Gravitational waves of moving or vibrating masses

[yahastu]

I am curious if the motion of massive object can effect it's gravitational influence due to the fact that gravitational waves travel at the speed of light.

For a weak analogy, consider how a small object can make bigger ripples in the water if it is moving around more. I am curious if there are any conditions where the movement of a mass would create similar ripples in spacetime similar to the appearance of a larger object

 

[Ibix]

I think you are asking if the gravitational field of a mass can ever look like the gravitational field of a larger mass. In short, no. However, I'm not sure where you think gravitational waves come into this, so I'll talk around it a bit.

If you have an isolated mass, its speed isn't a well-defined quantity. So it can't really have an effect on anything. That said, your experience of its gravitational field is very different depending on your speed relative to the object. It doesn't look like a straight mass increase, though. In the limit where your relative speed approaches c, it is described by the impressively named Aichelburg-Sexl ultraboost.

When there are two (or more) masses in relative motion then there is an absolute sense in which something is moving, and the result is quite different - energy is lost to gravitational radiation. But, again, this doesn't look like a mass increase. The paths of two objects that have masses $m_1$ and $m_2$ will be quite different from two objects that have masses $M_1$ and $M_2$, with consequently different emission signatures, both in terms of power and frequency.

 

[LURCH]

Perhaps it is worth pointing out that gravity waves are not caused by an object moving at tremendous speeds, but by an object undergoing tremendous acceleration.

With that in mind; Are you asking whether an object of small mass under extreme acceleration would generate gravity waves similar to those of a greater mass under slightly less acceleration?

 

[Ibix]

but by an object undergoing tremendous acceleration.

Orbiting black holes emit gravitational waves and are inertial, not accelerating in any absolute sense. A time-varying quadropole moment is the actual source term for gravitational waves.

 

[yahastu]

With that in mind; Are you asking whether an object of small mass under extreme acceleration would generate gravity waves similar to those of a greater mass under slightly less acceleration?

Sort of. I guess my question could be better phrased as follows:

Suppose you want to estimate the mass of some object based on its observed gravitational influence on other objects in its vicinity. You have a good estimate of the low-frequency overall movement of all bodies in question, however you failed to account for some high frequency oscillations in its acceleration. Would the incorrect assumptions about high frequency accelerations cause you to incorrectly estimate its mass? In other words, is it possible for unaccounted high frequency accelerations of a massive object to cause it to appear as if it had a different mass?

 

[LURCH]

As far as I know, no. Gravitational waves do not, in any model of which I am aware, increase gravitational pull. A gravitational wave distorts spacetime first in one direction, then the opposite. The overall net result is null. Gravitational waves don’t increase the amount of gravitational pull in the same way that waves in water don’t increase the amount of water.

 

[yahastu]

As far as I know, no. Gravitational waves do not, in any model of which I am aware, do not increase gravitational pull. A gravitational wave distorts spacetime first in one direction, then the opposite. The overall net result is null. Gravitational waves don’t increase the amount of gravitational pull in the same way that waves in water don’t increase the water level.

I appreciate your answer, although your analogy seems to overlook the confusing aspect of this...you can make a big splash either by moving a large object a little bit, or by moving a small object a lot...in other words, a small object with high energy can also make a big splash in water. I thought that perhaps the same might be true with gravitational waves...meaning that if you added energy to the system in the form of additional movement, it might make a bigger gravitational wave. After all, mass is convertible to energy.

Consider the following:

There are three masses M1, M2, M3 arranged in a line.

M2 is very close to M1, and emits a gravitational wave that accelerates M1 towards the center of the line.
Then, M2 zips over to M3 at half the speed of light and emits a gravitational wave that accelerates M3 towards the center.
M2 can keep going back and forth and giving them tugs toward the center.
An observer sees both M1 and M3 being attracted towards the center, and may conclude there is a fixed point mass located at the midpoint between them -- but what is the apparent mass of this object?
I think that the apparent mass would have to be larger than M2, because the force of gravity is a nonlinear function of distance.

 

[PeterDonis]

Suppose you want to estimate the mass of some object based on its observed gravitational influence on other objects in its vicinity. You have a good estimate of the low-frequency overall movement of all bodies in question, however you failed to account for some high frequency oscillations in its acceleration.

High frequency oscillations in the acceleration of what? Of the massive body? Or of the bodies in its vicinity whose motion you are using to estimate the massive body's mass?

If you are estimating the mass of a massive body from motion of bodies orbiting the massive body, your estimate will be as accurate as your observations of the orbiting bodies are. This method of estimating does not "care" about the motion of the massive body itself.

 

[LURCH]

I appreciate your answer, although your analogy seems to overlook the confusing aspect of this...you can make a big splash either by moving a large object a little bit, or by moving a small object a lot...in other words, a small object with high energy can also make a big splash in water. I thought that perhaps the same might be true with gravitational waves...meaning that if you added energy to the system in the form of additional movement, it might make a bigger gravitational wave. After all, mass is convertible to energy.

Looks like there are two parts to this. I want to address the second part first, because then we can get to the part that I think is the heart of the matter.

Consider the following:

There are three masses M1, M2, M3 arranged in a line.

M2 is very close to M1, and emits a gravitational wave that accelerates M1 towards the center of the line.
Then, M2 zips over to M3 at half the speed of light and emits a gravitational wave that accelerates M3 towards the center.
M2 can keep going back and forth and giving them tugs toward the center.
An observer sees both M1 and M3 being attracted towards the center, and may conclude there is a fixed point mass located at the midpoint between them -- but what is the apparent mass of this object?
I think that the apparent mass would have to be larger than M2, because the force of gravity is a nonlinear function of distance.

This is the matter that I was addressing in my earlier post. M2, by emitting gravity waves, does not accelerate M1 or M3. Gravitational waves do not exert a push or a pull on objects. At least not in the sense that you describe. If M2 emits strong gravitational waves toward M1, assuming M1 was a spherical object, M1 will become somewhat elongated along one axis, then compressed along that same axis and compressed in the opposite direction, but the center of mass of M1 will not be moved. So, the motions of M1 and M3 cannot be used to measure, or even detect, gravitational waves. Just wanted to clear that up.

However, I suspect that this might be beside your point, since gravitational waves can be detected by other means (LIGO, for example). What you are asking about, if I understand correctly, is whether a certain mass at a certain acceleration will produce gravitational waves identical to those from a smaller mass at greater acceleration, or a greater mass at lesser acceleration. I do not have a definitive answer, but I hope I have made the question more clear for others who might read it.

I can tell you that gravitational waves have many characteristics in common with other waves; they have wavelength, amplitude and frequency. Based on that knowledge, let’s try to reason this out. Assume gravitational waves are being generated by two separate sources of equal energy. Each source is a massive object being accelerated back and forth in place. One source is far more massive than the other. Keeping in mind that both sources have equal total energy, it would seem that the more massive one is going to be moving back and forth more slowly, so the wave frequency would be lower, and this, I think, could be used to calculate the difference in mass.

Again, that is only my reasoning, and I hope someone more knowledgeable than I will address this further.

 

[Ibix]

however you failed to account for some high frequency oscillations in its acceleration.

Where would these come from? Unlike your water analogy, there's no way to "stand on the bank and wiggle the pebble". So whatever is making it oscillate is in spacetime, and is of comparable mass and also oscillating. Where is this in your description?

M2 is very close to M1, and emits a gravitational wave

Why? Things don't just emit gravitational waves. There needs to be a changing quadropole moment - so you need other masses in relative motion. Again, this doesn't seem to be present in your description.

Furthermore, a gravitational wave causes strains perpendicular to its direction of propagation. It doesn't make things accelerate towards the source.

What you are asking about, if I understand correctly, is whether a certain mass at a certain acceleration will produce gravitational waves identical to those from a smaller mass at greater acceleration, or a greater mass at lesser acceleration.

The problem with answering this is, as I tried to point out before, things don't just accelerate. There has to be something of similar mass (rocket exhaust, or another planet/star/black hole if we interpret "acceleration" loosely) around that is involved in making it accelerate. And that is also a source of gravity that seems to be completely neglected in the OP's writing.

 

[yahastu]

M2, by emitting gravity waves, does not accelerate M1 or M3. Gravitational waves do not exert a push or a pull on objects. At least not in the sense that you describe. If M2 emits strong gravitational waves toward M1, assuming M1 was a spherical object, M1 will become somewhat elongated along one axis, then compressed along that same axis and compressed in the opposite direction, but the center of mass of M1 will not be moved. So, the motions of M1 and M3 cannot be used to measure, or even detect, gravitational waves. Just wanted to clear that up.

Huh? Gravitational waves don't exert a push or a pull? The center of mass of two objects can't be moved by gravity? I don't understand what you're saying. Clearly, gravity is a force that can move the center of mass of objects...the Earth is a mass which is attracted to the Sun for example, and it's center of mass relative to the sun is constantly being moved while it is in orbit. We also know the influence of gravity travels through gravitational waves that propagate at the speed of light. So how is it not the case that gravitational waves exert a push or pull?

 

[Ibix]

Huh? Gravitational waves don't exert a push or a pull? The center of mass of two objects can't be moved by gravity? I don't understand what you're saying. Clearly, gravity is a force that can move the center of mass of objects...

Gravity, in the "I let something go and it falls" sense, is very different from gravitational waves.

It's closely analogous to charging a balloon by rubbing it on your jumper versus using a radio. The balloon will pull your hair towards it due to its electric field, but the electromagnetic radiation from the radio won't. They are both electromagnetic phenomena, but don't do the same thing.

We also know the influence of gravity travels through gravitational waves that propagate at the speed of light.

This is an overly simplistic picture, at best, as noted above.

 

[PeterDonis]

Gravitational waves don't exert a push or a pull? The center of mass of two objects can't be moved by gravity?

"Gravity" and "gravitational waves" are not the same. Gravitational waves, as @Ibix noted, are transverse; they produce strains perpendicular to their direction of motion. They do not push things along their direction of motion.

gravity is a force that can move the center of mass of objects

No, in GR gravity is not a force. Objects that are affected only by gravity move on geodesics--freely falling paths through spacetime. They feel no force. "Gravity" affects their paths by affecting the geometry of spacetime, not by pushing or pulling on the objects.

We also know the influence of gravity travels through gravitational waves that propagate at the speed of light.

No, this is not correct. Static gravity, the kind of "gravity" that makes rocks fall towards the Earth or the Earth orbit the Sun, is not propagated by gravitational waves.

 

[yahastu]

"Gravity" and "gravitational waves" are not the same. Gravitational waves, as @Ibix noted, are transverse; they produce strains perpendicular to their direction of motion. They do not push things along their direction of motion.

No, in GR gravity is not a force. Objects that are affected only by gravity move on geodesics--freely falling paths through spacetime. They feel no force. "Gravity" affects their paths by affecting the geometry of spacetime, not by pushing or pulling on the objects.
No, this is not correct. Static gravity, the kind of "gravity" that makes rocks fall towards the Earth or the Earth orbit the Sun, is not propagated by gravitational waves.

I apologize for calling it a "force"...though I'm pretty sure my textbook does also. It doesn't really matter to me what we call it, I just want to better understand how it works. I'll try to rephrase my question using the lingo of GR:

Is it not true that changes to the geometry of spacetime due to moving masses are limited by the speed of light? For example, if a massive object spontaneously appeared at point A (not possible, but makes the question simpler), then the spacetime geometry at a different point B would not be effected immediately -- there would be a delay before the spacetime geometry at B is changed, right? In other words, if we consider the typical visualization in GR of a 2d spacetime sheet being deformed by a ball mass, and the ball moves, then in this illustration we should expect to see ripples/waves in that spacetime as it moves, rather than the spacetime always being perfectly deformed underneath it at all times regardless of motion, right? And those ripples would be gravitational waves, right?

 

[PeterDonis]

Is it not true that changes to the geometry of spacetime due to moving masses are limited by the speed of light?

This is true, but you have to be careful when trying to figure out what it means. See below.

For example, if a massive object spontaneously appeared at point A (not possible, but makes the question simpler)

Sorry, but "not possible" means the question is meaningless, not simpler. There is no point in postulating a scenario that violates the laws of physics, and then asking what the laws of physics say about it.

It actually turns out to be very difficult to set up a scenario where you can actually test the "speed of gravity" in the sense of propagating changes to spacetime geometry due to changes in the sources (stress-energy, which includes moving masses but also changes in pressure and stresses). But what you can do is prove some very general theorems about the Einstein Field Equation, which basically amount to: if you want to know the spacetime curvature at a particular event in spacetime, all you need to know is the distribution of stress-energy in the past light cone of that event. That is what ensures that "gravity" cannot "propagate" faster than light.

those ripples would be gravitational waves, right?

Particular kinds of moving systems do cause ripples in spacetime that propagate outward at the speed of light, and those propagating ripples are gravtational waves, yes. Examples of such systems include binary pulsars and neutron star and black hole mergers.

However, the conditions required for a system to emit gravitational waves are not just "moving masses"; they are more complicated than that. As has already been noted in this thread (I think), the "source" of gravitational waves is the third time derivative of the quadrupole moment of the stress-energy. To get a nonzero third time derivative of the quadrupole moment, you need two unequal masses orbiting each other (and for the waves to be detectable the masses need to be large and dense, like neutron stars and black holes). At least, that's the only kind of system we've detected gravitational waves from so far.

 

[LURCH]

I’m afraid the entire conversation here may be a result of the failure to distinguish between “gravitational waves”, and “gravitons”. Gravitons are proposed (and still theoretical at the moment) quantum units of gravity, which are often described as being “wave-like”.

Gravitational waves are something completely different. Unlike gravity (and gravitons, if they are ever proven to exist), gravitational waves are not emitted by a massive object that is sitting stationary.

However, I do think there is legitimate inquiry to be explored, here. Suppose a GW detector (LIGO, or LISA, or some other) detects two different sources. We know that two massive objects are oscillating back and forth in place. We don’t know what is making these objects behave this way, but there they are (wouldn’t be the first time we saw something we didn’t fully understand). If one of the sources was a massive object undergoing acceleration, while the other is a considerably more massive object undergoing less acceleration, would we be able to tell the difference, just by the attributes of the wave? I would think that we could, just by comparing amplitude and frequency of each set of waves. Does that sound right?

 

[Vanadium 50]

I’m afraid the entire conversation here may be a result of the failure to distinguish between “gravitational waves”, and “gravitons

How is that possible if you are the only one to use the word here?

 

[LURCH]

I think the main question would be; is it possible to determine the mass and acceleration of a GW source strictly by examining the waves themselves? Could we determine the difference between a greater mass under less acceleration, vs a lesser mass under greater acceleration? Or would they appear the same?

 

[PeterDonis]

We know that two massive objects are oscillating back and forth in place.

No, they're not. They're orbiting each other. Every GW source we have directly detected thus far is a pair of neutron stars or black holes orbiting each other and then merging. And every GW source we have indirectly detected (by long-term effects on orbital parameters) is a binary pulsar, i.e., a pair of neutron stars orbiting each other.

We don’t know what is making these objects behave this way

Sure we do: they're a pair of massive bodies orbiting each other, which is exactly what they are expected to do.

is it possible to determine the mass and acceleration of a GW source strictly by examining the waves themselves?

Mass, yes, within limits that depend on a variety of factors. Have you looked at the published LIGO results? They cover exactly this point.

Acceleration is irrelevant since all of the sources we have seen are in free-fall orbits, i.e., zero acceleration.

 

[LURCH]

I notice that the OP has not responded since the distinction between gravitational waves and gravitation was discussed. Once the difference was pointed out, we moved into discussing one of the phenomena, that being gravitational waves (my suggestion, I’m afraid). I now begin to worry that OP wanted to discuss the effect of relativistic velocity on gravitation.

@yahastu , were you trying to start a conversation about the gravitational pull of an object increasing because of rapid motion? Also, are you still reading this thread?