Presentation #211.02 in the session “Cosmology II”.
The constancy of the speed of light c is the foundation of most physical theories and is found to be indeed constant from local measurements. Suggestions have recently been made that the temporal variation of c at cosmological time scale is possible to test with a combination of strongly lensed and unlensed type 1a supernovae (SNe1a) observations. Accordingly, the measurement of time delay difference in the peaking of the SNe1a luminosity between two gravitationally lensed images of the SNe1a should enable one to determine if c was different from its current value at the time the images were produced by a lensing galaxy. Since the geometrical time delay and the Shapiro time delay both scale as G/c3 we show that this method of constraining c is valid only when the possible variation of the gravitational constant G is ignored. Otherwise, the constraint determined is on the variation of G/c3, and is consistent with recently developed variable physical constant theory [MNRAS 498, 4481 (2020)] according to which (dG/dt)/G=3(dc/dt)/c.