I just saw the Einstein's thought experiment about train

Question

In the experiment, two lightning bolts strike at the same time and the stationary observer at the train sees the lightning simultaneously but the one in the middle of the train station would see at different times because the light has to travel more in one direction and less in the other. My question is: does the observer in the moving train experience the lighting for more time as the time slows down for a moving object? So the stationary observer at the station will experience it for $t$ seconds but the observer on the train will experience it for more than $t$ seconds. Please explain if this is correct and if not then why.

Answer 1

At the risk of making the experiment sound more complicated, there are two considerations here. The first is that the local duration of a flash is frame dependent. In a frame in which the flash occurs in one spot, the duration is less than the duration in another frame in which the flash is moving. (Note that while you might think a flash of lightning is instantaneous, the individual flashes last tens of microseconds, during which time light can travel a few miles.) In the example you give, I assume the lightning flashes are stationary in the Earth frame, so they would be moving relative to the train, so the duration of the flashes would be slightly longer in the frame of the train, which is just the usual time dilation effect.

However, if you are asking how long the flash would seem to last to an observer some distance from it, you need to take into account the relativistic Doppler effect, which would blue-shift, or shorten, the flash that the observer was heading toward, and red-shift, or lengthen, the flash that the observer was heading away from.

Answer 2

Does the observer in the moving train experience the lighting for more time as the time slows down for a moving object?

If by the "time experiencing the lightning" we understand the time elapsed since the strike until both pulses are absorbed by the detectors at the front and at the end of the train, then no, quite the opposite.

If the train has length $L$, then for the observer inside the train both rays take a time $t'=L/2c$ to get to the detectors.

For the observer outside in the station, the pulse that goes to the back of the train arrives before the one going to the front part. So this observer will continue to see light until the pulse arrives at the front of the train. This happens after a time

$$t_{\rm front}=\frac{L\sqrt{1-v^2/c^2}}{2(c-v)}$$

as measured by the observer in the station. This can be obtained via the inverse Lorentz boost

$$t=\gamma\left(t'+\frac{vx'}{c^2}\right)$$

with $x'=L/2$ and $t'=L/2c$.

One can check that $t_{\rm front}>t'_{\rm front}=L/2c$, i.e., the pulse going to the front of the train takes more time to arrive for the observer at the station.

Answer 3

As per Theory of Relativity time spans can be different for different observers. You may experience only 1 year while travelling at some speed near the speed of light while your buddy at home experience 7 years say.

That ratio ofcourse can be varied. At speed even nearer to speed of light the ratio can be increased to say 80. 1 year for you, 80 years for your buddy.

The key here is time span. Your clock will tick slower, water boil slower, you will have only two wheat crops etc.

In the Einstein's thought experiment, the lightning strike is supposed to be instantaneous. Einstein build his theory on that thought experiment so he couldn't talk about time spans there. That would trap him in an infinitely recursive need of explanations.

Real lightning strikes ofcourse are not instantenous. They are spread in time i.e. have time spans. Therefore any moving observer will experience it for smaller period of time.

All this is as per Theory of Relativity which assume constant speed of light and therefore speed limit for everything. Its proved wrong by observation of galaxies moving away faster than speed of light.