Galaxy Simulation
galaxym.ovh
galaxym.ovh
This is technically true, but not in a way that matters for practical purposes.
Changes in the gravitational field -- that is, the metric structure of spacetime -- do propagate at the speed of light. So for instance, if a massive object were to suddenly appear in space, then nearby objects would only experience a gravitational attraction to it after a delay. But of course that can't actually happen because of mass-energy conservation.
It turns out that if you use general relativity to calculate a more realistic scenario, where conservation laws are obeyed -- say, a pair of massive objects moving at a constant relative velocity -- then no matter how far apart they are, the speed-of-light delay is almost exactly canceled out by velocity-dependent effects, so that from each object's perspective it appears to be attracted to the other's instantaneous position, without any delay.
(If this weren't true, orbits would be extremely unstable. If the Earth was feeling a gravitational force corresponding to the relative position where the sun appeared to be 8.5 minutes ago, instead of where it currently is, then it would lose orbital angular momentum and spiral into the sun on a timescale of millennia.)
In the case of objects that are accelerating (not moving at a constant velocity) this cancellation is not quite perfect, which is what leads to the existence of gravitational waves. But the difference is exceedingly small under almost all circumstances.
See also:
https://math.ucr.edu/home/baez/physics/Relativity/GR/grav_sp...
https://en.wikipedia.org/wiki/Speed_of_gravity#Static_fields
https://physics.stackexchange.com/questions/458136/does-grav...
But that is exactly it. Earth is experiencing gravitational force from where the sun appears to be. Which is already “corrected” for speed of light effect, since both the light (where the sun appears to be) and the gravity (where it appears to pull from) is delayed by the same amount.
If we would be living in a simulation which neglects to take delay in gravity into account we would be experiencing a pull from the direction where the sun will appear in 8.5 minutes.
Now, I can totally believe you that this effect is not significant, or can be neglected for other reasons. But that sentence where you say that orbits would be extremely unstable if gravity would not be delayed indicates otherwise.
This is actually pretty much what happens. The point that the earth accelerates towards is, to first (second?) order, the predicted point that the sun would be assuming it continued accelerating at its current rate.
It is not accelerating towards where the sun was 8 minutes ago, nor where the sun appears now or 8 minutes ago.
So it's very nice that Newtonian physics work to some scale in a limited context. I consider it a fast-inverse-square-root style shortcut the universe has given to people like me.
I can’t understand why. If we imagine a completely dark universe of pointlike massive bodies, orbits still should work. Light and gravity not in sync should not change gravity? If that was obvious, why LIGO(iirc?) wanted to detect gravitational waves?
Surely where the sun currently is depends entirely on the position and frame of reference of the observer?
What you are talking about is how that point is named by different observers, and there is indeed great ambiguity there. But ultimately, if two persons are starting from different places towards the same goal following a map, the fact that they don't both eventually arrive at the same place has implications about the map they used, not about where the place is.
Likewise in a galaxy, the gravitational field always points to the centre of the galaxy. Lots of tiny wobbles due to stars moving around, but mostly just points directly to the centre (and the giant black hole lurking there maybe?).
An example of an effect that may actually be relevant to galaxy rotation curves: A strong gravitational well focuses light like a lens, and it ought to focus gravity like a lens also! This means that a star at the edge of a galactic disk ought to see "more" of the gravity from stars on the opposite edge due to the focusing effect of the galactic bulge in between.
A similar effect I've heard talked about is that the the entire galaxy is effectively warping spacetime, which means that the edge moves through time faster than the centre. It's a small effect, but it compounds with the one above to further increase the apparent velocity of the stars at the edge.
Since you sound well-versed in the subject -- what do you think of entropic gravity?
It's like predicting climate vs. weather.
Answer 1: Gravity is just like electrodynamics in this respect: as you say, the force vector is determined by the position of the other mass at the so-called retarded time not the current time. Specifically toward the position the other mass would occupy right now, had it kept moving at constant velocity using the velocity its velocity at the retarded time.
Hence, all deviations of the force vector from current position are due to the acceleration of the gravitating mass. The significance of the deviation is roughly estimated by the dimensionless ratio : a*x / v^2, where v is speed, a is acceleration, x is distance from gravitating mass. Accelerations are very very tiny in galactic contexts, so numerator is smaller than denominator.
Answer 2: A galaxy is like a fluid with approximately steady flow; hence, even if a given gravitating mass has moved since the retarded time, some other mass has taken its place.
I haven’t put numbers on these though.
Also I drug the "number of stars" thing all the way to the right and poof went my Firefox, haha.
Set to Universe, Gravity Force to max.
Trippy!