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 greater by approaching at speed towards the material source that is emitting light. It is not possible to make the speed of light appear less 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 the light pulse 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 2L and 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.
Read more about this topic: Time Dilation
Famous quotes containing the words simple, inference, time, due and/or relative:
“How many desolate creatures on the earth
Have learnt the simple dues of fellowship
And social comfort, in a hospital.”
—Elizabeth Barrett Browning (1806–1861)
“Rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either.”
—Nelson Goodman (b. 1906)
“Fair Hope! our earlier Heaven! by thee
Young Time is taster to Eternity.
The generous wine with age grows strong, not sour,
Nor need we kill thy fruit to smell thy flower.
Thy golden head never hangs down
Till in the lap of Love’s full noon
It falls and dies: Oh no, it melts away
As doth the dawn into the day,
As lumps of sugar lose themselves, and twine
Their subtle essence with the soul of wine.”
—Abraham Cowley (1618–1667)
“The creation of “strong-minded” women, so-called, is due to the individualism of men, to the modern selfish and speculative spirit which absorbs everything within itself and leaves women nothing but self-assertion for their protection and support.”
—“Jennie June” Croly 1829–1901, U.S. founder of the woman’s club movement, journalist, author, editor. Demorest’s Illustrated Monthly and Mirror of Fashions, p. 44 (February 1870)
“She went in there to muse on being rid
Of relative beneath the coffin lid.
No one was by. She stuck her tongue out; slid.”
—Gwendolyn Brooks (b. 1917)