Elastic properties of spacetime

[AbsoluteChaos]

As a complete amature, I have a question about gravity and spacetime. Gravity is seen as a distortion of spacetime and we have the traditional view of a mass resting on a rubber sheet, distorting the space around it. But most masses are moving in space - usually fast or very fast. Is there a distortion in space, either infront or behind the direction of movement which acounts for the movement of the mass in space? Is there a delay in the mass passing a region of space and the spacetime returning back to its previous state?

Grateful for your view. Please remember my status as a complete amature and answers requiring a knowledge of advance physics will go completely over my Neanderthal head.

Many thanks

Absolute Chaos
PS - I have include some simple diagrams to help my simple brain

 

[Chalnoth]

Well, for the most part the distortions tend to move along with the objects in question. There is essentially no delay, for instance, in the Earth's gravitational field. What happens is that the field itself around the object moves and even accelerates along with the object in question. Now, this effect isn't perfect, and the fact that there is some limitation to how well the gravitational field can follow objects is why some systems emit gravitational radiation (such as binary neutron stars).

One way of thinking about how it basically has to be this way is just the simple fact that in General Relativity, any coordinate system is as good as any other. So in GR, one can literally not distinguish between the "Earth is stationary" and the "Earth is moving around the Sun". In terms of General Relativity, we only pick the latter point of view because the system is vastly, vastly easier to describe in that way. But if, in GR, the "Earth is stationary" view is valid, then the gravitational field of the Earth must not be distorted by the Earth's motion.

 

[Passionflower]

As a complete amature, I have a question about gravity and spacetime. Gravity is seen as a distortion of spacetime and we have the traditional view of a mass resting on a rubber sheet, distorting the space around it. But most masses are moving in space - usually fast or very fast. Is there a distortion in space, either infront or behind the direction of movement which acounts for the movement of the mass in space? Is there a delay in the mass passing a region of space and the spacetime returning back to its previous state?

Spacetime is fixed, it never changes. Space however can constantly be deformed, these deformations are "propagated" with the speed of light.

So in GR, one can literally not distinguish between the "Earth is stationary" and the "Earth is moving around the Sun". In terms of General Relativity, we only pick the latter point of view because the system is vastly, vastly easier to describe in that way. But if, in GR, the "Earth is stationary" view is valid, then the gravitational field of the Earth must not be distorted by the Earth's motion.

Could you please support your argument that one view is "vastly, vastly easier" in GR?

I don't think that the difficulty is in the choice of a coordinate chart, it is the difficulty in describing a two body with different masses problem analytically in GR.

Am I wrong perhaps?

 

[Chalnoth]

Could you please support your argument that one view is "vastly, vastly easier" in GR?

Basically, because the Sun's motion is perturbed less by the planets due to its large mass, describing the Sun as stationary is a much closer approximation to reality than describing the Earth as stationary. Of course, you still can't produce an analytically exact description of the behavior in GR, but it's easy enough a system to solve numerically.

 

[Passionflower]

Basically, because the Sun's motion is perturbed less by the planets due to its large mass, describing the Sun as stationary is a much closer approximation to reality than describing the Earth as stationary. Of course, you still can't produce an analytically exact description of the behavior in GR, but it's easy enough a system to solve numerically.

I think that both ways are very hard to solve numerically as well. Again, I do not think the difficulty is in the chosen coordinate chart or the chosen observer.

 

[Chalnoth]

I think that both ways are very hard to solve numerically as well. Again, I do not think the difficulty is in the chosen coordinate chart or the chosen observer.

Well, one strategy to follow here is find a system that provides an analytical solution to a simpler situation, and use perturbation theory to compute deviations from that. The solar system is much more easily modeled as having nothing but the Sun than it is having nothing but the Earth.

 

[Buckethead]

As a complete amature, I have a question about gravity and spacetime. Gravity is seen as a distortion of spacetime and we have the traditional view of a mass resting on a rubber sheet, distorting the space around it. But most masses are moving in space - usually fast or very fast. Is there a distortion in space, either infront or behind the direction of movement which acounts for the movement of the mass in space? Is there a delay in the mass passing a region of space and the spacetime returning back to its previous state?

You might wiki the Lense–Thirring effect which describes the dragging of space around a rotating massive body. This effect is also seen in a body moving in a linear direction and even more interesting is that GR also shows that the mass of a body changes in the vicinity of nearby passing objects which is also related to this.

With reagard to delay, an accelerating body causes ripples in the spacetime fabric called gravitational waves and these (are currently accepted) travel at the speed of light. Non-accelerating bodies however do not cause gravitational waves.

These distortions in space do not AFAIK contribute to the movement of a mass in space and I'm assuming you are simply asking if any possible distortion as you describe might be a reason for Newton's first law of motion? This would not be the case. Newton's first law occurs simply because of the law of relativity which states it's not possible to know if a body is in (non-accelerated) motion or not except with respect to another object. Logic dictates this as well.

 

[Passionflower]

With regard to delay, an accelerating body causes ripples in the spacetime fabric called gravitational waves and these (are currently accepted) travel at the speed of light. Non-accelerating bodies however do not cause gravitational waves.

Why do you think that non-accelerating bodies cannot cause gravitational waves?

For instance consider two orbiting bodies.

 

[Chalnoth]

Why do you think that non-accelerating bodies cannot cause gravitational waves?

For instance consider two orbiting bodies.

Orbiting bodies are accelerating towards one another.

What you need for gravitational radiation is a time-dependent quadrupole of the gravitational field (a time-dependent dipole is not sufficient, as it is for producing electromagnetic waves).

 

[Buckethead]

Why do you think that non-accelerating bodies cannot cause gravitational waves?

For instance consider two orbiting bodies.

Orbiting bodies are accelerating.

 

[Passionflower]

Orbiting bodies are accelerating towards one another.

What you need for gravitational radiation is a time-dependent quadrupole of the gravitational field (a time-dependent dipole is not sufficient, as it is for producing electromagnetic waves).

Orbiting bodies are accelerating.

Conform GR, orbiting test masses do not undergo proper acceleration while they do radiate gravitational waves.

Correction: corrected (test) bodies to test masses

 

[Chalnoth]

Conform GR, orbiting (test) bodies do not undergo proper acceleration while they do radiate gravitational waves.

I guess I don't understand how a test body can emit gravitational waves when, by definition, a test body does not perturb the gravitational field.

 

[Passionflower]

I guess I don't understand how a test body can emit gravitational waves when, by definition, a test body does not perturb the gravitational field.

Ok, you got a point.

I meant to say a test mass.

 

[Buckethead]

Conform GR, orbiting (test) bodies do not undergo proper acceleration while they do radiate gravitational waves.

I can see what you are saying and yes you are technically correct in that an orbiting body is in free fall and therefore is not experiencing proper acceleration, however a free falling body is said to be accelerating at the rate of the gravitational attraction, so on the other hand it can be said to be accelerating, it just depends on how you look at it.

Let me restate that to say a body will radiate grav waves when and only if it either changes direction or linearly accelerates. So this would include an orbiting body as well as a linearly accelerating body.

 

[mattp913]

The mass(potential energy) of matter can change the shape of space-time so possibly temperature(kinetic energy) can as well. The universe is said to have started out much smaller than it is today and with a great amount of heat and energy. Today, it is expanding and cooling. Could this expansion be simply because the universe is cooling? A rubber band is elastic much in the same way that the fabric of space-time is. Rubber, unlike most matter, contracts when it is heated because the molecules become more entangled and it cools when it expands, actually becoming more elastic. Also, according to general relativity, as an object approaches the speed of light, distances actually shorten. Could the heat that an object gives off warp the fabric of space-time and explain these length contractions? Are temperature and distance somehow inversely proportional? I believe it somehow may be...

 

[Chalnoth]

The mass(potential energy) of matter can change the shape of space-time so possibly temperature(kinetic energy) can as well.

Yes, in General Relativity this is the case.

Are temperature and distance somehow inversely proportional?

This is the case for radiation. This can be understood relatively easily in terms of the redshift: if the universe expands by a factor of two, then photons are redshifted by a factor of two in that time. Double the wavelength of a photon and you cut its energy in half. Since the temperature is just the average energy of the photons, cutting the energy of every photon in half also cuts the temperature in half.

So yes, for photons, temperature is inversely proportional to the expansion.

This is not the case, however, with either normal matter or dark matter.

 

[mattp913]

I am talking about the fabric of space-time itself. Not for photons or matter

 

[Chalnoth]

I am talking about the fabric of space-time itself. Not for photons or matter

Space-time has no temperature in and of itself.

 

[mattp913]

The universe is cooler today than it was right after the big bang

 

[Chalnoth]

The universe is cooler today than it was right after the big bang

Yes, but that temperature exists as radiation.

 

[mattp913]

Right, so my question was could that temperature be inversely proportional to the distance of space-time? The universe is cooling and expanding. Also, as an object approaches the speed of light, distances contract. The mass(potential energy) of matter can affect the shape of space-time, so the temperature(kinetic energy) of matter in space-time may also affect its shape.

 

[Chalnoth]

Right, so my question was could that temperature be inversely proportional to the distance of space-time? The universe is cooling and expanding. Also, as an object approaches the speed of light, distances contract. The mass(potential energy) of matter can affect the shape of space-time, so the temperature(kinetic energy) of matter in space-time may also affect its shape.

Yes, the temperature of matter in space-time has an impact. However, normal matter and dark matter are effectively zero-temperature today for this sort of consideration (temperature only really matters when it is high enough that the particles are relativistic). It was a significant consideration very early on, when the temperature of normal matter was so high that the typical energy of, say, an electron was much higher than its mass energy. But that isn't the case any longer.

And while the photons are obviously still relativistic (they are relativistic at any temperature), their total energy density is only a tiny fraction of the energy density in matter, so that their effect on the curvature of space-time is minimal.