Constraints on variation in the speed of light based on gravitational constant constraints

We consider the possibility of a varying speed of light based on a unit of length defined with a rigid rod or atomic standard. The reference for comparison is the international standard for the meter based on the transit of light, defined so that c is constant. If these two units do not correspond over time, then the gravitational constant G as measured with each will not be in agreement. We relate changes in the speed of light in atomic units of length to changes in G measured in the two systems. Reported experimental data that constrain yearly changes in G are sufficient to bound changes in c. Experimental constraints on vertical bar(over dot(G))/G vertical bar based on spacecraft microwave ranging and on helioseismology indicate that presently vertical bar(over dot(c))/c vertical bar <= .55 x 10(-12) yr(-1). If this result is extended in epoch by relating c to a power of the scale factor, a(n), then variation in c is constrained by vertical bar n vertical bar < .0080. The approach is distinct from other efforts to constrain (over dot(c)) in being based on data from within the Solar system instead of cosmological observations. A relationship between c and the fine-structure constant is identified that potentially provides tighter constraints.

Automated summary

The study explores the relationship between the speed of light and gravitational constant, using experimental data to determine the range of variation in the speed of light over time. It is noted that constraints on the speed of light variation are based on data from within the Solar system rather than cosmological observations. Additionally, a relationship between the speed of light and the fine-structure constant is identified as potentially offering tighter constraints.