S11. Simultaneity

" From different reference frame there can never be an agreement on the simultaneity of events.."

The concept of events happening at the same time is called the “simultaneous events”.  In Newtonian physics there was a notion of the universal time, and hence simultaneous events  in all inertial frame was a consequences of such assumption. In simple words, observers in all reference frame would agree on particular events irrespective of their motion. However, as we have seen that from the postulate of special relativity that the concept of time is relative one, we would thus expect the need for the revision of the concept of simultaneity.

As you can guess from the equations for the Lorentz transformation, the concept of time becomes a relative concept since we no longer have the simple relation $t=t'$. What we actually mean here is that the concept of simultaneity will depend on which frame you are in. This is a simple consequence of the fact that the speed of light is the same no matter which inertial frame you are in.

Consider a moving train at speed close to speed of light $c$.Imagine a long platform with an observer located at its midpoint. At either end, at the places marked $A$ and $B$, there are two momentary lightning flashes. The light propagates from these events to the observer. Noticing that they arrive at the same moment as they come from places of equal distances away, the observer will decide that the two events happened simultaneously.

However, from the point of view of the person on the train, the front of the train is moving towards the lightning  coming from the point $B$, while the back of the train moves away from the point of the lightning flash point $A$. This means that the distance covered by light coming from point $B$ will be shorter than the light coming from the point $A$. And since the speed of light is $c$ in both directions for the observer on the train too, the light will reach the front of the train before it reaches the back of the train. Hence, the observer on the train will claim the two events were not simultaneous events.

In short, Simultaneity is the property of two events happening at the same time in a frame of reference. According to Einstein's Theory of Relativity, simultaneity is not an absolute property between events; what is simultaneous in one frame of reference will not necessarily be simultaneous in another. For inertial frames moving at speeds small compared to the speed of light with respect to one another this effect is small and can for practical matters be ignored such that simultaneity can be treated as an absolute property.

A short video on the simultaneity can be found here.