be conserved in nanostructures by an increase in temperature. Conservation may only proceed by the QED induced frequency up-conversion of absorbed heat to non-thermal EM radiation at the fundamental EM confinement frequency of the nanostructure, typically in the UV and beyond. The EM confinement is quasi-bound allowing leakage of QED induced radiation from the nanostructure to be absorbed in the macroscopic surroundings. See Ibid.

But QED emission in the UV and beyond from nanostructures is not readily observed – even by standard photomultipliers because of the UV cut-off, and therefore heat balances of nanostructures do not include QED emissions as heat losses. Hence, thermal conductivity is inferred to be reduced from that of the bulk to be consistent with the measured temperature difference across the body, e.g., as in thin films. If QED emissions are included in heat losses, the bulk conductivity need not be reduced for consistency with temperature differences thereby precluding any modification of Fourier’s theory of heat conduction by the Boltzmann transport equation (BTE). See Ibid.  

 Molecular Dynamics and Periodic Boundaries  Molecular Dynamics (MD) describes the classical solution of atomic motion based on Newton’s equations. To determine bulk transport properties, there are no QM restrictions on kT energy of atoms, i.e., atoms are assumed to have kT energy because the MD solution for the bulk is obtained by imposing periodic boundary conditions on the computational box. Historically, Monte Carlo (MC) preceded MD simulations, however. MC simulations of spherical particles in a submicron computational square with periodic boundaries were used to determine the 2D virial coefficients for the PVT equation of state. See Metropolis et al. Ibid.For a discrete nanostructure, periodic boundaries do not apply, and therefore the atoms in the nanostructure are subject to QM restrictions of zero kT energy.

Heat transfer of discrete nanostructures which are unambiguously not periodic is generally simulated by MD on the invalid assumption the atoms have kT energy. See e.g.,  Extending specific heat from macroscopic samples to the nanoscale is just as invalid as extending the Dulong-Petit law for specific heat at ambient temperature to low temperatures about 200 years ago. Nevertheless, MD simulations of nanostructures today are proudly displayed in the belief they provide precise atomistic explanations of conduction heat transfer when in fact they are not valid because the simulations are performed on the assumption the atoms have finite kT energy. See Ibid, and


1. QM requires zero specific heat capacity at the nanoscale be specified as a new thermophysical property of all materials.

2. The classification of specific heat as an intensive thermophysical property of a body should be changed to an extensive property depending on the dimensions of the body.

3. Nanoscale heat transfer based on the assumption of macroscopic specific heat is likely to produce unphysical results, e.g., reduced thermal conductivity in thin films.

4.  There is no need for the BTE to determine the thermal conductivity in thin films as bulk conductivity may be assumed without any loss in accuracy.

5. Macroscopic Debye and Einstein theories should be revised to include zero specific heat at the nanoscale.

6. Lacking specific heat at the nanoscale, absorbed EM energy is not conserved by an increase in temperature, but rather by the emission of non-thermal QED induced EM radiation.

7. MD and MC simulations of bulk thermal conductivity based on full kT energy of atoms in submicron computational boxes under periodic boundary conditions are consistent with QM.

8. Zero specific heat is required for atoms in MD and MC simulations of discrete nanostructures without periodic constraints.

9. Absorbed EM energy in discrete nanostructures may be a priori assumed to be emitted as high frequency EM radiation that is absorbed in the macroscopic surroundings, thereby obviating any need to perform MD and MC simulations of the nanostructure itself.

Redshift by Cosmic Dust trumps Hubble and Tired Light Theories

Hubble and Tired Light Theories
In 1929, Hubble formulated a law that the velocity of a receding galaxy is proportional to its distance to the Earth. The Hubble relation held in all directions suggesting to de Sitter that the Universe was consistent with the expansive metric of Einsteins theory of general relativity. However, others thought the Hubble redshift was caused by mechanisms without Universe expansion. Zwicky proposed that galaxy photons redshift because they lose energy as they scatter upon collision with cosmic dust particles (DPs) before entering the Earth, a redshift theory called Tired Light. See Recently, Ashmore extended Tired Light to loss of energy in galaxy photons upon collisions with electrons. See

Objections to Tired Light theories are generally based on the argument that scattered light should blur the galaxy image, and therefore are dismissed because the images are clear and not blurred. See However, claims that Tired Light theories do not explain all the predictions of Big Bang cosmology should be set aside because there is no mandate in science that any theory must totally stand alone, e.g., the anisotropy of the cosmic microwave background (CMB) in the current epoch may be simply explained by the static Universe in the current epoch having nearly uniform temperature everywhere of about 2.726K.

Alternative QED Induced Light Theory
An alternative to the Hubble and Tired Light theories is the theory of QED induced redshift caused by the absorption of galaxy light in DPs. QED stands for quantum electrodynamics. See at “Dark Energy and Cosmic Dust” and “Reddening and Redshift”, 2009. QED theory asserts the redshift Z is spontaneous upon the absorption of light. Here Z = (Lo – L)/L, where L is the wavelength of galaxy light and Lo is the wavelength of the light emitted from the DP.

QED induced redshift may be understood by treating the absorbed galaxy photon as electromagnetic (EM) energy confined within the DP geometry. Recall from quantum mechanics (QM) that photons of wavelength Lo are created by supplying EM energy to a QM box with walls separated by Lo/2. For a spherical DP of diameter D, the QED photons are produced at a wavelength Lo = 2Dn, where n is the index of refraction which for the typical DP of amorphous silicate has n = 1.45. Hence, DPs having D = 0.25 microns redshift the Lyman-alpha line at 0.121 microns to a red line at 0.725 microns with Z ~ 5. If the QED induced redshift in DPs at Z = 5 is erroneously interpreted by the Hubble law, the galaxy recession velocity is 95 % of the speed of light when in fact the Universe is not expandingl.

Tolman Test and Supernovae Spectra Aging
Shortly after the Hubble discovery, Tolman devised a test to distinguish between a static and expanding Universe. See In a static Universe, the light intensity of an object drops inversely with the square of its distance from the observer, but the apparent area of the object also drops inversely with the square of the distance, so the brightness given as the intensity per unit area of the object is independent of the distance. However, if the Universe is expanding, astronomers claim the brightness is reduced by the fourth power of (1+Z). In 2001, Lubin and Sandage showed the redshift gave a reduction in brightness by the cube of (1+Z). Although the brightness is not reduced by the fourth power of (1+Z), the conclusion was the brightness test is consistent with the reality of Universe expansion.

However, there is a problem with the Tolman test because the brightness B of an object in the static Universe is not assumed reduced by absorption in DPs. By QED theory, a single interaction with a DP emits light at wavelength Lo = (1+Z)L. Therefore the brightness Bo at the observer is Bo = hc/Lo = hc/L(1+Z) = B/(1+Z), or the object brightness is reduced by (1+Z), but not by the cube of (1+Z) as measured. Closer agreement is found for multiple interactions, e.g., for N interactions, B drops inversely with the product (1+Z1)(1+Z2)…(1+ZN), where ZK is the redshift for interaction K.

The Tolman test aside, the aging of Supernovae spectra is found to drop inversely with (1+Z) at the observer. See Blondin et al. at For spectra defined by brightness/unit area, Bo = B divided by the respective wavelength. Equivalence is found by Bo/Lo = B/L(1+Z). Hence, QED theory for the spectra at the Supernovae is consistent with the measured spectra showing an inverse drop by (1+Z).

Time Dilation of Supernova Light Curves
Tired Light theories are claimed unable to explain the observed time dilation of Supernova light curves at high Z redshift, i.e., nearby supernovae that take 20 days to decay will take 40 days to decay when observed at redshift Z =1 See e.g., However, redshift in the QED theory differs from Tired Light in that it is proportional to the number of DPs in the light path that in turn is proportional to the total dust mass emitted in the Supernova explosion. Time dilation in observing Supernova explosions is nothing more thermal cooling of the dust mass, i.e, at high Z the Supernovae having larger dust mass takes a longer time to cool than at low Z. Hence, QED redshift theory based on DPs is consistent with Supernova light curves.

ISM Lights
A more compelling argument that DPs are the source of redshift of galaxy light is found on a far larger scale everywhere by the visible (VIS) light observed throughout the Universe. Ultraviolet (UV) radiation is known to permeate the Universe including the interstellar medium (ISM). Indeed, astronomers explain the infrared (IR) spectra measured in the ISM by the thermal emission following the increase in temperature in DPs upon the absorption of single UV photons. But this is unlikely, because an increase in DP temperature is negated by the QM restriction that the specific heat of DPs vanishes. Also unlikely is VIS light produced in DPs by photoluminescence (PL) because a single UV photon is more likely to be absorbed anywhere in the DP than at the PL color center.

Without thermal emission and PL, the IR and VIS spectra can only be produced by QED induced redshift upon the absorption of single UV photons in DPs. VIS colors in the ISM require DPs having D < 0.5 microns while IR spectra depend on larger DPs found in molecular clouds. Similar to the Hubble redshift of galaxy light, the vivid ISM colors observed are produced without Universe expansion, e.g., single UV photons at 0.15 microns absorbed in a D = 0.125 to 0.25 micron silicate DPs, blue to red light corresponding to wavelengths from 0.362 to 0.725 microns is produced at redshift Z from 1.41 to 3.83. ISM light does not depend Universe expansion.


1. The measured Hubble redshift Z is caused by DPs and has nothing to do with an expanding Universe. DPs make moot the existence of dark energy because it is no longer necessary in a static Universe.

2. Tired Light theories based on scattering are likely to produce blurring of the object image. QED theory based on absorption and not scattering do not produce blurring.

3. QED theory does not agree with brightness reduction to the cube of (1+Z) in the Tolman test, but is found in agreement with the (1+Z) reduction in aged Supernovae spectra.

4. QED theory based on redshift of DPs is consistent with the observed time dilation of Supernova light curves.

5. The vivid VIS color variations in the ISM are caused by variations in DP diameter D and far less likely by PL from the chemical composition of the DPs. Larger DPs necessary to produce the IR spectra are found in molecular clouds.

Redshift in cosmic dust resolves the galaxy rotation problem without dark matter and MOND

Background  The Tully-Fisher relation based on Newtonian mechanics requires the rotation velocity of spiral galaxies to vary inversely with the square root of the distance from the galactic center. See  However, observations of galaxy rotation velocities obtained with the Doppler shift show the velocity is nearly constant with distance suggesting the presence of a substantial amount of dark matter in a halo surrounding the galactic center. See

Dark matter halos are an important feature of the Lambda Cold Dark Matter (LCDM) model of the Universe, but dark matter lacks experimental verification, and remains an unsolved problem in physics. The question may be asked:

Is dark matter responsible for the difference between galaxy rotation velocities given by Newtonian mechanics and those observed, or is there another explanation?  

MOND asserts the galaxy rotation problem may be resolved by assuming the physics of gravity changes at the large scale allowing rotation velocities in galaxies to remain constant with distance from the galactic center instead of decreasing as required by Newtonian mechanics. But like dark matter, MOND lacks experimental verification. Moreover, MOND requires motions of galaxies around a galactic center, and therefore fails to explain the collapse of cluster galaxies having motion emanating from  other points. See Clowe, et al. ApJ Letters, 648, L109, 2006 in However, the failure of MOND to explain collapsing galaxies is not proof dark matter exists, as other explanations are possible.

Redshift in Cosmic Dust
Redshift in cosmic dust claims the galaxy rotation problem is caused by Doppler shift and is resolved by replacing the latter with a theory called QED induced radiation. See “Dark Energy and Cosmic Dust” at  By this theory, the validity of the Doppler shift as the measure of velocities in the Universe is held in question by the redshift that accompanies the absorption of light in submicron dust particles (DPs). It is important to note that the redshift upon the absorption of light in DPs differs from scattering in that the latter does not redshift light. The impact of DPs on velocity measurements in cosmology is significant in that the very first redshift measurements by Hubble giving recession velocities of galaxies are refuted leaving the notion of an expanding Universe without experimental verification. Astronomers are therefore required to find other ways of proving Universe expansion or abandon the cosmology of the expanding Universe including the Big Bang. No matter how unpleasant these options may be, the fact remains the Universe is only observed by light, and therefore the significance of absorption of galactic light by cosmic dust may by default require astronomers to return to the cosmolog of a static Universe once proposed by Einstein.

Indeed, the redshift measurements by Hubble and interpreted by the Doppler shift were most likely caused by QED induced redshift and have nothing to do with the recession velocities of galaxies. In fact, cosmological events that produce large amounts of debris have large redshifts because of the proportionality of submciron DPs that form to the debris produced. In this regard, QED induced redshift of galaxy light in DPs observed by Hubble may be almost insignificant compared to the large quantities of  DPs produced in Supernovae Type 1a explosions. See The interpretation of Supernova light curves and respective time dilation therefore cannot proceed without considering the absorption of light in DPs.

Cosmic Dust and Galaxy Rotation Curves
Similar to light from receding galaxies and Supernovae explosions, astronomers use the Doppler shift of light from different parts of a spiral galaxy to determine its rotation velocities. In the plane of rotation, the galaxy is described by spiral arms of stars emanating from the galactic center while the edge view shows a bulge at the center of a thin disk.  In edge view, galaxy rotation consists of half of the disk moving away from us leaving a trailing cloud of DPs in the light path to us. However, there are far less DPs present in the half moving toward us. Our edge view of a rotating galaxy is therefore altered by an asymmetric cloud of DPs.

Light from the galaxy passing through the asymmetric cloud of DPs undergoes more QED induced redshift on the half moving away than that moving toward us. Away from the galaxy, the DPs in the light path to us induce the same QED redshift for both halves of the disk, but compared to the cloud of trailing DPs may be neglected. The asymmetry in QED induced redshift if interpreted as a Doppler shift suggests the galaxy is rotating faster than it actually is. Since the trailing cloud of DPs is always present at any distance from the galactic center, the galaxy rotation appears to be flat with distance. By QED induced redshift, the galaxy rotation problem is resolved by treating the Doppler shift as anomaly of cosmic dust having nothing to do with rotation velocities, thereby allowing the dynamics of spiral galaxies to be governed solely by Newtonian mechanics.

1.  Cosmic dust refutes velocities determined by Doppler shift leaving Newtonian mechanics alone to govern the Tully-Fisher relation for spiral galaxy rotation curves. Rotation velocities inferred from Doppler shifts should be not used in explaining galaxy dynamics, and instead treated as anomolies of cosmic dust . There is no need for dark matter and MOND to explain the galaxy rotation problem.
2. The failure of the LCDM model to explain galaxy rotation curves began with Hubble who proposed the observed redshift of galaxies be interpreted as recession velocities given by the Doppler shift instead of by absorption in cosmic dust.
3. Astronomers may want to consider abandoning the LCDM model in favor of a static Universe once proposed Einstein.

Olbers paradox is explained by cosmic dust instead of the Big Bang


The German astronomer Heinrich Olbers in 1823 is credited with the paradoxical observation that the night sky is dark, but in a static infinite universe the night sky should be bright. Indeed, Olbers paradox is often cited as evidence for the Big Bang theory.’_paradox

In a static infinite Universe, the observer would see a nearby galaxy in one region of the sky and another galaxy in a more distant region. Although the nearer galaxy would appear brighter, there would be more galaxies in the more distant region of the sky. Therefore, the total light from the nearer region of the sky would be the same as that from the more distant region. No matter where the observer looks in the sky, the total light coming from every line-of-sight would be the same. Olbers paradox concludes the night sky should be bright and not dark if the Universe is infinite.

Astronomers explain Olbers paradox as an artifact of a finite and expanding Universe In the Big Bang. By Hubble’s law, distant galaxies in an expanding Universe are moving away from us faster than nearby galaxies, i.e., a galaxy at distance d from us moving away at velocity V = Hd, where H is Hubble’s constant. Hence, light from distant galaxies is redshift so much that visible light is moved to the infrared and microwave regions that are invisible to the observer.

An alternative to the Big Bang explanation of Olbers paradox is that the static and infinite Universe is not transparent, and the light from distant galaxies is absorbed by cosmic dust, so that there is a bound on the distance from which light can reach the observer. However, astronomers dismiss this explanation based on the second law of thermodynamics that states there can be no material hotter than its surroundings that does not give off radiation. Hence, there is no material which can be uniformly distributed through space and yet able to absorb galaxy light without increasing in temperature. Therefore, the cosmic dust would heat up and soon reradiate the energy that again results in intense uniform radiation as bright as the collective of the galaxies themselves, once again giving a bright night sky which is not observed.’s_paradox.html


The problem with Big Bang explanation of Olbers paradox is that the Universe is unequivocally not transparent because of ubiquitous submicron cosmic dust, and therefore the distance from which galaxy light can reach the observer is indeed bounded. The second law is not violated, however. In fact, QED induced redshift based on QM allows submicron cosmic dust to redshift visible light to infrared and microwaves regions of the EM spectrum without increasing in temperature. QM stands for quantum mechanics, QED for quantum electrodynamics, and EM for electromagnetic. Therefore, a static infinite Universe without the Big Bang explains Olbers paradox.

QED redshift in Cosmic Dust instead of Hubble’s Doppler shift

QED induced redshift is a consequence of QM constraints placed on the conservation of energy in submicron dust particles. QM precludes cosmic dust from having the specific heat capacity necessary to conserve absorbed galaxy photons by an increase in temperature. Photons are created from the EM confinement of the absorbed galaxy photon within the dust particle. See at “Dark Energy and Cosmic Dust” and “Reddening and Redshift,” 2009.

QED induced redshift may be understood from QM by the creation of photons of wavelength Lo upon supplying EM energy to a QM box with walls separated by Lo/2. For a galaxy photon absorbed in a spherical particle of diameter D, the QED photons are created at a wavelength Lo = 2nD, where n is the index of refraction of the particle. Cosmic dust is generally amorphous silicate having n = 1.45 and diameters D < 0.5 microns. For example, at D = 0.25 microns, the QED created photons has Lo = 0.745 microns, and therefore an absorbed Lyman-alpha photon having L = 0.1216 microns in galaxy light is redshift to Z = (Lo – L)/L. ~ 5. If the QED redshift is interpreted by Doppler shift, the galaxy recession velocity is 95 % of the speed of light when in fact the Universe is not expanding at all, thereby negating any and all need for the Big Bang to explain our Universe.

Moreover, QED redshift in cosmic dust has been suggested to explain brightness in the Tolman test and time dilation in Supernova explosions. In this regard, a critique of Doppler redshift from Hubble theory in relation to QED induced redshift is given in  Moreover, QED redshift in cosmic dust resolves the galaxy rotation problem and negates the need for MOND. See


1. Olbers paradox need not rely on the Doppler redshift in light from distant galaxies in a finite and expanding Universe.
2. QED redshift of galaxy light by submicron cosmic dust explains Olbers paradox in an infinite and non-expanding static Universe.
3. Given the fact the Universe is permeated by cosmic dust, it is highly likely that the redshift measured by Hubble was QED induced redshift having nothing to do with the Big Bang and an expanding Universe.
4. In a static infinite Universe, there is no gravitational collapse and no need for the cosmological constant or the Big Bang.