Thursday, July 28, 2011

Faster-Than-Light Expansion? Not So Fast, Buddy!

This is a very common question that I come across. Is the universe expanding faster than the speed of light? If so, then isn't this proof that SR basic postulate is incorrect?

Most people who asked that question usually don't have an understanding of General Relativity. But even for those who do, especially students studying that subject, a serious confusion can occur when it is applied to outlying, sufficiently-far away celestial bodies, where speed greater than c can be achieved.

This is a nice paper, to be published in AJP, that addressed this issue, and the restriction on the application of the Hubble Law.

Abstract: Naively applying Hubble's law to a sufficiently distant object gives a receding velocity larger than the speed of light. By discussing a very similar situation in special relativity, we argue that Hubble's law is meaningful only for nearby objects with non-relativistic receding speeds. To support this claim, we note that in a curved spacetime manifold it is not possible to directly compare tangent vectors at different points, and thus there is no natural definition of relative velocity between two spatially separated objects in cosmology. We clarify the geometrical meaning of the Hubble's receding speed v by showing that in a Friedmann-Robertson-Walker spacetime if the four-velocity vector of a comoving object is parallel-transported along the straight line in flat comoving coordinates to the position of a second comoving object, then v/c actually becomes the rapidity of the local Lorentz transformation, which maps the fixed four-velocity vector to the transported one. 

It also contains several references that tackle this apparent faster-than-light issue in terms of universe expansion. Hopefully, this will answer that vexing and common question.


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