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Space and Time in Einstein Theory of Relativity Revision Notes

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18.3Space and Time in Einstein Theory of Relativity


In these revision notes for Space and Time in Einstein Theory of Relativity, we cover the following key points:

  • Why the classical theory of relativity is not suitable to explain relativistic events?
  • What contradictions of the classical theory of relativity did Einstein's Special Theory of Relativity addressed?
  • What are synchronized clocks? Why clocks' synchronization is important in relativistic events?
  • What happens to the time in relativistic events?
  • What happens to the length of objects in relativistic events?
  • In which direction do the change in time and length during a relativistic event occur?

Space and Time in Einstein Theory of Relativity Revision Notes

The old theory of relativity led to many contradictions, which led to the formulation of the modern theory of relativity by Einstein, based on his two famous postulates.

From the first postulate, it derives that we are not able to determine whether a system is at rest or it is moving; this can neither be achieved by analyzing the mechanical phenomena nor optical ones. The speed of light is not involved in any of calculations.

The second postulate is even stranger and unexpected. The common understanding on relativity is based on the concept of a changeable speed that depends on the system of reference used to describe the motion. According to Einstein, this is valid for all material objects but not for the light. These findings led to the formulation of "Special Theory of Relativity".

According to this theory, the simultaneity of the events observed is relative - a conclusion that contradicts the Newtonian concept of absolute time, which was believed to be equal for all inertial frames of reference. From this viewpoint, Einstein in his theory formulated the idea of different-flowing times in different inertial frames of reference. There is no absolute time anymore. The time flow that characterizes the chronology of events is an inner property of a given inertial frame of reference.

Since the time of event occurrence is not the same in two inertial systems, as in the case of the Newtonian system, a procedure for measuring the time that is typical for a given system, is necessary. This procedure is known as clocks' synchronization. All events are absolute as objective facts, however, their time (and place) of appearance is different in different inertial frames of reference. Thus, the same event is shown at coordinates (x, y, x, t) in the system S and (x', y', z', t') in the system S'.

The time interval of an event's occurrence when measured from a reference frame connected to the moving object, is

∆t' = ∆t ∙ √1 - V2/c2

where V is the speed of moving object (of S') and Δt is the time interval of event's occurrence when measured from a fixed point outside the moving object (in S). This formula is known as the formula of time dilation in relativistic events.

On the other hand, the length of an object contracts during a relativistic event as a counterbalance towards the dilation of time. The formula of length contraction in relativistic events is

L = L'·√1 - V2/c2

where L is the length of moving object when it is measured from a fixed point on the ground (in S) and L' is the length of object measured from any point connected to it (in S').

Any object in a relativistic event still looks in the original shape however, despite the "pressing" effect caused by the motion at very high speed.

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