Mach's principle and variable speed of light.

[CarlB]

Mach's Principle and a Variable Speed of Light
Alexander Unzicker

Mach's principle, according to which the origin of gravitational interaction depends on the presence of all the masses in the universe, was expressed in a quantitative form by Sciama (1953). Since this idea suggests a variable speed of light (VSL), it is shown here that the arising variability of c is in agreement with all GR tests regarding time and length scales which are subject to variation as well. Moreover, VSL opens the possibility to write the total energy of a particle as $$E=mc^2$$; this necessarily leads to the proportionality of inertial and gravitating mass, the equivalence principle. Furthermore, a formula for c depending on the mass distribution is given that reproduces Newtons law of gravitation. This mass distribution allows to calculate a slightly variable term that corresponds to the `constant' G. The present proposal may also supply an alternative explanation to the flatness problem and the horizon problem in cosmology.
http://www.arxiv.org/abs/gr-qc/0511038

I just saw this on Arxiv and haven't read it yet. But I recognize the author as having written interesting papers before.

Carl

 

[Dale]

Note that this paper is more than a decade old and has not yet been published in a peer reviewed journal. Its quality and correctness is doubtful.

That aside, one problem that I have with all VSL theories is that the speed of light is an artifact of your choice of units. So a VSL simply means that you have units which change over time or space. There is no physical content to a VSL. In SI units the speed of light is fixed by definition and so in SI units any VSL theory is immediately falsified.

The physical content of a VSL is actually captured in a variable fine structure constant. That is a dimensionless constant which describes the actual physics and is not subject to the criticism above. The fine structure constant depends on other parameters besides c, such as e, the charge on an electron. There is no reason that you couldn’t interpret a variable fine structure constant as a variable e instead of a VSL. In my view this is more natural and is a major weakness of all VSL theories. In addition, there is currently no good evidence for a variable fine structure constant.

Furthermore, Mach’s principle is in doubt, in my opinion. To my knowledge, the best theoretical embodiment of Mach’s principle is Brans Dicke theory. As the Brans Dicke parameter gets larger it becomes closer and closer to GR, with the non-Machianness of GR. So far the parameter has a very large lower limit. So I am skeptical that Mach’s principle is a correct representation of physics, at least insofar as BD gravity does embody Mach’s principle and GR does not.

All in all, a theory that seeks to combine both Mach’s principle and a VSL is doubly-problematic in my view.