The second postulate should trouble your intuition. The idea that light will always approach an observer at light speed c regardless of whether the source is in motion relative to the observer or not is odd. You also don't increase the speed at which light approaches you if you run toward the light. Nor do you decrease the speed of its approach if you run away from it. This is NOT because you can't run fast enough, but would be true even if you could run at 100 million meters per second. I hope this troubles you. Light is strange.[br][br]Not only does light always approach at the same speed, but nothing with mass (light has none) can ever travel relative to anything else at speeds [math]v\ge c[/math]. In other words, velocity of a massive particle must always be [math]v<c.[/math]

We added velocities in relative frames in first semester when we carefully studied collisions. To get the correct results we had to be careful to look at collisions in the center of mass reference frame. Recall that when comparing the velocity of object A as measured by B, to the velocity of object B as measured by A, that [math]\vec{v}_{AB}=-\vec{v}_{BA},[/math] so that switching the reference frame reverses the vector.[br][br]Given a third frame C moving with respect to two other frames A and B, we can always relate the velocities by[br][center][math]\vec{v}_{AC}=\vec{v}_{AB}+\vec{v}_{BC}[/math][/center][br]in which the center indices match on the right side. This equation is valid, however, only for velocities slower than c. I'd be concerned using it above around v=c/10 or so.

The corresponding equation for quickly moving frames which may exceed c/10 is rather difficult for true 3D vectors. The equation in which the velocities are along the same axis (I'll use the x-axis) is very similar to the Galilean expression, but has a denominator. The expression looks like this:[br][br][center][math]v_{x,AC}=\frac{v_{x,AB}+v_{x,BC}}{1+\frac{|v_{x,AB}||v_{x,BC}|}{c^2}}[/math][/center] [br]Note that the denominator serves to guarantee that the sum will never exceed c. Even c+c=c. On the other hand 0.5c+0.5c = 0.8c. It is only with very small values that the expression gives values in line with the Galilean expression. For instance, you can verify that 0.1c+0.1c = 0.198c, and at 0.01c+0.01c=0.019998c, or very nearly 0.2c, etc.