# Why does everything rotate?

Jimster41
Gold Member
I keep thinking about this one... I can understand that Newton's approximation is a sufficient "how". It will provide an accurate a prediction of rotation (for all practical purposes).

But I think the OP's question was "why" (and I share that question).

We could use Newton if we wanted prediction of "how", but isn't that stopping short? Don't we know that it is a superficial answer because we have accepted that Einstein's "how" is a better... "why".

So it seems to me that to answer the OP, we need to try and explain the initial rotation from the perfectly motionless cloud set up by @Bandersnatch using GR. Am I wrong in invoking "Frame dragging" and the "Lense Thirring" effect to understand it? Is there a more correct/direct GR explanation?

 Even if it is not a montionless initial setup, the question of how gravity "propagates" angular momentum seems relevant, aside from the Newtonian approximation. Or is it all happening via "collisions"? What about the case where the density is low, and collisions are rare?

 I just saw the two more recent posts above regarding initial temperature. There was an initial finite temperature correct? If there was, doesn't uniform random motion reduce to motionlessness. Don't all the Newtonian moments cancel for any given particle over any interval of action?

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Bandersnatch
What I know about frame dragging can be very generously described as 'patchy'. My naive understanding is that it's more or less what it says on the tin: a compact rotating object will affect other objects in its orbit. So, even disregarding whether the effect is noticeable and not swamped by more mundane influences, you'd have to start by answering the question of why the compact object is rotating in the first place - which is because it retained the angular momentum of the collapsing cloud that it coalesced from. And to explain why the cloud was rotating you must use something other than frame dragging, otherwise the argument is circular and its elephants all the way down.

PeterDonis
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2019 Award
we need to try and explain the initial rotation from the perfectly motionless cloud set up by @Bandersnatch using GR
If the initial cloud is perfectly motionless--every single particle at rest relative to every other particle--then there will be no rotation; the cloud is perfectly spherically symmetric and it will stay that way as it collapses, as long as no other matter is present. In other words, this highly idealized system has zero angular momentum to start, and is completely isolated, so its angular momentum is conserved and it will never have any rotation.

However, this situation is never going to happen in the real universe; in any real cloud there will be some particles moving relative to other particles, and the collapse process won't occur in complete isolation, there will be other matter in the universe that can affect it. So in any real situation, the cloud is not going to have zero angular momentum.

Am I wrong in invoking "Frame dragging" and the "Lense Thirring" effect to understand it?
Yes. These effects are only present if the system already has nonzero angular momentum. They can't explain where the nonzero angular momentum came from.

Jimster41
Gold Member
Yes. These effects are only present if the system already has nonzero angular momentum. They can't explain where the nonzero angular momentum came from.
In a system that already has non-zero angular momentum. What is the mechanism by which Enstien's gravity conserves angular momentum between separated particles?

When you say it is "never" going to happen. Do you mean NEVER as in not over the entire history of the universe, past and present. So does this mean angular momentum is traced back all the way to initial conditions?

Jimster41
Gold Member
What I know about frame dragging can be very generously described as 'patchy'. My naive understanding is that it's more or less what it says on the tin: a compact rotating object will affect other objects in its orbit. So, even disregarding whether the effect is noticeable and not swamped by more mundane influences, you'd have to start by answering the question of why the compact object is rotating in the first place - which is because it retained the angular momentum of the collapsing cloud that it coalesced from. And to explain why the cloud was rotating you must use something other than frame dragging, otherwise the argument is circular and its elephants all the way down.
Does "turtles all the way up" have anything to do with "Elephants all the way down"?

 Nevermind, found it.

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PeterDonis
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2019 Award
What is the mechanism by which Enstien's gravity conserves angular momentum between separated particles?
Basically the same way Newtonian gravity conserves it. The only difference is that in GR, you can have gravitational waves, which can carry angular momentum, so you have to count that as well as the angular momentum contained in the particles.

Do you mean NEVER as in not over the entire history of the universe, past and present.
Yes, in the sense that a perfectly spherically symmetric, perfectly isolated system is in principle possible, but it is so unlikely that we should not expect it to have ever happened anywhere in the universe.

does this mean angular momentum is traced back all the way to initial conditions?
Yes. Our current best estimate of the initial conditions is that the overall angular momentum of the universe was zero, and therefore is and has always been zero.

Jimster41
Gold Member
So just to restate the thread as I understand it so far, big cloud of randomly moving particles

At some time t (or step) two specific particles experience a higher net moment on a line between them. After that they have non-random movement that is symmetrical along that line. But at some infinitesimally subsequent step a third particle moment is affected/involved - and I can see how this non-equilateral triangular relationship between Newtonian moment arms defines rotation about an axis perpendicular to the plane of that asymmetry.

If on the other hand all moments are simultaneously involved at time t, as Newton's law would say

Asymmetry can't form in this way (from some sequential propagation of Newtonian relationships) right?

So is it because of the distribution of discete-particles, from any specific location, cannot be symmetric for all radii?

 latex fail

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wabbit
Gold Member
Yes. Our current best estimate of the initial conditions is that the overall angular momentum of the universe was zero, and therefore is and has always been zero.
This is something I find mysterious at two levels : for the universe as a whole, either there should be a principle forbidding global rotation, or there should be some rotation, however small - exactly zero cannot happen by chance. But for the observable universe (and presumably this is where we have estimates), it seems rather extraordinary that while, as a general rule, everything rotates, this should not be true at that particular scale (even if there is no global rotation of the whole universe).
Amd even if not exactly zero, an undetectable rotation rate for the observable universe would seem to warrant some explanation. Could it possibly be a consequence of a theoretical upper bound on angular momentum in the dense early stage combined with the "dilution" of that momentum by expansion ? Or is there some other reason ?

PeterDonis
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2019 Award
for the universe as a whole, either there should be a principle forbidding global rotation, or there should be some rotation, however small - exactly zero cannot happen by chance
Observationally, of course, we can't say the global rotation is exactly zero; all we can do is place limits on it. I think those limits are pretty strict, but I have not seen a lot of detailed discussion of this.

As far as why the global rotation should be small, I don't know that there is a good explanation at this point. My best guess would be that, assuming some form of inflation is true, the process of inflation would impose a high degree of symmetry on the resulting bubble of expanding universe. Inflation itself should be rotationally invariant, because it occurs in a vacuum state and the vacuum should be rotationally invariant (in fact it should be Lorentz invariant); so the end state of inflation should be a universe with almost zero rotation--the only rotation would be due to unavoidable quantum fluctuations in the inflating vacuum state.

Chalnoth
This is something I find mysterious at two levels : for the universe as a whole, either there should be a principle forbidding global rotation, or there should be some rotation, however small - exactly zero cannot happen by chance. But for the observable universe (and presumably this is where we have estimates), it seems rather extraordinary that while, as a general rule, everything rotates, this should not be true at that particular scale (even if there is no global rotation of the whole universe).
Amd even if not exactly zero, an undetectable rotation rate for the observable universe would seem to warrant some explanation. Could it possibly be a consequence of a theoretical upper bound on angular momentum in the dense early stage combined with the "dilution" of that momentum by expansion ? Or is there some other reason ?
Perhaps, but because the observable universe has not and probably will not collapse, any small net rotation is not likely to ever be observable.

Jimster41
Gold Member
This is what I'm confused about. If Newton is the mechanism of conservation. I don't see how asymmetry can "develop". It has to just suddenly exist? What am I missing?

${ L }[t]\quad ={ \quad I }_{ { R } }{ \omega }_{ { R } }+\sum _{ i=0 }^{ \infty }{ { I }_{ i } } { \omega }_{ i }\quad \\ { L }[t+\tau ]\quad =\quad { I }_{ { R } }{ \omega }_{ { R } }+\sum _{ i=0 }^{ \infty }{ { I }_{ i } } { \omega }_{ i }$

If there is some sense in which gravitational propagation is required between particles, then "spontaneous" asymmetry seems natural, because you can have that third (or eventually uneven) moment.

wabbit
Gold Member
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.

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PeterDonis
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2019 Award
If Newton is the mechanism of conservation. I don't see how asymmetry can "develop".
Global asymmetry being zero is not the same as no asymmetry at all. The global asymmetry is the total of it over the entire universe. You can have individual systems within the universe that have nonzero angular momentum, as long as the total of all of them works out to zero.

HallsofIvy
Homework Helper
If you rephrase the question- "why is there nothing in the universe that has rate of rotation exactly equal to 0?" you should be able to see that it would be extremely unlikely for any object to have exactly any given rate of rotation, including 0.

It makes sense that locally condensing gas clouds can have an angular momentum, but the net momentum of the Universe is zero.
Hard to imagine it being otherwise because then you have to figure out what the Universe is rotating in.

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Jimster41
Gold Member
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.

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.

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Bandersnatch
If this was not "last scattering", there still had to be a that instant, right
I think you're getting too hung up on this perfect-homogeneity picture. While it's an alright analytic tool, there's no reason to think there actually ever was such a state in the history of the universe.

There were periods when the universe was in a state of high homogeneity, such as before recombination (last scattering) when all the plasma constituting the (our patch of) universe was thermalised, and any overdensities tended to rebound due to overpressure, or after inflation (which was invented to deal with the question how come all the universe was thermalised in the first place). But it never was a perfect homogeneity.

A good analogy, I think, would be any arbitrary close volume of gas at a set temperature. You can say it's globally homogeneous, you can say it's got no momentum, angular or otherwise, but look close enough at a small enough volume and you'll see how neither of those qualifiers apply.
If you then cool this volume of gas to a low enough temperature, the thermal motion keeping it globally homogeneous will drop and the particles will start to clump, and all that motion and overdensities that required special attention to notice earlier will become immediately apparent.

wabbit
Gold Member
I'm not sure I understand your question, but I see two points : first, starting from a perfectly symmetrical universe, it seems to me pretty much any quantum fluctuation results in some asymetry.

In a classical setup, symmetry is preserved if it is there to start with - those are the FRW solutions, where all matter is comoving and nothing happens at all in the universe except global uniform expansion or contraction. But these are extremely special spacetimes and it would be rather extraordinary if our universe matched that exactly - it doesn't of course, not any more than the surface of the earth is a perfect sphere, these are just simplifying asumptions valid as a first approximation.

In general, asymmetry is generic, symmetry is very special and requires an explanation. This is the case even if the underlying equations are symmetric, only in rare cases are generic solutions symmetric too I think.

Chronos
Gold Member
The issue of the univetse rotating with respect to 'what' remains unanswered.

wabbit
Gold Member
The issue of the univetse rotating with respect to 'what' remains unanswered.
If about the whole universe, hypothetically, rotating in the sense that inertial observers see each other rotate I suppose, as in a Gödel spacetime. I don't know what the "standard rotating cosmological model" might be or if it exists.

Jimster41
Gold Member
I had been operating on from the point of view that primordial anisotropy was a puzzle? (for information conservation purposes I guess)?

http://arxiv.org/pdf/1410.1562v1.pdf
Quantum collapse as source of the seeds of cosmic structure during the radiation era
Authors: Gabriel León, Susana J. Landau, María Pía Piccirilli
(Submitted on 29 Sep 2014)
Abstract: The emergence of the seeds of cosmic structure, from a perfect isotropic and homogeneous Universe, has not been clearly explained by the standard version of inflationary models as the dynamics involved preserve the homogeneity and isotropy at all times. A proposal that attempts to deal with this problem, by introducing "the self-induced collapse hypothesis," has been introduced by D. Sudarsky and collaborators in previous papers. In all these works, the collapse of the wave function of the inflaton mode is restricted to occur during the inflationary period. In this paper, we analyse the possibility that the collapse happens during the radiation era. A viable model can be constructed under the condition that the inflaton field variable must be affected by the collapse while the momentum variable can or cannot be affected. Another condition to be fulfilled is that the time of collapse must be independent of k . However, when comparing with recent observational data, the predictions of the model cannot be distinguished from the ones provided by the standard inflationary scenario. The main reason for this arises from the requirement that primordial power spectrum obtained for the radiation era matches the amplitude of scalar fluctuations consistent with the latest CMB observations. This latter constraint results in a limit on the possible times of collapse and ensures that the contribution of the inflaton field to the energy-momentum tensor is negligible compared to the contribution of the radiation fields.

Which is why I am sort of hung up on a mechanism by which something uniform, or "perfectly gaussian" goes to a "differentiated" cloud of randomly moving particles then to "swirling" around specific loci.

If when gravity "turned on" it was Newtonian then all Newtonian moments were accounted for everywhere weren't they? At time 0, it is instantly an n-body solution where n is all bodies there are. And at time t+tau it is a continuous extension of the same solution. So if it started off gaussian at time 0, how did it get non-gaussian later. Sine it was non-gaussian later, it couldn't have been gaussian at t=0. So if things were swirling around specific locations later, then the distribution of moments (and momenta) had to contain that outcome to begin with. And maybe that's what happened.

On the other hand if when gravity "turned on", it had to "flow" to connect masses over time (through some sequence) then the swirling foci seen later were just those locations where the differentiated and "suddenly massive" particles were closest to each other. It is a subtle distinction. But it just seems more direct, simpler. And it's what I thought the theory said. It still leaves the question of information content, why the initial quanta were distributed spatially the way they were. But it is more easily flipped in my mind as information contained in the expansion field. And that seems nice.

... because it means that the fact everything rotates now, does not necessarily separate from the reason it started rotating then. If expansion/inflation (I do conflate them) and "geometry flow" were the cause then, what has changed? There is a vast backdrop of resulting "helicity" but that doesn't mean it is not an ongoing process?

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Jimster41
Gold Member
"closest to each" other, as in entangled?

PeterDonis
Mentor
2019 Award
something uniform, or "perfectly gaussian"
When that paper says "a perfect isotropic and homogeneous Universe", it is talking about an idealized model, not the real universe. The real universe was never perfectly isotropic and homogeneous. So we don't need an explanation of how something perfectly uniform could produce non-uniformity; that never happened. That's why you should stop being "hung up" on finding such an explanation; it's a wild goose chase.

If when gravity "turned on" it was Newtonian
Gravity never "turned" on; it was always there. And gravity was never Newtonian; it was always described by GR.