# Relativity - facing backwards on a train

#### rczmiller

I am an amateur and I have a question about time and relativity. It is my understanding that Einstein theorized that time slows down for a moving object based on his thought experiment of an individual shining a light in the forward direction on a moving train. Since the speed of light is constant for the person on the train as it is for the person on the bank outside the moving train, time would slow down for the person on the train observing the light moving forward.

Here is my question: With everything else being equal, does this mean that if the person on the train was shining the light to the back of the train, that time would speed up for the observer on the train (so that the speed of light remained constant)?

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#### James R

Homework Helper
Gold Member
The observer on the train doesn't notice any strange effects at all inside the train. Light travels with the normal speed in either direction.

A person viewing the inside of the train while standing still on the tracks will see time slowed inside the train, regardless of which direction the light is shining.

no. $$t'=\frac{t}{\sqrt{1-\frac{v^2}{c^2}}}$$

the velocity term is squared, so negative velocity doesn't change dilation

#### JesseM

To understand how both observers measure light moving at the same speed relative to themselves, you have to know not just about time dilation, but also about length contraction and about the fact that the two observers define "simultaneity" differently (for example, if an observer in a middle of a train car sends light beams out in both directions, in his the beams hit either end of the car 'at the same time', but in the frame of an observer on the track, the beam moving backwards hits the back end of the car before the beam moving forwards hits the front end). You may want to take a look at this thread where some similar issues were discussed.

#### rczmiller

Thanks for the posts!

JesseM said:
To understand how both observers measure light moving at the same speed relative to themselves, you have to know not just about time dilation, but also about length contraction and about the fact that the two observers define "simultaneity" differently (for example, if an observer in a middle of a train car sends light beams out in both directions, in his the beams hit either end of the car 'at the same time', but in the frame of an observer on the track, the beam moving backwards hits the back end of the car before the beam moving forwards hits the front end). You may want to take a look at this thread where some similar issues were discussed.
JesseM - Thanks for the reference thread. I have read this and I am still confused. This thead uses a box with lightbulbs on either end set to flash at the same time (Noon) and the question was do these flashes reach the middle of the box at the same time. The answer that I pulled out this was that the flashes do hit the middle at the same time, but even though the observer inside the box sees the clocks as being synced, an outside observer (an observer seeing the box as in motion) will see the back clock ahead of the front clock. This would mean that the outside observer would see the back lightbulb flash prior to the lightbulb in the front. This would allow the 2 flashes to reach the middle of the box at the same time.

Even though the inside observer sees no time warping, as the box's velocity is increased, an outside observer would see time traveling slower in the front part of the box and speeding up in the back part of the box inorder to allow this experiment to continue with the same results.

Is this correct?

#### Doc Al

Mentor
rczmiller said:
Even though the inside observer sees no time warping, as the box's velocity is increased, an outside observer would see time traveling slower in the front part of the box and speeding up in the back part of the box inorder to allow this experiment to continue with the same results.

Is this correct?
No. The outside observer would measure all clocks used by the inside observers (whether at the front or back of the train) to be running uniformly slowly. The outside observer will also measure the clocks at the front and rear of the train to be out of synch.

#### JesseM

rczmiller said:
Even though the inside observer sees no time warping, as the box's velocity is increased, an outside observer would see time traveling slower in the front part of the box and speeding up in the back part of the box inorder to allow this experiment to continue with the same results.
No, unlike time dilation and length contraction, the clocks-being-out-of-sync effect is not something that just happens "naturally" when you increase the velocity, it's a consequence of how each inertial observer synchronizes their clocks using the procedure described by Einstein involving light-signals. If the box accelerates, then acheives a new constant velocity, and then the observer in the box resets the clocks at both ends using Einstein's procedure, then as a consequence we will see the clock in the front behind the clock in the back by an even larger amount, but both clocks will tick at the same slowed-down rate in our frame.

#### rczmiller

If the inside observer has to reset the clocks, wouldn't he conclude that he was already traveling is a certain direction prior to his acceloration?

#### Doc Al

Mentor
rczmiller said:
If the inside observer has to reset the clocks, wouldn't he conclude that he was already traveling is a certain direction prior to his acceloration?
This is where things get a bit tricky in this thought experiment.

Whether or not the observers in the train have to reset their clocks depends on how they were accelerated. If the train is accelerated in such a way that each piece of the train is simultaneously accelerated according to the outside observers, then the train observers will find that their clocks are no longer synchronized. (Realize that to the observers on the train this means that parts of the train were accelerated at different times. The train will most likely be ripped apart.)

On the other hand, if the train is accelerated in such a way that each section of train is simultaneously accelerated according to the observers on the train, then they will not have to reset their clocks. (Imagine the acceleration taking place in little bursts along the length of the train. Each set of simultaneous bursts--simultaneous according to the train observers!-- gives the train a little more speed.) But realize that according to the outside observers, this means that different parts of the train accelerated at different times, so they will measure the train clocks to be out of synch.

#### rczmiller

Thank you, thank you, thank you. All of these post have given me a lot to think about.

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