B How fast are gravitational forces transmitted?

[maxelcat]

I understand that if the sun where to 'disappear' then it would take several minutes for the us on the earth to notice as the light takes time to travel. Does this mean that it would also take the same time for us to notice that the gravitational (or electromagnetic) force would disappear too since the exchange particles are photons and therefore take time to arrive? I am coming at this as an 18 year old, pre university student.

 

[haruspex]

I understand that if the sun where to 'disappear' then it would take several minutes for the us on the earth to notice as the light takes time to travel. Does this mean that it would also take the same time for us to notice that the gravitational (or electromagnetic) force would disappear too since the exchange particles are photons and therefore take time to arrive? I am coming at this as an 18 year old, pre university student.

Yes. Gravity is mediated by gravitons, but they also travel at light speed.
https://en.wikipedia.org/wiki/Speed_of_gravity

 

[Vanadium 50]

Except.

There are no solutions where a star's mass can completely disappear. So there is no prediction for how fast the signal can travel - as there is no description of the signal to begin with.

 

[berkeman]

I understand that if the sun where to 'disappear' then it would take several minutes for the us on the earth to notice as the light takes time to travel

Except.

There are no solutions where a star's mass can completely disappear.

So a better way for you to think of the question @maxelcat would be more like, "If our Sun blew up and two hemispheres shot apart from each other at high speed, how long would it take for us to see that happen and how long for our gravitational attraction to the Sun to change?"

 

[Ibix]

Does this mean that it would also take the same time for us to notice that the gravitational (or electromagnetic) force would disappear too since the exchange particles are photons and therefore take time to arrive?

As @Vanadium 50 says, it is not possible to describe the Sun just vanishing in General Relativity. Attempting to force this scenario into the maths will inevitably lead you to the implication that 0=1 somewhere, so it's simply impossible to consider this case. If we were ever to see a chunk of matter just vanish (not get converted to radiation or something) then we would have to discard relativity theory.

Where people answer the question with "it would take eight minutes" they are either unaware of the problem with this scenario or choosing to answer based on related scenarios (such as the one proposed by @berkeman) that emit gravitational waves. These do propagate at the speed of light. In fact we expect all changes in anything to propagate at or below the speed of light, and finding a case that did propagate faster than light would invalidate relativity (if it doesn't turn out to be a loose wire in the sensor circuitry, as with the OPERA faster-than-light neutrino detection a few years ago). So far, though, everything seems to operate in accordance with relativity.

 

[russ_watters]

My suspicion is "if the sun vanished..." is just an easy to conceive way to frame a question on "the speed of gravity" and not meant to be a real scenario to investigate.

 

[Ibix]

My suspicion is "if the sun vanished..." is just an easy to conceive way to frame a question on "the speed of gravity" and not meant to be a real scenario to investigate.

I would tend to agree, but I think it's interesting to point out that you can't do it, even in principle. It's one aspect of what makes relativity's maths nastier and harder to work with than, e.g., electromagnetism.

 

[Nugatory]

Part of the confusion here comes from the way the question is framed: "How fast are gravitational forces transmitted?". The problem is that GR uses a different paradigm, one in which gravity is not a force, let alone one that can be transmitted from one point to another. Even phrasing it in the language of fields, which works so well with electromagnetic forces ("changes in the field propagate at the speed of light") doesn't work with gravity - there's no analogue to the retarded potential.

Perhaps we should say that the curvature of space at any given point in spacetime is determined by what's in the past light cone of that event?

 

[PeterDonis]

My suspicion is "if the sun vanished..." is just an easy to conceive way to frame a question on "the speed of gravity" and not meant to be a real scenario to investigate.

But the question framed that way cannot be analyzed at all, because it violates the laws of physics, and the only tool we have to analyze the scenario is the laws of physics. For us to even be able to address the question, it has to be framed in a way that does not violate the laws of physics.

 

[PeterDonis]

Perhaps we should say that the curvature of spacetime at any given point in spacetime is determined by what's in the past light cone of that event?

I would say that (with the bolded addition in the quote above) is the best brief way to describe "propagation of gravity" in GR, yes.

 

[russ_watters]

But the question framed that way cannot be analyzed at all, because it violates the laws of physics, and the only tool we have to analyze the scenario is the laws of physics. For us to even be able to address the question, it has to be framed in a way that does not violate the laws of physics.

Respectfully, I don't think you're hearing the real question but are stopping before you get to it because of the impossible framing.

Substitute: if two black holes collide 1 light year away, how long would it take before we detect the gravitational waves/at what speed do they propagate?

The question is not about black hole collisions, it's about the speed of propagation of gravity/gravitons.

 

[PeterDonis]

I don't think you're hearing the real question

I understand perfectly well the kind of question the OP wanted to ask. I'm just pointing out that that kind of question can't be answered unless it is formulated in a way that doesn't violate the laws of physics. Good answers to a properly formulated question of that kind have already been given in this thread.

 

[Ibix]

I don't think you're hearing the real question.

We can hear the question. But we're also aware of the difficulties of answering it honestly.

The question is not about black hole collisions, it's about the speed of propagation of gravity/gravitons.

The reason that "the Sun vanishes" is very attractive to try to study is that you have gravity that you can attribute to the Sun and nothing else, and then you have no gravity, and you hope you can ask how quickly the change propagates. Unfortunately it can't be analysed.

So the only thing you can really do is consider manipulating the Sun somehow. But anything massive or energetic enough to manipulate the Sun would, on its own, have a gravitational field comparable to the Sun. And the Einstein field equations are non-linear, so when you bring the Sun and the manipulator thing together it isn't really possible to separate the combined gravitational field into "the Sun's contribution" and "the other thing's contribution". So you can't really define what is a "change in the field coming from the Sun", so you can't ask what speed it's going at.

You can ask about the speed of gravitational waves in the weak field limit, because then we can neglect all the non-linearities and separate "the wave" from "the background" and make measurements with respect to the background. In that case, the answer is $c$. But the general answer is probably "you need to understand enough GR to understand why an answer in terms of domains of dependency of some part of a Cauchy surface is the best you're getting".

 

[Ibix]

Incidentally, if you find that kind of answer frustrating then you are very far from alone. It's where we are in this particular field, however.

 

[Orodruin]

Respectfully, I don't think you're hearing the real question but are stopping before you get to it because of the impossible framing.

I have seen this question waaay too often to be respectful towards it. In fact, it is one of my strongest pet peeves. If I see someone asking the question honestly, fine. I may be gentle. When I see educators throw the scenario around casually without any sort of disclaimer or remorse, I will not. The scenario is non-sensical and could have any answer you wish it to have.

The respectful thing is to point this out while offering the alternative scenario of gravitational wave propagation.

 

[Vanadium 50]

There is also a lurking problem with the question related to aberration and the direction in which the force...er...acceleration points. It is better to get off the bad example as quickly as possible rather than compounding the problem.

 

[renormalize]

Even phrasing it in the language of fields, which works so well with electromagnetic forces ("changes in the field propagate at the speed of light") doesn't work with gravity - there's no analogue to the retarded potential.

I don't think that's true, at least for weak gravitational perturbations. For example: The speed of gravity in general relativity and theoretical interpretation of the Jovian deflection experiment states in its abstract:
... The post-Newtonian series expansion in the $c_g$-parametrized general relativity is with respect to a small parameter that is proportional to the ratio of the characteristic velocity of the bodies to the speed of propagation of the gravitational interaction $c_g$. The Einstein equations are solved in terms of the Liénard–Wiechert tensor potentials which are used for integrating the light-ray propagation equations. An exact analytic expression for the relativistic time delay in the propagation of a radio wave from a quasar to an observer is calculated under the assumption that the light-ray deflecting bodies move with constant velocities. ...

 

[berkeman]

The respectful thing is to point this out while offering the alternative scenario of gravitational wave propagation.

Whew, glad I got IBTL with the exploding hemispheres thing.

But I still want to hear more about this scenario; it sounds intense (pun intended)!

If we were ever to see a chunk of matter just vanish (not get converted to radiation or something)

 

[PAllen]

I don't think that's true, at least for weak gravitational perturbations. For example: The speed of gravity in general relativity and theoretical interpretation of the Jovian deflection experiment states in its abstract:
... The post-Newtonian series expansion in the $c_g$-parametrized general relativity is with respect to a small parameter that is proportional to the ratio of the characteristic velocity of the bodies to the speed of propagation of the gravitational interaction $c_g$. The Einstein equations are solved in terms of the Liénard–Wiechert tensor potentials which are used for integrating the light-ray propagation equations. An exact analytic expression for the relativistic time delay in the propagation of a radio wave from a quasar to an observer is calculated under the assumption that the light-ray deflecting bodies move with constant velocities. ...

I don’t want to derail this thread, but it should be pointed out that the author’s claim that the measurement discussed says anything about the speed of gravity is hotly disputed among GR experts. My impression is that the majority do not agree this experiment says anything about the speed of gravity.

 

[renormalize]

I don’t want to derail this thread, but it should be pointed out that the author’s claim that the measurement discussed says anything about the speed of gravity is hotly disputed among GR experts. My impression is that the majority do not agree this experiment says anything about the speed of gravity.

Understood. What then is your take on the appropriateness of using "Liénard–Wiechert tensor potentials" i.e., retarded potentials, in gravitation?

 

[PeterDonis]

What then is your take on the appropriateness of using "Liénard–Wiechert tensor potentials" i.e., retarded potentials, in gravitation?

It might be worth looking at this classic paper by Carlip and comparing the way he analyzes the EM and gravitational cases:

https://arxiv.org/abs/gr-qc/9909087

 

[PAllen]

Understood. What then is your take on the appropriateness of using "Liénard–Wiechert tensor potentials" i.e., retarded potentials, in gravitation?

I’ve looked at a few of the papers in the debate. I am partial to Carlip’s argument that to discuss measuring the speed of gravity distinct from the speed of light, you need a framework where they can be different. Then, using a plausible such framework, one finds that the Kopeikin, et.al. measurement measures the speed of light.

A good summary of the debate is: https://arxiv.org/abs/astro-ph/0412401

 

[Vanadium 50]

I am going to take a somewhat iconoclastic (but nevertheless, correct ) point of view. There is no "the speed of gravity".

You can talk about particular observations of given systems, and that's well defined, but the idea that there is a single speed agreed upon by all observers and all phenomena in curved spacetime is, well, less than useful and in some cases misleading.

With that as a backdrop, using non-physical examples adds more confusion than clarification.

Additionally, some of the "improved" examples need to be very carefully specified. If I blow an object apart, the energy to do that had to come from somewhere, and that energy gravitates. In many of these examples it is easy to describe an incomplete system and confuse rather thjan clarify.

 

[PeterDonis]

There is no "the speed of gravity".

The paper by Samuel that @PAllen referenced appears to me to take basically that position, for the case where all objects involved are moving inertially. However, the Carlip paper I referenced analyzes the case of an object with nonzero proper acceleration, the Kinnersley photon rocket, and gives a well-defined concept of "the speed of gravity" for that case (and the Samuel paper acknowledges that a well-defined speed of gravity might exist for such a case).

IMO, a simpler way to look at all of this is the one @Nugatory gave earlier: the spacetime geometry at a given event is entirely due to what is in the past light cone of that event. This formulation has the virtue that it works for anything, not just gravity--for example, one can make the same statement for electromagnetism.

 

[PAllen]

For reference, here is Carlip's direct contribution to this debate (this is referenced in the Samuel review paper I gave earlier):

https://arxiv.org/abs/gr-qc/0403060

 

[ohwilleke]

Yes. Gravity is mediated by gravitons, but they also travel at light speed.
https://en.wikipedia.org/wiki/Speed_of_gravity

In classical general relativity, gravitational waves propagate at the speed of light, but gravitons, a hypothetical quantum gravity concept, are not involved.

Observationally, the best evidence of "the speed of gravity" involves the infall, collision, and merger of compact massive objects like neutron stars.

In these events, gravitational waves are detected at essentially the same time as light from that event is detected, even when these events are many light years distant. Any discrepancy in the arrival times can fairly be attributed to the sequence of events in the original event. From the link above:

The detection of GW170817 in 2017, the finale of a neutron star inspiral observed through both gravitational waves and gamma rays, at a distance of 130 million light years, currently provides by far the best limit on the difference between the speed of light and that of gravity. Photons were detected 1.7 seconds after peak gravitational wave emission; assuming a delay of zero to 10 seconds, the difference between the speeds of gravitational and electromagnetic waves, vGW − vEM, is constrained to between −3×10⁻¹⁵ and +7×10⁻¹⁶ times the speed of light.

The speed of light is, of course, exactly and by definition, 299,792,458 meters per second. The discrepancy between the speed of gravitational waves and the speed of light is at most about -1 to + 0.2 micrometers per second from the speed of light.

A brief detour regarding quantum gravity

Quantum gravity is a hypothesis that is very plausible and probably the single most widely expected to exist deviation from "core theory" out there, but there is no experimental or observational confirmation of it. The mathematics involved in quantum gravity have also proven much more difficult to work out in a rigorous, consistent manner that is a match to all observations than one would naively expect.

If massless gravitons did exist, however, they, like all massless particles, would travel at the speed of light, which is really, due to special relativity, the speed of all massless particles.

There are qualitative reasons that gravitons should be massless, but there are also theories about hypothetical massive gravitons. If the graviton were massive, its mass would be constrained to be less than 1.76 x 10^-23 eV/c² according to the Particle Data Group based upon the GW170817 event in 2017 and special relativity.

 

[DaveC426913]

Observationally, the best evidence of "the speed of gravity" involves the infall, collision, and merger of compact massive objects like neutron stars.

In these events, gravitational waves are detected at essentially the same time as light from that event is detected, even when these events are many light years distant. Any discrepancy in the arrival times can fairly be attributed to the sequence of events in the original event.

I'd say this succinct answer is faithful to both the spirit of the OP's question and the letter of the law(s of physics).

 

[sophiecentaur]

The respectful thing is to point this out while offering the alternative scenario of gravitational wave propagation.

And there are plenty of examples which have been observed and are 'sort of' familiar in popular cosmology. e,g, So there's no excuse for a disappearing Sun any more.

 

[Vanadium 50]

My question is "if the OP disappears suddenly, how long does it take the thread to notice?"
(He hasn't been here since the OP)

 

[Orodruin]

My question is "if the OP disappears suddenly, how long does it take the thread to notice?"
(He hasn't been here since the OP)

Unlike stress energy, there is no conservation law of posters.

 

[sophiecentaur]

My question is "if the OP disappears suddenly, how long does it take the thread to notice?"
(He hasn't been here since the OP)

The speed of postitons?

 

[DaveC426913]

Posters are a field. They're always there; it's simply the contribution that fluctuates.

 

[jbriggs444]

Posters are a field.

Sometimes quite far afield.

 

[PAllen]

Posters are a field. They're always there; it's simply the contribution that fluctuates.

Well, the smallest field has 2 elements, so ...