The thermodynamic properties of the medium are directly related to the gravitational wave, just as a phonon is related to the properties of a fluid (semi-solid state)> The entire possible gravitational waves will have to be described as a dispersion relation - which is something already implemented in my equations which feature drag as an analogue to a correction term predicted by Lorentz. The density of those states will determine the available heat capacity of the gravitational medium (aether). We can demonstrate some of the master equations which explain this:

The drag in three dimensions was derived from a set of equations using simple algebra:

[math] \frac{1}{n^2} - \frac{1}{n^2} + \frac{\lambda}{n^2} \cdot \frac{dn^2}{d\lambda} = 1 + f [/math]

[math]f = \frac{2F}{\rho v^2 A}[/math]

[math] 1 + \frac{2F}{\rho v^2 A} = \frac{1}{n^2} - \frac{1}{n^2} + \frac{\lambda}{n^2} \cdot \frac{dn^2}{d\lambda}[/math]

[math]f = \frac{A_b}{A_f} \frac{B}{Re^2_L}[/math]

[math] 1 + \frac{A_b}{A_f} \frac{B}{Re^2_L} = \frac{1}{n^2} - \frac{1}{n^2} + \frac{\lambda}{n^2} \cdot \frac{dn^2}{d\lambda}[/math]

With the following term [math]\frac{\lambda}{n^2} \cdot \frac{dn^2}{d\lambda}[/math] as a correction to the drag formula first predicted by Lorentz [and is] a dispersion relationship, one which possibly has implications to the gravitational transverse waves. While gravitational waves are understood to be transverse, their possible polarizations are not described under vectors, but instead a transverse tensor. However, this may be up to debate, because for a complete analogy to a sound wave passing through a medium, such as a desired fluid model, sound waves are often seen as longitudinal waves which are basically compression waves – we know the gravitational wave compresses as it passed through a detector – a fluid however also allows a sound wave to be described under both longitudinal and transverse waves. So a prediction may be made, that a gravitational wave is not only transverse, but also longitudinal.

The realization was that the index of refraction had to be quantized, revealing that the principal quantum number plays the identical role:

[math]\frac{1}{n^2} + \frac{1}{n^2} + \frac{1}{n^2} = - \frac{1}{\rho v^2 A} \cdot \rho v^2 f A = -f[/math]

[math]\frac{1}{n^2} + \frac{1}{n^2} + \frac{1}{n^2} = -f[/math]

[math]\frac{1}{n^2} + \frac{1}{n^2} + \frac{1}{n^2} - 1 = f + 1[/math]

If we take the first three terms of the spatial dimensions, than its last part has to be associated to the timelike dimension:

[math]\frac{1}{\lambda}(\frac{x}{n^2} + \frac{y}{n^2} + \frac{z}{n^2} - ct) = f + 1[/math]

The heat related to entropic gravity with correspondance to the drag coefficient was:

[math]F = \frac{1}{2} \rho v^2\ f\ A = m\frac{2 \pi c\ k_BT}{\hbar} = m\frac{4 \pi c}{\hbar} \frac{E}{N} = m\frac{4 \pi c^2}{\hbar} \frac{M}{N} = \frac{4 \pi GMm}{A} = G \frac{Mm}{r^2}[/math]

and a heat flow as

[math]\dot{F} = \frac{1}{2} \rho v^2\ f\ A_f = \dot{m}\frac{2 \pi c\ k_BT}{\hbar} = \dot{m}\frac{4 \pi c}{\hbar} \frac{E}{N} = \dot{m}\frac{4 \pi c^2}{\hbar} \frac{M}{N} = \dot{m}\frac{A_b}{A_f}\frac{4 \pi GM}{r^2} = \dot{m}\frac{GM}{r^2}[/math]

The pressure and stress energy was related also as

[math]P = f \cdot q = \frac{1}{2}f \cdot \rho v = \frac{1}{2}f \cdot \mathbf{j} = \frac{1}{2n^2A_f}(x + y + z - \sigma_{x,t})^2\ T_{00} [/math]

[math]T^{00} = g^{00}(\rho + P_0 - P) = (\rho_m + \frac{P_0 - P}{c^2})v^0v^0 = (\rho_m + \frac{q}{c^2})v^0v^0[/math]

In such a case, the gravitaional wave is an acoustic wave and also a pseudo-fluctuation as presented in previous idea's from already known models existing in literature. We know experimentally-speaking, the gravitational wave does not always move at light speed, in fact the acousting properties are also affected by the field itself - this has been tested to quite a good degree of accuracy, in which gravitational waves arriving at Earth had a slighter delay time than the photons from the same source. This at the core of it, demonstrates how light speed cannot reach zero velocities with current idea's, but can in fact escape a black hole solving the information paradox... It might take light a long time to leave the core of a black hole but in theory it should be possible which solves itself the information paradox.

The index of refraction related to a principal quantum number was purely an intuitive idea, but after heated exchanges on a specific forum in which people had declared there was no reason to think this, I did finally do some research and found that this approach has at least been speculated:

https://www.researchgate.net/post/Is_there_a_quantum_model_for_the_refractive_index

This demonstrated to me at least that the idea was not bizarre at all and in fact was intuitively correct from a quantum physical viewpoint. Let’s describe what a gravitational aether means and what it involves as it has quite a history, but to keep it simple with modern physics, we have to go to a paper that has modified the refractive index in terms of the gravitational aether properties of a permittivity and permeability which are inescapable since the discovery of gravitational waves.

As just explained, excellent arguments exist now for the existence of the gravitational permittivity and permeability with the discovery of gravitational waves. The constancy of the speed of light only holds in a vacuum - but the density of gravitation varies between celestial objects and therefore the speed of light does technically vary.

In fact, authors Masanori Sato and Hiroki Sato in their paper ‘’Gravitational wave derived from fluid mechanics applied on the permittivity and the permeability of free space’’ suggests that gravitational waves are simply fluctuations of the medium, which appears as the product of the permittivity of free space and the permeability of free space. That is, the gravitational wave is an acoustic wave in the medium - the proposal shows how the phase velocity of the fluctuation relates to the speed of light

[math]c = \frac{1}{\sqrt{\epsilon_G \mu_G}}[/math]

The model has some interesting consequences, first being that permittivity and permeability are allowed to vary. A second is that the speed of light is variable in gravitational fields. Another interesting property is that while both Newtonian mechanics and Einstein’s relativity theories predict the confinement of light by gravity, neither theory defines the escape velocity or the Schwarzschild radius; in fact, the actual speed of light can only approach zero but never reach it - so in effect light is allowed to escape from a black hole.

Let’s be clear about something - I do not believe that the thickness of space (the medium) is an aether made from any particle. In fact there cannot be any motion associated to this aether because it would violate the first principles of relativity. In fact you can argue as I have already done, that any true quantization of gravity would be at odds concerning how we actually think about the roles of pseudo forces. There is also a different kind of question that comes into the market, an anomaly concerning the measurement of Newtons constant.

Many experiments have been performed to measure the value of the Newtonian [math]G[/math] but has come up with varied results and up until this year another measurement has cast a shadow over settling why we keep measuring different values for the constant. Since in this aether theory I have chosen, both permittivity and permeability will depend on [math]G[/math] ~

[math]\frac{1}{\epsilon_G} = 4 \pi G[/math]

[math]\frac{1}{\mu_G} = \frac{c^2}{4 \pi G}[/math]

This leaves open a question of whether the deviations in the value of [math]G[/math] has something to do with variations spacetime permittivity and permeability. This particular theory of the aether, as a dynamical ''thickness'' of space due to varying gravitational density, the refractive index for radiation is proportional to [math]\sqrt{\epsilon_G \mu_G}[/math] (permittivity and permeability) and is represented as:

[math]n = \sqrt{\frac{\epsilon_G \mu_G}{\epsilon_0 \mu_0}}[/math]

A high refractive index for the equation [math]\frac{1}{\sqrt{\epsilon_G \mu_G}}[/math] causes a low speed of light (such as found round strong gravitational fields of black holes). It has been argued in literature that the refractive index is more intuitive than curvature; this suggestion is probably quite true, since curvature is the presence of a dynamic metric but we know not what causes this ''dynamic feature'' other through the presence of matter - which is well-known to tell spacetime how to curve, but still doesn't explain why the dynamic phenomenon exists. In a sense, the gravitational explanation for a refractive index supposes a type of mechanical explanation to curvature.

I proposed that the Von Klitzing constant may be subject fundamentally to the permittivity and permeability of space:

[math]\frac{\mathbf{J}}{e^2} = \sqrt{\epsilon_G \mu_G}[/math]

At first, how to make any sense from this hypothesis so far had proven to be difficult, but in gravielectromagnetism, the term kept popping up from the equations.

**Edited by Dubbelosix, 27 June 2019 - 05:56 AM.**