Monogravitational materials (hypothetical, per Strano)

[WrathfulSpatula]

I've been experimenting with a dialectric-like theory of materials for speculative graviton thermal interactions, per earlier work by Strano, (me). Nuclei in rigid body objects would hypothetically act like (composite) graviton monopole emitters. Because of the single pole rather than dipole, all material permittivity should be equal to vacuum. Radiative emission and absorption should act like in the theory of dialectrics. Single nucleus spontaneous emission should follow Wien's law up to the Higgs vacuum fundamental mass, under the assumption that emission happens as spin-anti-aligned pairs (or higher even integers) of gravitons. (I have argued that removing the assumption of metric tensor symmetry from general relativity allows this degree of freedom in the Hilbert space of gravitons, in earlier work.)

This is still incomplete/bugged, for simple cases.

[WrathfulSpatula]

I'm still confused on Planck's/Wien's considerations, for the moment. Those apply as per usual, but I need to figure out peak frequency from a single nuclear mass monopole emitter, and I'm trying to do it with a Gaussian surface, with Fermi's Golden Rule to consider.

(Thermodynamically, we're no longer talking about kinetic particles in a gas or a lattice, but rather weakly-interacting boson temperature from the mass excitation of the nuclei.)

[WrathfulSpatula]

We're not working backwards from a temperature to a spectral frequency, in this case, as per Planck's and Wien's laws. We have a system of independent free point sources for gravitational monopole radiation, as opposed to quantized, (at least, that I can figure). This radiation is emitted in packets of E=h nu. These point sources can absorb each other's radiation. We can draw a Gaussian surface around any single point emitter in the material bulk, and we can model its flux across that boundary. Per Fermi's golden rule, the transition probability is linearly proportional to the density of states at the energy level after transition. The emitters can emit up to their entire excitation energy as a single massless boson. We call the energy level state density of all available excitation energy being emitted as 1 or more particles, rho(h nu).

I think that rho(h nu) is actually exactly equal for all states from 0 to complete emission of excitation. 1/2 the energy emitted in 1 or more particles, for example, would have half the available combinatoric states available compared to full excitation energy, but can happen twice at once, and so on linearly across the spectrum. So, peak frequency should be 1/2 total excitation energy for an emitter, if I have that right. Further, I think this matches the expectation from the virial theorem in statistical mechanics, such that the average energy per oscillator works out to be 1/2 k * T. I don't know that I've argued it with sufficient rigor, but I think this means our estimate of 1/2 the excitation energy emitted as peak frequency from every point emitter might be right.

[WrathfulSpatula]

In other words, the average energy per source is 1/2 k T, and we work backwards from Wien's law due to quantization of radiation temperature, to avoid an ultraviolet catastrophe, I think. I might have guessed right, last night.

[WrathfulSpatula]

Rethinking this, say that virial theorem tells us that the average energy carried by each degree of the system is 1 / 2 k T. Say that this corresponds to our average excitation energy per nucleus, "x." Further, the Maxwell-Boltzmann distribution would seem to apply as (k T / m)^(1/2) goes to (1 / 2 k T), for our case, (velocity versus kinetic energy). The mode of the Maxwell-Boltzmann distribution is k T in our case, hence the peak thermal frequency is 2 * x. Then, work backwards from Wien's law, (dividing by Wien's displacement constant).

[WrathfulSpatula]

Sorry for the rapid-fire comment edits, but that's basically it, now. To state it simply: virial theorem and Maxwell-Boltzmann both apply. However, Maxwell-Boltzmann gives a distribution of velocities corresponding to kinetic energies, assuming kinetic energy is 1 / 2 m v^2. We convert the quantities of Maxwell-Boltzmann to a distribution of energies, corresponding via the definition of the kinetic energy. We know average energy per nucleus, and this is 1 / 2 k T. Mode energy is therefore k * T, corresponding to the peak of Wien's displacement law.

[WrathfulSpatula]

Wait, it's even simpler: extrinsically, we know the total excitation energy, and we know the nucleus count, so this average energy is 1 / 2 k T. Divide by (1 / 2 * k) to get the temperature. (Duh.) No Wien's law necessary. I'll correct this when I have the chance.

[WrathfulSpatula]

Short of continuity equations for localized heat transfer within a material, I think the current round of updates is done, here. I conclude that all we need is virial theorem, since we already know the extrinsic total excitation energy, and we know the nucleus count. Average energy per nucleus is E=1 / 2 k T, and we have the temperature of rigid body objects. Emissivity should probably be very high, since the "black body" interacts with a "weakly interacting" (composite scalar) boson gas to which it is nearly transparent, and permittivity should be equal to that of vacuum, since these are monopole materials rather than dipole.

[WrathfulSpatula]

See my personal blog, ultraphrenia.com, for details, and particularly this preprint: Monopole waves in general relativity. If Rindler horizons evaporate via Hawking radiation the same way black hole event horizons do, I'm arguing that we have to abandon the assumption of metric tensor symmetry, (which Einstein questioned himself back during his own career,) since the metric connection must vary from strictly global Levi-Civita. We develop a theory of a composite scalar boson graviton gas that results, from allowing an asymmetric rank-2 potential.