A spinning Universe?

[Always curious]

From a universe according to General Relativity can we ascertain if the Universe can be said to be spinning?

Spinning relative to what is a tough question - I would say perhaps a rate of spin relative to the age of the Universe might give a framework if it can be agreed that say 1 second after the BB the Early Universe was spinning or perhaps more properly could at least be said to have had Angular Momentum as it expanded?

I have no Grand Theory attched to this question I was just - as always - curious.

[selfAdjoint]

The famous logician and pal of Einstein, Kurt Goedel devised a spinning Einstein style universe and showed that it contained closed timelike paths - code for achievable time travel.

[Always curious]

The famous logician and pal of Einstein, Kurt Goedel devised a spinning Einstein style universe and showed that it contained closed timelike paths - code for achievable time travel.
That sounds interesting - time travle is always interesting though doubtful- what say the theorists?

[Garth]

A Machian view would say that the universe could not spin as a whole as it would need to rotate relative to something else; although one 'half' could rotate relative to the other 'half'.

Goedel's model could then, in a Machian view, to be construed as a refutation of GR.

Alternatively, from a GR point of view, it could construe a refutation of Mach's Principle. Perhaps Gravity Probe B will resolve the issue?

Garth

[Nereid]

Alternatively, from a GR point of view, it could construe a refutation of Mach's Principle. Perhaps Gravity Probe B will resolve the issue? How?

More precisely, what limits could the 'best' (= most sensitive) results from GPB set on the rotation of the universe?

On another tack, there is at least one research effort underway to measure 'local rotation', using ring lasers ... could that work also constrain 'universal rotation'?

Finally, didn't I read that Hipparcos set some limits (not very stringent) on rotation of FK5? (I'll check later ...).

[Garth]

Perhaps Gravity Probe B will resolve the issue?How?My cryptic reference to possible non-GR results of that experiment! -and possible Machian alternative results.

As I said on another thread "Mach's Principle", my post #37:
Gravity Probe B will be able to tell, the predictions for General Relativity, the Brans Dicke theory and Self Creation Cosmology are:
Gravity Probe B:
GR prediction: Geodetic effect 6.6144 arcseconds/yr
Gravitomagnetic effect 40.9 millarcseconds/yr

BD prediction: Geodetic effect {(3w+4)/3w+6)}6.6144 arcseconds/yr
Gravitomagnetic effect {(2w+3)/(2w+4)}40.9 millarcseconds/yr

SCC prediction:Geodetic effect 5.5120 arcseconds/yr
Gravitomagnetic effect 40.9 millarcseconds/yr

Wait and see!


Garth

[Always curious]

Thanks guys

When do we get the results of this probe you refer to?

PS: If the Universe is spinning would there be a different rate of spin from the early universe to the present Universe?

If expansion is increasing what would occur to the spinrate?

[Garth]

Thanks guys

When do we get the results of this probe you refer to? The experiment will end this (northern) Summer. Analysis of the results may take several months and results should be published early next year (06). However everything about GPB has taken twice as long as expected so I wouldn't hold your breath!

PS: If the Universe is spinning would there be a different rate of spin from the early universe to the present Universe?

If expansion is increasing what would occur to the spinrate?
If there is an absolute inertial frame relative to which the universe is spinning, and in which angular momentum is conserved, then its spin rate would slow down with expansion. Conversely as you plot back into the Big Bang the spin rate should go up - infinitely so as t -> 0?? Perhaps that is a possible cause of a bounce?

Garth

[Always curious]

The experiment will end this (northern) Summer. Analysis of the results may take several months and results should be published early next year (06). However everything about GPB has taken twice as long as expected so I wouldn't hold your breath!

If there is an absolute inertial frame relative to which the universe is spinning, and in which angular momentum is conserved, then its spin rate would slow down with expansion. Conversely as you plot back into the Big Bang the spin rate should go up - infinitely so as t -> 0?? Perhaps that is a possible cause of a bounce?

Garth

Thanks Garth - I will look forward to these fascinating results (or more correctly the results of this fascinating experiment!)

Anyone else have any thoughts on the "bounce" Garth mentions?

[Garth]

Of course if would be a pancake bounce normal to the axis of rotation.

Garth

[dedpoet777]

i have thought for years that it is spinning personally. and i thought this because i knew that galaxies, and everything else, is spinning. so the question is if a galaxy is spinning, then to what is its spin relative? and as far as what is relative to the spin of the universe that is impossible to ever prove. however, it is possible that one universe is spinning realtive to another, or to something bigger. we will just never know. but what we do know is that everything we know of is made of smaller couterparts down to the quark level. so it would make sense that our universe is maybe something similar to a cell in that makes up something even bigger. because to a cell our body would be a universe. and since everything is made on the atomic level, perhaps our universe makes up a bigger part of the "atom" per se.:rofl:

[JesseM]

A rotating universe in the context of general relativity isn't rotating in quite the sense we usually think of it--there's no center of rotation, for example. As this page (http://www.ettnet.se/~egils/essay/essay.html) says: When I tell people about the possibility of a rotating universe, their reaction is usually either a silly smile, or the very well motivated question: With respect to what would the universe rotate? I viciously reply: With respect to something that does not rotate, that is, something that does not experience any centrifugal forces. OK, this is correct, but it needs some elaboration.

First of all, don't try to imagine the universe as rotating as a whole. That way of thinking is misleading. I'll come back to rotation as a whole later.

Second, don't think that this implies some center of rotation. According to the Copernican principle, all places in the universe are equivalent. This is a simplifying assumption adopted by most cosmologists; whether it holds in reality is an open question. On smaller scale the universe is badly inhomogeneous, but there is still hope that the large scale structure is homogeneous.

Third, study carefully the following attempt to visualize a rotating universe.

Imagine you are in a laboratory without windows floating around somewhere in the universe. If you and the other objects in the laboratory get pressed against the walls, you would say that the laboratory is rotating, and centrifugal forces are responsible for the effects. Now, the laboratory happens to be equipped with small engines that can be used to control the rotation. Use the engines until you have totally eliminated the centrifugal forces, and thereby the rotation. When done, drill some peepholes in the laboratory (but please make sure you don't lose your air supply). Observe the galaxies. If you find that the galaxies rotate around you, then the universe is said to be rotating.

You have actually only seen that the universe rotates around the point where you are, but if the Copernican principle holds, then it rotates around any point. That's a rotating universe.

So keep in mind that when I talk about a rotating universe, I mean that the matter of the universe rotates around the non-rotating observer. There is a better word for it: vorticity. In classical hydrodynamics, the vorticity w of a velocity field v is defined using the rot operator:

[see page for image of equation]

In general relativity, there is a similar definition. One expresses the vorticity four-vector in terms of matter four-velocity field (a four-vector is a vector with one 'time' and three 'space' components).

[MeJennifer]

"...On smaller scale the universe is badly inhomogeneous, but there is still hope that the large scale structure is homogeneous...."

What an odd remark from someone writing about science. :smile:

[notknowing]

From a universe according to General Relativity can we ascertain if the Universe can be said to be spinning?

Spinning relative to what is a tough question - I would say perhaps a rate of spin relative to the age of the Universe might give a framework if it can be agreed that say 1 second after the BB the Early Universe was spinning or perhaps more properly could at least be said to have had Angular Momentum as it expanded?

I have no Grand Theory attched to this question I was just - as always - curious.
An interesting topic ..
When one talks about a spinning universe, does one mean that all the galaxies and mass are spinning or does one mean that space (in between the galaxies) is also spinning ? If space itself is spinning, what does this actually mean ? There exists in general relativity also the so-called "frame-dragging" effect (a topic of investigation for the gravity probe B experiment). Could this also be interpreted that space is actually spinning around a rotating body ?

[Chris Hillman]

Hi, Always curious,

Just thought I'd recommend some more reading:

You can find a new arXiv eprint with fabulous illustrations of closed timelike curves CTCs in the Goedel lambdadust solution as http://www.arxiv.org/abs/gr-qc/0611093. The classic description is in Hawking and Ellis, The Large Scale Structure of Space-Time, and if you search the arXiv you should find a dozen or so eprints discussing various aspects of this fascinating solution.

I also recommend Cuifolini and Wheeler, Gravitation and Inertia, for more about Mach's principle, frame dragging, gravitomagnetism, and rotating cosmological models, even though I don't feel this book comes up the high standards of exposition set in the classic textbook by Misner, Thorne, and Wheeler, Gravitation, Freeman, 1973.

A rotating universe in the context of general relativity isn't rotating in quite the sense we usually think of it--there's no center of rotation

That's not true in general; the so-called LRS (locally rotationally symmetric models) and the well-known Van Stockum dust are examples of cosmological models in which the matter (source of the gravitational field) is rotating about an axis with a definite location "in space". However, the Goedel lambdadust is homogeneous (not isotropic), so it does have the property you mentioned.

The issue of how to define "rotation" in curved spacetimes gets quite tricky and much ink has been spilled--- unfortunately, some contributions seem to involve "independently committing" the same errors which have been made (and corrected) in the past, so discussion can easily become contentious.

As always, the local versus global distinction is critical. There are distinct notions of "rotation" which are local in the sense of "jet space", principally vorticity (MTW, Hawking and Ellis, the book by Eric Poisson, A Relativist's Toolkit, are all good sources for the kinematical quantities known as the vorticity tensor, expansion tensor, and acceleration vector), and neccessarily more sophisticated notions which are global.

One thing to watch out for (for those who know what these buzzwords mean): in many "rotating" dust models, the "obvious" coframe read off the metric is often already inertial and even comoving with the dust particles, but the frame may be spinning. With luck, as in the Goedel lambdadust, you can "despin" the frame by applying, as you run along the world line of each dust particle, just the right rotation as a function of proper time about one of the spatial frame vectors. Here, note that in curved spacetimes, nonspinning inertial frames correspond to Lorentz frames in flat spacetime. Spinning but inertial frames correspond to, well, you probably get the idea.

Similar remarks hold for circularly polarized plane waves. Speaking of which, the Osvath-Shuecking circularly polarized gravitational plane wave solution is often touted as a "rotating" cosmological solution (although it is an exact vacuum solution, indeed a Petrov type N vacuum, not a fluid solution, so no matter is anywhere in sight!).

Chris Hillman