<p>The perturbation to the metric of spacetime (known as the strain), caused (for example) by an oscillating mass quadrupole, obeys a wave equation of the form
<span class="math-container">$$ \nabla^2 h^{\mu \nu} = \frac{1}{c^2} \frac{\partial^2 h^{\mu \nu}}{\partial t^2}\, , $$</span>
where <span class="math-container">$h^{\mu \nu}$</span> is a 4x4 tensor.</p>
<p>The solutions to this equation are plane waves travelling with a speed <span class="math-container">$c$</span>, i.e., the speed of light.</p>
<p>Why is this so? Well, I suppose it is because General Relativity is a relativistically covariant theory that works for all frames of reference. This inevitably involves the speed of light as the fastest speed that information can travel. The speed of light, along with <span class="math-container">$G$</span>, is present in the fundamental Einstein Field Equations in much the same way that the speed of light is present in Maxwell's equations for electromagnetism.</p>
<p>Hence GR predicts that these disturbances should travel at the speed of light and the limited measurements so far indicate that is the case.</p>

CC BY-SA 4.0
2021-06-10T13:08:20.087Z
But still, it is *presumed* those spacetime variations travel at the same speed as the stuff that moves *in* spacetime. If you "allow" these variations to travel at another speed (or infinite speed, which would make it more symmetrical), there would be no difference in the theory. All distortions would act sooner or later (or instantaneously) on masses than light. The covariance would imply though that gravity must travel at the same speed in all frames.
Deschele Schilder
CC BY-SA 4.0
2021-06-10T13:16:36.790Z
@Barberium Maxwell's Equations and the Einstein Field Equations cannot be derived. You are correct - the speed could be any speed but would be the same for both. But I am not sure what you mean by presumption? The laws are hypothesised as a way of explaining what happens.
ProfRob
CC BY-SA 4.0
2021-06-10T13:22:35.050Z
Hi! Well, when Einstein "made up" his theory, it was already known that light traveled at the speed of, well, light. About the speed of gravity (the speed of the distortions), there was nothing known (yet). So he *assumed* the two speeds to be equal. Only to be proven right after the LIGO measurements. I don't see exactly how in the classical (GR) view the two speeds should be equal. It could be just as well that the speeds are different (but that both speeds are the same in every frame).
Deschele Schilder
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2021-06-10T13:28:51.267Z
@Barbierium There is no *assumption* that the waves travel at the speed of light.  It is a feature of any covariant theory.
ProfRob
CC BY-SA 4.0
2021-06-10T13:35:17.213Z
But won't the theory be still covariant if the speed of gravity (when different from c) is the same in every frame of reference?
Deschele Schilder
CC BY-SA 4.0
2021-06-10T13:43:24.733Z
@Barbierium no, I'm sure it would not be. Lorentz covariance means that all the laws of physics need to be the same under the same Lorentz transformation.
ProfRob
CC BY-SA 4.0
2021-06-10T13:50:43.573Z
Can't there be two Lorentz transformations? One to apply for light and one for gravity? So one containing the lightspeed and one containing the speed of gravity? Mass-energy will not be able to travel faster than light, but gravity waves will? Gravity waves contain no mass-energy in the classical sense. So the physics would still be the same in every reference frame.
Deschele Schilder
CC BY-SA 4.0
2021-06-10T17:24:51.247Z
Newtonian gravity can be cast in mathematically covariant form, but the gravitational information would propagate instantaneously, right? So how is the statement *Well, I suppose it is because General Relativity is a relativistically covariant theory that works for all frames of reference.* justified? I think this has more to do with the fact that solutions to the wave equation, as you've written, propagate to infinity at finite speed. So when one derives the wave equation from GR, that is the prediction, and it seems to hold pretty well experimentally.
Daddy Kropotkin
CC BY-SA 4.0
2021-06-10T17:30:41.593Z
@Barbierium There cannot be multiple distinct invariant speeds in the same spacetime, because each one would necessarily require that the other must vary. If something travels at the same speed in all inertial reference frames, then it travels at the speed of light.
Douglas
CC BY-SA 4.0
2021-06-12T15:36:38.640Z
@DaddyKropotkin: the instantaneous propagation of gravity would allow instantaneuous propagation of information (by changing the distribution of mass in your vicinity), which violates causality in a relativistic universe.
TonyK
CC BY-SA 4.0
2021-06-09T22:16:52.680Z
2021-06-10T14:18:03.897Z
2021-06-10T14:18:03.897Z
ProfRob
<p>This is actually a very good question! I think you find it strange that gravity (or gravitational waves) travels at the same speed as photons, which travel <em>in</em> spacetime. How come that a spacetime disturbance &quot;knows&quot; to travel at the same speed as the photons inside it? If a photon travels inside a gravitational wave, why will it stay in the wave? Which of the two will arrive at the finish first, if they started from the same place (though the place for the wave is a bit hard to formulate, as the GW is a distortion of spacetime itself, while the photon has a position <em>in</em> it) if they are traveling side by side? The photon or the wave?<br />
Both will arrive at the finish first (that is at the same time). They travel in time too. That is, their traveling velocity in time is zero. You can compare this with an infinite traveling speed in classical, absolute spacetime (the one that Newton used). There is simply no higher speed than that. <em>If</em> the gravitational waves were traveling at a higher speed they would get younger which means that they would take the shape they had a moment before. But that would be exactly the shape they had upon leaving, which again means that they wouldn't be able to go forward at all.<br />
So the main point is that the waves simply can't travel at a higher speed than an infinite speed when considered as traveling in absolute spacetime (Newton thought indeed that the gravitational interaction was instantaneous). This translates in a lightspeed in relative spacetime.</p>
<p>In a quantum theory of gravity, gravitons are thought to be traveling through spacetime after a source of matter-energy has produced them. Just as photons are produced by an electric charge. The gravitons travel through flat spacetime just as the photons. They are thought to be massless, and as such they can't travel at a higher speed than the lightspeed. But how can they travel through flat spacetime when the wave is a non-flat piece of spacetime? It is exactly this that makes the finding of a quantum theory of gravity hard. For example, spacetime around a massive object is curved. How can this field be seen as (virtual) gravitons traveling in <em>flat</em> spacetime? For small fields (small masses), you can approximate the spacetime as being flat. But if the field is strong every graviton travels in a spacetime that the other gravitons have already disturbed. This is a bit similar to how gluons in the strong interaction behave. The action of each gluon is affected by the other gluons They emit gluons themselves, like gravitons emit gravitons. The difference is though that gluons are supposed to travel always in a flat spacetime, while gravitons travel in a spacetime that is curved already (by themselves).</p>

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2021-06-10T14:00:56.383Z
But practical measurements of the light part would be affected by the (non-empty) intergalactic medium(?).
Peter Mortensen
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2021-06-10T14:28:51.703Z
@PeterMortensen Do you mean that lightwaves have a velocity that is less than that of gravitational waves (because they travel in a non-empty medium)?
Deschele Schilder
CC BY-SA 4.0
2021-06-10T05:34:53.127Z
2021-06-10T12:11:09.940Z
2021-06-10T12:11:09.940Z
Deschele Schilder
<p>Here is a simple aspect that has not been stressed enough (in my opinion) in the answers given so far.</p>
<p>GR states (I’m not sure if as a result or axiom) that there exists a finite maximum speed. This maximum speed is <em>not</em> the speed of light and <em>not</em> the speed of gravitational waves, but all massless particles and gravitational waves <em>happen to</em> (as a consequence of the theory) propagate with that same maximum speed.</p>
<p>If you think it this way there is nothing suspicious about the fact that gravitational waves and light propagate with the same speed. There is nothing suspicious about the fact that the driver of a car happens to travel at the same speed as the passengers.</p>

CC BY-SA 4.0
2021-06-10T10:15:45.813Z
To what refers the car and to what the passengers? The axiom refers to massless particles *in* spacetime, not to the speed of a spacetime distortion. you can *state* that they travel at the same speed, but that doesn't explain *why* they travel at the same speed. Only in the graviton picture (which didn't exist at the time when GR was invented), this equality is explained.
Deschele Schilder
CC BY-SA 4.0
2021-06-10T10:29:17.783Z
@Barbierium Light and gravitational waves *both* travel at the same speed because they travel with the *one* maximum speed. My car example would be better stated as follows: consider there is a speed limit and some drivers (for whichever reason) always have the need to travel with the maximum allowed speed. Then all those drivers travel with the same speed, nothing suspicious about it. This, of course, does not explain why they have *the need* to travel with that speed. But this seemed not to be the question in the first place, right?
Hartmut Braun
CC BY-SA 4.0
2021-06-10T10:45:11.647Z
I think the need to travel at a maximum speed is that at the maximum speed through space the traveling speed through time is zero. This holds for the car (the wave) as well for the passengers (the EM field, or photons). It's a nice analogy! As long as you say that there is no frame in which the cars *don't* travel at the speed of light.
Deschele Schilder
CC BY-SA 4.0
2021-06-10T12:22:33.727Z
Only the “massless” cars feel the need to travel with maximum speed, the massive ones don’t (and can’t!). As far as I remember, the GR speed limit refers to the maximum speed *information* can travel. Light and gravitational waves carry information.
Hartmut Braun
CC BY-SA 4.0
2021-06-10T12:33:16.850Z
Precisely! You can't inform other people faster than the time it takes for lightspeed information to reach them. It would be strange if you could use gravity to inform them sooner than with light.
Deschele Schilder
CC BY-SA 4.0
2021-06-10T20:47:16.330Z
GR doesn't state that there's a finite maximum speed.  What it states is that there is a singularity in the equations at a speed "c".  For objects with mass, those equations only give a result if the speed is faster than "c" or slower than "c"; for massless objects, they only give a result if the speed is equal to "c".
Mark
CC BY-SA 4.0
2021-06-11T04:30:43.457Z
@Mark Thank’s for the clarification. So instead of a *maximum* speed it’s better to call it a *particular* speed. But then my answer seems still valid, at least for the “suspicious” aspect of OPs question.
Hartmut Braun
CC BY-SA 4.0
2021-06-12T14:56:24.017Z
@BenCrowell having read your answer, I don’t see a contradiction to my answer, while admittedly mine seems to be incomplete not taking into account the limit of low amplitudes and flat background. Well, the car example needs improving.
Hartmut Braun
CC BY-SA 4.0
2021-06-10T09:58:59.920Z
2021-06-10T09:58:59.920Z
Hartmut Braun
<p>It is very suspicious!  It points to the fact that the speed of light isn't just some random speed that light happens to travel at, but is a fundamental property of the universe.</p>
<p>In fact, any massless particle will move at the speed of light. This is a consequence of relativity. Energy, mass and momentum(<span class="math-container">$p$</span>) are related by</p>
<p><span class="math-container">$$E^2 = m^2c^4 +p^2c^2$$</span></p>
<p>for a particle moving at velocity <span class="math-container">$v$</span> less than <span class="math-container">$c$</span>,
<span class="math-container">$$p = mv\sqrt{\left(\frac{1}{1-(v/c)^2}\right)}$$</span></p>
<p>if a massless particle (<span class="math-container">$m=0$</span>) is moving at velocity less than <span class="math-container">$c$</span>, then it would have zero momentum and zero energy.  Such a particle could never be detected (since to be detected a particle has to transfer some of its energy and momentum to the detector). Is it possible for a fundamentally undetectable object to exist?  That is a matter for philosophers.  For the sake of developing models of reality, such particles don't exist.</p>

CC BY-SA 4.0
2021-06-09T19:07:18.037Z
Quarks are fundamentally undetectable, but they are assumed to exist by every physicist.
Deschele Schilder
CC BY-SA 4.0
2021-06-09T19:39:30.730Z
You can detect quarks, you just can’t isolate them
Steve Linton
CC BY-SA 4.0
2021-06-09T20:58:34.550Z
So confirmation of gravitational waves would seem to confirm graviton existence - or suggest its existence?
PunchyRascal
CC BY-SA 4.0
2021-06-09T21:18:39.277Z
Very strongly suggest. quantum mechanics tends to infect everything. However, this is veering away from anything astronomical, and towards particle physics.
James K
CC BY-SA 4.0
2021-06-09T22:17:43.750Z
General Relativity, like Electromagnetism, is a classical theory. No need for photons or gravitons.
ProfRob
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2021-06-09T22:25:55.157Z
Yet photons do exist...which merely shows that General Relativity is incomplete.  Nothing surprising about that.
James K
CC BY-SA 4.0
2021-06-10T10:33:33.970Z
What about particles with a mass smaller than zero? Will they travel backward in time? Like tachyons? Or will they simply have the opposite effect as a positive mass particle traveling forward in time? That is, will they push mass away, instead of attracting them?
Deschele Schilder
CC BY-SA 4.0
2021-06-10T11:41:10.073Z
@James K I find the use of "infect" hillariously precise
George Menoutis
CC BY-SA 4.0
2021-06-10T11:59:52.103Z
All is well here, but "This is a consequence of general relativity." - this needs to be the other way round. Einstein did not invent the universe... :)
AnoE
CC BY-SA 4.0
2021-06-10T13:55:38.620Z
@AnoE Some tales say that that is how he derived his theories of relativity: by sitting down and imagining how _he_ would do things.
wizzwizz4
CC BY-SA 4.0
2021-06-10T15:29:39.670Z
*"if a massless particle (m=0) is moving **in empty space** at velocity less than c, then it would have zero momentum and zero energy."*  ftfy ;)
J...
CC BY-SA 4.0
2021-06-10T15:57:54.737Z
$E^2 = m^2c^4 + p^2c^2$ is a Special Relativistic formula and only applies in local inertial frames. But that's ok - we measure the speed of light (and GWs) *locally* to be $c$.
ProfRob
CC BY-SA 4.0
2021-06-11T14:29:25.250Z
@AnoE I disagree. It is indeed a consequence of general relativity. Einstein didn't invent general relativity, he discovered it.
Auspex
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2021-06-12T04:20:12.390Z
@Auspex given that General Relativity isn't *exactly* how the universe works (quantum gravity and all that) maybe he *did* invent it!
Michael
CC BY-SA 4.0
2021-06-14T07:43:19.727Z
@Auspex, that comment was half tongue in cheek... half a bit of OCD/nitpicking. ;)
AnoE
CC BY-SA 4.0
2021-06-09T18:19:44.780Z
2021-06-10T18:25:53.130Z
2021-06-10T18:25:53.130Z
James K
<p>Thinking about gravitational waves and the fact that they propagate at the speed of light, I was wondering if it isn't suspicious - the speed of light I mean. Does it perhaps point to something fundamental about the spacetime? Is there maybe some connection between EMR and spacetime itself? Or am I seeing things in the tea leaves?</p>

CC BY-SA 4.0
2021-06-09T19:09:54.303Z
You think it strange that gravity (spacetime distortion) travels at the same speed as photons, which travel *in* spacetime?
Deschele Schilder
CC BY-SA 4.0
2021-06-09T19:49:15.023Z
It's kind of a historical accident that we call *c* the speed of light. https://physics.stackexchange.com/a/291346/123208
PM 2Ring
CC BY-SA 4.0
2021-06-09T20:54:47.023Z
@Barbierium Yes that is what I meant
PunchyRascal
CC BY-SA 4.0
2021-06-10T12:02:58.093Z
Perhaps it is rather surprising that there are things *not* traveling at *c.*
Peter - Reinstate Monica
CC BY-SA 4.0
2021-06-10T12:20:35.983Z
@Peter-ReinstateMonica In fact, *all* objects travel at the speed of light. In spacetime, that is. Massive objects travel with a speed less than the lightspeed in space and a speed through time, while massless ones travel at lightspeed and no speed through time. Stationary objects travel through time only. The difference between the two is that massless particles *always* travel at the speed of light through space (as they *always* travel trough time with zero velocity).
Deschele Schilder
CC BY-SA 4.0
2021-06-10T14:48:00.660Z
I always wondered if "gravity" did travel at the speed of light. Does that mean that when making calculations for "big" stuff where it could make a difference, that a correction has to be made.

eg when calculating the earth's orbit around the sun. The sun orbits around the centre of mass of the solar system (roughly), so the orbit calculation must know where the sun was ~500 seconds ago. But obviously that 500s changes depending on where we are in our elliptical orbit.
Max Allan
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2021-06-10T15:55:07.357Z
@MaxAllan GR effects produce *small* differences in the orbit of the Earth around the Sun.
ProfRob
CC BY-SA 4.0
2021-06-10T17:11:52.167Z
@MaxAllan Indeed. The big paradigm shift from Newton to Einstein: There is no immediate impact, gravitational or otherwise, of one object on another. Gravity, light, the mere *existence* behaves much like the sound of an airplane high in the sky overhead: It lags.
Peter - Reinstate Monica
CC BY-SA 4.0
2021-06-10T22:06:03.993Z
As far as observational evidence is concerned, I think you can not call the speed of gravitational waves, or even their existence, a fact yet. The evidence for this is still rather thin, and some physicists even question the evidence. See http://backreaction.blogspot.com/2019/09/whats-up-with-ligo.html for details. I think the jury is still out for this one.
Thomas
CC BY-SA 4.0
2021-06-12T15:04:02.710Z
@Thomas, the existence of gravitational waves is on a very sound footing, and has been for years. They are the only explanation we have for [the decay of binary pulsar orbits](https://en.wikipedia.org/wiki/Gravitational_wave#Indirect_detection) (Hulse and Taylor won the 1993 Nobel prize in physics for this); and they are an exceptionally good explanation, too. What more do you need?
TonyK
CC BY-SA 4.0
2021-06-12T16:26:21.267Z
@TonyK If the decay of binary pulsar orbits would have established gravitational waves as a fact, there would have been no need to build LIGO. And as I said, the results obtained by LIGO are not beyond doubt either. Healthy scepticism is always advised before accepting something as fact, especially in astronomy where the objects are not directly accessible and only indirect evidence can be obtained.
Thomas
CC BY-SA 4.0
2021-06-12T16:36:35.107Z
@Thomas, the decay of binary pulsar orbits established gravitational waves as sound, empirical fact. They built LIGO to find out more about these waves. (And I said nothing about the results obtained by LIGO -- that's a different matter entirely.)
TonyK
<light><space-time><gravitational-waves>
Is it suspicious that gravitational waves propagate at the speed of light?
PunchyRascal
# Is it suspicious that gravitational waves propagate at the speed of light?

(Asked by: username_0 on 2021-06-09)

Thinking about gravitational waves and the fact that they propagate at the speed of light, I was wondering if it isn't suspicious - the speed of light I mean. Does it perhaps point to something fundamental about the spacetime? Is there maybe some connection between EMR and spacetime itself? Or am I seeing things in the tea leaves?

**Tags:** light, space-time, gravitational-waves

> **Comments:**
> **username_1**: You think it strange that gravity (spacetime distortion) travels at the same speed as photons, which travel *in* spacetime?  
> **username_2**: It's kind of a historical accident that we call *c* the speed of light. https://physics.stackexchange.com/a/291346/123208  
> **username_0**: @Barbierium Yes that is what I meant  
> **username_3**: Perhaps it is rather surprising that there are things *not* traveling at *c.*  
> **username_1**: @Peter-ReinstateMonica In fact, *all* objects travel at the speed of light. In spacetime, that is. Massive objects travel with a speed less than the lightspeed in space and a speed through time, while massless ones travel at lightspeed and no speed through time. Stationary objects travel through time only. The difference between the two is that massless particles *always* travel at the speed of light through space (as they *always* travel trough time with zero velocity).  
> **username_4**: I always wondered if "gravity" did travel at the speed of light. Does that mean that when making calculations for "big" stuff where it could make a difference, that a correction has to be made.  eg when calculating the earth's orbit around the sun. The sun orbits around the centre of mass of the solar system (roughly), so the orbit calculation must know where the sun was ~500 seconds ago. But obviously that 500s changes depending on where we are in our elliptical orbit.  
> **username_5**: @MaxAllan GR effects produce *small* differences in the orbit of the Earth around the Sun.  
> **username_3**: @MaxAllan Indeed. The big paradigm shift from Newton to Einstein: There is no immediate impact, gravitational or otherwise, of one object on another. Gravity, light, the mere *existence* behaves much like the sound of an airplane high in the sky overhead: It lags.  
> **username_6**: As far as observational evidence is concerned, I think you can not call the speed of gravitational waves, or even their existence, a fact yet. The evidence for this is still rather thin, and some physicists even question the evidence. See http://backreaction.blogspot.com/2019/09/whats-up-with-ligo.html for details. I think the jury is still out for this one.  
> **username_7**: @username_6, the existence of gravitational waves is on a very sound footing, and has been for years. They are the only explanation we have for [the decay of binary pulsar orbits](https://en.wikipedia.org/wiki/Gravitational_wave#Indirect_detection) (Hulse and Taylor won the 1993 Nobel prize in physics for this); and they are an exceptionally good explanation, too. What more do you need?  
> **username_6**: @username_7 If the decay of binary pulsar orbits would have established gravitational waves as a fact, there would have been no need to build LIGO. And as I said, the results obtained by LIGO are not beyond doubt either. Healthy scepticism is always advised before accepting something as fact, especially in astronomy where the objects are not directly accessible and only indirect evidence can be obtained.  
> **username_7**: @username_6, the decay of binary pulsar orbits established gravitational waves as sound, empirical fact. They built LIGO to find out more about these waves. (And I said nothing about the results obtained by LIGO -- that's a different matter entirely.)  

---

## 4 answers

### Answer by username_13 on 2021-06-09. Score: 42 | Accepted answer

It is very suspicious! It points to the fact that the speed of light isn't just some random speed that light happens to travel at, but is a fundamental property of the universe.

In fact, any massless particle will move at the speed of light. This is a consequence of relativity. Energy, mass and momentum($p$) are related by

$$E^2 = m^2c^4 +p^2c^2$$

for a particle moving at velocity $v$ less than $c$,
$$p = mv\sqrt{\left(\frac{1}{1-(v/c)^2}\right)}$$

if a massless particle ($m=0$) is moving at velocity less than $c$, then it would have zero momentum and zero energy. Such a particle could never be detected (since to be detected a particle has to transfer some of its energy and momentum to the detector). Is it possible for a fundamentally undetectable object to exist? That is a matter for philosophers. For the sake of developing models of reality, such particles don't exist.

> **Comments:**
> **username_1**: Quarks are fundamentally undetectable, but they are assumed to exist by every physicist.  
> **username_14**: You can detect quarks, you just can’t isolate them  
> **username_0**: So confirmation of gravitational waves would seem to confirm graviton existence - or suggest its existence?  
> **username_13**: Very strongly suggest. quantum mechanics tends to infect everything. However, this is veering away from anything astronomical, and towards particle physics.  
> **username_5**: General Relativity, like Electromagnetism, is a classical theory. No need for photons or gravitons.  
> **username_13**: Yet photons do exist...which merely shows that General Relativity is incomplete.  Nothing surprising about that.  
> **username_1**: What about particles with a mass smaller than zero? Will they travel backward in time? Like tachyons? Or will they simply have the opposite effect as a positive mass particle traveling forward in time? That is, will they push mass away, instead of attracting them?  
> **username_15**: @username_13 I find the use of "infect" hillariously precise  
> **username_16**: All is well here, but "This is a consequence of general relativity." - this needs to be the other way round. Einstein did not invent the universe... :)  
> **username_17**: @username_16 Some tales say that that is how he derived his theories of relativity: by sitting down and imagining how _he_ would do things.  
> **username_18**: *"if a massless particle (m=0) is moving **in empty space** at velocity less than c, then it would have zero momentum and zero energy."*  ftfy ;)  
> **username_5**: $E^2 = m^2c^4 + p^2c^2$ is a Special Relativistic formula and only applies in local inertial frames. But that's ok - we measure the speed of light (and GWs) *locally* to be $c$.  
> **username_19**: @username_16 I disagree. It is indeed a consequence of general relativity. Einstein didn't invent general relativity, he discovered it.  
> **username_20**: @username_19 given that General Relativity isn't *exactly* how the universe works (quantum gravity and all that) maybe he *did* invent it!  
> **username_16**: @username_19, that comment was half tongue in cheek... half a bit of OCD/nitpicking. ;)  

---

### Answer by username_5 on 2021-06-09. Score: 12

The perturbation to the metric of spacetime (known as the strain), caused (for example) by an oscillating mass quadrupole, obeys a wave equation of the form
$$ \nabla^2 h^{\mu \nu} = \frac{1}{c^2} \frac{\partial^2 h^{\mu \nu}}{\partial t^2}\, , $$
where $h^{\mu \nu}$ is a 4x4 tensor.

The solutions to this equation are plane waves travelling with a speed $c$, i.e., the speed of light.

Why is this so? Well, I suppose it is because General Relativity is a relativistically covariant theory that works for all frames of reference. This inevitably involves the speed of light as the fastest speed that information can travel. The speed of light, along with $G$, is present in the fundamental Einstein Field Equations in much the same way that the speed of light is present in Maxwell's equations for electromagnetism.

Hence GR predicts that these disturbances should travel at the speed of light and the limited measurements so far indicate that is the case.

> **Comments:**
> **username_1**: But still, it is *presumed* those spacetime variations travel at the same speed as the stuff that moves *in* spacetime. If you "allow" these variations to travel at another speed (or infinite speed, which would make it more symmetrical), there would be no difference in the theory. All distortions would act sooner or later (or instantaneously) on masses than light. The covariance would imply though that gravity must travel at the same speed in all frames.  
> **username_5**: @Barberium Maxwell's Equations and the Einstein Field Equations cannot be derived. You are correct - the speed could be any speed but would be the same for both. But I am not sure what you mean by presumption? The laws are hypothesised as a way of explaining what happens.  
> **username_1**: Hi! Well, when Einstein "made up" his theory, it was already known that light traveled at the speed of, well, light. About the speed of gravity (the speed of the distortions), there was nothing known (yet). So he *assumed* the two speeds to be equal. Only to be proven right after the LIGO measurements. I don't see exactly how in the classical (GR) view the two speeds should be equal. It could be just as well that the speeds are different (but that both speeds are the same in every frame).  
> **username_5**: @Barbierium There is no *assumption* that the waves travel at the speed of light.  It is a feature of any covariant theory.  
> **username_1**: But won't the theory be still covariant if the speed of gravity (when different from c) is the same in every frame of reference?  
> **username_5**: @Barbierium no, I'm sure it would not be. Lorentz covariance means that all the laws of physics need to be the same under the same Lorentz transformation.  
> **username_1**: Can't there be two Lorentz transformations? One to apply for light and one for gravity? So one containing the lightspeed and one containing the speed of gravity? Mass-energy will not be able to travel faster than light, but gravity waves will? Gravity waves contain no mass-energy in the classical sense. So the physics would still be the same in every reference frame.  
> **username_8**: Newtonian gravity can be cast in mathematically covariant form, but the gravitational information would propagate instantaneously, right? So how is the statement *Well, I suppose it is because General Relativity is a relativistically covariant theory that works for all frames of reference.* justified? I think this has more to do with the fact that solutions to the wave equation, as you've written, propagate to infinity at finite speed. So when one derives the wave equation from GR, that is the prediction, and it seems to hold pretty well experimentally.  
> **username_9**: @Barbierium There cannot be multiple distinct invariant speeds in the same spacetime, because each one would necessarily require that the other must vary. If something travels at the same speed in all inertial reference frames, then it travels at the speed of light.  
> **username_7**: @DaddyKropotkin: the instantaneous propagation of gravity would allow instantaneuous propagation of information (by changing the distribution of mass in your vicinity), which violates causality in a relativistic universe.  

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### Answer by username_1 on 2021-06-10. Score: 7

This is actually a very good question! I think you find it strange that gravity (or gravitational waves) travels at the same speed as photons, which travel *in* spacetime. How come that a spacetime disturbance "knows" to travel at the same speed as the photons inside it? If a photon travels inside a gravitational wave, why will it stay in the wave? Which of the two will arrive at the finish first, if they started from the same place (though the place for the wave is a bit hard to formulate, as the GW is a distortion of spacetime itself, while the photon has a position *in* it) if they are traveling side by side? The photon or the wave?  
Both will arrive at the finish first (that is at the same time). They travel in time too. That is, their traveling velocity in time is zero. You can compare this with an infinite traveling speed in classical, absolute spacetime (the one that Newton used). There is simply no higher speed than that. *If* the gravitational waves were traveling at a higher speed they would get younger which means that they would take the shape they had a moment before. But that would be exactly the shape they had upon leaving, which again means that they wouldn't be able to go forward at all.  
So the main point is that the waves simply can't travel at a higher speed than an infinite speed when considered as traveling in absolute spacetime (Newton thought indeed that the gravitational interaction was instantaneous). This translates in a lightspeed in relative spacetime.

In a quantum theory of gravity, gravitons are thought to be traveling through spacetime after a source of matter-energy has produced them. Just as photons are produced by an electric charge. The gravitons travel through flat spacetime just as the photons. They are thought to be massless, and as such they can't travel at a higher speed than the lightspeed. But how can they travel through flat spacetime when the wave is a non-flat piece of spacetime? It is exactly this that makes the finding of a quantum theory of gravity hard. For example, spacetime around a massive object is curved. How can this field be seen as (virtual) gravitons traveling in *flat* spacetime? For small fields (small masses), you can approximate the spacetime as being flat. But if the field is strong every graviton travels in a spacetime that the other gravitons have already disturbed. This is a bit similar to how gluons in the strong interaction behave. The action of each gluon is affected by the other gluons They emit gluons themselves, like gravitons emit gravitons. The difference is though that gluons are supposed to travel always in a flat spacetime, while gravitons travel in a spacetime that is curved already (by themselves).

> **Comments:**
> **username_10**: But practical measurements of the light part would be affected by the (non-empty) intergalactic medium(?).  
> **username_1**: @PeterMortensen Do you mean that lightwaves have a velocity that is less than that of gravitational waves (because they travel in a non-empty medium)?  

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### Answer by username_11 on 2021-06-10. Score: 5

Here is a simple aspect that has not been stressed enough (in my opinion) in the answers given so far.

GR states (I’m not sure if as a result or axiom) that there exists a finite maximum speed. This maximum speed is *not* the speed of light and *not* the speed of gravitational waves, but all massless particles and gravitational waves *happen to* (as a consequence of the theory) propagate with that same maximum speed.

If you think it this way there is nothing suspicious about the fact that gravitational waves and light propagate with the same speed. There is nothing suspicious about the fact that the driver of a car happens to travel at the same speed as the passengers.

> **Comments:**
> **username_1**: To what refers the car and to what the passengers? The axiom refers to massless particles *in* spacetime, not to the speed of a spacetime distortion. you can *state* that they travel at the same speed, but that doesn't explain *why* they travel at the same speed. Only in the graviton picture (which didn't exist at the time when GR was invented), this equality is explained.  
> **username_11**: @Barbierium Light and gravitational waves *both* travel at the same speed because they travel with the *one* maximum speed. My car example would be better stated as follows: consider there is a speed limit and some drivers (for whichever reason) always have the need to travel with the maximum allowed speed. Then all those drivers travel with the same speed, nothing suspicious about it. This, of course, does not explain why they have *the need* to travel with that speed. But this seemed not to be the question in the first place, right?  
> **username_1**: I think the need to travel at a maximum speed is that at the maximum speed through space the traveling speed through time is zero. This holds for the car (the wave) as well for the passengers (the EM field, or photons). It's a nice analogy! As long as you say that there is no frame in which the cars *don't* travel at the speed of light.  
> **username_11**: Only the “massless” cars feel the need to travel with maximum speed, the massive ones don’t (and can’t!). As far as I remember, the GR speed limit refers to the maximum speed *information* can travel. Light and gravitational waves carry information.  
> **username_1**: Precisely! You can't inform other people faster than the time it takes for lightspeed information to reach them. It would be strange if you could use gravity to inform them sooner than with light.  
> **username_12**: GR doesn't state that there's a finite maximum speed.  What it states is that there is a singularity in the equations at a speed "c".  For objects with mass, those equations only give a result if the speed is faster than "c" or slower than "c"; for massless objects, they only give a result if the speed is equal to "c".  
> **username_11**: @username_12 Thank’s for the clarification. So instead of a *maximum* speed it’s better to call it a *particular* speed. But then my answer seems still valid, at least for the “suspicious” aspect of OPs question.  
> **username_11**: @BenCrowell having read your answer, I don’t see a contradiction to my answer, while admittedly mine seems to be incomplete not taking into account the limit of low amplitudes and flat background. Well, the car example needs improving.  

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