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?
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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.
James K
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Quarks are fundamentally undetectable, but they are assumed to exist by every physicist. – Deschele Schilder Jun 09 '21 at 19:07
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So confirmation of gravitational waves would seem to confirm graviton existence - or suggest its existence? – PunchyRascal Jun 09 '21 at 20:58
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5Very strongly suggest. quantum mechanics tends to infect everything. However, this is veering away from anything astronomical, and towards particle physics. – James K Jun 09 '21 at 21:18
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2General Relativity, like Electromagnetism, is a classical theory. No need for photons or gravitons. – ProfRob Jun 09 '21 at 22:17
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3Yet photons do exist...which merely shows that General Relativity is incomplete. Nothing surprising about that. – James K Jun 09 '21 at 22:25
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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 Jun 10 '21 at 10:33
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8All 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 Jun 10 '21 at 11:59
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2@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 Jun 10 '21 at 13:55
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"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... Jun 10 '21 at 15:29
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$E^2 = m^2c^4 + p^2c^2$ 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 Jun 10 '21 at 15:57
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@AnoE I disagree. It is indeed a consequence of general relativity. Einstein didn't invent general relativity, he discovered it. – Auspex Jun 11 '21 at 14:29
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@Auspex given that General Relativity isn't exactly how the universe works (quantum gravity and all that) maybe he did invent it! – Michael Jun 12 '21 at 04:20
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@Auspex, that comment was half tongue in cheek... half a bit of OCD/nitpicking. ;) – AnoE Jun 14 '21 at 07:43
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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.
ProfRob
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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 Jun 10 '21 at 13:08
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@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 Jun 10 '21 at 13:16
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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 Jun 10 '21 at 13:22
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3@Barbierium There is no assumption that the waves travel at the speed of light. It is a feature of any covariant theory. – ProfRob Jun 10 '21 at 13:28
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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 Jun 10 '21 at 13:35
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1@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 Jun 10 '21 at 13:43
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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 Jun 10 '21 at 13:50
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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 Jun 10 '21 at 17:24
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2@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 Jun 10 '21 at 17:30
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@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 Jun 12 '21 at 15:36
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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).
Deschele Schilder
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But practical measurements of the light part would be affected by the (non-empty) intergalactic medium(?). – Peter Mortensen Jun 10 '21 at 14:00
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@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 Jun 10 '21 at 14:28
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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.
Hartmut Braun
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1To 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 Jun 10 '21 at 10:15
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@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 Jun 10 '21 at 10:29
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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 Jun 10 '21 at 10:45
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1Only 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 Jun 10 '21 at 12:22
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2Precisely! 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 Jun 10 '21 at 12:33
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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 Jun 10 '21 at 20:47
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@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 Jun 11 '21 at 04:30
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@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 Jun 12 '21 at 14:56
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This is actually pretty complicated to answer, and you should beware of oversimplified answers. And BTW you'd probably be better off asking this on physics.SE.
The state of the art in physics at this point is that we have two totally successful theories that contradict each other. These are quantum mechanics and general relativity.
Quantum mechanics says the way forces are created is that material particles (fermions) exchange bosons. If the boson is massless, then in the classical limit you get a $1/r^2$ force. Massless particles travel at $c$. Therefore if we observe a force that, like gravity, falls off with distance as $1/r^2$, we suspect that it arises from a massless boson. Massless bosons travel at $c$, ergo gravitational signals should travel at $c$. This all sounds great, except that quantum mechanics doesn't work as a theory of gravity, which throws everything into doubt.
General relativity (GR) works great as a classical theory of gravity, and it's been spectacularly confirmed in the strong-gravity regime by recent observations of gravitational waves and the event horizons of black holes. But GR does not really predict that gravitational waves travel at $c$. Actually GR tells us that speed is not really a very meaningful concept. For example, it refuses to answer the question of whether a distant galaxy is actually moving away from us at some speed, or whether both our galaxy and that one are at rest, while the space in between expands. All GR really says is that in the limit of low amplitudes, on a background of flat spacetime, it's meaningful to talk about the speed of gravitational waves, and in that same limit they travel at $c$.
So it's not really true and not really predicted by the known laws of physics that gravitational waves travel at $c$. However, it's intuitively obvious to physicists, in the view from 40,000 feet, that it must be so in cases of practical interest, based on a general feel for how physics works.
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 Jun 10 '21 at 14:48