Caption: The vacuum light speed c = 2.99792458*10**8 m/s ≅ 3*10**8 m/s = 3*10**5 km/s ≅ 1 ft/ns and relative velocity.

Features:

1. The two Aliens are moving with respect to a local inertial frame in outer space: i.e., a free-fall frame unrotating with respect to the observable universe.

2. Our everyday life experience and classical physics tells us that the Aliens in the two spacecraft should measure different speeds for the light beam: c - v and c + v.

3. But this is WRONG. Both Aliens measure the vacuum light speed c = 2.99792458*10**8 m/s ≅ 3*10**8 m/s = 3*10**5 km/s ≅ 1 ft/ns.

   How can this be?

4. The short answer is special relativity.

   The slightly longer answer is that length and time flow rate depend on relative velocity according to special relativity in just such a way that both Aliens measure the vacuum light speed to be c.

   There is a sort of "cancelation of paradoxes".

   By the by, mass also depends on relative velocity---but that's another story.

   The mathematics of these dependencies is simple. Wrapping your head around them is hard.

   Also by the by:

   1. The length dependence is called the FitzGerald contraction.
   2. The time flow rate dependence is called time dilation.

5. The invariance of the vacuum light speed relative to local inertial frames is a universal observation (as always to within experimental uncertainty) and is the invariance principle, one of the two major postulates of special relativity (see also Wikipedia: Postulates of special relativity).

   All of the special relativity depends on the invariance principle and if it were wrong, all of special relativity would be wrong somehow---but it is all right to within experimental uncertainty.

   So we have overwhelming confidence in the invariance of the vacuum light speed.

6. Why do we NEVER observe the weirdness of special relativity in everyday life and in many other kinds of observations?

   The weird effects of special relativity usually scale as v/c or (v/c)**2, where v is relative velocity. In everyday life and in many other cases, v/c << 1 and the weird effects are unnoticeably small.

   But they are real enough and can be measured with accurate/precise equipment. For example, Global Positioning System (GPS) would NOT work well if special relativity (and general relativity too) were NOT accounted for. In fact, GPS confirms special relativity and general relativity every second of the day.