Permittivity And Permeability In Gravitoelectromagnetism

[Dubbelosix]

There is a special relationship between permittivity and permeability in the Sciama model that I am not aware that Sciama himself was aware of.

 

There does exist in literature, a direct analogy of the gravitational permeability and permittivity. It is stated that [math]\epsilon_G = \frac{1}{4 \pi G}[/math] is the gravitational analogue of the vacuum permittivity [math]\epsilon[/math]. Gravitational waves have been experimentally varified to move at the speed of light - this is related in analogy (Sivaram, Sabatta) with electromagnetism [math]c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}[/math] and that a corresponding gravitational interpretation is [math]c = \frac{1}{\sqrt{\epsilon_G \mu_G}}[/math]. This implies the gravitational permeability is [math]\mu_G = \frac{4 \pi G}{c^2}[/math]. Sciama defined the gravielectric field as using cgs units for the gravitational constant:

 

[math](\frac{\Phi + \phi}{c^2}) = -\frac{1}{G}[/math]

 

*the units chosen for G ensures that the ratio of the scalar and the speed of light squared is not dimensionless, as often encountered in physics.

 

This equation may be understood when reformulated to represent an inverse gravitational permeability:

 

[math]\Phi = -\frac{c^2}{4 \pi G}[/math]

 

That mean's Sciama's gravielectric scalar potential is itself the definition of the inverse permeability. A unique property of these special units is that the ratio and inverse ratio have the relationships:

 

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

 

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

 

Both these quantities appear within the framework of a single gravitomagnetic coupling equation to angular momentum

 

[math]\mathbf{B} = \frac{1}{mc^2 r}(\frac{\Phi}{c^2})\frac{\partial v}{\partial t} \mathbf{J} \approx \frac{1}{mc^2 r}(\frac{1}{c^2} \frac{c^2}{4 \pi G})\frac{\partial v}{\partial t} \mathbf{J} = -\frac{1}{mc^2 r}\frac{1}{4 \pi G}\frac{\partial v}{\partial t} \mathbf{J}[/math]

 

Sciama never attributed the inverse G to the permeability but doing so makes Sciama's equation an approximate.

Edited March 28, 2018 by Dubbelosix

[exchemist]

In case any readers might be confused, the relationship between the speed of light, c, and the electrostatic permittivity, ε₀ and magnetic permeability, μ₀ of free space is:

c = 1/√(ε₀.μ₀),

 

not  c = √(ε₀.μ₀), which anyone with a reasonable grasp of physics will immediately realise would lead to a laughably slow speed for light! 

Edited March 21, 2018 by exchemist

[exchemist]

I have edited the main work to account for the discrepancy. It didn't effect the work, I did after all know what I meant :)

Affect. 

[Super Polymath]

The quantum eraser deletes the past, it deletes time, which is a part of space. Einstein's spacetime ether is permeatitive gravity, it's also non-vanishing in contrary to planck mass, this permativity you refer to.

 

So in my DID theory posted last night I said that if de sitter space has 2.6 dimensions, ADS will have 2.4, & motion/gravitoelectromagnetism will not exist because this bi-dimensional ether is stable, nothing is getting quantum mechanically erased.

 

However, at points with low thermodynamic conductivity in de sitter space where the dimensions are greater than 2.6 the ether has to stabilize via the quantum eraser. Where they were less than 2.4, the dimensions had to compensate via expansion.

 

I showed this by adding a special case bi-brane inequality operation that held up to every possible piece of factual LCDM data I could throw at it, even regarding what's known about expansion, electromagnetism, the nuclear forces, and quantum electrodynamics.

Edited March 24, 2018 by Super Polymath