They sound kooky. They refer to a paradigm shift. Actually, you can find a lot of Americans physicists who think relativity needs to be revised. Most astrophysicists now believe that the expansion of the universe is accelerating, and relativity doesn't explain that.
Joe writes: "Uh-oh. I'm reading a book by Davies right now - "The Fifth Miracle." He's written a lot of books and has always seemed pretty mainstream to me."
Andy writes: "I can't imagine a meaningful revision. Relativity consists entirely of two simple postulates: (1) all frames of reference are identical for the laws of physics and (2) the speed of light is invariant and insurpassable. Relativity is a math transformation system based entirely on those two postulates, rather than data. Any revision to postulate (1) or (2) would be a big change."
Yes, it is hard to imagine physics that is not based on the Lorentz group (relating space and time coordinates). That is, the spacetime manifold is locally based on SO(3,1). But gravitation and quantum mechanics have never been reconciled, and it is inevitable that relativity theory will have to be revised somehow.
Andy writes: "That's a problem for the theory of relativity, not for physics. There is no difficulty imagining variations to the speed of light, or a preferential frame of reference. Computer-based Newtonian mechanics handles many-bodied problems (like our solar system) much better than relativity. I did a Google search on "many bodied problem" and "relativity" and only 3 cites even mention it! Relativity remains consistent with two-body problems, but becomes incoherent with additional bodies. Does relativistic mass of a fast-moving object influence the third body?"
Relativity doesn't have anything to do with the number of bodies. Newtonian mechanics is easier to compute, and is a good approximation for bodies on the scale of the solar system.