Is it possible that speed of a gravitational waves are greater than c?

[Ravi Mandavi]

Since at event horizon, the escape velocity of black hole must be greater than speed of light but even light can't escape from black hole so is it possible that speed of gravitational wave > c?

 

[alexg]

Since at event horizon, the escape velocity of black hole must be greater than speed of light but even light can't escape from black hole so is it possible that speed of gravitational wave > c?

When the Black Hole formed, the gravitational field was already there, permeating space. It doesn't go away because an event horizon formed.

 

[skeptic2]

It would be hard to explain a 21 billion solar mass black hole by saying that the gravitational field was already there when the star collapsed. I think most cosmologists accept that the field grows as the BH accretes mass. But from where does the gravitational field originate?

While a static field is not affected by an event horizon, the process of accreting mass is hardly static. If the gravitational field were an indication of the mass at the singularity then there is a problem of how the increases in the mass of the singularity, resulting in the changes in the gravitational field, propagate from the singularity backwards in time and faster than light in order to escape the event horizon.

On the other hand, there is an explanation that as matter falls through the EH, it leaves its gravitational field frozen at the horizon.

 

[Chronos]

Under quantum electrodynamics, gravity should be mediated by virtual particles. Virtual particles are not bound by event horizons.

 

[Aidyan]

I wonder instead why physicists/astronomers are so sure that gravitational waves travel with the speed of light? Why can it not be slower? Is it just an assumption that waits to be tested, or is there a deeper reason for that?

 

[phyzguy]

The reason we believe that gravitational waves travel at the speed of light is that gravity is very accurately described by Einstein's equations of General Relativity. General Relativity has passed every experimental test to which it has been subjected, and General Relativity predicts gravitational waves, and predicts that they travel at the speed of light. While gravitational waves have never (yet) been detected directly, their consequence has been seen in the Hulse-Taylor binary pulsar, the discovery and explanation of which earned them the Nobel prize. When gravitational waves are directly seen, probably within the next decade, I would bet a large sum of money that they are seen to travel at the speed of light.

 

[Chronos]

Lorentz invariance is the part of GR that limits the propogation speed of fields to 'c' and it is assumed Lorentz invariace also applies to gravity. Hulse and Taylor received the 1993 Nobel for their work on binary pulsars, which showed timing increases that precisely matched those predicted by GR. If gravity were not Lorentz invariant, the results would not have matched the predictions of GR.

 

[jambaugh]

Remember that we have not quite yet observed gravitational waves. The theory that predicts them predicts their speed as c. Until or unless they are observed it is not appropriate to simply speculate whether this one point may vary. You must rather bite off a bigger chunk.

One would be speculating whether there is an alternative theory, also predicting gravity waves but traveling at different speeds, which is self consistent and consistent with observed phenomena.

 

[DaveC426913]

On the other hand, there is an explanation that as matter falls through the EH, it leaves its gravitational field frozen at the horizon.

Good, you answered you own question.

All mass (thus all sources of gravity) started off either before or outside the BH, thus their gravitational fields were indeed already in effect when they fell into the BH.

 

[Orion1]

Power radiated by orbiting bodies:
$$P = \frac{dE}{dt} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}$$

Orbital decay from gravitational radiation:
$$\frac{dr}{dt} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}$$

If gravitational wave velocity was greater than luminous velocity, then the amount of power radiated and the orbital decay of binary pulsars would be much less.

If gravitational wave velocity was less than luminous velocity, then the amount of power radiated and the orbital decay of binary pulsars would be much more.

However, the measurements of these functions in nature indicate agreement with these equations in which the intrinsic velocity of gravitational waves is exactly equal to luminous velocity.

Could the gravitational wave velocity be measured directly from nature with is equation?

Gravitational wave velocity:
$$c = \left[ \left( \frac{64 G^3}{5} \, \frac{(m_1m_2)(m_1+m_2)}{r^3} \right) \left( - \frac{dr}{dt} \right)^{-1} \right]^{\frac{1}{5}}$$


Reference:
Gravitational wave - Wikipedia

 

[Chronos]

Jimbaugh, do you think Hulse was not compelling evidence of gravitational waves and their Lorentz invariance? phyzguy, apologies I was still pecking away when you posted essentially the same thing.

 

[Nabeshin]

Power radiated by orbiting bodies:
$$P = \frac{dE}{dt} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}$$

Orbital decay from gravitational radiation:
$$\frac{dr}{dt} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}$$

If gravitational wave velocity was greater than luminous velocity, then the amount of power radiated and the orbital decay of binary pulsars would be much less.

If gravitational wave velocity was less than luminous velocity, then the amount of power radiated and the orbital decay of binary pulsars would be much more.

However, the measurements of these functions in nature indicate agreement with these equations in which the intrinsic velocity of gravitational waves is exactly equal to luminous velocity.

Could the gravitational wave velocity be measured directly from nature with is equation?

Gravitational wave velocity:
$$c = \left[ \left( \frac{64 G^3}{5} \, \frac{(m_1m_2)(m_1+m_2)}{r^3} \right) \left( - \frac{dr}{dt} \right)^{-1} \right]^{\frac{1}{5}}$$


Reference:
Gravitational wave - Wikipedia

This is an incredibly naive analysis... If you assume gravitational radiation does NOT travel at c, a lot has to change within relativity. If it's slower, well you have a massive graviton which among having a speed <c also admits longitudinal polarizations. The whole situation becomes significantly more complicated. If it's faster, all kind of crazy things go out the window and I don't even know where to start there.

 

[jambaugh]

Jimbaugh, do you think Hulse was not compelling evidence of gravitational waves and their Lorentz invariance?

Yes I do. But I do not consider it direct observation. The pulsar observations make it that much harder to speculate outside of GR. One must explain them.

If however we can build a grav. wave detector we needn't speculate, we could measure the speed. Thus it is meaningful to ask what value we might measure.

Until then, this question is of a different type, (i.e. what does theory say) and so supposing a different answer than theory supposes a distinct theory.

Now personally I'll be shocked if we observe other than speed c grav waves...beyond shocked, flabbergasted.

 

[Chronos]

Thanks for the clarification, jambaugh. As you probably recall, Kopeikin and Formalont attempted a direct measurement of the speed of gravity about a decade ago, but, it is considered controversial. I believe it was Steve Carlip who basically accused them of making a backdoor measurement of the speed of light.

 

[Orion1]

What is the gravitational wave frequency equation for the Hulse–Taylor binary pulsar system?

Reference:
Gravitational wave - Wikipedia
PSR B1913+16 - Wikipedia
http://www.nobelprize.org/nobel_prizes/physics/laureates/1993/hulse-lecture.pdf
http://www.nobelprize.org/nobel_prizes/physics/laureates/1993/taylor-lecture.pdf
General relativistic model for experimental measurement of the speed of propagation of gravity by VLBI - University of Missouri - Kopeikin and Fomalont

 

[poioip]

what basically happens is that gravity bents space & time fabric. the light travels parallel to space & time fabric so at a point the fabric is stretched and light have to travel twice as long so that's why they say light cannot escape a black hole. As Eisenstein said that c is the optimum speed limit so let's say a particles with mass zero (energy) can travel at the velocity of c

 

[Nabeshin]

What is the gravitational wave frequency equation for the Hulse–Taylor binary pulsar system?

Reference:
Gravitational wave - Wikipedia
PSR B1913+16 - Wikipedia
http://www.nobelprize.org/nobel_prizes/physics/laureates/1993/hulse-lecture.pdf
http://www.nobelprize.org/nobel_prizes/physics/laureates/1993/taylor-lecture.pdf
General relativistic model for experimental measurement of the speed of propagation of gravity by VLBI - University of Missouri - Kopeikin and Fomalont

2x the orbital frequency.

 

[strat1227]

Pardon if this is a naive understanding of it, but I was under the impression that describing gravity in waves is just a way for us to visualize it, but in actuality that's not what's happening.

My understanding is just that mass alters space-time, so for example while the moon appears to be going in a circle to us, it's actually not going in a circle through space-time, because that's an entirely different plane than our spatial 3 dimensions.

So if that's the case (if it's not then please just correct my misunderstanding and ignore this question), why does it take any time at all for gravity to permeate? If you drop a billiard ball onto a outstretched blanket, all points of the blanket are affected at the same time. Similarly, if you just spontaneously created a large amount of mass in the middle of empty space, would not the space-time field be instantly altered?

 

[Nabeshin]

So if that's the case (if it's not then please just correct my misunderstanding and ignore this question), why does it take any time at all for gravity to permeate? If you drop a billiard ball onto a outstretched blanket, all points of the blanket are affected at the same time. Similarly, if you just spontaneously created a large amount of mass in the middle of empty space, would not the space-time field be instantly altered?

No, even within your analogy your intuition is failing here. If you imagine a really large sheet and dropping a bowling ball on it, say the sheet goes from New York to Paris, do you really think the guy in Paris will feel the ball that was dropped in NY instantly? No, he will not. The disturbance propagates at something like the sound speed of the material (I have no idea what this is for a taut sheet, but certainly finite!). The analogy with spacetime is decent, in that the disturbance propagates our at the speed of light.

Note that within GR, if I just imagine the moon orbiting the earth, nothing is changing about the spacetime (assume the moon mass is so much smaller than the Earth that it doesn't alter the geometry). The Earth creates some well, and the moon is just moving in a straight line through that well. 'Gravity' is encoded in the curvature of that well, which never changes, so it doesn't make any sense to talk about anything propagating here. Only when I change the situation (remove some mass somehow, or something like that), does the geometry need to respond, and these ripples travel outwards like waves on a pond at precisely the speed of light.

 

[strat1227]

The disturbance propagates at something like the sound speed of the material (I have no idea what this is for a taut sheet, but certainly finite!).

Ok, that explanation makes sense :) I was thinking about it from a mathematical standpoint and not a physical one ... Mathematically speaking, all points would feel it at the same time, but that obviously can't be the case physically

Only when I change the situation (remove some mass somehow, or something like that), does the geometry need to respond, and these ripples travel outwards like waves on a pond at precisely the speed of light.

That was the question that inspired my post, if I just created a bunch of mass spontaneously in the middle of empty space, how long would it take surrounding planets to feel the effects of it.

 

[DaveC426913]

Mathematically speaking, all points would feel it at the same time

Why would this be so? Why does 'mathematically' mean you'd ignore propagation velocity?

 

[strat1227]

Why would this be so? Why does 'mathematically' mean you'd ignore propagation velocity?

All the points are connected, so if you pull down on any of them they all move ... Similar to if you held a light-year long pole and extended your arm, if you just consider that a line segment then the end of the line moves simultaneously with the end you're holding, which obviously isn't true of the physical world.

But that's just a tangent of mine and not a point of contention, as I mentioned earlier I realized a had a fundamental misunderstanding of the information and now it's been corrected, no reason to argue :)

 

[DaveC426913]

All the points are connected, so if you pull down on any of them they all move ...

Yeah but the movement must still propagate.

 

[strat1227]

Yeah but the movement must still propagate.

Haha not to be off topic, but why? It doesn't in the line segment example ... The stretching of the plane could just as easily be simultaneous across the whole plane, the only limiting reason it wouldn't be are physical limitations

 

[DaveC426913]

Haha not to be off topic, but why? It doesn't in the line segment example ...

A line segment doesn't move. You could measure the distance from your hand to your target as being one light year, then move your hand and measure again. But it's not the same line segment (since it's just a measurement), and it took a finite time between measurements.

The stretching of the plane could just as easily be simultaneous across the whole plane, the only limiting reason it wouldn't be are physical limitations

The model you used was a billiard ball on a blanket. You can ignore the physical traits of the system and only examine it mathematically, but it is a central cause and a radiating sequence of effects. In a cause/effect system the effect must propagate from the central cause at a finite speed.

 

[strat1227]

A line segment doesn't move. You could measure the distance from your hand to your target as being one light year, then move your hand and measure again. But it's not the same line segment (since it's just a measurement), and it took a finite time between measurements.


The model you used was a billiard ball on a blanket. You can ignore the physical traits of the system and only examine it mathematically, but it is a central cause and a radiating sequence of effects. In a cause/effect system the effect must propagate from the central cause at a finite speed.

Haha ok, we're just kinda talking past each other at this point, and since it's not really relevant to the topic in any real way anymore I'll just say that I understand my mistake from earlier and thanks for helping me :)

 

[DaveC426913]

Haha ok, we're just kinda talking past each other at this point, and since it's not really relevant to the topic in any real way anymore I'll just say that I understand my mistake from earlier and thanks for helping me :)

It's cool. I like discussing.

 

[strat1227]

It's cool. I like discussing.

Haha ok, cool :)

Basically what I was thinking is that the reason motion propagates is on the molecular level. If you push one atom it moves and then pushes the next one, and so on. Similar to how when a light turns green, the first car starts moving THEN the next car starts moving, etc, instead of all of them moving as soon as it turns green.

However, (presumably), the fabric of space-time isn't molecular. I'm not particularly knowledgeable about the subject, but I would assume that space-time is continuous, not discrete. So if I tug on a string of space-time, it's not individual atoms moving, it's a continuous string so as I pull on my end, the other end moves simultaneously.

 

[Steely Dan]

Haha ok, cool :)

Basically what I was thinking is that the reason motion propagates is on the molecular level. If you push one atom it moves and then pushes the next one, and so on. Similar to how when a light turns green, the first car starts moving THEN the next car starts moving, etc, instead of all of them moving as soon as it turns green.

However, (presumably), the fabric of space-time isn't molecular. I'm not particularly knowledgeable about the subject, but I would assume that space-time is continuous, not discrete. So if I tug on a string of space-time, it's not individual atoms moving, it's a continuous string so as I pull on my end, the other end moves simultaneously.

From the perspective of general relativity, that's exactly correct. Just like a string, spacetime itself has some characteristic speed at which waves propagate through it (although in the case of space, it's the speed of light, which is a bit higher than your average wave speed in a string).

Anyway, this bit about propagation speeds of physical effects is quite important, and it's important to always be aware of it. It's often easy to write down a mathematical model for a certain situation that extends off to infinity, and forget that far away from your local area of interest, signal speeds become important. That can be important when dealing with boundary conditions for PDEs, for example.

 

[Orion1]

Since at event horizon, the escape velocity of black hole must be greater than speed of light but even light can't escape from black hole so is it possible that speed of gravitational wave > c?

A black hole event horizon has perfect spherical symmetry, therefore it does not radiate gravitational radiation.

Reference:
Gravitational wave - sources of gravitational waves - Wikipedia

 

[Ravi Mandavi]

what i got is this- http://metaresearch.org/cosmology/speed_of_gravity.asp
According to it gravitational wave's speed faster than light, though i don't think so and feel its rubbish.

 

[Steely Dan]

what i got is this- http://metaresearch.org/cosmology/speed_of_gravity.asp
According to it gravitational wave's speed faster than light, though i don't think so and feel its rubbish.

The article is clear to point out that it does not dispute the idea that gravitational waves travel at the speed of light. What it questions is whether changes to the gravitational field necessarily propagate as gravitational waves, or whether they are different and therefore not bound to the requirement of traveling at $c$.

 

[GTOM]

If gravity is the thing that defines spacetime, why is it necessary bounded by a speed, that is only meaningful, when we know exact parameters of spacetime, what is exactly one meter and one sec?
One sec in strong gravity and week gravity isn't exactly the same.

 

[Whovian]

If gravity is the thing that defines spacetime, why is it necessary bounded by a speed, that is only meaningful, when we know exact parameters of spacetime, what is exactly one meter and one sec?
One sec in strong gravity and week gravity isn't exactly the same.

To the person in strong/weak gravity, one second is the same.

Why is it necessarily bounded by a speed? A gravitational wave does distort spacetime, and can also be detected. A physicist with an instrument that detects that wave can know that there's a mass at the source of the wave, so the wave can be thought to contain the information that a mass is there. But information can't travel faster than light.

 

[Drakkith]

If gravity is the thing that defines spacetime, why is it necessary bounded by a speed, that is only meaningful, when we know exact parameters of spacetime, what is exactly one meter and one sec?
One sec in strong gravity and week gravity isn't exactly the same.

Gravity does not define spacetime. Gravity is merely a property of energy and mass occupying an area of spacetime that causes an effect we call "curvature". We measure distance and time using measuring devices, such as a meter stick and a clock and have defined a specific distance and a specific interval on the clock as one meter and one second. There is no known reason that the speed of light be the limiting speed at which information can travel through the universe. It is only known that this limit exists.