Hypersphere, gravity waves and dark matter

[Frog march]

On another thread it was stated that if a gyroscope where to traverse the hypersphere that is the Universe, ie make a complete circuit, that it would no longer be orientated in the same direction.

I just wondered, if gravity waves(what ever they may be) where to do a similar circuit, whether they would also undergo some kind of alteration or inversion of properties such that they would repulse matter.

Could this be a better explanation for the acceleration of the expansion of the Universe, than dark matter?

[Digix]

I suppose gyroscope orientation will change because of completely normal reasons, for example because you move its front will feel dufferent forxe than rear, so you can expect that to integrate and give visible results.

also it is quite interesting how gravity afects itself.

[publiusr]

It should be possible to circumnavigate the Universe and NFAL speeds.

But you can't go home again.

[Ken G]

The universe isn't thought to be a hypersphere, so the question is moot, though cute. Note however that the analog of a gyroscope changing orientation is just a change in polarization of the gravity waves, which is nothing so profound as turning gravity into antigravity (despite how often they 'reverse the polarity' in Star Trek).

[Frog march]

If the Universe is not a hypersphere(meaning a closed universe with no boundaries) what is it? I don't think it can be infinite.

[Frog march]

It should be possible to circumnavigate the Universe and NFAL speeds.

But you can't go home again.

I suppose by NFAL means Near Fast As Light?

If the universe were expanding at the speed of light then nothing would return to where is started but half way across the universe might mean some altering of the properties of light or gravity perhaps?

[Ken G]

If the Universe is not a hypersphere(meaning a closed universe with no boundaries) what is it? I don't think it can be infinite.

Well, if you don't think it can be infinite, then I guess it is likely to be a hypersphere. But if it can be infinite... What really matters is that the part of it we can observe is not a hypersphere.

[Frog march]

well, I personally believe it to be a hypersphere. And if it is, surely it would have hypersphere properties over 2feet even if the curve of that space were unmeasurable.

do you think, if it was a hypersphere, that that could be the reason for redshift? I mean the change in properties as with the change of a gyroscope orientation.

[Ken G]

No, because even an open universe, or the nearly flat one we seem to have, would still have redshifts. But you're right that there is a geometric interpretation of the redshift, something like curvature of the time axis. I've never really understood geometric interpretations, to be frank. I prefer to think of the redshift as being due to time passing more slowly when the universe was younger.

[publius]

I suppose gyroscope orientation will change because of completely normal reasons, for example because you move its front will feel dufferent forxe than rear, so you can expect that to integrate and give visible results.

also it is quite interesting how gravity afects itself.

No, the change in the orientation of a gyro is due to a GR effect called the "geodetic effect". Consider the curved 2D surface of a sphere. Now define a local 2D coordinate system at some point on that sphere. Now move the origin along a geodesic and watch what happens to your local directions relative to initial point. They change because of the curvature.

You can define a path that gets you back to where you started by going first in one local direction, then another and so forth. You will find that when you get back to your starting point, your local directions have flipped around on you.

Besides gravitomagnetism (frame dragging), Gravity Probe B is also looking for this geodetic effect. Both of these effects are very small (but I think the geodectic effect is actually stronger than the frame dragging), and its a testament to the engineering that devised a way to accurately measure such small effects. Results will be in next year, and we'll see if GR's predictions hold up.

My money is on GR passing with flying colors. I would love to see some anomaly, something a bit different from GR's predictions in these small regimes [I'm suspicious that gravity behaves slightly differently than we think it does], but if I were a betting man, my money would be on no anomalies and everything within GR's predictions.


-Richard

[publiusr]

It will be interesting to watch.

[agingjb]

If the universe, well our particular space-time, isn't a hypersphere, then it's either infinite or some perhaps less likely manifold. A hypersphere is parallelisable, which means that whole thing could be, in sense, rotating along what are (I stand to be corrected) called Clifford parallels. I'd guess that most of the other possible manifolds, hypertoroid etc., would also admit such a rotation. But that would imply some sort of anisotropy at the very largest of scales - is there evidence for this?