Undergrad Doppler Gravity: Does it Exist? Why or Why Not?

[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