1 Does gravity travel at the speed of light?

2 Does gravity travel at the speed of light?

Such sound bites are rarely correct in GR. It will take me a page to explain....

This depends on what model you use, and how you apply it, and whether you can use an approximation. As an illustration of the difficulties, remember that in GR "now" is not well defined except at a single point.

First Model: In Newtonian mechanics (NM), gravity does not propagate at all. It is in general a function of the universal time, but anywhere you measure it the value depends only on the physical situation at the time of the measurement. Gravity is a function of each mass's position at the time of the measurement (Poisson's equation). Speaking loosely, gravity "propagates with infinite speed".

In GR this is not so, and the situation is considerably more complicated. First a digression to SR.

Interlude: classical electrodynamics (CE):
In CE one can compute the E and B fields at a a point (x,y,z,t) in inertial frame S [#] via the Lienard-Wiechert potential. This evaluates the location and velocity of each charge at a retarded point (x',y',z',t') [@] such that the interval between these two points is null -- i.e. a vacuum light ray would propagate from the primed point to the unprimed point. E and B are functions of the charge's position and velocity at the primed point. If you examine the math, you find that this potential in effect makes a linear extrapolation of each charge's position to t ("now") in S. As a result, E from a given charge points very close to where the charge is "now" (in S), and exactly there if the charge is moving inertially; even though the EM field propagates at c.

[#] Remember that in CE the EM field is really a 2-form which must be projected onto an inertial frame to obtain E and B. This requirement foreshadows much greater complexities in GR.

[@] Note the primes denote a different point in S, NOT a different frame.

Second model: In the linearized approximation to GR, the equivalent construction does a similar thing, in that it uses the retarded position of each mass, extrapolating its position, velocity, and acceleration to "now". So in this approximation the "gravitational force" at each point points very close to where the mass is "now", with magnitude 1/distance^2; exactly so if the mass is following a second-order curve in the equivalent to S. In this approximation the "gravitational force" from a mass points at its location "now"; even though gravity propagates at c.

Third model: In GR itself (i.e. NOT that approximation), there is no "gravitational force", the above construction does not apply, one cannot add "gravitational fields" from multiple masses (equations are nonlinear), energy other than mass contributes, and things are VASTLY more complicated. But still, one can say that CHANGES in gravity propagate at c, which yields gravitational waves.

Conclusion: GR goes smoothly into NM as long as one looks at a small enough region of spacetime in which all masses and velocities are "small" (so the above approximation applies). This is so even though speaking loosely one might say "gravity propagates at c in GR but with infinite speed in NM" -- as discussed above the actual situation is more complicated than such a sound bite can capture.

Tom Roberts

3 Does gravity travel at the speed of light?

4 Does gravity travel at the speed of light?

Am 18.03.2017 um 02:59 schrieb Richard D. Saam:

>

Given the well known reference: http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html The discussion is oriented around the earth orbiting the sun: "In the simple newtonian model, gravity propagates instantaneously: the force exerted by a massive object points directly toward that object's present position. For example, even though the Sun is 500 light seconds from the Earth, newtonian gravity describes a force on Earth directed towards the Sun's position "now," not its position 500 seconds ago. Putting a "light travel delay" (technically called "retardation") into newtonian gravity would make orbits unstable, leading to predictions that clearly contradict Solar System observations." How does this concept translate in to universe observations? It would appear that gravity travels instantaneously among all "now" time objects (galaxies etc). Is that correct?

Dynamical equations have time independent solutions.

This so called kernel of its time development operator consists of constant fields that have to be discussed away and fields that are watermarks of the geometry.

If such a field is present there is no need to discuss its "propagation". The prototyp of such watermark fields are the 1/r-potential in electrodynamics and in Newtons gravitation.

The 1/r fields count the number of elementary charges by measuring this field at infinity by its feature to have a constante E-field flow that integrates over any sphere to the same number now matter how large or small.

By this simple idea, "propagation" is what remains if these constant fields at infinity are removed from calculations.

The calculations are not so easy to perfom if many charged particles are moving, but the idea that no action can exceed speed of light simply excludes that the constant 1/r field at infinity can change at all over time because a change had to be instananeous of infinite distances in space.

This is at the heart of the fundamental law of electric charge conservation by Maxwells equation -Laplace(phi) =div E = rho.

For Einstein equations, the time independent solution with a central mass is again a mass/r-field that is simply a measure of the total mass-energy confined inside a ball. It yields by a rotation of the tangent space of test particles the trajectories as circles, ellipses and hyperbolas in the spatial 3d-projection of their world lines.

If one is considering not passive test particles but a two body problem, again, the combined mass-energy creates a static 1/r curvature at infinity and the dynamical part consists of two centers. Their relative coordinate is moving in the nonlinearly combined gravitational field of the common center of gravity plus a dymamical quadrupol correction.

The quadrupol is coupled to the gravitional radiation field and by this radiation the mass-energy content of the bound system decreases, the 1/r field at infinity changes changes too. In contrast to Maxwell charge this is possible because the equations are nonlinear.

So of course both bound masses react in every moment to the geometry created by their whole past and not only to the actual position.

Of course, since interaction with waves is small, in some way, the approximate conservation of total momentum and angular combined as seen from far away outside directly demonstrate, that actio=reactio remains intact and the two bodies, moving eg on circles, remain on circles with slowly decreasing radial coordinates for all times. Their angular displacement will be always pi exactly.

So their interaction by movement in the common 1/r fiels always looks as if their interaction "propagates" instantly along the diameter through the center.

But there is no propagation of modes with frequency=energy=0.

--

Roland Franzius

5 Does gravity travel at the speed of light?

The discussion about the speed of gravity is as long in this newsgroup as the road to Rome....

I prefer to say that considering Newton's law gravity acts instantantaneous. That means the force of gravity points to the present position of each object considered, independent of its distance. This is wrong, but from Newton's point of view very clever (handy).

Current main? opinion is that the speed of gravity is the same as the speed of light.
I prefer a different line of reasoning. What is the relation between gravity (force between objects) and the speed of light (photons or radiation in general)? IMO (If I'm allowed) physical almost nothing. IMO there exist a whole different question: Is the speed of light constant? IMO the answer is no. The speed of light is influenced by gravity.

What I myself have done is to simulate the movement of the planet Mercury (including many more planets) assuming that the speed of gravity is not infinite.
The problem is when you use cg = c than such a simulation is not possible. When you use much higher speeds such simulations become realistic.

That does not mean that the speed of light is not important to perform simultions. The speed of light is important to handle (initial) observations and in order to validate the results.

I have frequently asked in this newsgroup about results to do the same using GR. There is not much responds. My own experience with GR involves one object the Sun and the planet Mercury as a point mass. No other planets. The mathematics involved using GR is very tricky.

IMO the only way to simulate stars is using Newton's Law with a speed of gravity roughly 100 times c.

6 Does gravity travel at the speed of light?

Hmmmm. This depends in detail on what one means by "speed of gravity". See my recent post in this thread for details.

>	Is the speed of light constant? IMO the answer is no. The speed of light is influenced by gravity.

In GR the LOCAL speed of light (in vacuum) is not influenced by gravity. Over non-local paths one can certainly measure values different from c, but that's not a very useful measurement because it depends in detail on how it is made, and standard techniques won't hold (in particular, how to synchronize clocks and KEEP them synchronized).

>	What I myself have done is to simulate the movement of the planet Mercury (including many more planets) assuming that the speed of gravity is not infinite. The problem is when you use cg = c than such a simulation is not possible. When you use much higher speeds such simulations become realistic.

Well known. Simply modifying Newtonian gravity with a finite speed is a non-starter. You have to use the post-Newtonian approximation to GR, which is much more complicated, but accurate.

Also see my earlier post in this thread -- in the solar system the approximation holds, and even though gravity "propagates" with speed c, the "gravitational force" essentially extrapolates objects' positions to "now" so it is essentially as if gravity "propagated instantaneously".

I'm speaking loosely here; see that post for details.

>	I have frequently asked in this newsgroup about results to do the same using GR. There is not much responds. My own experience with GR involves one object the Sun and the planet Mercury as a point mass. No other planets. The mathematics involved using GR is very tricky.

Well known. Doing a full-up simulation of the 2-body problem in GR is HIGHLY non-trivial, and using more objects is even more difficult. Here there be dragons, and non-experts are unlikely to succeed. But the post-Newtonian approximation might be accessible to a person skilled in simulations and software development.

Tom Roberts

7 Does gravity travel at the speed of light?

8 Does gravity travel at the speed of light?

On Saturday, March 18, 2017 at 2:23:49 AM UTC-7, Tom Roberts wrote:

>

... Interlude: classical electrodynamics (CE): In CE one can compute the E and B fields at a a point (x,y,z,t) in inertial frame S [#] via the Lienard-Wiechert potential. This evaluates the location and velocity of each charge at a retarded point (x',y',z',t') [@] such that the interval between these two points isu null -- i.e. a vacuum light ray would propagate from the primed point to the unprimed point. E and B are functions of the charge's position and velocity at the primed point. If you examine the math, you find that this potential in effect makes a linear extrapolation of each charge's position to t ("now") in S. As a result, E from a given charge points very close to where the charge is "now" (in S), and exactly there if the charge is moving inertially; even though the EM field propagates at c. ... Tom Roberts

This is certainly true for radial motion, but is it true also for tangential motion, which is the relevant case here? The denominator in the Lienard-Wiechert potentials has a dot product with the radial separation vector. For a source moving tangential to this vector the denominator is just the radial separation. It isn't clear to me that this would cause a lateral deviation in the direction of the electrostatic force to where the source "would be" at the present time. Am I wrong about that?

Rich L.

9 Does gravity travel at the speed of light?

Just like the Lienard-Wiechert potentials of classical electrodynamics, this obeys the maximum speed of c. It is the extrapolation that makes it LOOK as if gravity "propagated instantaneously" -- but gravity does not actually do so in GR.

>	So something must be in power to avoid this.

Yes. The local Lorentz invariance of the equations. Such symmetries are the foundations of physics.

>	It could be that "nothing surprising" can happen in the world with regard to the gravity field in the sense that the extrapolation you mention must coincide with the real behavior.

Hmmm. The predictions of both CE and GR agree very well with the results of experiments. So they do "coincide with the real behavior", at least within their domains.

>	If one could "surprisingly" create a large amount of energy at a place, we would not expect this new information to be able to escape faster than light. This might indicate that such an event (a "surprising" creation of energy at a place) is not possible.

The local conservation of energy also prohibits that. GR has nothing to say about such an unphysical scenario. That is, it is not possible to construct a manifold in which that happens and which also satisfies the field equation. But also, nobody has ever reported observing such a scenario in the world we inhabit.

Tom Roberts

10 Does gravity travel at the speed of light?

The speed of gravity has to do with a gravitational event and the detection af that event a distant away (including gravitons) The speed of light has to do with a lightning event and the observation af that event a distant away (including photons)

Both events can be the 'same' (the same origin) but that does not mean that the detection resp observation are simultaneous. For example a collision between two large stars.

>	In GR the LOCAL speed of light (in vacuum) is not influenced by gravity. Over non-local paths one can certainly measure values different from c etc.

11 Does gravity travel at the speed of light?

You must include the terms related to object n's velocity and acceleration. These are part of the post-Newtonian approximation to GR, but are not in a simplistic extension of Newtonian gravity. These make the force from object n be very, very close to the Newtonian calculation using its current position [#] and infinite "propagation" speed.

[#] in suitable coordinates, such as BCRS.

>	In the solar system if you want to simulate the movement of the planet mercury, you 'must' use the approach explained above.

Depends on the accuracy you require; for many purposes Newtonian gravity is sufficiently accurate (and A LOT simpler). If going beyond NG, be sure to use the P-N approximation to GR, not a simplistic extension of NG.

>	Imo you also have to take the movement of the sun into account if you want to simulate for thousands of years.

OF COURSE! Because you surely will use the Barycentric celestial reference system (BCRS).

>	Sorry but imo in this approach you can not claim that gravity propagate instantaneously (or behaves as if it propagates instantaneously)

Sure. In the post-Newtonian approximation to GR, gravity propagates at c; but due to the extrapolation discussed above, results are APPROXIMATELY the same as Newtonian gravity in which it "propagates" instantaneously.

>	My, maybe biased, opinion is, that in case of n-body problem, using GR is practical 'impossible' when stars are evolved.

I'm not sure what you mean. The post-Newtonian approximation to GR applies when gravity and speeds are "small", and that can include many (but not all!) systems of stars. As I said before, it is is extremely challenging to apply GR without approximation to an n-body problem.

>	My first suggestion is why not simulate a system in which no moving clocks are involved?

Huh? Planets and stars are not clocks.

>	A whole different issue is how important are the Lorentz transformations in this context ( n-star problem) ?

The question does not make sense, as only one coordinate system is used. Lorentz transforms are irrelevant in GR, and in the post-Newtonian approximation to GR.

Tom Roberts