I was going to post this in my other thread, but the idea's are good enough to start a new investigation for a new post.

The phase velocity of a particle or wave in a medium is

[math]v = \frac{c}{n}[/math]

For light, in literature, the refractive index [math]n[/math] decreases with an increasing wavelength,

[math]1 < n(\lambda_{red}) < n(\lambda_{yellow}) < n(\lambda_{blue})[/math]

The alternative statement for this is

[math]\frac{dn}{d\lambda} < 0[/math]

In such a case, the dispersion is said to be normal.

https://en.wikipedia...ersion_(optics)

This however, takes us to the Fresnel drag coefficient, that is, the index of refraction is

[math]w_{+} = \frac{c}{n} + v[/math]

and in the other direction

[math]w_{-} = \frac{c}{n} - v[/math]

From it, Frizeau found that

[math]w_{+} = \frac{c}{n} + v(1 - \frac{1}{n^2})[/math]

If we replace the concept this was used in first context of light traveling against the flow of a fluid, with gravity, then the speed of the light will be seen travelling slower with the flow of the fluid. This brings us back to the well-known concepts now, that light is not truly a constant when inside a gravitational field.

But to do this, we require dragging coefficient [math]f[/math] which involves an experiment by Arago in which that an aether drags light propagating through it with only a fraction of the mediums speed. Gravitational aether theories are not very well-explored, but if we accept that light is not a constant in general truth when gravitational fields are involved, then the dragging coefficient should be no different to the one proposed

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

Then in 1895, Lorentz predicted the existence of an extra term, which brings us back to the dispersion formula, which is why we mentioned it in the beginning of this post:

[math]w_{+} = \frac{c}{n} + v(1 - \frac{1}{n^2} - \frac{\lambda}{n} \frac{dn}{d\lambda})[/math]

In particular, this term

[math]\frac{dn}{d\lambda}[/math]

in which we had noted the relationship

[math]\frac{dn}{d\lambda} < 0[/math]

Now, let's say a little about the gravitational aether, something which Einstein supported strongly, but did not appear to realize that the constancy of the speed of light in the medium of space is [not] generally constant like he believed his theory predicted.

**A Gravitational Aether**

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.

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 - it may not be the case the constant does change, but what it may have to do with is the gravitational acceleration which is proportional to 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 G 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] (the gravitational permittivity and permeaility) 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.

**Edited by Dubbelosix, 01 June 2019 - 09:46 AM.**