Invariant Relativistic Facts

I asked this a while back and am still awaiting an answer.If a passenger shoots a narrow laser beam straight up from within a train car the laser beam hits a mark at point A. If the car is moving at constant velocity the laser as viewed by the passenger still hits the mark A--since to the passenger the car is standing still. An observer on the platform (outside the car) sees the car (and the mark A on the ceiling) has traveled a bit. Will the laser beam hit the mark A?1) If yes, then the beam must appear as traveling on an angle, i.e., the motion of car as angled the beam.2) If no, then two mutually exclusive events (hit and not hit) have occurred!!
- Mehran (age 64)
Miami (previously)

Yes, you've put your finger on it. The simple observable, whether the light hit the spot or not, must be invariant, agreed upon by everybody who can observe it and communicate about it. That's because it leaves a record, e.g. an exposed photographic plate, which all those observers can come by and check without worrying about clock times, etc. So your first description is right: the ground observer seems the beam as angling away from the vertical.

Mike W.

(published on 03/30/2015)

Now assume, from the platform bystander's view, the train is moving to the right. This requires the light beam to appear to the bystander to angle to the right in order, as you mentioned, to hit the mark A. But suppose the laser beam comes out of a flash light that is fixed perpendicular to the floor of the car. Since the light emits in the direction of the flash light axis, hence the flash light itself must appear to the bystander as being angled to the right pointing to mark A on the ceiling. If the light is off, the flashlight still must appear to the bystander as angled to right pointing to the ceiling mark A. If the flash light is replaced by a rod, it must also appear to the bystander as angled to right to the ceiling point A. Hence, we may conclude that lines perpendicular to the direction of motion angle in the direction of motion from the floor to the ceiling. However, this requires artificial designation of "floor" and "ceiling". In outer space there is no "floor" or "ceiling". We may replace the word "floor" with "source" (of light) and "ceiling" with "target" (of light). However, a rod does not have source or target; both of its ends are physics-wise symmetrical--in fact this Einstein's principle that laws of physics are the same, i.e., space is isotropic with respect to laws of physics. Hence, we must conclude that rods perpendicular to the direction of motion angle in the direction of motion and opposite it at the same time: a contradiction. Where did I go wrong?
- Mehran (age 64)
Miami (previously)

Your symmetry argument that the flashlight will not be tilted is completely correct. The argument that the beams coming out the top (and let's have one out the bottom, too) must be lined up and parallel with the flashlight and each other isn't correct.  Both those beams are angled a bit forward. They have to be, as you showed before, if things are to look right in the flashlight frame too.

Mike W.

(published on 04/04/2015)