Concerning how quickly gravity takes to effect distant bodies

[acesuv]

I believe this is related to relativity, as it weighs in on how quickly information can travel through space; and I'm pretty sure this is the idea behind gravity's speed being that of light. However, I was wondering if you think it could be possible that gravity may be faster than light, as massive bodies are influencing the shape of space/time itself. From what I figure, the speed at which space/time is distorted (gravity) isn't necessarily equal to or less than the speed of light, since this doesn't seem to be information moving through space, but rather space itself moving.

In addition, perhaps the speed of gravity could be slower than light. I'm curious of the implications of this, such as gravitational influence from a speeding body (away from you) could become zero if it is traveling faster than the rate that the gravity can be propagated through space/time.

All this being said, what is the current consensus about the "speed of gravity"? Has it been measured? Are there any compelling reasons for a particular speed? Any interesting implications of these possibilities?... are they possible?

 

[Bill_K]

Although gravitational waves have never been detected directly, it is a firm prediction of general relativity that they exist and travel at the same speed as light waves.

 

[pervect]

I believe this is related to relativity, as it weighs in on how quickly information can travel through space; and I'm pretty sure this is the idea behind gravity's speed being that of light. However, I was wondering if you think it could be possible that gravity may be faster than light, as massive bodies are influencing the shape of space/time itself. From what I figure, the speed at which space/time is distorted (gravity) isn't necessarily equal to or less than the speed of light, since this doesn't seem to be information moving through space, but rather space itself moving.

In addition, perhaps the speed of gravity could be slower than light. I'm curious of the implications of this, such as gravitational influence from a speeding body (away from you) could become zero if it is traveling faster than the rate that the gravity can be propagated through space/time.

All this being said, what is the current consensus about the "speed of gravity"? Has it been measured? Are there any compelling reasons for a particular speed? Any interesting implications of these possibilities?... are they possible?

Note that the speed of light is measured by changes in the electromagnetic field - i.e. it's the speed of electromagnetic radiation. You can't measure the speed of light just by looking at the direction of the force, and if you have a medium where light is slow, you won't be able to "outrun" the attraction due to differing charges.

Similar remarks apply to the speed of gravity - it's not measured by looking at the direction of the gravitational attraction, and while it is theoretically possible to slow down gravitational waves, this won't allow you to "outrun" the attractive force anymore than you can "outrun" the attractive force of a charge by slowing light down.

 

[bcrowell]

We have a FAQ on this: https://www.physicsforums.com/showthread.php?t=635645

 

[Bill_K]

From the FAQ:

High-amplitude gravitational waves need *not* propagate at c. For example, GR predicts that a gravitational-wave pulse propagating on a background of curved spacetime develops a trailing edge that propagates at less than c.[MTW, p. 957] This effect is weak when the amplitude is small or the wavelength is short compared to the scale of the background curvature.

The development of wave tails should not be interpreted as a slower propagation speed. The leading edge of a gravitational wave always propagates along a characteristic surface, i.e. at speed c. The development of a tail is better seen as a backscattering effect, i.e. the wave being partially reflected as it traverses a changing background, for example as it climbs out of a Schwarzschild.

 

[Samshorn]

We have a FAQ on this: https://www.physicsforums.com/showthread.php?t=635645

That post includes the statement "based on symmetry properties of spacetime, one can prove that there must be a maximum speed of cause and effect". That seems misleading at best, because to answer questions such as "Is the force of gravity propagated instantaneously?" we need to know about the existence of a FINITE upper bound on speeds (of mass-energy and information, in terms of standard inertial coordinates). If we omit the word "finite" then the proposition has no relevance to whether effects can propagate instantaneously. So we need to stipulate "finite", but the symmetry properties of spacetime (at least the ones invoked by Ignatowski, et al) do NOT imply a finite upper bound on speeds. The existence of a finite upper bound on speeds is put in as a separate premise. The "symmetry arguments" are just as consistent with Galilean relativity (in which gravity COULD conceivably propagate instantaneously) as they are with Einsteinian relativity (in which it couldn't). So those "symmetry arguments" are a red herring in this context.

 

[bcrowell]

[...] the symmetry properties of spacetime (at least the ones invoked by Ignatowski, et al) do NOT imply a finite upper bound on speeds. The existence of a finite upper bound on speeds is put in as a separate premise. [...] The "symmetry arguments" are just as consistent with Galilean relativity (in which gravity COULD conceivably propagate instantaneously) as they are with Einsteinian relativity (in which it couldn't). So those "symmetry arguments" are a red herring in this context.

Yeah, I agree that the way I wrote that part is not optimal. The symmetry arguments lead to two cases: case 1 being Galilean relativity and 2 being SR. However, I don't think the symmetry arguments are a red herring. They establish the entire theory, except for the question of which case it is, 1 or 2. The only additional input is that you choose 2 over 1.

 

[bcrowell]

The development of wave tails should not be interpreted as a slower propagation speed. The leading edge of a gravitational wave always propagates along a characteristic surface, i.e. at speed c. The development of a tail is better seen as a backscattering effect, i.e. the wave being partially reflected as it traverses a changing background, for example as it climbs out of a Schwarzschild.

We discussed this before and failed to convince one another: https://www.physicsforums.com/showthread.php?t=634813

 

[Bill_K]

Ben,

I had forgotten about that discussion. I'm still right, of course!

The Wikipedia articles on hyperbolic PDEs and characteristics are typically overloaded with math. (Who writes these things??) The concepts are much simpler than they're made out to be, and are used in all fields wherever PDEs are involved. I'd say the very first subject covered in a PDE course is the division into hyperbolic, parabolic and elliptic systems. The wave equation is the prototype hyperbolic equation, and appearance of the wave operator is usually a dead giveaway that the system is hyperbolic.

To tackle nonlinear PDEs, we linearize the problem and look at small disturbances. This is already familiar for Einstein's Equations, where we put g_μν = η_μν + h_μν for weak fields, or more generally g_μν = g⁰_μν + h_μν where g⁰_μν is a background metric. Note that g⁰_μν can be any Einstein solution at all, including spacetimes that are dynamic. Then h_μν obeys a set of linear PDEs,

◻h_μν - h^α_ν;αμ - h^α_μ;αν - h^α_α;μν = 0

where everything (wave operator, raising/lowering and covariant derivative) is wrt the background metric.

Characteristics come in when we take the high frequency limit. That is, we look at a disturbance which is not only small but also abrupt: a step function, a "shock wave", a discontinuity. Low frequency waves are spread out, while high frequency waves are completely localized. In the equation, all we have to do is focus on the highest derivative terms, i.e. discard the first derivatives. The result is just the wave equation in the background metric, ◻h_μν = 0.

Is this hyperbolic? Of course it is. At any point, the background is locally Minkowskian and you have local coordinates in which ◻ = ∂_t² - ∂_x² - ∂_y² - ∂_z². There's a local light cone, and solutions to the wave equation have all the usual local properties - they propagate at the speed of light. Again, this is a standard element of general relativity - in vacuum, discontinuities can only occur across null surfaces. Which are, in general terms, what we call characteristic surfaces.

In the high-frequency limit, information (i.e. a small localized perturbation) travels along the bicharacteristics, which are the null geodesics that lie in the null surface.

 

[pervect]

Ben,

Again, this is a standard element of general relativity - in vacuum, discontinuities can only occur across null surfaces. Which are, in general terms, what we call characteristic surfaces.

In the high-frequency limit, information (i.e. a small localized perturbation) travels along the bicharacteristics, which are the null geodesics that lie in the null surface.

Is this still true in a medium - i.e. a non-vacuum?

 

[bcrowell]

Hi, Bill -- Thanks for your #9, which is very illuminating. I think the real issue here is one of definition, and there is no satisfactory way to resolve it. I'm happy to concede that gravitational effects propagate at c locally. Whether they propagate at c globally is a different issue. GR simply doesn't offer a way of describing velocities non-locally. Since it doesn't allow us to define velocities non-locally, it can't define whether gravitational waves propagate at c globally. This means that when we observe the behavior of gravitational disturbances in GR, there is an inevitable ambiguity in defining whether we think they are propagating at c. I can interpret the existence of wave tails as demonstrating propagation at less than c, and you can interpret it the opposite way. It seems to me that GR doesn't offer the tools that would allow us to settle who is right.

 

[Bill_K]

High-amplitude gravitational waves need *not* propagate at c. For example, GR predicts that a gravitational-wave pulse propagating on a background of curved spacetime develops a trailing edge that propagates at less than c.

The development of wave tails should not be interpreted as a slower propagation speed. The leading edge of a gravitational wave always propagates along a characteristic surface, i.e. at speed c. The development of a tail is better seen as a backscattering effect,

Another reason to consider this a backscattering effect rather than a slower wave speed is that backscattering is a more general phenomenon. An outgoing electromagnetic wave, for example, thanks to the stress-energy it carries, will produce an ingoing gravitational wave tail.