Laboratory Observability of a Cosmologically Changing Light Speed

Einstein's axiom of special relativity was not an invariant light speed, but less restrictive: The velocity of light is independent of the motion of the light source. This is compatible with an expanding hyperbolic position space tangent to Minkowski four-space [1]. In this geometry $c$ decreases as $t^{-1/2}$ and a new Hubble-Lorentz expansion constant appears, $\sigma =c_0 ^2H_0 ^{-1}=3.89\times 10^{34}$ m$^2$s^{-1}$. The practical choice of $c$ as a defined constant is then not relativistically invariant, and should be modified. The logarithmic rate of change of $c$ is directly connected with the Hubble parameter, $d\ln c/dt=-H\left( t \right)/2$, with the present value $-3.65\times 10^{-11}\mbox{ y}^{-1}$. In 1972 $c$ was measured to 3.5 parts in $10^9$. If this precision can now be improved by 10 or 100, the predicted rate of change of $c$ can be tested. The issues involved in converting between cosmological and laboratory time and distance scales will be reported. Ultimately, a laboratory measurement of $H_0 $ may be in prospect. \newline \newline [1] F. T. Smith, Ann. Fond. L. de Broglie, \textbf{30}, 179 (2005); http://www.ensmp.fr/aflb/AFLB-302/table302.htm