"Doppler" Gravity

[Ibix]

I don't understand this 3:1 ratio thing you keep quoting. A test particle swinging around a (non-rotating) massive body is obviously symmetric under time reversal. That is, a video of an object approaching from the left is indistinguishable from a video of it approaching from the right, played backwards.

 

[jbriggs444]

compared to the 3:1 ratio in the exposure rate to the receding and approaching masses

If you imagine an object experiencing an increased gravitational acceleration on approach to a massive object and a reduced gravitational deceleration on recession, then you have a perpetual motion machine.

 

[Nugatory]

such a global frame is small when compared to the 3:1 ratio

You are still missing the point of coordinate dependence. That ratio is 3:1 instead of 1:1 or 1000000:1 or 1:100000 only if you choose coordinates that make it come out to be 3:1 (which requires more specification of how you're assigning coordinates than you've provided so far). @Ibix was able to dial the ratio down to 1:1 in post 26 just by choosing coordinates in which the gravitating object is at rest.

 

[.Scott]

I don't understand this 3:1 ratio thing you keep quoting. A test particle swinging around a (non-rotating) massive body is obviously symmetric under time reversal. That is, a video of an object approaching from the left is indistinguishable from a video of it approaching from the right, played backwards.

Actually, that time-reversal issue is interesting. When I look at EM radiation, time reversal changes the direction of the EM radiation. But time reversal doesn't do that with gravity. Gravity pulls in both time directions.

 

[Nugatory]

Actually, that time-reversal issue is interesting. When I look at EM radiation, time reversal changes the direction of the EM radiation. But time reversal doesn't do that with gravity. Gravity pulls in both time directions.

Time reversal (understood here in @Ibix's sense of playing the video backwards) changes the direction in which EM radiation travels, but it does not change the direction the fields point, nor does it change the direction in which the forces pull. What reverses under time reversal is the velocity of a test particle, and gravity works the same way. Compare a video of a positive-charged particle ejected from and falling back to a negative-charged surface with a video of a ball thrown up in the air and falling back to earth.

 

[PeterDonis]

Let's have a flat universe with many stationary (in their frame) gravitation sources (perhaps galaxies) evenly disbursed.

Do you mean spatially flat (as in our best current model of our universe)? If there are gravitation sources present, spacetime can't be flat.

(Strictly speaking, isolated gravitating bodies, even if they are evenly distributed, won't lead to a spatially flat spacetime. But it could be spatially flat on average.)

Taking this galaxy as our frame, will this galaxy accelerate?

Since you are assuming that all of the other gravitating bodies are evenly distributed, my answer would be no.

If it does not, then gravity is doing something that I don't understand. Somehow it isn't really propagating at the speed of light - because our moving galaxy isn't "running into" this propagation and causing it to "bunch up".

I don't understand this reasoning; I don't know what you mean by "bunch up" or why you think this would happen. I suspect you have a confused concept of how gravity in GR works. Rather than try to use that confused intuition to try to analyze a scenario, you should try to retrain your intuition. The best way to do that is to work through a good textbook on GR. (Carroll's online lecture notes are a good start.)

 

[Grinkle]

I don't know what you mean by "bunch up" or why you think this would happen.

The OP has prompted me to ask a very B level question -

Why is it invalid to compare a moving mass and its radiation of gravity to a moving light-bulb and its radiation of photons? Doesn't all matter emit gravitons all the time, and don't these gravitons move at c?

 

[jbriggs444]

Why is it invalid to compare a moving mass and its radiation of gravity to a moving light-bulb and its radiation of photons? Doesn't all matter emit gravitons all the time, and don't these gravitons move at c?

That's mixing classical and quantum pictures. And we have no quantum theory of gravity.

But, here is a simple question: Does a charge that is moving radially inward toward a stationary charged body encounter a different Coulomb force than a charge that is moving radially outward from that stationary body?

 

[PeterDonis]

Why is it invalid to compare a moving mass and its radiation of gravity to a moving light-bulb and its radiation of photons?

It's not invalid as a heuristic; the fact that moving charge emits EM radiation does make it reasonable to hypothesize that moving stress-energy emits gravitational radiation.

However, once you dig into the details, you find that there are significant differences. The Carlip paper I linked to in post #21 discusses the key ones, which can be summarized as:

(1) EM radiation is dipole at lowest order, whereas gravitational radiation is quadrupole. In other words, EM radiation is produced by any accelerating charge--i.e., when the second time derivative is nonzero--since that is sufficient to produce a time-varying dipole moment; but to produce gravitational radiation you need a time-varying quadrupole moment, which requires the third time derivative to be nonzero. (This is connected to the fact that the EM force is spin 1 while gravity is spin-2, and to the constraints imposed by conservation of momentum, which leads to the next point.)

(2) EM sources can be accelerated without having to add any further charges or currents to the system. However, gravitational sources (stress-energy) cannot be accelerated without adding further gravitational sources to the system, the sources of whatever energy is being used to produce the acceleration. This drastically constrains the kinds of scenarios you can consistently set up to test how gravity propagates; for example, as has already been commented, you can't just have a gravitating body like the sun disappear and ask how long it takes us to notice here on Earth.

 

[Grinkle]

Does a charge that is moving radially inward toward a stationary charged body encounter a different Coulomb force than a charge that is moving radially outward from that stationary body?

If both particles are the same distance away, I think no since the Coulomb force is a function of the distance.

 

[MikeGomez]

So light will blue shift (higher energy) and sound is louder and at a higher pitch.

So does that mean that you have or have not read up on gravitational redshift?

 

[.Scott]

So does that mean that you have or have not read up on gravitational redshift?

That's a different topic.

 

[Dale]

the total change in momentum applied to the observer from the gravitational force

Umm, in general relativity there is no gravitational force, and the four momentum of an object in free fall does not change. The only way to get any of these quantities is to introduce a coordinate system and then you can look at the three momentum and the Christoffel symbols. That will be the closest you can get, but to do that you will have to specify the coordinates fully.

 

[skanskan]

You should read about the transverse Doppler effect.

https://en.wikipedia.org/wiki/Relativistic_Doppler_effect