Simultaneity and Time Dilation
Simultaneity describes the occurrence of two events at the same time. In accord with the postulates of special relativity, simultaneity is a perception governed by the speed of light that depends upon the reference frame and the relationship of observers to phenomena. Accordingly, simultaneity is a relative phenomenon rather than an absolute and is affected by time dilation.
In 1916, German-American physicist Albert Einstein wrote, "There is hardly a simpler law in physics than that according to which light is propagated in empty space. Every child at school knows that this propagation takes place in straight lines with a velocity c = 300,000 km/sec... Who would imagine that this simple law has plunged the conscientiously thoughtful physicist into the greatest intellectual difficulties?" Those intellectual difficulties, as described by Einstein, concern the relativity of simultaneity, and observer-dependent time.
In order to understand the relativity of simultaneity, the concept of simultaneity itself must be defined. There is no problem determining whether two events that occur at the same place are simultaneous; if they occur at the same time (the same reading of a clock at that point), they are simultaneous. But what of events which are separated in space? Einstein proposed an operational definition. Consider an observer equidistant between the locations of two events (for example, two strokes of lightning). Einstein states, the events are simultaneous if that observer measures or sees the two events as occurring at the same time.
Seeing the two events involves light rays propagating from the two events to the observer's eye. If each stroke is the same distance from the observer, the light signals carrying news of each stroke take the same amount of time to reach the observer. If he sees the strokes simultaneously, they occurred simultaneously. What if there are two different observers, each equidistant from the events, but in relative motion with respect to one another? Are two events, which are judged simultaneous by one observer, also judged simultaneous by the other?
To analyze this situation, Einstein proposed his famous thought-experiment involving two observers and a railroad train moving, for example, to the right along a straight embankment. One observer, Jonathan, is on the train, at the center, while the other, Nicholas, stands alongside the embankment. Remembering the principle of relativity, there is no experiment either physicist can perform that can determine which one is moving. All that can be said is that Jonathan is moving uniformly with respect to Nicholas, and Nicholas is moving uniformly (although in the opposite direction) with respect to Jonathan.
At the instant when the positions of Jonathan and Nicholas coincide, two strokes of lightning hit the embankment at the front and rear of the train. Both observers are equidistant from the lightning strokes. The light from each stroke travels with the same speed, c, with respect to each observer (this is the constancy of the speed of light). Nicholas, on the embankment, judges the strokes to be simultaneous, as the light from each reaches him at the same time. He sees the flashes simultaneously.
But what does Jonathan see? Since he is moving towards the position of the front stroke, light from it will have less distance to travel by the time it reaches him. Conversely, light from the rear stroke will have a greater distance to traverse. Thus, the light from the front stroke reaches Jonathan before that from the rear. Each observer employs Einstein's intuitive definition of simultaneity, as each was equidistant from the two events. Nicholas judges them to be simultaneous, while Jonathan does not. Simultaneity is thus relative: two events, which are simultaneous for one observer, will not be simultaneous for another in motion with respect to the first.
Considering time interval, the amount of time that elapses between two events, Einstein's thought experiment shows that the time interval between strokes is different for each observer. It is zero as measured by Nicholas's clock, but greater than zero as measured by Jonathan's. According to Jonathan, who, like all inertial observers can consider himself to be at rest, the time interval as measured by a moving clock (Nicholas and his clock are, according to Jonathan, moving to the left) is less than that measured by his. This is a particular example of what is known in general as time dilation, often summed up by the statement that "moving clocks run slow."
According to the postulates of relativity related to time dilation, time in a moving system will be observed by a stationary observer to be running slower by a factor that is the reciprocal of the Lorentz contraction equation. Although the effects are negligible for small velocities, the effects increase asymptotically as velocity approaches the speed of light.
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