B Temporal differences across a galaxy?

[narrator]

TL;DR Summary

Do the temporal differences across a galaxy create any issues for how a galaxy holds together, maybe affecting it's shape?

Hi. I'm a science enthusiast. I haven't been here in a long while. This is something I've wondered about for quite some time.

I'm wondering if the temporal differences across something so vast as our milky way galaxy might pose any implications for how our galaxy holds together (ours and other galaxies, of course). This is probably simple math for a cosmologist.

I was thinking a while back. If I held a model of our galaxy in my hand and twirled it, that spiral shape might seem kind'a natural. Though, from one side of that model to the other, there is effectively no time differential. The real galaxy has a differential of about 100 thousand years. Even locally, our next nearest star system is just over 4 years. It made me wonder about bodies within a galaxy whose gravitational effects would be delayed years or even aeons, and how that might affect things. Is it just simple math, and does it impact on the shape of the galaxy?

(As for my Math level, 40 years ago I could do basic dy/dx calculus, but not now. I should have kept it up, hey.)

Andrew

 

[jbriggs444]

Summary: Do the temporal differences across a galaxy create any issues for how a galaxy holds together, maybe affecting it's shape?

Consider something simpler. A binary star. Does the force of gravity from the other star point toward where the other star was or to where it is now? Answer: it points to where it is now.

[At least until we get into effects like the precession of the perihelion of Mercury]

 

[PeterDonis]

whose gravitational effects would be delayed

The gravitational effects of a given part of the galaxy "now" are delayed, but what you are feeling "now" from, say, the other side of the galaxy are the gravitational effects of that part of the galaxy 100,000 years ago. And since the galaxy has not changed significantly on that time scale (it takes about 250 million years for a star system at the distance from galaxy center of our solar system to orbit the galaxy center), the gravity you feel now from the other side of the galaxy 100,000 years ago is pretty close to the gravity being "emitted" by the other side of the galaxy "now". In other words, the galaxy is a (nearly) stationary system, and in a stationary system, which doesn't change significantly with time (at least on the time scale of light travel time across the system), "time delay" for an effect like gravity doesn't matter, because the system one light travel time ago is the same as the system now.

The galaxy is not perfectly stationary, so there are small effects due to its departure from being perfectly stationary, but they're too small to measure (and we don't know enough detail about the other side of the galaxy anyway to be able to attempt to measure such effects). In addition, in GR, gravity is not a Newtonian force, and even in the approximation (low speeds and weak fields) where we can treat it as close to being a Newtonian force, there are still extra corrections that have the effect of canceling out most of the effects of propagation delay. (Most, not all: effects like the precession of the perihelion of Mercury that @jbriggs444 mentioned are due to the fact that the cancellation is not complete.)

The classic paper on this is Carlip 1997:

https://arxiv.org/abs/gr-qc/9909087

 

[narrator]

Thanks Peter, great explanation! The paper, I've downloaded and quickly read a couple of pages. Hopeful that I'll understand enough, look forward to reading it.

 

[narrator]

@PeterDonis
Could you help me unpack this quote from that paper?
"By analyzing the motion of the Moon, Laplace concluded in 1805 that the speed of (Newtonian) gravity must be at least 7×10⁶c "

Thanks

 

[PeterDonis]

Could you help me unpack this quote from that paper?
"By analyzing the motion of the Moon, Laplace concluded in 1805 that the speed of (Newtonian) gravity must be at least 7×10⁶c "

Laplace was assuming that gravity was a Newtonian inverse square law force that depended only on the distance between the two bodies. On that assumption, you can use the lack of observed aberration in gravity (i.e., that the force points towards the position of the other body "now", not at any time delayed time in the past) to place a lower limit on the speed at which the Newtonian force of gravity must propagate. (It can only be a lower limit because of the finite accuracy of our measurements; we can't say that the observed aberration is exactly zero, only that it is smaller than the smallest amount that we could detect.)

But of course with GR we now know that Laplace's assumption was false. Gravity is not a Newtonian inverse square law force that depends only on the distance between the two bodies. It can be approximated as such a force under certain conditions, but that is only an approximation, and one that we can easily detect corrections to, such as the perihelion shift of Mercury (and now other planets as well). And that means we cannot use the lack of observed aberration to infer the kind of lower limit on propagation speed that Laplace did. We have to use the actual, GR-correct behavior to make such inferences, and Carlip shows in his paper how all of our observations, once we use the correct GR equations, are consistent with the propagation speed of gravity being $c$.

 

[narrator]

Thanks Peter. Grateful for your explanation.