Replies

Wait a minute.

According to Einstein, the laws of physics are the same in any inertial reference frame, that is for anyone going at constant velocity and not accelerating. If so then the velocity of incoming cosmic rays should be independent of the velocity of the platform you are on. If that wasn't the case then you could measure the average velocity of these incoming high speed particles and calculate your actual speed relative to ... to what, that's the problem. There isn't any what. So your velocity can't make a difference.

OTOH, feel free to educate me on what really happens.

According to Einstein, the laws of physics are the same in any inertial reference frame,

I think you need to read up a little. According to your example, if you hit a person head on walking 2 mph toward you, he wouldn't be hurt (from the car's reference frame).

How Do You Add Velocities in Special Relativity?
Suppose an object A is moving with a velocity v relative to an object B and B is moving with a velocity u (in the same direction) relative to an object C. What is the velocity of A relative to C?

In non-relativistic mechanics the velocities are simply added and the answer is that A is moving with a velocity w = u+v relative to C. But in special relativity the velocities must be combined using the formula

w = (u + v)/(1 + uv/c2)

If u and v are both small compared to the speed of light c, then the answer is approximately the same as the non-relativistic theory. In the limit where u is equal to c (because C is a massless particle moving to the left at the speed of light), the sum gives c. This confirms that anything going at the speed of light does so in all reference frames.

This change in the velocity addition formula is not due to making measurements without taking into account time it takes light to travel or the Doppler effect. It is what is observed after such effects have been accounted for and is an effect of special relativity which cannot be accounted for with Newtonian mechanics.

The formula can also be applied to velocities in opposite directions by simply changing signs of velocity values or by rearranging the formula and solving for v. In other words, If B is moving with velocity u relative to C and A is moving with velocity w relative to C then the velocity of A relative to B is given by,

v = (w - u)/(1 - wu/c2)

Cosmic "rays" (a terrible misnomer) are protons, neutrons, atomic nuclei, etc., that have been accelerated (probably by supernovae and other cosmic processes) to relativistic speeds. Einstein said the speed of light is constant for all observers... Doesn't apply to these subatomic particles; i.e., the speed of a carbon nuclei is not constant for all observers, e.g.