B What would happen if the speed of light were different?

No

 

This topic has come up several times. You'll often get a faster answer with a forum search.

You can't just change the speed of light, because the physical constants are linked. So you also have to specify what else you are changing and what you are not - and at least one other thing must change.

Generally, if you work through the consequences of such a change there is no effect. It turns out to be a Byzantine way of changing your units. Obviously we can halve the value of the speed of light by defining the metre to be twice what it is, and obviously this makes no difference to anything.

The exception turns out to be if you change the fine structure constant, which is a dimensionless number which relates the speed of light to the strength of the electromagnetic interaction. Since you (and everything else) are held together by electromagnetic interactions between your atoms, this changes the relationship between your size and the speed of light. In other words, this actually changes the relationship between monkey arm lengths (~1m), monkey heart beats (~1s), and the speed of light (a natural scale factor between distance and time units).

I don't think mucking around with the fine structure constant has any effect classically beyond changing the speed of light (or, at least, being interpretable as a change in the speed of light). My quantum (what I ever knew of it) is way too rusty to know if there are effects there - others may know.

 

In case you didn't know....

That's the speed of light in a vacuum. It's different in other media like water (about 25% slower).

 

As others have mentioned, experimental tests to see of the speed of light changes with time usually revolve around looking for changes in the fine structure constant.

The fine structure constant is something that one can measure that doesn't depend on one's units system. If you believe that plank's constant, the charge on the electron and the permittivity of free space are all constant, then detecting a change in the fine structure constant would be equivalent to saying the speed of light varies. Such experimental tests as have been done for changes in c really measure the fine structure constant (as far as I know), so if you want to look at the experimental literature, that's a good place to start.

Talking about changes in the fine structure constant eliminates trivial "changes" in the speed of light that amount to changes in units. For instance, the speed of light is about 9.8e8 feet/second. If one called a meter a foot, one might claim that the change of nomenclature "changed" the speed of light, but it was really just a changing in words, not a change in physics.

Considering only dimensionless quantities such as the fine structure constant eliminates this sort of confusion, because the units all cancel out and it's a pure number that's independent of one's choice of units.