Time dilationTime dilation is the phenomenon whereby an observer finds that another's clock which is physically identical to their own is ticking at a slower rate as measured by their own clock. This is often taken to mean that time has "slowed down" for the other clock, but that is only true in the context of the observer's frame of reference. Locally, time is always passing at the same rate. The time dilation phenomenon applies to any process that manifests change over time.
In Albert Einstein's theories of relativity time dilation is manifested in two circumstances:
In special relativity, clocks that are moving with respect to an inertial system of observation (the putatively stationary observer) are found to be running slower. This effect is described precisely by the Lorentz transformations.
In general relativity, clocks at lower potentials in a gravitational field-- such as in close proximity to a planet --are found to be running slower. This gravitational time dilation is only briefly mentioned in this article but is described elsewhere (see also gravitational red shift).
In special relativity, the time dilation effect is reciprocal: as observed from the point of view of any two clocks which are in motion with respect to each other, it will be the other party's clocks that is time dilated. (This presumes that the relative motion of both parties is uniform; that is, they do not accelerate with respect to one another during the course of the observations.)
In contrast, gravitational time dilation (as treated in General Relativity) is not reciprocal: an observer at the top of a tower will observe that clocks at ground level tick slower, and observers on the ground will agree. Thus gravitational time dilation is agreed upon by all stationary observers, independent of their altitude.
Overview
The formula for determining time dilation in special relativity is:
where
is the time interval between two colocal events for an observer in some inertial frame (e.g. ticks on his clock),
is the time interval between those same events, as measured by another observer, inertially moving with velocity v w.r.t. the former observer,
is the relative velocity between the observer and the moving clock,
is the speed of light, and
is the so-called Lorentz factor.
Thus the duration of the clock cycle of a moving clock is found to be increased: it is "running slow." As indicated, the Lorentz transforms can be used for more general cases.
As shown, the effect increases in an exponential manner with respect to relative speed or gravitational differences. The range of such variances in ordinary life, even considering space travel, are not great enough to produce easily detectable time dilation effects, and such vanishingly small effects can be safely ignored. It is only when an object approaches speeds on the order of 30,000 km/s (1/10 of the speed of light), or lies deep within the gravitational "well" of massive stellar objects, that it becomes important.
Time dilation by the Lorentz factor was predicted by Joseph Larmor (1897), at least for electrons orbiting a nucleus. Thus "... individual electrons describe corresponding parts of their orbits in times shorter for the [rest] system in the ratio :" (Larmor 1897). Time dilation of magnitude corresponding to this (Lorentz) factor has been experimentally confirmed, as described below.
Experimental confirmation
Time dilation has been tested a number of times. The routine work carried on in particle accelerators since the 1950s, such as those at CERN, is a continuously running test of the time dilation of special relativity. The specific experiments include:
http://en.wikipedia.org/wiki/Time_dilationhttp://en.wikipedia.org/wiki/Time_travel
