[aristeides]

If the speed of light varies from one time to another, will it also vary from one place to another? (In fact, if I remember my relativity accurately, what is a difference in time to one observer can be a difference in place to another. Which raises another question -- again as I remember relativity, one space-time point is unambiguously earlier than another if the distance between the two cannot be covered in time at the speed of light. Otherwise, different observers can decide that two different space-time points are both earlier and later. So, if the speed of light varies, how do we decide?)

[Alamo-Girl]

I think what you are speaking of in #35 is called the Lorentz Transformations. Here is a link to some interesting notes on the subject.

[Alamo-Girl]

Aha, I found a much better one with graphics! Construction of Lorentz Transformation

[OBAFGKM]

Which raises another question -- again as I remember relativity, one space-time point is unambiguously earlier than another if the distance between the two cannot be covered in time at the speed of light. Otherwise, different observers can decide that two different space-time points are both earlier and later. So, if the speed of light varies, how do we decide?

You remember right. The hitch comes when we assume that different observers must agree upon which space-time point is earlier and which later. Having different light-speeds in different parts of the universe guarantees that there can be observers who disagree.

Looked at in different ways, it guarantees that somewhere and somewhen a traveler could set out on a journey and return to the same place and time he started, or that he could travel backwards in time. The bottom line is that cause and effect need not be absolute, but may just depend on who's doing the looking. Lots of people object to such a universe on religious grounds and reject its possibility out of hand.