grav

2009-Jan-08, 11:24 PM

I have a dilemma, mentioned here (http://www.bautforum.com/questions-answers/83164-simple-relativity-question-2.html#post1404895). Here is the first part of it. Observers are positioned stationary every few hundred meters within a very, very long tunnel. One observer in the center of the tunnel then instantly accelerates to some relative speed toward one end. Due to the new relative speed, the length of the tunnel is now contracted to the observer and the distance between all of the stationary observers has contracted according to the moving observer as well. The moving observer also measures all of the stationary observers travelling past him at the same relative speed regardless of distance. Light coming from stationary observers behind him is all redshifted by the same amount regardless of the distance of the source and light coming from stationary observers in front of him is all blueshifted by the same amount regardless of distance.

Okay, so now, instead of an instant acceleration to v, let's just give our observer a constant acceleration toward one end of the tunnel. As the observer's relative speed to the rest frame increases, contraction of the tunnel takes place. Since the entire length steadily contracts, that means that our observer will see the stationary observers pull closer to him in front and in back at a rate that is proportional to the distance. He will see stationary observers at some distance to the front and back pulling closer to him at some rate due to the contraction while stationary observers at twice the distance pull closer at nearly twice the rate, only limited by the speed of light at the greatest distances. So from his point of view, minus the local relative speed between himself and the tunnel, all stationary observers are moving toward him with a relative speed which increases with distance from him as he accelerates.

First of all, is my scenario correct? If so, what happens when he simply turns off his engines and ceases to accelerate? Shouldn't all stationary observers which are now moving toward him from front and back with relative speeds that increase with distance continue to move toward him inertially at those same speeds? Or would turning off the engines somehow affect space-time since he is no longer accelerating and space-time contracting, so that the stationary observers suddenly stop travelling toward him except for the local relative speed to the tunnel which continues to persist, now all along the length?

Okay, so now, instead of an instant acceleration to v, let's just give our observer a constant acceleration toward one end of the tunnel. As the observer's relative speed to the rest frame increases, contraction of the tunnel takes place. Since the entire length steadily contracts, that means that our observer will see the stationary observers pull closer to him in front and in back at a rate that is proportional to the distance. He will see stationary observers at some distance to the front and back pulling closer to him at some rate due to the contraction while stationary observers at twice the distance pull closer at nearly twice the rate, only limited by the speed of light at the greatest distances. So from his point of view, minus the local relative speed between himself and the tunnel, all stationary observers are moving toward him with a relative speed which increases with distance from him as he accelerates.

First of all, is my scenario correct? If so, what happens when he simply turns off his engines and ceases to accelerate? Shouldn't all stationary observers which are now moving toward him from front and back with relative speeds that increase with distance continue to move toward him inertially at those same speeds? Or would turning off the engines somehow affect space-time since he is no longer accelerating and space-time contracting, so that the stationary observers suddenly stop travelling toward him except for the local relative speed to the tunnel which continues to persist, now all along the length?