The speed of gravity revisited
On Mar 6, 3:41*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. We know that in any medium
longitudinal waves travel faster than transverse waves.
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).
xxein: 'Knowing' doesn't appear reliable because it had already been
just a product of 'ifs' and 'suggestions'. Somewhere along the way a
chameleon math told the physic how it operated. Think of how stupid
that is. You can mathematically describe the physic in countless
ways, but you can't change the physic, itself. If each notion
associated with any line of math were taken as truth, the physic loses
its integrity. We know that can't happen and yet we continually will
it.
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