## The speed of gravity revisited (nueva revisión de la velocidad de la gravedad)

Posted by Albert Zotkin en abril 10, 2013

Hola amable lector, hoy me gustaría traerte un thread de usenet que inicé hace ya algunos años. En el grupo de usenet sci.physics.relativity creé un thread con el título de “The speed of gravity revisited”. Dicho thread llegó a alcanzar los 368 posts, y entre los numerosos comentaristas podemos encontrar nombres como Tom Van Flandern, Steve Carlip, Tom Roberts, ó Juan R. González-Álvarez.

Una breve presentación de estos cuatro relevantes comentaristas científicos:
1. Tom Van Flandern, era un prestigioso astrónomo americano especializado en mecánica celeste, y entre otras muchas cosas, contribuyó notablemente a mejorar el GPS.
2. Steve Carlip es un prestigiso profesor de física en la Universidad de California, Davis. Son destacables sus papers en gravedad cuántica (2+1) dimensional, fundamentos gravitacionales cuánticos de la termodinámica de los agujeros negros, o en triangulaciones dinámicas causales.
3. Tom Roberts, PhD en fisica, prolífico comentarista en usenet, y acérrimo defensor de la relativdad Einsteniana, trabaja en Fermilab, es autor, entre otros trabajos, de “What is the experimental basis of Special Relativity?”

4. Juan R. González-Álvarez. Cientifico español, con una sólida base académica. Estudió físca y quimica en la Universidad de Vigo. Trabajó en temas científicos en el Ilustre Colegio de Químicos de Galicia y fue investigador asistente de bioquímica de las Rias en el CSIC, participó en varios simposios, conferencias e informes. Puedes encontrar algunos de sus papers en FQXi Community, por ejemplo este.

Lo que sigue son los primeros posts de ese histórico thread en sci.relativity.

 1. Albertito: 6 mar 2008, 22:41 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, cL, and transverse cS, in a medium, with Young’s modules E, Poison’s ratio v and mass density d0, are $\displaystyle c_L^2 = \left (\cfrac{E}{d_0(1+v)}\right ) \cfrac{1-v}{1-2v} \\ \\ \\ c_S^2 = \left (\cfrac{E}{d_0(1+v)}\right ) \cfrac{1}{2}$ We also know there exists a relation between those elastic constants, as $\displaystyle E=2G(1+v)=3K(1-2v),$ where G is shear modulus and K is bulk modulus. So, we have $\displaystyle c_L^2 = \left (\cfrac{2G}{d_0}\right ) \cfrac{1-v}{1-2v} \\ \\ \\ c_S^2 = \cfrac{G}{d_0}$ Therefore, for a Poison’s ratio of v=1/2, it would result an infinite longitudinal speed. In general we have $\displaystyle c_L^2 +c_S^2 = \cfrac{G}{d_0} \cfrac{2(1-v)}{1-2v}+1 \\ \\ \\$ This quadratic relation suggests it is a universal constant for vacuum. This suggests $\displaystyle \cfrac{G}{d_0} \cfrac{2(1-v)}{1-2v}+1 = \cfrac{R^2}{t_p^2}$ where R is a scale parameter and tp is Planck time, or $\displaystyle \cfrac{G}{d_0} \cfrac{2(1-v)}{1-2v}+1 = \cfrac{c^2}{l_p^2}$ where lp is Planck length $\displaystyle c_L^2 + c_S^2 = c^2 \cfrac{R^2}{l_p^2}$ So, for a speed of light being cS=c, it would yield $\displaystyle c_L^2 + c_S^2 = c^2 \cfrac{R^2}{l_p^2} \\ \\ c_L = c \sqrt{\frac{R^2}{l_p^2} -1},$ which is roughly $\displaystyle c_L = \cfrac{c L}{l_p}$ if R is meaningfully larger than lp. If we define R = R_h (Hubble radius), then the speed of gravity, there where the local speed of light is c, would be $\displaystyle c_L = \cfrac{c R_h}{l_p}$ it is saying it would be a very superluminal speed (i.e. infinite velocity, for practical purposes).

 2. Tom Roberts: 7 mar 2008, 17:44 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. Sure. But this is MODEL DEPENDENT. In the model of Newtonian gravitation, gravity propagates INSTANTLY (i.e. with infinite speed). In the model of GR, gravity does not propagate at all, but changes in gravity propagate with speed c. The GR model agrees with all these “evidences”, and indeed it accounts MUCH more accurately than the Newtonian model for measurements in the solar system (including the perihelions of Mercury and other planets, the Shapiro time delay, the bending of EM radiation by the sun, the operation of the GPS, the frame dragging measured by the LAGEOS satellites, etc.). Bottom line: it is MUCH better to discuss models and their agreement with experiments than to discuss MODEl-DEPENDENT quantities like “speed of gravity”. That is, discuss science (experiments) rather than engineering (measurements), and avoid unacknowledged puns (such as model-dependent meanings of words that are treated as if they had a single meaning) like “speed of gravity”. > [… further nonsense based on unrealistic models (“aetherists”)…] Tom Roberts

 3. Juan R. González-Álvarez: 7 mar 2008, 20:17 Tom Roberts wrote on Fri, 07 Mar 2008 15:44:38 +0000: > 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. > Sure. But this is MODEL DEPENDENT. In the model of Newtonian > gravitation, gravity propagates INSTANTLY (i.e. with infinite speed). Being a AAAD theory, nothing propagates in Newtonian gravitation. speaking about infinite speed is misleading also. Infinite speed of what? > In > the model of GR, gravity does not propagate at all, Gravitational waves travel at c like changes in spacetime geometry do. >> but changes in > gravity propagate with speed c. The GR model agrees with all these > “evidences”, and indeed it accounts MUCH more accurately than the > Newtonian model for measurements in the solar system (including the > perihelions of Mercury and other planets, the Shapiro time delay, the > bending of EM radiation by the sun, the operation of the GPS, the frame > dragging measured by the LAGEOS satellites, etc.). GR gives better results (i would not say “MUCH”) for purely relativistic effects. Since NG is non-relativistic, this is not kind of surprising. The problem with NG is that lacks an adequate Newtonian limit. GR literature is incorrect at this point. Moreover, NG is free from several difficulties affecting GR: energy problem, systems of reference problems, unphysical boundaries, quantization, N-body theory… — I apply http://canonicalscience.org/en/miscellaneouszone/guidelines.txt
4. Tom Roberts: 8 mar 2008, 04:11
Juan R. González-Álvarez wrote:
> Tom Roberts wrote on Fri, 07 Mar 2008 15:44:38 +0000:
>> In the model of Newtonian
>> gravitation, gravity propagates INSTANTLY (i.e. with infinite speed).
> Being a AAAD theory, nothing propagates in Newtonian gravitation.
> speaking about infinite speed is misleading also. Infinite speed of what?

Infinite speed of gravity, of course. You are just saying the same thing
using different words (AAAD == infinite speed of propagation of influence).
>> In
>> the model of GR, gravity does not propagate at all,
> Gravitational waves travel at c like changes in spacetime geometry do.

Of course — gravitational waves _ARE_ changes in spacetime geometry.
>> The GR model agrees with all these
>> “evidences”, and indeed it accounts MUCH more accurately than the
>> Newtonian model for measurements in the solar system (including the
>v perihelions of Mercury and other planets, the Shapiro time delay, the
>v bending of EM radiation by the sun, the operation of the GPS, the frame
>v dragging measured by the LAGEOS satellites, etc.).
> GR gives better results (i would not say “MUCH”) for purely relativistic
> effects. Since NG is non-relativistic, this is not kind of surprising.

Hmmm. If you mean NG is accurate in the non-relativistic regime, then
sure. But such a statement carries no information. And the usual meaning
of “relativistic effects” does not apply to any of the measurements I
mentioned. In any case, my “MUCH” is certainly justified — NG fails to
predict ANY of them anywhere close to correctly (why else do you suppose
I chose them?):

 Measurement NG GR Perih. of Mercury et al zero correct Shapiro time delay zero * correct Bending of EM radiation zero * correct operation of GPS hopeless correct frame dragging zero correct

Where “correct” means within the appropriate experimental resolution.
* For NG applied to EM waves, I use the fact that
such waves are massless in making the NG prediction.
> The problem with NG is that lacks an adequate Newtonian limit. GR
> literature is incorrect at this point.

If this is not a typo it makes no sense. If it is a typo, writing “NG”
when you meant “GR”, then you are wrong — there is nothing “inadequate”
about the Newtonian limit of GR.
> Moreover, NG is free from several difficulties affecting GR: energy
> problem, systems of reference problems, unphysical boundaries,
> quantization, N-body theory…

Some of those “difficulties” are merely complications that are
inescapable: energy problem, systems of reference problems. Some are (as
best I can tell) figments of your imagination: unphysical boundaries,
N-body problem. Yes, quantization is a problem for GR and severely
limits its domain of applicability, but NG has much worse problems
(disagreement with numerous experiments within its domain of applicability).
Tom Roberts