 Train thought experiment 

This is about Einstein's famous 'train thought experiment' ('Gedankenexperiment') proving Relativity of Simultaneity. It is not part of Einstein's original 1905 paper where relativity of simultaneity is explained mathematically (which I treat here).
I really love this train experiment. It shows Einstein's genius. Simple, easy exercise. Big consequences. But beware! At first sight this experiment looks an easy piece of cake, but it demands rather sharp thinking to grasp the essence. Some people (especially ether fanatics) never do. In the video the crucial words are said at 1:23 min.: "If she sees the front strike first, it actually happened first!" 
The text you find on the Youtube page (the written out text of what's been said in the video) is fine. Proof of it I copy it here, although there are a few little but crucial typing errors (but correctly said in the video) that I correct between square brackets. The blue text (crucial for understanding the experiment!) is not said in the video, but was added by the author in the text!
<< Imagine two observers, one seated in the center of a speeding train car, and another standing on the platform as the train races by. As the center of the car passes the observer on the platform, he sees two bolts of lightning strike the car  one on the front, and one on the rear. The flashes of light from each strike reach him at the same time, so he concludes that the bolts were simultaneous, since he knows that the light from both strikes traveled the same distance at the same speed, the speed of light. He also predicts that his friend on the train will notice the front strike before the rear strike, because from her [edit: his] perspective on the platform the train is moving to meet the flash from the front, and moving away from the flash from the rear.
But what does the passenger see? As her friend on the platform predicted, the passenger does notice the flash from the front before the flash from the rear. But her conclusion is very different. As Einstein showed, the speed of the flashes as measured in the reference frame of the train must also be the speed of light. So, because each light pulse travels the same distance from each end of the train to the passenger, and because both pulses must move at the same speed, he [edit: she] can only conclude one thing: if he [edit: she] sees the front strike first, it actually happened first ... for her (my addition).
Whose interpretation is correct? The observer on the platform, who claims that the strikes happened simultaneously, or the observer on the train, who claims that the front strike happened before the rear strike? Einstein tells us that both are correct, within their own frame of reference. This is a fundamental result of special relativity: From different reference frames, there can never be agreement on the simultaneity of events. >>
<< Imagine two observers, one seated in the center of a speeding train car, and another standing on the platform as the train races by. As the center of the car passes the observer on the platform, he sees two bolts of lightning strike the car  one on the front, and one on the rear. The flashes of light from each strike reach him at the same time, so he concludes that the bolts were simultaneous, since he knows that the light from both strikes traveled the same distance at the same speed, the speed of light. He also predicts that his friend on the train will notice the front strike before the rear strike, because from her [edit: his] perspective on the platform the train is moving to meet the flash from the front, and moving away from the flash from the rear.
But what does the passenger see? As her friend on the platform predicted, the passenger does notice the flash from the front before the flash from the rear. But her conclusion is very different. As Einstein showed, the speed of the flashes as measured in the reference frame of the train must also be the speed of light. So, because each light pulse travels the same distance from each end of the train to the passenger, and because both pulses must move at the same speed, he [edit: she] can only conclude one thing: if he [edit: she] sees the front strike first, it actually happened first ... for her (my addition).
Whose interpretation is correct? The observer on the platform, who claims that the strikes happened simultaneously, or the observer on the train, who claims that the front strike happened before the rear strike? Einstein tells us that both are correct, within their own frame of reference. This is a fundamental result of special relativity: From different reference frames, there can never be agreement on the simultaneity of events. >>
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Let me elaborate on this a bit.
Sketch A.
The lady passenger is blue, her friend on the platform is green.
As seen from the platfrom.
Light from the front flash reaches blue passenger first. A few moments later both light beams are at the platform observer. And a split second later the light from the rear light beam reaches the blue passenger. Does this mean that for the passenger the two flashes didn't happen simultaneously?
Why is it that BECAUSE the light beams do not reach the passenger at one and the same moment in time, it follows that for the passenger both flashes did not HAPPEN simultaneously?
Maybe she only sees the events not happening simultaneously (because she is moving and therefore the distance the rear light beam has to cover to reach her is longer than the distance the front light beam has to cover? In other words: maybe the light beams reach the passenger at different times, but for the passenger both light beams left at the same time (as shown in sketch A)?
Wrong! To find out what happens in green passenger's reality we have to consider her train immobile and the platform moving:
Sketch B.
As seen from the train.
Speed of light is the same for green and blue observer.
If the two flashes would happen simultaneously for the passenger when she crosses the platform observer (i.e. when she is halfway between the two flashes), then relative to her (and the train) the distances both lightbeams have to cover to reach her are equal. And because the speed of both light beams are equal (=light speed), the two lightbeams should reach her at the same time (the light beams cover equal distances in equal times). But ... it doesn't happen that way (sketch B is wrong), because we know (sketch A) that the two light beams do not reach the passenger simultaneously (the arrival of the rear and front beams are two different events that can not be replaced by one event only in another reference frame), which means that for the passenger the two flashes did not happen simultaneously.
When the passenger crosses the platform observer both flashes happen for the platform observer, but for the passenger the front flash already happened, the rear flash not yet. In this exercise you can apply some abstract mathematical coordinate calculations, but for the thought experiment proper wristwatch time indications will suffice. In other words: for the passenger there is some proper passenger's wristwatch time ticking (a sequence of successive proper wristwatch time indication events) between the two flashes occuring, whereas for the platform observer the two flashes happen at one and the same platform observer's wristwatch time indication.
Sketch C
Sketch C shows what happens for the passenger. First lightning hits the front of the train, and only a few moments later (physically real time ticking on the passenger's wristwatch) lightning hits the rear of the train!
After going through my 'Relativity for Dummies' tutorial you should have no problems reading my Sketch D: a (Minkowski) 4D spacetime diagram (for dummies: to be read from bottom up!) with horizontal green lines representing the platform's worlds of simultaneous events. The blue oblique lines represent the passenger's worlds of simultaneous events.
Sketch E shows the same scenario in a Loedel diagram, in which all unit lengths are calibrated (which makes it easier to read time dilation and length contraction, but of no importance in Einstein's thought experiment). What's important here is: different green and blue 3D worlds cut through one and the same total 4D Spacetime (Block Universe). If you keep that in mind next time you face a Special Relativity topic, nothing can go wrong. Trust me ;)
Let me elaborate on this a bit.
Sketch A.
The lady passenger is blue, her friend on the platform is green.
As seen from the platfrom.
Light from the front flash reaches blue passenger first. A few moments later both light beams are at the platform observer. And a split second later the light from the rear light beam reaches the blue passenger. Does this mean that for the passenger the two flashes didn't happen simultaneously?
Why is it that BECAUSE the light beams do not reach the passenger at one and the same moment in time, it follows that for the passenger both flashes did not HAPPEN simultaneously?
Maybe she only sees the events not happening simultaneously (because she is moving and therefore the distance the rear light beam has to cover to reach her is longer than the distance the front light beam has to cover? In other words: maybe the light beams reach the passenger at different times, but for the passenger both light beams left at the same time (as shown in sketch A)?
Wrong! To find out what happens in green passenger's reality we have to consider her train immobile and the platform moving:
Sketch B.
As seen from the train.
Speed of light is the same for green and blue observer.
If the two flashes would happen simultaneously for the passenger when she crosses the platform observer (i.e. when she is halfway between the two flashes), then relative to her (and the train) the distances both lightbeams have to cover to reach her are equal. And because the speed of both light beams are equal (=light speed), the two lightbeams should reach her at the same time (the light beams cover equal distances in equal times). But ... it doesn't happen that way (sketch B is wrong), because we know (sketch A) that the two light beams do not reach the passenger simultaneously (the arrival of the rear and front beams are two different events that can not be replaced by one event only in another reference frame), which means that for the passenger the two flashes did not happen simultaneously.
When the passenger crosses the platform observer both flashes happen for the platform observer, but for the passenger the front flash already happened, the rear flash not yet. In this exercise you can apply some abstract mathematical coordinate calculations, but for the thought experiment proper wristwatch time indications will suffice. In other words: for the passenger there is some proper passenger's wristwatch time ticking (a sequence of successive proper wristwatch time indication events) between the two flashes occuring, whereas for the platform observer the two flashes happen at one and the same platform observer's wristwatch time indication.
Sketch C
Sketch C shows what happens for the passenger. First lightning hits the front of the train, and only a few moments later (physically real time ticking on the passenger's wristwatch) lightning hits the rear of the train!
After going through my 'Relativity for Dummies' tutorial you should have no problems reading my Sketch D: a (Minkowski) 4D spacetime diagram (for dummies: to be read from bottom up!) with horizontal green lines representing the platform's worlds of simultaneous events. The blue oblique lines represent the passenger's worlds of simultaneous events.
Sketch E shows the same scenario in a Loedel diagram, in which all unit lengths are calibrated (which makes it easier to read time dilation and length contraction, but of no importance in Einstein's thought experiment). What's important here is: different green and blue 3D worlds cut through one and the same total 4D Spacetime (Block Universe). If you keep that in mind next time you face a Special Relativity topic, nothing can go wrong. Trust me ;)

Events
A and B are the lightning flashes. Simultaneous for Mr Green.
Not simultaneous for Mr Blue.
Are the clock time indications only mathematical data with no real significance in reality? Is Mr Green's clock time indication real, but Mr Blue's clock time only fictitious? Do the clock time indications only 'appear' to be 9 and 11? No. Green and Blue time are all physically real clock time indications! For the man on the platform (Mr Green in the sketch) the two lightning events occur when his wristwatch indicates one specific physical time, one event. Say the two events happen when the hand on his (old classic) wristwatch points to 10. Physically real proper time indication.
For Mr Blue lightning B is simultaneous with his wristwatch at 9 o'clock, whereas flash A occurs simultaneous with his wristwatch showing 11 o'clock. Wristwatch 9 and later wristwatch 11. Two different physically real events. And between those two events proper wristwatch time indications tick away (meaning between those two events there are other Blue events of time ticks). For Mr Green on the platform the two flashes happen simultaneous with one Green clock time event only.
Mr Blue's time coordinates are of course different from Mr Green's time coordinates. It tells them that for Mr Green no proper (real green wristwatch) time ticks on his wristwatch between the happening of the flashes: both flash events happen in one green 3D world only. For Mr Blue some physically real proper (real Blue wristwatch) time indication events tick away between the two flash events. For Mr Blue the flash events happen in different physically real 3D worlds. All 3D worlds are sections through one and the same 4D Block Spacetime Universe.
Are the clock time indications only mathematical data with no real significance in reality? Is Mr Green's clock time indication real, but Mr Blue's clock time only fictitious? Do the clock time indications only 'appear' to be 9 and 11? No. Green and Blue time are all physically real clock time indications! For the man on the platform (Mr Green in the sketch) the two lightning events occur when his wristwatch indicates one specific physical time, one event. Say the two events happen when the hand on his (old classic) wristwatch points to 10. Physically real proper time indication.
For Mr Blue lightning B is simultaneous with his wristwatch at 9 o'clock, whereas flash A occurs simultaneous with his wristwatch showing 11 o'clock. Wristwatch 9 and later wristwatch 11. Two different physically real events. And between those two events proper wristwatch time indications tick away (meaning between those two events there are other Blue events of time ticks). For Mr Green on the platform the two flashes happen simultaneous with one Green clock time event only.
Mr Blue's time coordinates are of course different from Mr Green's time coordinates. It tells them that for Mr Green no proper (real green wristwatch) time ticks on his wristwatch between the happening of the flashes: both flash events happen in one green 3D world only. For Mr Blue some physically real proper (real Blue wristwatch) time indication events tick away between the two flash events. For Mr Blue the flash events happen in different physically real 3D worlds. All 3D worlds are sections through one and the same 4D Block Spacetime Universe.
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Click here for my own Relativity of Simultaneity visualization.
Click here for a simular but not identical Relativity of Simultaneity case.
Click here for an analysis of the train thought experiment that got it all wrong. The author seems to understand the essence of the train thought experiment, but at the bottom of page 2 when he jumps frames he proves he doesn't. His statement, quote: <<Mike would als deduce that flash B must have occurred first given thet he knows that he is the one in motion. He saw them at the same time at a place closer to A than B and so deduces that B must have occurred earlier as it has had further to travel >> is totally absurd knowing the setup of the exercise starts with two flashes occurring simultaneously for Mike. The author doesn't understand the meaning of different reference frames. He guesses that in Nina's frame of reference, i.e. based on the two flashes not occurring simultaneously in her frame, Mike agrees the two flashes do not occur simultaneously. It's wrong. Mike does not agree. For him both flashes do occur simultaneously: for him both flashes occur simultaneously when he is in front of Nina, and both light signals reach him simultaneously. Unfortunately, if Nina does not know the facts of the setup of the exercise, she will never be able to deduce relativity of simultaneity from what she experiences in her frame. That's the reason why Einstein starts with both flashes occuring simultaneously for Mike as a given.
Click here for my own Relativity of Simultaneity visualization.
Click here for a simular but not identical Relativity of Simultaneity case.
Click here for an analysis of the train thought experiment that got it all wrong. The author seems to understand the essence of the train thought experiment, but at the bottom of page 2 when he jumps frames he proves he doesn't. His statement, quote: <<Mike would als deduce that flash B must have occurred first given thet he knows that he is the one in motion. He saw them at the same time at a place closer to A than B and so deduces that B must have occurred earlier as it has had further to travel >> is totally absurd knowing the setup of the exercise starts with two flashes occurring simultaneously for Mike. The author doesn't understand the meaning of different reference frames. He guesses that in Nina's frame of reference, i.e. based on the two flashes not occurring simultaneously in her frame, Mike agrees the two flashes do not occur simultaneously. It's wrong. Mike does not agree. For him both flashes do occur simultaneously: for him both flashes occur simultaneously when he is in front of Nina, and both light signals reach him simultaneously. Unfortunately, if Nina does not know the facts of the setup of the exercise, she will never be able to deduce relativity of simultaneity from what she experiences in her frame. That's the reason why Einstein starts with both flashes occuring simultaneously for Mike as a given.