A big confusion regarding to the 2 thought experiments of Relativity of Simultaneity leading to other confusions

I will just present my arguments because the correct arguments would be known facts.

So in the experiment where a flash of light is given off at the center of a moving train just as the 2 observers pass each other ( one observer is standing at the midpoint of the train and the other observer on the platform), the platform observer sees the rear end of the train moving towards the flash of light and front end moving away from the speed of light. As the speed of light is constant and light has to move considerably a less distance to meet the rear end , the ground observer says that the flash of light reaches the rear end first and then reaches the front end. But the train observer is at rest with respect to train and the distance between the front end and him and rear end and him is the same. Also the speed of light is the same in his frame and hence he says the light flashes reach the rear and the front end at the exactly the same time ( this point is crucial).

Now taking the other experiment in which the flashes of light hit the ends of the train and the platform just as the 2 observers (1 at the middle of the train and the 2nd at the centre of the platform). The platform observer sees the light flashes at the same time because the flashes travel at the same speed the same distance (Important point in this ground frame discussion , as I think is that the ground observer is at rest w.r.t to the ground and hence sees the flashes at the same time). But since the train observer is moving towards the front end and away from the rear end , he sees the light flash from the front end first (this is the argument followed). But in the frame of of the train , the train observer is at rest (just as the ground observer is at rest w.r.t to the ground and the train observer was at rest w.r.t to the train in previous example). So since in the frame of the train the train observer is at rest and the distance between the front end and him and rear end and him is the same and the speed of light is the same in his frame , he should say that the flashes of light reach him at the same time (just as he had said in the previous example ).

He should say that the flashes reach him at the same time (case is exactly similar to the previous case of train observer. In both the cases he is at rest w.r.t ti the train ).

So, as far as I think:

1)The ground observer should say -"According to me I see the flashes at the same time but the train observer should see the flashes at different times." 2)And the train observer should say that " I see the flashes at the same time but the ground observer shouldn't. "

So the ground observer should say that the flashes are seen by the train observer at different times but the train observer says that he sees the flashes at the same time.

So why and where I am wrong ? I must be missing some ridiculously simple fact ? I am sorry if it's too ridiculous a question but I am missing some simple fact and unable to find it.

Also following from the 2nd experiment and lines below it in bold (my conclusions) , I say that that if the ground observer measures time on his clock to be Ta and predicts that time on train observer's clock to be $T_{ab}$, then he would say $T_{ab}>T_a$ (This should be time dilation. $T_{ab}$ is precisely calculated using Lorentz transformations). But the train observer would measure time in his frame to be $T_b$ and this $T_b$ should be equal to $T_a$.

So time dilation (similar arguments fir length contraction) should be that the ground observer should say " according to me a certain amount of time has passed in my frame but according to me the time passed in the train observer's frame should be more than that passed in my own frame (for the same 2 events that occurred in my and in his frame). But the train observer would maintain to say that i experienced exactly the same time in my frame as is experienced by the ground frame observer in his own frame , but it is the ground observer that according to me has measured a greater time.

In a nutshell I am saying that both the observer's experience the same time in their own frames (no time dilation in their own frame w.r.t to they themselves) but according to them the other one should experience a longer time interval ( time dilation ).

Is this reasoning wrong and if so where ?

Forgive me if my arguments are ridiculously silly because I am a beginner to Relativity !!

• Aren't you missing that the platform moves backwards in the reference frame of the train? – Prof. Legolasov Sep 20 '16 at 11:15
• @SolenodonParadoxus No I am not missing that fact. Infact the train observer will say that the ground observer didn't see the flashes together because to him the ground moves backwards. – Shashaank Sep 20 '16 at 11:37
• It is a bit strange for one observer to hypothesize what would another observer say. Suppose both observers make observations. The observer in the train sees two events occurring one after another, and the ground observer sees them simultaneously. The situation is an exact opposite of the (commonly known) thought experiment, you just have to replace the train and the platform. Or is this not what you are asking? – Prof. Legolasov Sep 20 '16 at 11:45
• @SolenodonParadoxus No , I am saying that the train observer should say that the flashes reach him at the same time because he is at rest in his train frame . Since he is at rest in his frame , to him the flashes should reach at the same time. It is exactly similar to the 1st experiment where the flash of light is given off at center of a MOVING train and the train observer said that the flashes reached the ends at the same time. This time the flashes start from the end and will obviously reach the center at same time because the observer is at rest in train – Shashaank Sep 20 '16 at 11:53
• That is if the flashes happen simultaneously, yes. But in this case they happen one at a time in the ground observer reference frame, so the ground observer sees them one at a time (not because something moves towards or against the light beam, but simply because of the relativity of simultaneity). – Prof. Legolasov Sep 20 '16 at 12:20

Lets start with the ground observer. Suppose that in his reference frame, the two flashes happen simultaneously. The light beams approach him from both sides with the same speed, so he sees the flashes happen at the same time.

But the train is moving, and so the ground observer sees that the first beam reaches the person in the middle of the wagon before the second.

Now consider the train observer. Because we have already presupposed that the two flashes happen simultaneously at the ground reference frame, by the relativity of simultaneity they happen one by one in the train frame. So despite the fact that the light still approaches the observer with the same speed from both sides, the train observer does see them consequently simply because they do happen consequently, and the ground observer is not mistaken.

The same thing happens if we suppose that both flashes happen simultaneously in the train reference system, but in this case you have to exchange the two observers.

Thus Special Relativity triumphs once again to survive another day until another young enthusiast questions its self-consistency :)

• I got everything till the point "by the Relativity of Simultaneity they happen one by one in the train frame ." But why due Relativity of simultaneity they happen one by one ( probably this is where I am not getting the reasoning and this is the point of confusion ). Do you mean that the train observer sees the flashes together but still they don't occur simultaneously in his frame. I was just thinking that he should see them simultaneously because he is at rest (refer to the 1st thought experiment in which the train observer sees the flashes hit the ends of the moving train simultaneously... – Shashaank Sep 20 '16 at 13:00
• Simultaneity of events is relative. If one frame they happen at the same time, it is not true for another frame. This is a well-known consequence of special relativity. Actually, the thought experiment that you described proves the relativity of simultaneity, cause otherwise the two observers wont agree. – Prof. Legolasov Sep 20 '16 at 13:03
• So am I wrong in saying that the flashes reach the train observer simultaneously according him ? – Shashaank Sep 20 '16 at 13:19
• @Shashaank Yes. They reach the observer sequentially because the flashes happen sequentially. – Prof. Legolasov Sep 20 '16 at 13:38
• Oh ok , they reach sequentially since they happen sequentially. I think , I got it. Your last comment made it clear. – Shashaank Sep 20 '16 at 13:54

The key to understanding time dilation lies in the idea that acceleration/deceleration is not relative, while velocity/momentum is relative. I didn't read your whole post but i can almost guarantee this is the confusion you're having.

• But I haven't talked about acceleration anywhere in the entire question. The train has a constant velocity only – Shashaank Sep 20 '16 at 13:56
• Ok sorry, your question seems to be ridiculously over complicated it's kind of hard for me to follow. A flash in the middle of the train will reach both people at the same time from the perspective of the laser. From the perspective of each person on the train it will reach them first because light has to travel from the other person back to them. From the person on station it depends on where the travelers are located relative to him and which light reaches him first. It's simple math and geometry. – Yogi DMT Sep 20 '16 at 14:27
• I think you didn't get the question. Please read the question again and @ SolenodonParadoxus answer. – Shashaank Sep 20 '16 at 14:34
• I mean it's the same thing i just said with different semantics. The reason the stationary observer sees the light reaching the back on the train first is because the back of the train is closer to him than the front, less distance = quicker for light to travel. The only way he sees the what the train passenger sees is if he observes the lights hitting the front and the back of the train at the same time he is equidistant from those locations. Anything else will be skewed one way or the other because the distance the light from the front and back has to travel will be different. – Yogi DMT Sep 20 '16 at 15:16