4 ms·

Something I've been confused about for a while: Simulations like this typically use Newtonian mechanics. Ie F=MA n-body. Doesn't gravity propagate at the speed

Something I've been confused about for a while: Simulations like this typically use Newtonian mechanics. Ie F=MA n-body. Doesn't gravity propagate at the speed of light, which is important at these scales? Even if not using curved spacetime, wouldn't there be a big delay in when objects "feel" the gravity of distant ones? Ie the gravity should still propogate out at the speed of light.

teraflop 4y ago
> Doesn't gravity propagate at the speed of light 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_speed.html https://math.ucr.edu/home/baez/physics/Relativity/GR/grav_sp... https://en.wikipedia.org/wiki/Speed_of_gravity#Static_fields https://en.wikipedia.org/wiki/Speed_of_gravity#Static_fields https://physics.stackexchange.com/questions/458136/does-gravity-sometimes-get-transmitted-faster-than-the-speed-of-light https://physics.stackexchange.com/questions/458136/does-grav...
- krisoft 4y ago
  > If the Earth was feeling a gravitational force corresponding to the relative position where the sun appeared to be 8.5 minutes ago 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.
  - sebzim4500 4y ago
    >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. 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.
    - pyinstallwoes 4y ago
      If the sun disappeared, would it take 8 minutes to know?
      - petschge 4y ago
        Yes.
        pyinstallwoes 4y ago
        What would happen during this 8 minutes from beginning to end? Genuinely curious at a high level
adgjlsfhk1 4y ago
the short answer as to why this doesn't matter is that objects fast away from each other don't move quickly enough relative to each other for it to matter. since gravity falls off with distance squared, changes in gravity go with 1/r^3, so at large distances the difference in gravitational pull will be very small.
- dreamcompiler 4y ago
  And the contribution to the field from the center of mass of the overall system will be huge -- even predominant in many cases -- but it never moves.
- uoaei 4y ago
  The Lyapunov exponent of such a system is positive -- and probably substantially so, since there are thousands to millions of massive objects being simulated -- so it seems at first pass as if the absence of any determining factor in the dynamical model will hugely affect the simulation's evolution.
  - sebzim4500 4y ago
    Sure, but the goal of these simulations is qualitive results about how galaxies behave, not a quantitative prediction of exactly where every star will be in a billion years. It's like predicting climate vs. weather.
    - uoaei 4y ago
      Any smoothed and incomplete approximation to climate models is also devestating for qualitative similarities of results to data. The point is that the chaos inherent in the dynamics means that n-body solvers that aggregate e.g. spatial regions into low-rank approximations are losing enough detail that it could result in different dynamics being expressed. Like using too large of a mesh size in CFD calculations.
jiggawatts 4y ago
Related effects have been the topic of numerous papers, and often get hand-waved away without a coherent argument. I've seen statements along the lines of: "That might be true, but then we'd have to rewrite our simulation codes, and that's expensive... so... you see..." 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.
- uoaei 4y ago
  Do you have any papers (for a reading group for interested yet naive physicists) that discuss this lensing-of-gravity phenomenon? As I understand it, what you describe could be an alternative to dark matter that isn't MOND. Since you sound well-versed in the subject -- what do you think of entropic gravity?
  - jiggawatts 4y ago
    I don’t have hyperlinks handy, unfortunately. The other paper I’m thinking of basically stated that the full GR model could also explain most of the rotation curves. That paper was disregarded because it had a discontinuity at the rotation axis, which is non-physical. They turned out to be a side effect of a simplifying assumption and can be corrected, but by then it was too late and the dark matter people moved on…
    - simonh 4y ago
      Arguably if the originators of a theory can't be bothered to properly work it out and demonstrate it's viability, why should anyone else?
superposeur 4y ago
I’m not an expert in this but know the relevant physics well. Here are my thoughts on this good question. 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.

teraflop 4y ago

> Doesn't gravity propagate at the speed of light 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_speed.html https://math.ucr.edu/home/baez/physics/Relativity/GR/grav_sp... https://en.wikipedia.org/wiki/Speed_of_gravity#Static_fields https://en.wikipedia.org/wiki/Speed_of_gravity#Static_fields https://physics.stackexchange.com/questions/458136/does-gravity-sometimes-get-transmitted-faster-than-the-speed-of-light https://physics.stackexchange.com/questions/458136/does-grav...

krisoft 4y ago
> If the Earth was feeling a gravitational force corresponding to the relative position where the sun appeared to be 8.5 minutes ago 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.
- sebzim4500 4y ago
  >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. 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.
  - pyinstallwoes 4y ago
    If the sun disappeared, would it take 8 minutes to know?
    - petschge 4y ago
      Yes.
      - pyinstallwoes 4y ago
        What would happen during this 8 minutes from beginning to end? Genuinely curious at a high level

adgjlsfhk1 4y ago

the short answer as to why this doesn't matter is that objects fast away from each other don't move quickly enough relative to each other for it to matter. since gravity falls off with distance squared, changes in gravity go with 1/r^3, so at large distances the difference in gravitational pull will be very small.

dreamcompiler 4y ago
And the contribution to the field from the center of mass of the overall system will be huge -- even predominant in many cases -- but it never moves.
uoaei 4y ago
The Lyapunov exponent of such a system is positive -- and probably substantially so, since there are thousands to millions of massive objects being simulated -- so it seems at first pass as if the absence of any determining factor in the dynamical model will hugely affect the simulation's evolution.
- sebzim4500 4y ago
  Sure, but the goal of these simulations is qualitive results about how galaxies behave, not a quantitative prediction of exactly where every star will be in a billion years. It's like predicting climate vs. weather.
  - uoaei 4y ago
    Any smoothed and incomplete approximation to climate models is also devestating for qualitative similarities of results to data. The point is that the chaos inherent in the dynamics means that n-body solvers that aggregate e.g. spatial regions into low-rank approximations are losing enough detail that it could result in different dynamics being expressed. Like using too large of a mesh size in CFD calculations.

jiggawatts 4y ago

Related effects have been the topic of numerous papers, and often get hand-waved away without a coherent argument. I've seen statements along the lines of: "That might be true, but then we'd have to rewrite our simulation codes, and that's expensive... so... you see..." 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.

uoaei 4y ago
Do you have any papers (for a reading group for interested yet naive physicists) that discuss this lensing-of-gravity phenomenon? As I understand it, what you describe could be an alternative to dark matter that isn't MOND. Since you sound well-versed in the subject -- what do you think of entropic gravity?
- jiggawatts 4y ago
  I don’t have hyperlinks handy, unfortunately. The other paper I’m thinking of basically stated that the full GR model could also explain most of the rotation curves. That paper was disregarded because it had a discontinuity at the rotation axis, which is non-physical. They turned out to be a side effect of a simplifying assumption and can be corrected, but by then it was too late and the dark matter people moved on…
  - simonh 4y ago
    Arguably if the originators of a theory can't be bothered to properly work it out and demonstrate it's viability, why should anyone else?

superposeur 4y ago

I’m not an expert in this but know the relevant physics well. Here are my thoughts on this good question. 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.