Bear with me, this is something that has been bugging me awhile...
I'm trying to get a clear picture of how rotation "starts" in isolation. I'm picturing a uniform volume, isotropic, homogenous, that super high z instant, whenever it was, where suddenly the volume was differentiated. If this was not "last scattering", there still had to be a that instant, right. I want to say, at that instant the number of degrees of freedom has just gone up.
wabbit said:
But even if the total momentum is zero, any finite region will generically have some (perhaps small) angular momentum.
I suspect this is true except for subsystems relative to which the rest of the universe is exactly spherically symmetric.
What subsystem get's to start off being different, in the homogenous isotropic case?
I am totally fine with saying, "a random one". The part I'm just trying to clarify, is what mechanism of clumping, can account for it.
Newtons law of gravity, because it is not a function of time (is it?), or sequence, doesn't seem to me to be able to explain how angular assymetry developed in that initial situation, where we really do have to account for it spontaneously occurring. In that first differentiated instant, For Newton, aren't all angular gravitational moments, from all random motions, in all random regions exactly what they were one instant to the next. Unless angular asymmetry is introduced into that gravitationally "frozen" system, what can cause it to change?
A propagation limit suddenly applied to those Newtonian relations however, a flow, seems to me to provide the means by which a single random movement, or all single (pair wise) random movement, suddenly becomes candidate for the formation of the first ever "plane of gravitational asymmetry".
To me it seems to require picturing a "medium" through which gravity must travel at some limit, through which gravity propagates... over time.
And this then fits the bill of a mechanism that took off in lots of random places, more or less at once. That still abides.
In our highly asymmetrical angularly rotating neighborhood way down the cloud of spacetime helictites, (which should represent any neighborhood of course), it's easy to invoke the "initiating" assymetric moment. But that doesn't mean the same process of spontaneous angular symmetry breaking isn't still all over the place.
Where my head is truly stuck, is in associating the instant of "propagation limit begins" with the instant of "+1d for g" with the instant of "start expansion". Suddenly, at that moment, a counting process in 3d+1 gravity requires helical trajectories of all worldlines, henceforth.
@PeterDonis, you said awhile back that not everything rotates. I'm prepared to agree but I'm having trouble thinking of an example. Don't all quantum particles (except the Higgs Boson, which as I understand it is responsible for giving mass to other particles!) have spin, even if in combinations, some spins cancel.