Yes, it's a possibility that has to be considered. But in the 4-dimensional
space-time way of understanding special relativity, c is simply a factor for the
conversion of units used for distances in spacelike directions (meters) & those in
timelike directions (seconds). The use of those different units (& therefore of a
value of c differing from 1) is due to historical convention, not basic physics. The
value of c therefore plays the same type of role as the mechanical equivalent of heat.
While we usually call the quantity c which occurs in the Lorentz transformation
"the speed of light" & that was its historical origin, the 2 quantities are logically
distinct. What special relativity requires is that there be an absolute speed. Whether
or not light travels at that speed (& it doesn't if the photon has a rest mass) is
It isn't hard to formulate a relatvistic theory in which "the speed of light"
isn't constant - e.g., with a nonzero photon mass. A theory in which the conversion
between seconds and meters varied would be - I think - a lot harder to formulate in a
way which agreed with what we know about relativity.
George L. Murphy