Answer to Question #130716 in Mechanics | Relativity for stephanie robles

Question

Darth Vader is traveling at 0.3 c toward Luke Sky Walker. Darth Vader fires a pulse of light at Sky Walker.

A. According to classical mechanics, what is the speed of the light pulse seen by Luke Sky Walker?

B. According to electromagnetism, what is the speed of the light pulse seen by Luke Sky Walker?

Answer 1

A. According to pure classical mechanics (without special relativity), to find the velocity we need to use Galilean velocity-addition formula:

$v_1 = u+v = c +0.3c = 1.3c$

that is obviously is not correct (as we know now).

B. Maxwell's equations predict and describe electromagnetic waves. Here $c$ for the first time appears as a fundamental constant, that is not connected with any reference frame. Light (EM waves) propagate in vacuum with velocity $c$ relatively to any frame. So, the answer is $c.$

Exactly this fact from electromagnetism was used by Einstein as a postulate for special relativity. In special relativity there was introduced new velocity-addition formula, that gives correct answer to A:

$v_1 = \frac{u+v}{1+\frac{uv}{c^2}} = \frac{c+0.3c}{1+\frac{0.3c^2}{c^2}}= c$.

Answer: A. 1.3c, B. c.