The Relativity of Simultaneity
Hello Friends,In this section we will get to know about the relativity simultaneity.But before going to that let me ask you a very simple question that what is simultaneity? May be you find yourself unable to express your feelings. Ok... then to make it a little easier for you, I ask you another question. If I say there are two lightning strokes at Points A and B simultaneously, then is it there any sense in the statement? It is very definite that that you will answer it with a yes. Now to be a bit more precise if I ask you the sense in the statement you find yourself in trouble while explaining.Then let me help you a bit.For arriving at the definition of simultaneity we will use the concept of Light's speed being constant.So if an observer stands in the mid of the line joining A and B then he observes the two events occurring at the same time i.e. simultaneously.
Up to now, our considerations have been referred to a particular body of reference, which we have styled a 'railway embankment'. We suppose a very long thin train travelling along the rails with the constant velocity V. People in this train have the advantage of using this train as the rigid reference system and they can regard all the events with respect to this coordinate system.Here comes our old question back but with a different approach.Are the events simultaneous with respect to the embankment also simultaneous with respect to the carriage? The very obvious answer that comes is a clear 'No'.
When we say that the lightning strokes A and B are simultaneous, we mean that the ray of light reaches the midpoint of A and B simultaneously.Let M' be the point on train corresponding to the point M on the embankment.Let the train starts moving with moving velocity V towards point B.Hence the observer sitting at the middle of the train see light from B coming early that light from A.
Thus we arrive at an important result that the event simultaneous with respect to the embankment is not simultaneous with respect to the train.Now Before the advent of the Theory of Relativity it had been assumed that the time is independent of the state of motion of body of reference.But then this thing with corresponds to 'The Theorem of addition of velocities' and we have just seen in the above case that this is incompatible with the the thing that if a body transverses uniform straight line motion with respect to an inertial frame then the uniformly moving body can also be considered inertial frame and all the observations and laws are same for it as for the inertial frame.If we discard the assumption of independency of time with respect to state of motion of body of reference frame then the apparent incompatibility between The Theory of Relativity and The Law of propagation of light in vacuum disappears.
We led to this conflict by the considerations of 'The Theorem of addition of velocities', which we no longer be tenable.In that section we led to the conclusion that walking man in the carriage transverses equal distance in equal time with respect to both the embankment and the carriage.which is now clearly wrong.This conclusion is what they call as 'Time Dilation'.
Up to now, our considerations have been referred to a particular body of reference, which we have styled a 'railway embankment'. We suppose a very long thin train travelling along the rails with the constant velocity V. People in this train have the advantage of using this train as the rigid reference system and they can regard all the events with respect to this coordinate system.Here comes our old question back but with a different approach.Are the events simultaneous with respect to the embankment also simultaneous with respect to the carriage? The very obvious answer that comes is a clear 'No'.
When we say that the lightning strokes A and B are simultaneous, we mean that the ray of light reaches the midpoint of A and B simultaneously.Let M' be the point on train corresponding to the point M on the embankment.Let the train starts moving with moving velocity V towards point B.Hence the observer sitting at the middle of the train see light from B coming early that light from A.
Thus we arrive at an important result that the event simultaneous with respect to the embankment is not simultaneous with respect to the train.Now Before the advent of the Theory of Relativity it had been assumed that the time is independent of the state of motion of body of reference.But then this thing with corresponds to 'The Theorem of addition of velocities' and we have just seen in the above case that this is incompatible with the the thing that if a body transverses uniform straight line motion with respect to an inertial frame then the uniformly moving body can also be considered inertial frame and all the observations and laws are same for it as for the inertial frame.If we discard the assumption of independency of time with respect to state of motion of body of reference frame then the apparent incompatibility between The Theory of Relativity and The Law of propagation of light in vacuum disappears.
We led to this conflict by the considerations of 'The Theorem of addition of velocities', which we no longer be tenable.In that section we led to the conclusion that walking man in the carriage transverses equal distance in equal time with respect to both the embankment and the carriage.which is now clearly wrong.This conclusion is what they call as 'Time Dilation'.
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