How can we tell if the universe is rotating?

[jackiefrost]

How can we tell whether the universe is rotating or not?

Have we made a definitive determination yet?

How does the notion of a rotating universe even have any meaning?

What would a rotating universe be rotating in reference to?

And lastly, if the universe were somehow rotating, would it produce similarly observed red shifting of star light as a function of distance as we have in an expanding spacetime model?

Thanks in advance,
jf

 

[mfb]

What do you even mean with "rotating"?
The universe is not an object in space, it IS space(time). There is no external "thing" where it could rotate in.

 

[WannabeNewton]

http://en.wikipedia.org/wiki/Godel_metric
See the section on cosmological interpretation. Note that any kind of rotation would have to be codified by an angular velocity since GR has no way to define angular momentum of space-times (e.g. Komar angular momentum) for cosmological space-times (they are not asymptotically flat).

More links:
http://arxiv.org/ftp/gr-qc/papers/0106/0106070.pdf
http://iopscience.iop.org/1367-2630/15/1/013063/pdf/1367-2630_15_1_013063.pdf

 

[WannabeNewton]

By the way, while we're on the topic of rotation, one thing you might also want to read up on is the role of Mach's principle in GR as compared to its role in other theories of gravity such as the Brans-Dicke theory.

See, for example, this beautiful paper: http://systems-eth.webs.com/Mach's ...c Theory of Gravitation (PhysRev.124.925).pdf

 

[jackiefrost]

By the way, while we're on the topic of rotation, one thing you might also want to read up on is the role of Mach's principle in GR as compared to its role in other theories of gravity such as the Brans-Dicke theory.

See, for example, this beautiful paper: http://systems-eth.webs.com/Mach's ...c Theory of Gravitation (PhysRev.124.925).pdf

I've read a good bit on Mach's principal as related to GR - esp. as portrayed in "Gravitation and Inertia" - Ciufolini and Wheeler, etc. I'll check out that paper. When someone calls a paper "beautiul, how can I resist? :-)

 

[WannabeNewton]

I would love to read Komar's PhD thesis that Brans and Dicke reference in which he tries to make Mach's principle more apparent in GR but unfortunately it is unpublished. Komar is the one who defined certain absolute physical invariants of special classes of space-times e.g. the total angular momentum $J = \frac{1}{16\pi} \int _{S}\epsilon_{abcd}\nabla^{c}\psi^{d}$ of an axisymmetric asymptotically flat space-time.

Ciufolini and Wheeler is a great reference although I have only used it when learning about the physical implications of a thin rotating massive shell in GR (e.g. Lens-Thirring effect). I don't know if the reference touches on the philosophical implications of this with regards to Mach's principle. Brans and Dicke's paper however mentions the issue of Mach's principle in the case of Birkhoff's theorem.

EDIT: BTW, if you're interested, Wald talks about the role of Mach's principle in GR in section 1.4 of his GR text. Also see problem 3 of chapter 4 of the same text (problem 4.3 is the reason I sought out Ciufolini and Wheeler in the first place).

 

[George Jones]

Consider all the possible (timelike) geodesics for a non-interacting bunch of galaxies in a region of spacetime. These possible geodesics form a congruence, i.e., any event in the region lies on one, and only one, geodesic. Think of flow lines.

Roughly, the universe is rotating everywhere in the region if every geodesic in the congruence rotates about every other geodesic in the congruence. This is measurable. There is non-zero rotation when the the vorticity tensor \omega_{ab} = \nabla_{\left[ a \right.} U_{\left. b \right]} is non-zero

Here:

1) \nabla is the covariant derivative operator;
2) the square brackets denote an anti-symmetrizer;
3) U is th (4-velocity) field of tangent vectors to the geodesics.

A good reference for this is section 4.6 in the book "Relativistic Cosmology" (2012) by Ellis, Maartens, and MacCallum.

http://en.wikipedia.org/wiki/Godel_metric
See the section on cosmological interpretation.

See also the section "Rigid rotation" in this Wiki article.

 

[Chronos]

The idea of a rotating universe has been around since at least Gödel, who proposed the first model of a rotating universe in his Gödel metric [circa 1949] as an exact solution to Einstein's field equations. Einstein briefly commented on this model saying it would be interesting to see if it could be excluded on physical grounds. Attempts to fine tune the model have persisted to the present, but, all have had problems. The existence of closed timelike curves in the model is particularly troubling which makes it look decidedly unphysical. The oft heard objection 'rotating relative to what?' is not easily answered. Some of the answers have included other causally disconnected universes, which is unappealing to most people. The Sagnac effect also offers a way to detect rotation of a coordinate system [i.e., the universe]. This was discussed at length in the paper by Kajari, et. al., Rotation in relativity and the propagation of light, http://arxiv.org/abs/0905.0765. It is, of course, difficult to prove a negative, so the best we have been able to do is constrain the amount of rotation. One of the tightest constraints to date was offered by Su, et. al in Is the universe rotating?, http://arxiv.org/abs/0902.4575. This result is model dependent [LCDM], which is objectionable to some people. It is, however, nearly impossible to devise a test that is not model dependent.

 

[Chronos]

The most recent entry into this field was by Longo using data from the Sloan Digital Sky Survey [SDSS] to check galactic rotations. His results suggested a statistically significant preferred direction of rotation for galaxies - Evidence for a Preferred Handedness of Spiral Galaxies, http://arxiv.org/abs/0904.2529] , and a dipole - Detection of a Dipole in the Handedness of Spiral Galaxies with Redshifts z ~ 0.04, http://arxiv.org/abs/1104.2815. These results were confirmed by Shamir, also using SDSS - Handedness asymmetry of spiral galaxies with z<0.3 shows cosmic parity violation and a dipole axis, http://arxiv.org/abs/1207.5464. It remains to be seen if any selection effects can account for this.

 

[jackiefrost]

Ciufolini and Wheeler is a great reference although I have only used it when learning about the physical implications of a thin rotating massive shell in GR (e.g. Lens-Thirring effect). I don't know if the reference touches on the philosophical implications of this with regards to Mach's principle. Brans and Dicke's paper however mentions the issue of Mach's principle in the case of Birkhoff's theorem.

EDIT: BTW, if you're interested, Wald talks about the role of Mach's principle in GR in section 1.4 of his GR text. Also see problem 3 of chapter 4 of the same text (problem 4.3 is the reason I sought out Ciufolini and Wheeler in the first place).

I bought Ciufolini and Wheeler to get some insights into GR handling of inertia and Lense-Thirring frame dragging. Unfortunately I can't seem to find it and MTW doesn't seem get into it quite as well. I also was looking for some good background stuff on Gravity Probe B (the experiment was still in the making at that time). Very interesting book!

 

[Hernik]

The most recent entry into this field was by Longo using data from the Sloan Digital Sky Survey [SDSS] to check galactic rotations. His results suggested a statistically significant preferred direction of rotation for galaxies - Evidence for a Preferred Handedness of Spiral Galaxies, http://arxiv.org/abs/0904.2529] , and a dipole - Detection of a Dipole in the Handedness of Spiral Galaxies with Redshifts z ~ 0.04, http://arxiv.org/abs/1104.2815. These results were confirmed by Shamir, also using SDSS - Handedness asymmetry of spiral galaxies with z<0.3 shows cosmic parity violation and a dipole axis, http://arxiv.org/abs/1207.5464. It remains to be seen if any selection effects can account for this.

It is very interesting. Is the nature of this effect so that the further from the axis the more significant are the prefedrred directions?

Henrik

 

[Naty1]

Is the nature of this effect so that the further from the axis the more significant are the prefedrred directions?

Can an 'axis' for a possibly infinite universe be defined?? identified??

 

[WannabeNewton]

The axis is simply defined by the direction about which the rotation occurs. For a homogenous solution, such as the Godel space-time, there is no preferred location of the axis but it has a preferred direction which defines the axis. As you can see such solutions are necessarily anisotropic.

 

[WannabeNewton]

Naty, in case I wasn't clear, let me be a bit more precise. Consider the form of the Godel metric given in the wiki article and the basis vectors fields making up the frame field. We have a time-like geodesic congruence defined by the integral curves of the time-like basis vector field $(e_0)^{a} = \sqrt{2}\omega (\partial_{t})^{a}$ (this congruence represents a family of locally inertial observers who are comoving with the swirling dust that generate this space-time solution; imagine that at each event $p$ in space-time, the vector $(e_0)^{a}(p)$ points along the "time axis" of the frame setup at $p$ by the locally inertial observer in the family who is present at $p$). To see that this is indeed a geodesic congruence, note that $(e_0)^{\nu}\nabla_{\nu}(e_0)^{\mu} = 2\omega^{2}(\partial_{t})^{\nu}\nabla_{\nu}(\partial_{t})^{\mu} = 2\omega^{2}\Gamma ^{\mu}_{tt} = 0$.

Now consider a geodesic in this congruence and attach separation vectors from this geodesic to all infinitesimally nearby geodesics in the congruence. We have a vector quantity called the twist of the congruence, defined as $\omega^{a} = \epsilon^{abcd}(e_0)_{b}\nabla_{c}(e_0)_{d}$. As you can tell, it is a purely spatial vector because $\omega_{\mu}(e_0)^{\mu} = \epsilon_{\mu\nu\alpha\beta}(e_0)^{\mu}(e_{0})^{\nu}\nabla^{\alpha}(e_{0})^{\beta} \propto \epsilon_{tt\alpha\beta}\nabla^{\alpha}(e_{0})^{\beta} = 0$ so it is orthogonal to the "time axis" of this frame field. Physically, it will measure how much these separation vectors twist/swirl around the chosen geodesic. If we compute it we get $\omega^{a} = -\omega (\partial_{y})^{a}$ so an observer following the chosen geodesic will see separation vectors attached to nearby geodesics twisting about the $y$-axis with some angular velocity, in the coordinate chart used in the wiki article. This picks out an axis following that preferred direction.

 

[CowedbyWisdom]

Isn't it also true that man has not been recording the heavens long enough in order to determine the rotation of something that large? Isn't that the type of thing you would have to record the movements of over at least 100,000 years+/-? Couldn't in theory the universe itself be a rotating object that at the same time is expanding?

 

[WannabeNewton]

http://physics.stackexchange.com/questions/1048/what-if-the-universe-is-rotating-as-a-whole
See Ben Crowell's post (the very first answer). It contains a great summary of the issues involved in the measurement of a universal rotation and contains references to many papers which go into further detail on said issues.

I would avoid Hawking's paper if your goal is to just learn about the operational issues involved in measuring a universal rotation. Hawking's paper is more about theoretical models of rotating universes, solving the Einstein field equations, arising from transitive Lie groups that fall under different Bianchi types.

 

[Naty1]

Wannabe: thanks for the link to Crowell's answer...turns out that post is a Cosmology FAQ of these forums...I'm not a big fan of the FAQ's in general but that one IS good.


Your mathematical based explanation is just a smidgen [smidgen here being a near cosmological distance!] over my head...but I get the gist from your last few sentences...

For those who might want a simple conceptual test approach, the Wiki's Sagnac Interferometer introduction is interesting. I had never seen that before nor thought about it.

 

[WannabeNewton]

Two papers referenced in the above posts, which I will reference again in this post, will be of great interest to you with regards to the visualization of rotation (in general and in the Godel space-time), lightcones in the Godel space-time, and the Sagnac Interferometer:
http://iopscience.iop.org/1367-2630/15/1/013063/pdf/1367-2630_15_1_013063.pdf
http://arxiv.org/pdf/0905.0765v1.pdf

 

[jackiefrost]

The most recent entry into this field was by Longo using data from the Sloan Digital Sky Survey [SDSS] to check galactic rotations. His results suggested a statistically significant preferred direction of rotation for galaxies - Evidence for a Preferred Handedness of Spiral Galaxies, http://arxiv.org/abs/0904.2529] , and a dipole - Detection of a Dipole in the Handedness of Spiral Galaxies with Redshifts z ~ 0.04, http://arxiv.org/abs/1104.2815. These results were confirmed by Shamir, also using SDSS - Handedness asymmetry of spiral galaxies with z<0.3 shows cosmic parity violation and a dipole axis, http://arxiv.org/abs/1207.5464. It remains to be seen if any selection effects can account for this.

Shamir uses some interesting algorithms for detecting spiral galaxy rotation direction. Given the various caveats listed in the Conclusion section, it'll be interesting to see how results from the Large Synoptic Sky Survey compares to these more local results.

I suppose that even though the results are for z<0.3, still "far beyond the scale of a galaxy supercluster", the rotational asymmetry could be a minor statistical anomaly in the relatively local observational data as opposed to a larger scale (universal) phenomena.

It should be noted that the experiment is limited to the local universe, although the range of z<0.3 exceeds far beyond the scale of a galaxy supercluster. Higher resolution analysis of the cosmic parity violation in the more distant universe will be possible when the Large Synoptic Sky Survey (LSST) starts operating, providing a much larger galaxy dataset and seeing deeper space.

Shamir

LSST is in Obama's 2014 budget which is great news. Imagine surveying the entire sky with an 8.4 meter base, three-billion pixel digital camera ("the world’s largest digital camera")! That sucker will gather over 30 Terabytes of digital image info each night!