# Q & A: light in different frames

Q:
Question regarding special relativity. If you were on earth and switched on a laser pointing into space, that light would travel at rate c, and the leading edge of the beam could be calculated as to how far away it is from earth. After the laser is switched on, a person leaves Earth in a spacecraft parallel to the laser beam. The spacecraft quickly accelerates to 99.9% speed of light. Would the person in the spacecraft see the leading edge of the laser beam continue to get further away from him, at rate c? From Earth, the position of the spacecraft and the leading edge of the laser beam would be nearly static though? I understand (sort of) that time would change on the spacecraft to allow for the beam to appear to be moving at rate c, but from earth it wouldn't so wouldn't this really be an illusion? I don't understand how the spacecraft can appear in two places at the same time, from different observation points (the spacecraft and earth).
- Jason (age 42)
Indianapolis, IN, USA
A:

Your questions are very nice and right along the lines people wonder about when they first see Special Relativity. The rules for translating the space-time coordinates from one reference frame to another turn out to be different from the ones we intuitively assume. There are many good little books introducing SR, including one by Einstein and one by Jim Smith.

"Would the person in the spacecraft see the leading edge of the laser beam continue to get further away from him, at rate c? "  Yes.

"wouldn't this really be an illusion?" Which would be an illusion: the rate at which the beam leads the ship according to Earth (0.01c) or according to the ship  (c) ?

" I don't understand how the spacecraft can appear in two places at the same time..." Same time according to whom? Each viewpoint has the ship at one place at any time.