1

Suppose in the universe, there are inertial frames in the vicinity of galaxies. Suppose also that these frames rotate slightly with respect to each other - that the universe is not quite a 'mill pond'.

If this were true, our Galaxy would have its own inertial frame, rotating wrt distant galaxies.

The rotation of our galaxy's frame would affect astronomical observations.

Does anyone know the upper bound on the rotation rate of our galaxy's inertial frame which is consistent with observations?

Qmechanic
  • 201,751
RERT
  • 19
  • 1
  • I think you're asking if there is a net rotation of the universe about us. Is that so? – John Rennie Oct 07 '17 at 14:47
  • That is how it would appear, though I am explicitly not asking if the universe as a whole is rotating. – RERT Oct 07 '17 at 15:25
  • 1
    Your second supposition has no physical meaning. Two inertial frames cannot rotate relative to each other. – safesphere Oct 07 '17 at 15:32
  • This is in the context of general, not special relativity. I think it would be easy to write down a metric with a central zone an inertial frame which was rotating relative to another inertial frame at infinity. Harder I admit to be sure that the field equations were satisfied in the evolution of the system over time. But that is all moot if the experimental bound is too small to be interesting. @safesphere – RERT Oct 07 '17 at 21:15
  • Sorry, my first question @John Rennie – RERT Oct 07 '17 at 21:18
  • +1 I'd like to hear what the experts say, but intuitively I don't think such a metric can be a field solution without frame dragging by some enormous exotic dark matter. – safesphere Oct 08 '17 at 08:38
  • I was looking at some galaxy rotation profiles before asking this question. I realised that if the space in which the galaxy sat was rotating in the same direction as the stars in it, it would add apparent velocity to those stars orbits, as seen from elsewhere - the phenomenon currently ascribed to dark matter. The relevant rotation rates were tiny - maybe of the order 10^-21 rads/s. The usual objection to the rotating space theory is that we don't see the universe rotate - our galaxy is therefore special - yuk. But - 10^-21 rads/s may be invisible. @safesphere – RERT Oct 10 '17 at 11:29
  • I don't believe that the postulated metric would be stable in the absence of matter. Only a guess, but I'd expect the rotation of the central section to rapidly decay to that of the surrounding space (because that space is infinite in the model). In the presence of matter - maybe - it might be more stable. In any event whatever slows the rotation of the frame also needs to deal with the implied changes in kinetic energy of the masses involved. Intuition fails, really. @safesphere – RERT Oct 10 '17 at 11:48
  • To explain galaxy rotation, space would have to rotate faster at the edges of the galaxy than closer to the center, right? Not sure what would cause such a rotation of space. Have you actually played with the field equations or metric? – safesphere Oct 10 '17 at 14:23
  • I've posted a follow-up question https://physics.stackexchange.com/questions/362097/can-empty-space-rotate-without-frame-dragging – safesphere Oct 10 '17 at 14:48
  • No I don't think so: from just browsing a couple of Galaxy rotation curves thrown up by Google, if you take out (on the back of an envelope) the expected Keplerian velocity, what is left is the anomalous velocity. That anomalous velocity is roughly consistent with a rate of rotation either constant or falling off with distance. The central points have wide error bars. If you conceptualise overall velocity as tending to constant at large r, that corresponds to angular velocity in the metric going like 1/r. @safesphere – RERT Oct 11 '17 at 07:38
  • Right, but it's still unclear what would cause space to rotate. Doesn't seem possible without frame draggging by some super massive object, whose presence kind of defeats the purpose of this explanations. – safesphere Oct 11 '17 at 08:17
  • Helpfully the Kerr metric (on the back of my envelope) has a space rotation rate which falls off like 1/r for low rates of rotation. I'm being asked to avoid lengthy discussions in comments, and do I want to move this discussion to chat? Is that good for you - I don't know how that works. Else wise how do you want to continue the conversation? @safesphere – RERT Oct 11 '17 at 09:30
  • Looks to me like sa/r. (Wiki notation). For the Milky Way r is 0-10^21. s (schwarzschild) is about 210^15. So to match my observed scales we need a = 0.5 *10^-15. Plausible? @safesphere – RERT Oct 11 '17 at 10:04
  • To directly respond to your point above, I think the Kerr metric is actually a standard solution for a rotating mass. The Galaxy surely counts as a rotating mass, though to be sure not a point mass as in the metric. To be fair looking up orbital data for the Kerr metric is not giving me what I hoped for. Time for a bigger envelope... @safesphere – RERT Oct 12 '17 at 08:23

1 Answers1

0

I'd just like to cross-reference the top answer to the question What if the universe is rotating as a whole. The detection level there is given as 10^-9 to 10^-15 rads/year, so roughly 10^-16 to 10^-22 rads/sec.

Yes, it isn't answering the same question I asked, but it is a place to start until there is a better answer.

John Alexiou
  • 38,341
RERT
  • 19
  • 1