Quote:
Originally Posted by Ryanb9
If they are moving c/4 speed, and they shoot an object at you, and you calculate that objects speed to be c, then 3c/4 would be the speed that object was shot at you.
I'm wondering what's the biggest that number has been (the c/4 speed) in a test that actually measured c on the other end.
I'm assuming someone currently holds the record for the largest c/4 speed mentioned above. I'd like to find out what that number is and read about the test that made it. I'll start reading your links now, thanks masq.
You are mistaken in your formula for composition of velocity. Velocities are NOT additive, so a person moving at c/4 and shooting an object at speed 3c/4 in his reference frame would not give c for the object speed in your reference frame. If you are composing two velocities u and v, the correct formula is not u+v as is naively supposed, but rather (u+v)/(1+uv/c^2). Plugging c/4 and 3c/4 into that formula gives (c/4+3c/4)/(1+3c^2/16c^2) = c/(1+3/16) = 16c/19, not c.
Importantly, there are two things to note about this formula. First if u and v both are less than c, then the result of this formula is likewise less than c. Second, if u=c then the formula gives (c+v)/(1+cv/c^2) = (c+v)/(1+v/c). Multiply both the numerator and denominator of that expression by c and you get c(c+v)/(c+v) = c. Thus, if one velocity equals c, the composed velocity .also is c. Therefore if someone travels toward you at c/2 and shines a light at you, you measure the speed of that light as c. IOW, the speed of light is a constant regardless of the motion of either the source or detector.
This seems counterintuitive only because we don’t experience high speeds. Even the fastest military aircraft don’t move anywhere close to c. Velocities really are additive, or at least close enough that we can’t measure any deviation from additive type. Try for example u=v=c/100000. That gives 2c/100000 divided by the number 1+ 10^-10, which is very close to u+v.