Difference between revisions of "Time dilation"
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<math>t_2</math> is the time the events appear to occur, with the time dilation added. | <math>t_2</math> is the time the events appear to occur, with the time dilation added. | ||
− | This formula can be derived using a simple example. If there was a light clock that consisted of two mirrors with a light beam bouncing between them, the distance between the mirrors would be <math>ct_1</math>. If, the clock was inside a moving vehicle, than the distance the clock travels would equal <math>vt_2</math>. Finally, to an observer of the light clock, the light beam, instead of bouncing up and down, would move diagonally. The distance it appears to travel is <math>ct_2</math>. | + | This formula can be derived using a simple example. If there was a light clock that consisted of two mirrors with a light beam bouncing between them, the distance between the mirrors would be <math>ct_1</math>. If, the clock was inside a moving vehicle, than the distance the clock travels would equal <math>vt_2</math>. Finally, to an observer of the light clock, the light beam, instead of bouncing up and down, would move diagonally. The distance it appears to travel is <math>ct_2</math>. This forms a triangle, and using the Pythagorean theorem, it would obtain: |
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+ | <math>c^2(t_2)^2=c^2(t_1)^2+v^2(t_2)^2</math> | ||
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+ | Subtracting by <math>v^2(t_2)^2</math> yields | ||
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+ | <math>c^2(t_2)^2-v^2(t_2)^2=c^2(t_1)^2</math> |
Revision as of 23:24, 23 December 2008
In special relativity, the time dilation that will be experienced can be expressed with the formula:
where is the "proper" time experienced by the moving object.
is the relative velocity the ovject is moving to the observer.
is the speed of light; it can be simply expressed as 1, but then the velocity will have to be given in terms of .
is the time the events appear to occur, with the time dilation added.
This formula can be derived using a simple example. If there was a light clock that consisted of two mirrors with a light beam bouncing between them, the distance between the mirrors would be . If, the clock was inside a moving vehicle, than the distance the clock travels would equal . Finally, to an observer of the light clock, the light beam, instead of bouncing up and down, would move diagonally. The distance it appears to travel is . This forms a triangle, and using the Pythagorean theorem, it would obtain:
Subtracting by yields