The slowing of time for objects moving at velocities close to the velocity of light, as perceived by a stationary observer. If observer A watches the clock held by observer B as B moves past, A will see B's clock as running slowly. In turn, B will see A's clock as running slowly. The symmetry is consistent with the principle that no observer is more at rest than any other. Time dilation is observed in particle physics where moving unstable particles appear to decay more slowly than identical stationary particles.
Time 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. 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.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. 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 Δ t is a time interval measured by an observer in a stationary frame of reference, Δ t0 is that same time interval as measured by an observer in the moving frame, is the Lorentz factor, v is the relative speed between the clock and the stationary system, and c is the speed of light.Thus the duration of the clock cycle of a moving clock appears to be increased: it is "running slow."
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.
Time dilation by the Lorentz factor was predicted by Joseph Larmor (1897), at least for electrons orbiting a nucleus. 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:
Velocity time dilation tests
Ives and Stilwell (1938, 1941), “An experimental study of the rate of a moving clock”, in two parts. Although the travel time for the muons from the top of the mountain to the base is several muon half-lives, the muon sample at the base was only moderately reduced. This is explained by the time dilation attributed to their high speed relative to the experimenters. That is to say, the muons are decaying about 10 times slower than they would in a rest frame (that is, for "stationary observers"). For an invariant source frequency, there is no classical transverse Doppler shift, so, unlike the Ives-Stillwell experiment, the lower frequency of the moving source can be attributed to the time dilation effect alone.Gravitational time dilation tests
Pound, Rebka in 1959 measured the very slight gravitational red shift in the frequency of light emitted at a lower height, where Earth's gravitational field is relatively more intense. This effect is as predicted by gravitational time dilation.Velocity and gravitational time dilation combined-effect tests
Hefele and Keating, in 1971, flew cesium atomic clocks east and west around the Earth in commercial airliners, to compare the elapsed time against that of a clock that remained at the US Naval Observatory. The clocks were expected to age quicker (show a larger elapsed time) than the reference clock, since they were in a higher (weaker) gravitational potential for most of the trip (c.f. Pound, Rebka). The gravitational effect was the larger, and the clocks suffered a net gain in elapsed time. To within experimental error, the net gain was consistent with the difference between the predicted gravitational gain and the predicted velocity time loss. The in-orbit clocks are corrected for both special and general relativistic time-dilation effects so they run at the same (average) rate as clocks at the surface of the Earth.Time dilation and space flight
Time dilation would make it possible for passengers in a fast moving vehicle to travel into the further future while aging very little, in that their great speed retards the rate of passage of onboard time. That is, the ship's clock (and according to relativity, any human travelling with it) shows less elapsed time than stationary clocks. However, any such application of time dilation would require the use of some new, advanced method of propulsion.
Current space flight technology has fundamental theoretical limits based on the practical problem that, per other aspects of Einsteinian relativity affecting mass, an increasing amount of energy is required for propulsion as a craft approaches the speed of light. At the velocities presently attained, however, time dilation is not a factor in space travel.
Time dilation at constant acceleration
In Special Relativity, time dilation is most simply described in circumstances where relative velocity is unchanging. Nevertheless, the Lorentz equations allow one to calculate proper time and movement in space for the simple case of a spaceship whose acceleration, relative to some referent object in uniform (ie, unaccelerating) motion, equals g throughout the period of measurement.
Let t be the time in an inertial frame subsequently called the rest frame. Assuming the spaceship's position at time t = 0 being x = 0 and the velocity being v0, the following formulas hold:
Position:
Velocity:
Proper time:
Time in the rest frame as a function of x:
Simple inference of time dilation
Time dilation can be inferred from the constancy of the speed of light in all reference frames as follows:
Consider a simple clock consisting of two mirrors A and B, between which a photon 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 photon traces out a path of length 2L and the period of the clock is 2L divided by the speed of light. 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 slower.
c = v + 4L2
Time dilation is symmetric between two inertial observers
One assumes, naturally enough, that if time-passage has slowed for a moving object, the moving object would find the external world to be correspondingly "sped up."
The Einsteinian takes seriously the thesis that all motion is indeed relative to some actual (if specified only by implication) "benchmark" that is regarded as stationary, setting aside any issue as to whether what is treated as stationary "really is".
With respect to constant relative motion between two "clocks", a measurement of relative time must choose one clock as being "stationary" in spacetime, and that clock is the basis of a temporal coordinate system where time throughout is treated as synchronized with the stationary clock. The other "moving" clock is in motion with respect to this treated-as-stationary coordinated system, and its relative motion is the velocity value used in the applicable equations.
In the Special Theory of Relativity, the moving clock is found to be ticking slow with respect to the temporal coordinate system of the stationary clock. And as indicated, this effect is symmetrical: In a coordinate system synchronized, by contrast, with the "moving" clock, it is the "stationary" clocks that is found (by all methods of measurement) to be running slow.
It is a natural and legitimate question to ask how, in detail, Special Relativity can be self-consistent if clock A is time-dilated with respect to clock B and clock B is also time-dilated with respect to clock A.
Temporal coordinate systems and clock synchronization
In Relativity, temporal coordinate systems are set up using a procedure for synchronizing clocks, discussed by Poincaré (1900) in relation to Lorentz's local time (see relativity of simultaneity).
An observer with a clock sends a light signal out at time t1 according to his clock. At a distant event, that light signal is reflected back to, and arrives back to the observer at time t2 according to his clock. Since the light travels the same path at the same rate going both out and back for the observer in this scenario, the coordinate time of the event of the photon being reflected for the observer tE is tE = (t1 + t2) / 2.
Symmetric time dilation occurs with respect to temporal coordinate systems set up in this manner. Observers in rest in their coordinate system do not consider their own clock time to be time-dilated, but may find that it is understood to be time-dilated in another coordinate system.
The spacetime geometry of velocity time dilation
The green dots and red dots in the animation represent spaceships. The ships of the green fleet have no velocity relative to each other, so for the clocks onboard the individual ships the same amount of time elapses relative to each other, and they can set up a procedure to maintain a synchronized standard fleet time. One cycle of light-pulses between two green ships takes two seconds of "green time", one second for each leg.
As seen from the perspective of the reds, the transit time of the light pulses they exchange among each other is one second of "red time" for each leg. (As seen from the green perspective the reds travel 1.73 () light-seconds of distance for every two seconds of green time.)
One of the red ships emits a light pulse towards the greens every second of red time. These pulses are received by ships of the green fleet with two-second intervals as measured in green time. The lightpulses that are emitted by the reds at a particular frequency as measured in red time are received at a lower frequency as measured by the detectors of the green fleet that measure against green time, and vice versa.
Again, it is vital to understand that the results of these interactions and calculations reflect the real state of the ships as it emerges from their situation of relative motion.
Time dilation in popular culture
Time dilation caused by long distance space flight is central to the novel The Forever War, as well as Orson Scott Card's Ender novels.
Time dilation is used in The Matrix (called bullet-time by the directors) to exaggerate the speed of the "Agents" and Neo, as well as to further establish the fact that something is not right about the Matrix, relative to the real world.
Time dilation is used in Donnie Darko to show Donnie's power over the Tangent Universe.
Time dilation is a theme in the song "'39" by Queen.
Mostly in Japan, time dilation is commonly called the Urashima effect, after Urashima Tarō.
In the series Stargate SG-1, a time dilation device is used by the alien Asgard (Stargate) to try to contain the robotic Replicators. Another episode of Stargate SG-1 has a time dilation effect being created when a stargate connection is made to planet being devoured by a black hole.
Time Dilation was also put into use in Aim for the Top!
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