The tilted beam is a great counterexample. However, even if the assumption of a tilted flashlight is not made, and even if the person in the elevator has full knowledge that the beam was launched horizontally in the lab, the only thing that could be measured is the relative motion of the elevator versus the lab. The lab could equally well be moving downward relative to the elevator. None of this is a violation of Special Relativity because absolute motion is in no way being detected. The tilted beam in SR is analogous to being unable to tell if a car is accelerating or simply parked on a hill in GR. Locally, one cannot tell the difference.
Bob at PC
________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of John Denker
Sent: Tue 3/25/2008 1:39 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Relativistic elevator
If it is then the situation must be
equivalent to "looking outside".
Yes.
1) The shallow answer is that "looking outside" always means "looking
at light rays that came from outside". But I think the intent of
the question is deeper than that.
2a) To really understand the physics requires emphasizing the part
that states the beam is *horizontal* in the lab frame. That is,
the slope of the beam in the elevator frame tells you the velocity
relative to the frame where there was no slope. For you (the
elevator rider) to know that the beam was horizontal in the lab
frame requires rather detailed "looking outside".
2b) This is crucial because if you confine your attention to the
inside of the elevator, if you see a sloping beam you could perfectly
well attribute it to a source who is comoving with the elevator and
just holding the flashlight at an angle. This scenario (2b) would
tell you nothing about your velocity relative to the lab frame.