On Mar 6, 9:41 pm, Albertito wrote:
There are evidences showing that in Solar system,
the speed of gravity is many orders of magnitude higher
than the speed of light. But, what must we understand
by speed of gravity?. Aetherists often claim that gravity
are longitudinal waves, whereas light are transverse
waves through the aether.

I'm not sure I follow. Gravity are [sic] longitudinal waves??
Gravity is a force.. are you talking about gravitational waves?

Or are you saying that graviational forces are somehow carried out by
absorption and emission of some waves? That seems unlikely
considering gravitational lensing and other effects.


We know that in any medium
longitudinal waves travel faster than transverse waves.

Not "in any medium", but in a medium defined with elasticity/solid
stress parameters E,G,v and K you use below. Right?



We can find that longitudinal speed, c_L, and transverse
c_S, in a medium, with Young's modules E, Poison's ratio
v and mass density d_0, are

c_L^2 = (E/d_0(1+v))(1-v)/(1-2v)
c_S^2 = (E/d_0(1+v))(1/2)

We also know there exists a relation between those
elastic constants, as

E=2G(1+v)=3K(1-2v),

where G is shear modulus and K is bulk modulus.
So, we have

c_L^2 = (2G/d_0)(1-v)/(1-2v)
c_S^2 = G/d_0

Therefore, for a Poison's ratio of v=1/2, it would result an
infinite longitudinal speed. In general we have

c_L^2 + c_S^2 = (G/d_0)(2(1-v)/(1-2v) + 1)

This quadratic relation suggests (G/d_0)(2(1-v)/(1-2v) + 1) is
a universal constant for vacuum. This suggests

(G/d_0)(2(1-v)/(1-2v) + 1) = (R/t_p)^2,
where R is a scale parameter and t_p is Planck time.
or
(G/d_0)(2(1-v)/(1-2v) + 1) = c^2 (R/l_p)^2,
where l_p is Planck length.

c_L^2 + c_S^2 = c^2 (R/l_p)^2,

So, for a speed of light being c_S=c, it would yield

c_L^2 + c^2 = c^2 (R/l_p)^2,

c_L = c sqrt((R/l_p)^2 - 1), which is roughly

c_L = c R/l_p,

if R is meaningfully larger than l_p.

If we define R = R_h (Hubble radius), then the speed
of gravity, there where the local speed of light is c,
would be

c_L = c R_h/l_p,

it is saying it would be a very superluminal speed
(i.e. infinite for practical purposes).