The Confessing Seventh-day Adventist

IT’S DIFFICULT to sum up where VSL stands, as I finish this book, because it is still well within the maelstrom of scientific inquiry. VSL is now an umbrella for many different theories, all predicting, in one way or another, that the speed of light is not constant, and that revisions to special relativity are required. Some of these theories contradict the relativity of motion—for example, the model Andy and I first proposed—but others don’t. Some predict that the speed of light varies in space-time, such as my Lorentz-invariant VSL theory and Moffat’s theory.” (p. 256).

On the newsgroup sci.physics.research, Marc Millis wrote:An indirectly related theme to the idea of VSL is something that is sometimes called the "Optical-Analogy." Within GR, there exists some "Euclidean" interpretations, one of which is the "optical analogy." In this interpretation, the gravitational field is represented as an optical medium with an effective index of refraction [7-9]. Although different from the more common Geometric interpretation, this interpretation has been shown to be consistent with physical observables, and transformation rules between these two perspectives have also been published [8]. Little attention is typically focused on this perspective because it does not predict any new effects that aren't already covered by the more common Geometric perspective of GR, and because it raises unanswered issues with coordinate systems choices.

I hope that this adds to your repertoire of knowledge rather than to your confusion. This particular approach is easier to visualize.

7. de Felice, "On the Gravitational Field Acting as an Optical Medium", in General Relativity and Gravitation, 2, 347-357, (1971). 8. Evans, J., Nandi, and Islam, "The Optical-Mechanical Analogy in General Relativity: Exact Newtonian Forms for the Equations of Motion of Particles and Photons", in General Relativity and Gravitation, 28, 413-439, (1996). 9. Nandi, Kamal and Islam, "On the optical-mechanical analogy in general relativity", in American Journal of Physics, Volume 63, No. 3 (March 1995)

Also, I welcome comments from the other readers to highlight the strengths and weaknesses of this perspective. In particular, does anyone know a reference that critiques these from the point of view of issues with coordinate systems choices?

Marc

On the newsgroup sci.physics.research, Big Bird wrote:

Eugene Shubert wrote:I can easily imagine all "inertial" frames of reference being equivalent in a space that is homogeneous and isotropic, abandoning the homogeneity of time requirement and allowing a variable speed of light.

You can imagine that? I can't.

First off, it seems you'd be abandoning the concept of spacetime itself if you demand that space but not time be homogeneous. Surely this seems to say that the two are independent concepts -- and how, then, could there be Lorentz-like transforms that link the two?

Then, of course, abandoning homogeneity of time means abandoning conservation of energy via Noether's theorem. Certainly conservation of energy has all the experimental backup I could imagine any physical principle to have.

Thirdly I'd be curious to hear just what it would mean to write something as fundamental as "F = dp/dt" for an inhomogeneous "t". Derivative with respect to what? Or how would the Hamiltonian of a free particle look like?

This is approximately where my teeth start hurting just thinking about this and hence the question how you manage to imagine these things...