Consider picture 1.
The most important physical issue is that the observer does not see the two events b and c simultaneous. The event c comes to late and also event B, when lightning hits the back of moving train. This event B should come earlier. This should be the point (x-1,t-1), the point d. The back of the train is then at point Y.
In Picture 1 you can see that the two lines (B to a) and (d to b) run parallel.
However, and this is important, the moving observer O2, can claim, performing exactly the same experiment, that the observations will be the same.
In this experiment there are also two mirrors, one at the front and one back end of the (moving) train. That means, observer O2, standing in the middle of the train at point O, starts with a lightsignal, which will be emitted in both directions, towards the left and right mirror. This signal will be reflected by the two mirrors and observer O2 will observe the reflections simultaneous. That means Observer O2 can also claim that he is at rest.
The issue is, that if the same experiment is performed in all different directions and with different speeds, at the utmost only one observer can claim to be at rest.
When we use the word time it is important that it can mean two different things.
The first meaning is related to the age of the universe. This time we call universal time. What we mean that the universal time at any moment, throughout the universe at any place is the same. We can also call this moment: now. This is also the present moment. We can also define a past moment, which happend before the present moment and a future moment which will happen will happen later.
It is also important to define events. As such we can define: present events, past events and future events. An event can be a collision between two stars, between two cars and a erruption of a vulcan. All events that happen at the present moment, now, are happening simultaneous. The second meaning is time measured by a clock. The importance is that every clock is physical process, or mechanical device and based on the concept of an oscillator.
The major problem is that all clocks in general are different and that the time measured (duration) in universal time, between a fixed number of oscillations, is specific. However even for identical clocks the duration can be different.
But what is more important. The time
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