## APPENDIX 2: Radiant Energy Emission
## (i). Energy density of radiationThe energy density of emitted radiation, as distinct from the ZPE itself, is discussed first. The energy density, ρ, of electromagnetic waves is given by this equation in references [148-150]
Now electromagnetic waves are described by a sine function. The peak amplitude 1. We can now write /c
The increase in Radiation intensity, ## (ii). Stellar luminositiesThree factors determine the luminosity of a star with increasing ZPE strength, and decreasing c. First is the photon production rate, which depends on the stellar nuclear reaction rate. Second is the mass-density of the particles making up the star seen from the atomic frame of reference. Third is the star’s opacity, which inhibits the energy transport from the reaction centre out to where that energy radiates into space. Four key processes may contribute to opacity: free-free transitions, bound-free transitions, bound-bound transitions, and scattering by electrons. We note that bound-bound transitions play a negligible part in stellar interiors [151], but For the central area of stars, this leaves electron scattering of photons as the prime source of opacity. If
Here, σ is the Thomson scattering cross-section where σ = (8π/3)[e2/(εmec2)]2 which is constant, as is c2 as in (78). Some stars do not have the interior conditions for high energy Compton or inverse Compton effects to be relevant [156]. Still a formula for the Rosseland mean opacity for Compton scattering by free electrons in the non-degenerative limit exists [157]. It differs from (78) only by a dimensionless number. Let us consider bound-free transitions. Harwit states
Here, 2 and to U2 from (16). F contains correction and other factors independent of c, while <gbf> is the dimensionless mean Gaunt factor of the order of unity. X is a dimensionless number, and T is temperature. When the c-dependent terms are analysed, the result is that bound-free opacities are proportional to c2, the same as electron scattering. In [159], figure 8.3 reveals the stellar conditions allowing free-free transitions are restricted. Nevertheless Harwit repeats the above process for these free-free transitions. The resulting equation gives a result similar to (79), but an (X term is included in place of + Y) Z. Schwarzschild lists the complete equation as [161]:
Comparison with (79) shows the same
The other factor affecting a star’s luminosity is its rate of burning nuclear fuel. Since nuclear reactions are temperature sensitive, the proton-proton reactions dominate at lower temperatures with the carbon cycle prominent later [162]. The key reaction needed to get the proton-proton sequence started is given by the equation H1 + H1 → D2 + e
Here the temperature is c. Stellar nuclear reactions are thereby proportional to c, or 1/U, and so will be the photon production rate. When photon production rate and opacity are then considered together, the luminosity of a star with varying ZPE should be established. The key formula for stellar luminosity is given by Harwit as [164]:
Here the term
An approach by Schwarzschild is relevant [165]. He defines the fraction of energy a beam of light loses by scattering/absorption over distance
In (85), the term
Thus stellar photon emission rates are inversely proportional to
An example of what these principles mean in practice is given by a consideration of Cepheid variables and their observation in distant galaxies, and a discussion about supernova 1987A. ## (iii). Cepheid variablesThe near surface layers of Cepheid variable stars pulsate in and out like clockwork and their brightness pulsates inversely with the same period. The more massive the Cepheid, the brighter it shines, and the slower its pulsation rate. There is a direct link between a Cepheid’s period and its intrinsic luminosity. So Cepheids are used as distance indicators for galaxies in which their typical light curve is seen. Given the observed period, the intrinsic luminosity is known, and, when compared with the observed luminosity, the distance is deduced from the inverse square law [166]. This raises two matters; the observed luminosity, and the pulsation rate. Let us compare our observations of a distant Cepheid with one nearby us. Equation (86) shows the number of waves, or photons emitted per unit time, from each Cepheid is proportional to But what about Cepheid pulsation rates? To explain the pulsation process, Eddington suggested his ‘valve mechanism.’ If a specific layer of a star near the surface became more opaque upon compression, it would block the energy flowing towards the surface and push the surface layers upwards. Then, as this expanding layer became more transparent, trapped radiation would escape and the layer would collapse back down to begin the cycle again. He said
This means that Cepheid periods lengthen as the strength of the ZPE increases. Yet that is not the end of the story. At the time of reception, the wave-train carrying the information from the distant star is traveling more slowly than at the moment of emission. So the star’s period of variation appears longer at reception than at emission by a lengthening factor,
Thus the period of the distant Cepheid will appear to be the same as that for our local Cepheid. So measurements of distance based on Cepheid variability will be unaffected by ZPE changes. ## (iv). Supernova 1987 AIt has been claimed that two features of supernova SN1987A in the Large Magellanic Cloud (LMC) disprove changes in the ZPE and lightspeed. First was the measured exponential decay of the light intensity curve from the radioactive decay of cobalt 56. Second were the enlarging rings of light from the explosion that illuminated distant sheets of gas and dust. Since the both the distance to the LMC and the angular distance of the ring from the supernova are well-known, a simple calculation shows how long it takes light to get from the supernova to the sheets, and how long the peak intensity should take to pass. Now, as confirmed below in Appendix 4, radioactive decay rates are proportionally faster when lightspeed is higher and the ZPE energy density is lower. This means a shorter half-life for cobalt 56 than the light intensity curve revealed. For example, if The reason is the slow-down in the speed of light mentioned in Appendix 2 part (i) dealing with radiant energy density and part (iii) with Cepheid variables. Since ## (v). Chemical reactionsCollision theory suggests that chemical reactions could be affected by a ZPE and
Here, X*. It can be shown that the chance of forming the activated complex, A, at any instant is the number of ions approaching the reactant per second, Y*, multiplied by the time the ion spends in the vicinity of the reactant, X*. So that
Thus
[148] F.A. Jenkins & H.E. White, [212] C. Barnet, R. Davis, and W. L. Sanders, Go to: first page, section 1, 2, 3, 4, 5, 6, 7 or appendix 1, 2, 3, 4, 5, 6, 7, 8, or tables, or figures 1-7, or figure 8 or reference page. |