# How fast is gravity?

Does the force of gravity travel the speed of light? faster than the speed of light? or is it instantaneous?

Is there a distinction between propagating gravity waves and the force itself?

If gravity travels the speed of light, it could not escape a black hole, because the escape velocity is faster than light. So gravity must be faster.

If gravity is faster than light, but finite, wouldn't there exist an event horizon through which gravity could not escape? Depending on the speed of gravity and the density to which matter can compress, could there exist a "gravity hole" that would be undetectable (because no light or gravity can escape) unless it happens to directly collide with something. And would "red-shifted" gravity waves exist as well, due to a high gravity environment or the expansion of space?

One more musing: Do the other forces of nature have speeds, such as the electric, strong, and weak forces?

G01
Homework Helper
Gold Member
The Gravitational force as well as the electromagnetic force both travel at the speed of light. (I cannot comment on the other two forces with certainty, but I believe this is true for them as well.)

Your question about gravity escaping a black hole does not make much sense to me. Gravity is what keeps things inside a black hole. It seems to me that you are treating gravity as something else which is affected by gravity! Gravity does not pull on itself, so this question does not make much sense to me, maybe someone more versed in these topics can help you out if I'm missing something.

The proper way to think of gravity is a change or distortion of the shape of space/time in the presents of mass/energy. This view was first expressed by Einstine in his general therory of relativity. This shape is what causes a satelite to move around a planet in an eliptical path instead of a straight line. the satelite is actually following the path of least resistance and a force would be required to keep it from the curved path. The shape of space/time around the body is always there with it and its' influance extends indefinately but is reduced by the square of the distance from the body. Gravity is not a force and is the same thing as inertia, two aspects of the same thing. When you change direction in a car you feel a force which is actually Your body trying to NOT change direction. The so called force of gravity is the same thing, the change from the natural curved path. In orbit, you feel no force, unless you fire a rocket and change your path. -Robert

Assuming you talk about the theory of general relativity then:

Does the force of gravity travel the speed of light? faster than the speed of light? or is it instantaneous?
Gravitational waves travel at the speed of light.

Is there a distinction between propagating gravity waves and the force itself?
No.

If gravity travels the speed of light, it could not escape a black hole, because the escape velocity is faster than light. So gravity must be faster.
A black hole is a gravitational field. There is nothing to escape.

Last edited:
Thank you for the replies. I'm thinking about it wrong. Gravity does not interfere with itself (except perhaps when gravity waves cross paths just as when light waves cross paths). I was just thinking since photons are affected by gravity, maybe gravity waves and gravitons would be too.

Also, it is a good observation that gravity is a curvature in space-time.

I will continue to ponder gravity.

Gravity does not interfere with itself (except perhaps when gravity waves cross paths just as when light waves cross paths).
Gravitational fields do interfere with each other.

Take two gravitational fields, as soon as their light cones cross they will interfere with each other and create a resulting gravitational field.

gravity's influence is technically finite, though not if you count black holes. a singularity is infinintly dense, so it's gravitational influence is infinite. it's jsut the range that the gravity works on that is affected. once you take out black holes, gravity is finite. it depends on how dense the object is. if the earth were compressed to the size of roughly a golf ball, the gravitational effects would be similar to a black hole, in that it would not allow light to escape. so to answer your question, the effects of gravity are in direct proportion to to density, and how far it goes is in direct proportion to overall size.

I think what he is trying to get at is that the force of gravity extends through the black hole. As in, he is trying to figure out at what distance an object could be away from the black hole to where the black hole exerts no force on the object. If so then the answer is infinity because everything in the universe is exerting gravity on everything else, even at a great great distance, gravity exerts on other masses on a microscopic level.

It is kind of interesting too because gravity can travel through anything. Through any mass and medium all the way across the galaxy at every natural extreme.

Gravitational influence has never been shown to exceed or go below C. However, this is not set in stone... the complexities involved demand invesigating in this mystery.

George Jones
Staff Emeritus
Gold Member
Gravitational influence has never been shown to exceed or go below C. However, this is not set in stone... the complexities involved demand invesigating in this mystery.

I posted a little elaboration on this here.

The Gravitational force as well as the electromagnetic force both travel at the speed of light. (I cannot comment on the other two forces with certainty, but I believe this is true for them as well.)

Somebody could confirm this in one direction or another. I've thought that the fields of the nuclear interactions propagate below the speed of light.

hmhm... I wasn't thinking this carefully. The disturbances in KG fields propagate everywhere in the light cone, but on the other hand wave packets will travel with speeds below c if m!=0. I guess the question isn't simple enough to be given a simple answer.

In fact I don't know what kind of fields are used for nuclear forces, but are they something similar to the Klein-Gordon fields?

Last edited:
QuantumPion
Gold Member
I think what he is trying to get at is that the force of gravity extends through the black hole. As in, he is trying to figure out at what distance an object could be away from the black hole to where the black hole exerts no force on the object. If so then the answer is infinity because everything in the universe is exerting gravity on everything else, even at a great great distance, gravity exerts on other masses on a microscopic level.

It is kind of interesting too because gravity can travel through anything. Through any mass and medium all the way across the galaxy at every natural extreme.

What if gravity is quantized (gravitons)? In this case wouldn't there be a minimum unit for gravitational force, e.g. one graviton? So if you were far enough away from a mass, you would receive no gravitons and thus no force. Or looking at it another way, if a gravity well was actually a staircase, there would be a "top" of the stair case with maximum potential.

Last edited:
pervect
Staff Emeritus
What if gravity is quantized (gravitons)? In this case wouldn't there be a minimum unit for gravitational force, e.g. one graviton? So if you were far enough away from a mass, you would receive no gravitons and thus no force. Or looking at it another way, if a gravity well was actually a staircase, there would be a "top" of the stair case with maximum potential.

Electromagnetism is quantized. Yet there is no "top of the staircase" effect such as you describe in E&M.

One thing you have to realize is that just as the coulomb force between two charges is carried by virtual photons, the "gravitational force" would (probably) be carried by virtual gravitons. Note that even this may be an oversimplification.

AFAIK there isn't any "minimum value" for the energy or momentum of a virtual photon

So my general advice is to first get your ducks in a row for E&M, and then move on to gravity later.

You might try http://www.math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html

for some info on how virtual particles carry forces

http://www.math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html

on the speed of gravity

http://www.math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html
on "gravity getting out of a black hole".

Note that since GR is a classical theory, it doesn't have to deal with these issues. As the FAQ says:

Purely in terms of general relativity, there is no problem here. The gravity doesn't have to get out of the black hole. General relativity is a local theory, which means that the field at a certain point in spacetime is determined entirely by things going on at places that can communicate with it at speeds less than or equal to c. If a star collapses into a black hole, the gravitational field outside the black hole may be calculated entirely from the properties of the star and its external gravitational field before it becomes a black hole. Just as the light registering late stages in my fall takes longer and longer to get out to you at a large distance, the gravitational consequences of events late in the star's collapse take longer and longer to ripple out to the world at large. In this sense the black hole is a kind of "frozen star": the gravitational field is a fossil field. The same is true of the electromagnetic field that a black hole may possess.

Often this question is phrased in terms of gravitons, the hypothetical quanta of spacetime distortion. If things like gravity correspond to the exchange of "particles" like gravitons, how can they get out of the event horizon to do their job?

Gravitons don't exist in general relativity, because GR is not a quantum theory. They might be part of a theory of quantum gravity when it is completely developed, but even then it might not be best to describe gravitational attraction as produced by virtual gravitons. See the physics FAQ on virtual particles for a discussion of this.

i realize that this appears to be a resurrected post (or maybe it's a zombie post, if the sysops shoot it, will it die?), but i would be curious to see some response to this:

Do the other forces of nature have speeds, such as the electric, strong, and weak forces?

of course the "electric" force (EM) has, by definition, a speed of c.

but my understanding from SR and GR is that it is not just gravity (or the perturbation of space-time) and EM that move at a speed of c, but all interaction, otherwise information could move at the speed of the other fundamental interaction. is that not correct?

From discussions with some pretty heavy physicists (it's sorta amazing whom you can talk to, if you find their email address), the understanding from them that i gleaned was this: Nature has a single finite speed for these interactions (which may someday be all unified in a single theory). The salient physics is that speed is the same for all fundamental interactions and that it is finite. That is, whatever the interaction, if something changes over here, the effect over there, as observed by a third party somewhere else (but let's say equidistant from here and there), will happen at a time that is delayed by

$$\frac{ \left| \mathrm{locus}(here) - \mathrm{locus}(there) \right| }{c}$$

where c is that finite speed.

now the salient fundamental physics is that this speed of propagation, c, is finite, not infinite. physical reality would be different than it is if c were infinite. but it doesn't really matter what that finite speed is since it, along with G and $\hbar$, will simply define the scale of existence of things in the universe. as long as all of the dimensionless parameters of interaction remain the same (physicist John Baez has enumerated 26 such dimensionless parameters, but says there could be more as new interactions are discovered and that new physical theories might derive some of these parameters from others, thus reducing that number), a conceptual change in c could not be noticed by observers whose existence and scale is governed by that.

my interpretation: if God (or some "god-like" being) could reach over and turn the knob that controls c to half of its previous value so the new c is the old c/2, then the Planck Length would increase by a factor of $\sqrt{8}$ and so would the size of atoms, meter sticks, and people (from the POV of this "god-like" observer) if all the dimensionless parameters remained the same. but, also, the Planck Time would increase by a factor of $\sqrt{32}$ (from the perspective of this "god-like" observer) and, if all the dimensionless parameters remained the same, all of our clocks would have to tick slower by the same factor. so this "god-like" observer might observe that the speed of propagation of EM (and the other interactions) now is half of what it used to be, but for us that exist within the governing of physics, we could not tell any difference. light would still travel 299792458 of our new meters in the time elapsed by our new second. nothing operationally would change. from the POV of our existance, no new physics would be observed.

so if you're a theist (and running with this hyperbolic or parabolic imagery), God doesn't have a control knob on His/Her toy (that we call "The Universe") labeled "c", but He/She/It/whatever, might have one labeled "$\alpha$" and, perhaps 25 other such knobs (say for the cosmological constant or the masses of particles, all expressed in something like Planck units). i dunno, of course, it's just a speculative imagery that i found useful to think about what universal constants really matter and which ones do not (that is they only reflect our choice of units).

Last edited:
pervect
Staff Emeritus
i realize that this appears to be a resurrected post (or maybe it's a zombie post, if the sysops shoot it, will it die?), but i would be curious to see some response to this:

of course the "electic" force (EM) has, by definition, a speed of c.

but my understanding from SR and GR is that it is not just gravity (or the perturbation of space-time) and EM that move at a speed of c, but all interaction, otherwise information could move at the speed of the other fundamental interaction. is that not correct?

Right.

from discussions with some pretty heavy physicists (it's sorta amazing whom you can talk to, if you find their email address), the understanding from them that i gleaned was this: Nature has a single finite speed for these interactions (which may someday be all unified in a single theory). The salient physics is that speed is the same for all fundamental interactions and that is finite. That is, whatever the interaction, if something changes over here, the effect over there, as observed by a third party somewhere else (but let's say equidistant from here and there), will happen at a time that is delayed by

|locus(here) - locus(there)|/c

where c is that finite speed.

now the salient fundamental physics is that this speed of propagation, c, is finite, not infinite. physical reality would be different than it is if c were infinite. but it doesn't really matter what that finite speed is since it, along with G and $\hbar$, will simply define the scale of existence of things in the universe. as long as all of the dimensionless parameters of interaction remain the same (physicist John Baez has enumerated 26 such dimensionless parameters, but says there could be more as new interactions are discovered and that new physical theories might derive some of these parameters from others, thus reducing that number), a conceptual change in c could not be noticed by observers whose existence and scale is governed by that.

my interpretation: if God (or some "god-like" being) could reach over and turn the knob that controls c to half of its previous value so the new c is the old c/2, then the Planck Length would increase by a factor of $\sqrt{8}$ and so would the size of atoms, meter sticks, and people (from the POV of this "god-like" observer) if all the dimensionless parameters remained the same.

I'm not sure if I understand this. I was under the impression that if all the dimensionless parameters remained the same, the value of 'c' didn't matter, there was no new physics. I.e you could change 'c' to 'c/2' by doubling the length of the meter and leaving the second the same. This would double the size of atoms (I'm not sure where you got sqrt(8) - I would assume you had some sort of rationale, but that's not what I would guess would happen) You could also change 'c' to 'c/2' by doubling the length of the second - in this case, atoms would remain the same size, but the units of time would vary.

Right.

that's reassurring. i am trying to not misquote or mis-contextualize any of these pearls that i get from emails with the likes of Michael Duff or Lev Okun or Gabriel Veneziano. and if i f*ck something up, i wanna know.

I'm not sure if I understand this. I was under the impression that if all the dimensionless parameters remained the same, the value of 'c' didn't matter, there was no new physics.

that's what i understand, too.

I.e you could change 'c' to 'c/2' by doubling the length of the meter and leaving the second the same. This would double the size of atoms (I'm not sure where you got sqrt(8) - I would assume you had some sort of rationale, but that's not what I would guess would happen)

I was assuming an unchanged G and $\hbar$ (as well as the dimensionless parameters, which are the important ones). if c was halved, the Planck Length would increase by $\sqrt{8}$ (from the POV of the outside observer that is ungoverned by physics and who, hypothetically, could actually observe c getting cut in half) and if all the dimensionless ratios remained constant, so would atoms, meter sticks, and every other length. the Planck Time (from the POV of the outside observer that is ungoverned by physics) would be increased by a factor of $\sqrt{32}$. light would travel half as fast (from the POV of this supernatural observer), and would need to travel $\sqrt{8}$ times farther, but would have a factor of $\sqrt{32} = 2 \sqrt{8}$ more time to do it. assuming the dimensionless ratios of meter/PlanckLength and second/PlanckTime remain the same, this comes out to be the same number of new meters per new second.

so, in this thought experiment, if you, as this "god-like" observer/manipulator would "change 'c' to 'c/2' by doubling the length of the meter [and atoms] and leaving the second the same", but then (assuming the number of atoms in the meter stick remain constant) the dimensionless ratio of the atom sizes (approximately the Bohr radius) to the Planck Length would change (which is outside the axiom) if the dimensionless ratio of the second to the Planck Time remained the same. so i don't think that quite works, Pervect. if the second (and Planck Time) remained the same while c was cut in half the $G \hbar$ product would have to decrease by a factor of 32 but if the meter (and Planck Length) was doubled while c was cut in half, then the $G \hbar$ product would decrease by a factor of 2. 32 is not equal to 2. and i'm assuming that the number of atoms in the meter stick does not change, the number of Planck Lengths in the size of the atoms do not change, and the number of Planck Times per "period of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" remains the same.

You could also change 'c' to 'c/2' by doubling the length of the second - in this case, atoms would remain the same size, but the units of time would vary.

how can either doubling the length of the meter or doubling the length of the second both have the same effect to change c to c/2?

Edit: i thought about this a little, and i think what you meant to say, Pervect, is that you can change c to c/2 by halving the length of the meter (and the Planck Length), leaving the second (and Planck Time) unchanged, or you can change c to c/2 by leaving the meter unchanged and doubling the length of the second. That works, but besides a changing value of c (from the POV of the unaffected supernatural observer), there would also be changing G and/or $\hbar$. in any case, light, E&M, gravity, whatever interaction, will continue to travel 1 Planck Length during the period elapsed by 1 Planck Time.

Last edited:
pervect
Staff Emeritus
OK, I see where you're coming from now: if you assume that G and hbar remain constant, the planck length is just

$$\sqrt{\frac{G \bar{h}}{c^3}}$$

so that's where your factor of sqrt(8) came from.

As far as what I had in mind, if 1 new meter = 2 old meters, then

c = 3e8 old meter / second = 1.5e8 new meter / second

so doubling the meter halves the "speed of light" from 3e8 "old meters" per second to 1.5e8 "new meters"/ second.

OK, I see where you're coming from now: if you assume that G and hbar remain constant, the planck length is just

$$\sqrt{\frac{G \bar{h}}{c^3}}$$

so that's where your factor of sqrt(8) came from.

As far as what I had in mind, if 1 new meter = 2 old meters, then

c = 3e8 old meter / second = 1.5e8 new meter / second

so doubling the meter halves the "speed of light" from 3e8 "old meters" per second to 1.5e8 "new meters"/ second.

that doesn't quite work for me. i think that, if all of the dimensionless parameters remain constant,

c = 299792458 old_meters/old_second = 299792458 new_meters/new_second

and the new_second cannot be the same as the old_second if the meter had changed.

but i think we (as well as Duff) agree: ain't no operational difference. a change in c (or in G or h or any other sole dimensionful "constant") is not merely impossible, but is functionally meaningless.

i still don't know what to think of this inflationary universe theory where the universe expands faster than c at some time in its past.

Last edited:
Several of the comments re the speed of fields are not established by experiment - the speed of light in a vacuum is c, we all know that, but the speed with which a closed non-divergent magnetic field propagates in a loop of magnetic material is not readily explainable in terms of the field starting out at each pole of the energized magnet and meeting itself somewhere in middle - waves go from place to place - we do not know the mechanism by which fields make their forces felt at a distance -

It seems when physics needs to explain quantum entanglements and virtual photons the speed barrier is shunted to the side. In the case of gravity, it is usually assumed there is a graviton exchange between attracted particles - but gravity and inertia may be the result of global dynamics - the cosmological constant or, like expansion, an ongoing change that does not happen at one place and travel to another, but rather something that affects spacetime continuously. The curvature of GR may be the result of local mass interaction therewith, in which case it may not be meaningful to assign a propagation velocity to the curvature.

pervect
Staff Emeritus
Several of the comments re the speed of fields are not established by experiment

The speeds are certainly established by theory, though. And the theory has survived every experimental test thrown at it, to date.

For instance, if Maxwell's equations were wrong, we'd start to see disagreement with experiment, even if that experiment wasn't directly designed to measure some sort of "speed".

Maxwell's equations certainly give us a good reason to expect that electromagnetism, in general, travels at 'c' in the general sense that if you change something "here", it won't have any effect "there" until after a delay of at least c/distance.

Some care does need to be taken as to what means by speed. Specifically, one has to use the above defintion, and not try and guess the speed from the direction of the coulomb force, a common sorce of confusion that is also often repeated in "speed of gravity" threads.

GR is no different as far as the theoretical aspects go. (However, we don't have any direct measurements of the speed or even the existence of gravity waves, while of course we do have direct observations of light).

The equations are a lot messier than Maxwell's equation, but there is proof that GR is a well posed initial value problem, which implies that the "fields" propagate at less than 'c'. (You can regard the "fields" as changes in the metric, which will also change the Christoffel symbols and the curvature tensor).

The details of the proof that GR is a well posed initial value problem are rather complicated and I'm not especially familiar with them, but you can find the proof in Wald, "General Relativity". I've written a little about this in the past, as to what it means to be a well-posed initial value problem and what this implies about propagation speed.

Last edited:
The speeds are certainly established by theory, though. And the theory has survived every experimental test thrown at it, to date.

For instance, if Maxwell's equations were wrong, we'd start to see disagreement with experiment, even if that experiment wasn't directly designed to measure some sort of "speed".

Maxwell's equations certainly give us a good reason to expect that electromagnetism, in general, travels at 'c' in the general sense that if you change something "here", it won't have any effect "there" until after a delay of at least c/distance.

Would concur - there is much indirect/consequential evidence of c as the limiting communication velocity - but being the eternal skeptic, I always find myself compelled to comment when absolute assertions are made about propagation rates of fields

I sort of expected Eugene to jump into this thread somewhere as he has written a couple of papers on the subject

DaveC426913
Gold Member
gravity's influence is technically finite ... once you take out black holes, gravity is finite.
Do you mean in terms of distance? No it's not. It's infinite.

gravity's influence is technically finite, though not if you count black holes. a singularity is infinintly dense, so it's gravitational influence is infinite. it's jsut the range that the gravity works on that is affected. once you take out black holes, gravity is finite.

Do you mean in terms of distance? No it's not. It's infinite.

i thought he meant in terms of magnitude of field (or the degree of curvature of space-time).

haushofer