Time dilation is an observed difference of elapsed time between two observers which are moving relative to each other, or being differently situated from nearby gravitational masses. An observer will see the other observer's clock ticking at a slower rate than his/hers. This effect doesn't arise from technical aspects of the clock or the fact that any signal needs time to propagate, but from the nature of space-time described by the theory of relativity.
From the frame of reference of a moving observer traveling at the speed v (diagram at lower right), the light pulse traces out a longer, angled path. The second postulate of special relativity states that the speed of light is constant in all frames, which implies a lengthening of the period of this clock from the moving observer's perspective. That is to say, in a frame moving relative to the clock, the clock appears to be running more slowly. Straightforward application of the Pythagorean theorem leads to the well-known prediction of special relativity:
Relative velocity time dilation
When two observers are in relative uniform motion and uninfluenced by any gravitational mass, the point of view of each will be that the other's (moving) clock is ticking at a slower rate than the local clock. The faster the relative velocity, the greater the magnitude of time dilation. This case is sometimes called special relativistic time dilation. It is often interpreted as time "slowing down" for the other (moving) clock. But that is only true from the physical point of view of the local observer, and of others at relative rest (i.e. in the local observer's frame of reference). The point of view of the other observer will be that again the local clock (this time the other clock) is correct and it is the distant moving one that is slow. From a local perspective, time registered by clocks that are at rest with respect to the local frame of reference (and far from any gravitational mass) always appears to pass at the same rate.
Simple inference of time dilation due to relative velocity
Time dilation can be inferred from the observed fact of the constancy of the speed of light in all reference frames.
This constancy of the speed of light means, counter to intuition, that speeds of material objects and light are not additive. It is not possible to make the speed of light appear faster by approaching at speed towards the material source that is emitting light. It is not possible to make the speed of light appear slower by receding from the source at speed. From one point of view, it is the implications of this unexpected constancy that take away from constancies expected elsewhere.
Consider a simple clock consisting of two mirrors A and B, between which a light pulse is bouncing. The separation of the mirrors is L and the clock ticks once each time it hits a given mirror.
In the frame where the clock is at rest (diagram at right), the light pulse traces out a path of length 2Land the period of the clock is 2L divided by the speed of light:
From the frame of reference of a moving observer traveling at the speed v (diagram at lower right), the light pulse traces out a longer, angled path. The second postulate of special relativity states that the speed of light is constant in all frames, which implies a lengthening of the period of this clock from the moving observer's perspective. That is to say, in a frame moving relative to the clock, the clock appears to be running more slowly. Straightforward application of the Pythagorean theorem leads to the well-known prediction of special relativity:
The total time for the light pulse to trace its path is given by
The length of the half path can be calculated as a function of known quantities as
Substituting D from this equation into the previous and solving for Δt' gives:
and thus, with the definition of Δt:
which expresses the fact that for the moving observer the period of the clock is longer than in the frame of the clock itself.
0 comments:
Post a Comment