Expert: Philip Stahl - 12/27/2010

Question
QUESTION: Hi Philip,

I have finally gotten around to reading "A brief history of time". There was one statement in Chapter 10 of the book which was kinda offhand and unsupported, "The solution Godel found doesn’t correspond to the universe we live in because we can show that the universe is not rotating."

My question is, can we in fact show that the universe is not rotating? How can we possibly establish if it is or not with no access to any external frame of reference?

I am not particularly concerned about Godel's model, just the categorical no rotation.

Thanks and best regards,

Eric

ANSWER: Hello,

Actually, I just consulted my copy of 'A Brief History of Time' (Chapter 10, 'The Unification of physics') and can find no statements pertaining to the rotation (or otherwise) of the universe, or to Godel. Are you sure you have the right book, or is it a revised reprint of the original?

In any case, the solution of Godel is problematic to say the least. For one thing, because his solution (to the Einstein equations) allows closed timelike curves, it would mean that theoretically one could travel into one's past- which would imply the "grandfather paradox", i.e. one would be able to go back in time and kill his grandfather -but if he could do that, how could he exist in the present?

Anyway, we have no observations that would indicate any rotation of the universe. What might these observations be? Well, consider that in the extant cosmos any object moving from point A to a distant point B and expending energy E (assuming no black holes or other aberrant sources of gravity are in its path) does so in such a way that the path traversed represents the shortest distance - or what we call a "geodesic". (For example, on a sphere like the Earth - this geodesics are 'great circle' routes).

If the universe were rotating, however, one would see an additional motion superposed on the least action (geodesic) motion and this would somewhat resemble a corkscrew. Thus, to find any evidence for a rotation of the universe we'd examine the motions of distant objects (maybe quasars) and see if in fact they exhibit a type of 'corkscrew' motion. Up to now, we've seen no such signs or indicators - hence the assumption of no rotation seems to be a valid one.

Hope this sheds some light!

---------- FOLLOW-UP ----------

QUESTION: Hi Philip,

Thank you for the prompt and detailed reply. With regard to A Brief History of Time, My Chapter 10 is Wormholes and Time Travel, Chapter 11 is The Unification of Physics.

I assumed that if the universe is rotating, then it would not just be the objects in the universe spinning around some n-dimensional axis, but that space itself would also be rotating, which would tend to mask any coriolis effects, and would have no impact on a geodesic.

I am more concerned to discover if there is such a thing as proof that the universe cannot be rotating, rather than "we don't see any indication that it is".

Time travel is not my concern. I agree that the grandfather paradox makes time travel seem unlikely, though maybe I should make a list of major stock market changes, and keep it with me just in case I do get a chance to pass it to my younger self ;-)

Best regards,

Eric

Answer
Hello,

Thanks for your response which shows your 'Brief History of Time' must be an updated version, since mine has no such chapter (on Wormholes and Time Travel) in it.

Re: "space itself rotating", it wouldn't be if - as Hawking postulates- the universe is "boundary free". Then his no-boundary condition wouldn't allow any perceived, discrete perception or detection of overall rotation- since it's a non-starter for a non-bounded construct. The implicit conclusion of an exterior effect on geodesics is based on an assumption of inertia (for a "bounded cosmos" as a whole, e.g. in a Riemannian non -Euclidean manifold) and that conservative force fields and transits within the enclosed space-time would be affected by the exterior rotation since even if the universe had a uniform rotational velocity there'd still be a *centripetal acceleration v^2/r* directed inwards(which again, wouldn't apply to Hawking's no -boundary proposal. His solutions simply wouldn't admit of any rotation, period).

Unfortunately, there's no way to "prove" it one way or the other. One basically is constrained to adopt which solution he wishes and then accept the consequences of those solutions. This isn't very satisfactory, admittedly, but is all we have right now.