- #1
SlowThinker
- 474
- 65
I'm still having difficulty with the fully mathematical approach to GR (via metric and tensors), so I'm making thought experiments to get a feel for some issues.
Let's have a train moving at relativistic speed on a flat planet (so that the train goes straight). Also the gravity is supposed to be constant, say [itex]g[/itex].
The passengers set up an experiment, in which light is sent from the center of a train car horizontally forward and backward and they measure the height where it hits the walls.
There is a view which I call "stationary preferred", in which the light will be seen to fall with acceleration [itex]g[/itex] by a stationary observer. So the light will hit the back wall at nearly the original height, but it will hit the front wall a good bit lower - since it takes much more time to reach the front wall.
Another view is "passenger preferred", in which the light hits the walls nearly at the original height, same on back and front wall. It seems both views cannot be correct, and the "passenger preferred" is incorrect.
Some questions:
1. Is the "stationary preferred" view correct?
2. Does gravity create a preferred reference frame? Did I rediscover the Lens-Thirring effect?
3. If a passenger drops something, will it fall with acceleration [itex]g[/itex] as viewed by a stationary observer? This would mean that a passenger would feel her weight increased [itex]\gamma[/itex]-times. But some physicists say that the weight of objects in Einstein's train is not changed (http://arxiv.org/abs/physics/0504110 page 6).
4. I realize that objects dropped in the train will not fall perfectly vertically, since they would eventually exceed the speed of light for a stationary observer. Is there a simple way to compute the trajectory?
(4) seems to be similar to the case of a particle in a uniform electric field...
Let's have a train moving at relativistic speed on a flat planet (so that the train goes straight). Also the gravity is supposed to be constant, say [itex]g[/itex].
The passengers set up an experiment, in which light is sent from the center of a train car horizontally forward and backward and they measure the height where it hits the walls.
There is a view which I call "stationary preferred", in which the light will be seen to fall with acceleration [itex]g[/itex] by a stationary observer. So the light will hit the back wall at nearly the original height, but it will hit the front wall a good bit lower - since it takes much more time to reach the front wall.
Another view is "passenger preferred", in which the light hits the walls nearly at the original height, same on back and front wall. It seems both views cannot be correct, and the "passenger preferred" is incorrect.
Some questions:
1. Is the "stationary preferred" view correct?
2. Does gravity create a preferred reference frame? Did I rediscover the Lens-Thirring effect?
3. If a passenger drops something, will it fall with acceleration [itex]g[/itex] as viewed by a stationary observer? This would mean that a passenger would feel her weight increased [itex]\gamma[/itex]-times. But some physicists say that the weight of objects in Einstein's train is not changed (http://arxiv.org/abs/physics/0504110 page 6).
4. I realize that objects dropped in the train will not fall perfectly vertically, since they would eventually exceed the speed of light for a stationary observer. Is there a simple way to compute the trajectory?
(4) seems to be similar to the case of a particle in a uniform electric field...