Time dilation


Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity, a consequence of special relativity, or a difference in gravitational potential between their locations due to [|gravitational time dilation]. When unspecified, "time dilation" usually refers to the effect due to velocity. The dilation compares "wristwatch" clock readings between events measured in different inertial frames and is not observed by visual comparison of clocks across moving frames.
These predictions of the theory of relativity have been repeatedly confirmed by experiment, and they are of practical concern, for instance in the operation of satellite navigation systems such as GPS and Galileo.

Invisibility

Time dilation is a relationship between clock readings. Visually observed clock readings involve delays due to the propagation speed of light from the clock to the observer. Thus there is no direct way to observe time dilation. As an example of time dilation, two experimenters measuring a passing train traveling at.86 light speed may see a 2 second difference on their clocks while on the train the engineer reports only one second elapsed when the experimenters went by. Observations of a clock on the front of the train would give completely different results: the light from the train would not reach the second experimenter only 0.27s before the train passed. This effect of moving objects on observations is associated with the Doppler effect.

History

Time dilation by the Lorentz factor was predicted by several authors at the turn of the 20th century. Joseph Larmor wrote that, at least for those orbiting a nucleus, individual electrons describe corresponding parts of their orbits in times shorter for the system in the ratio:. Emil Cohn specifically related this formula to the rate of clocks. In the context of special relativity it was shown by Albert Einstein that this effect concerns the nature of time itself, and he was also the first to point out its reciprocity or symmetry. Subsequently, Hermann Minkowski introduced the concept of proper time which further clarified the meaning of time dilation.

Time dilation caused by a relative velocity

indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to the observer will be measured to tick more slowly than a clock at rest in the observer's frame of reference. This is sometimes called special relativistic time dilation. The faster the relative velocity, the greater the time dilation between them, with time slowing to a stop as one clock approaches the speed of light.
In theory, time dilation would make it possible for passengers in a fast-moving vehicle to advance into the future in a short period of their own time. With sufficiently high speeds, the effect would be dramatic. For example, one year of travel might correspond to ten years on Earth. Indeed, a constant 1 g acceleration would permit humans to travel through the entire known Universe in one human lifetime.
With current technology severely limiting the velocity of space travel, the differences experienced in practice are minuscule. After 6 months on the International Space Station, orbiting Earth at a speed of about 7,700 m/s, an astronaut would have aged about 0.005 seconds less than he would have on Earth. The cosmonauts Sergei Krikalev and Sergey Avdeev both experienced time dilation of about 20 milliseconds compared to time that passed on Earth.

Simple inference

Time dilation can be inferred from the observed constancy of the speed of light in all reference frames dictated by the second postulate of special relativity. This constancy of the speed of light means that, counter to intuition, the speeds of material objects and light are not additive. It is not possible to make the speed of light appear greater by moving towards or away from the light source.
The relativity of time can be illustrated with a thought experiment based on an abstract vertical clock consisting of two mirrors and, between which a light pulse is bouncing. The separation of the mirrors is and the clock ticks once each time the light pulse hits mirror.
In the frame in which the clock is at rest, the light pulse traces out a path of length and the time period between the ticks of the clock is equal to divided by the speed of light :
From the frame of reference of a moving observer traveling at the speed relative to the resting frame of the clock, the light pulse is seen as tracing out a longer, angled path. Keeping the speed of light constant for all inertial observers requires a lengthening of the time period between the ticks of this clock from the moving observer's perspective. That is to say, as measured in a frame moving relative to the local clock, this clock will be running more slowly, since tick rate equals one over the time period between ticks 1/.
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:
Elimination of the variables and from these three equations results in:
which expresses the fact that the moving observer's period of the clock is longer than the period in the frame of the clock itself. The Lorentz factor gamma is defined as
Because all clocks that have a common period in the resting frame should have a common period when observed from the moving frame, all other clocksmechanical, electronic, optical should exhibit the same velocity-dependent time dilation.

Reciprocity

Given a certain frame of reference, and the "stationary" observer described earlier, if a second observer accompanied the "moving" clock, each of the observers would measure the other's clock as ticking at a slower rate than their own local clock, due to them both measuring the other to be the one that is in motion relative to their own stationary frame of reference.
Common sense would dictate that, if the passage of time has slowed for a moving object, said object would observe the external world's time to be correspondingly sped up. Counterintuitively, special relativity predicts the opposite. When two observers are in motion relative to each other, each will measure the other's clock slowing down, in concordance with them being in motion relative to the observer's frame of reference.
Image:Eigenzeit.svg|right|thumb|Time UV of a clock in S is shorter compared to Ux′ in S′, and time UW of a clock in S′ is shorter compared to Ux in S.
While this seems self-contradictory, a similar oddity occurs in everyday life. If two persons A and B observe each other from a distance, B will appear small to A, but at the same time, A will appear small to B. Being familiar with the effects of perspective, there is no contradiction or paradox in this situation.
The reciprocity of the phenomenon also leads to the so-called twin paradox where the aging of twins, one staying on Earth and the other embarking on space travel, is compared, and where the reciprocity suggests that both persons should have the same age when they reunite. On the contrary, at the end of the round-trip, the traveling twin will be younger than the sibling on Earth. The dilemma posed by the paradox can be explained by the fact that the situation is not symmetric. The twin staying on Earth is in a single inertial frame, and the traveling twin is in two different inertial frames: one on the way out and another on the way back. See also.

Experimental testing

Moving particles

  • A comparison of muon lifetimes at different speeds is possible. In the laboratory, slow muons are produced; and in the atmosphere, very fast-moving muons are introduced by cosmic rays. Taking the muon lifetime at rest as the laboratory value of 2.197 μs, the lifetime of a cosmic-ray-produced muon traveling at 98% of the speed of light is about five times longer, in agreement with observations. An example is Rossi and Hall, who compared the population of cosmic-ray-produced muons at the top of a mountain to that observed at sea level.
  • The lifetime of particles produced in particle accelerators are longer due to time dilation. In such experiments, the "clock" is the time taken by processes leading to muon decay, and these processes take place in the moving muon at its own "clock rate", which is much slower than the laboratory clock. This is routinely taken into account in particle physics, and many dedicated measurements have been performed. For instance, in the muon storage ring at CERN the lifetime of muons circulating with γ = 29.327 was found to be dilated to 64.378 μs, confirming time dilation to an accuracy of 0.9 ± 0.4 parts per thousand.

    Doppler effect

  • The stated purpose by Ives and Stilwell of these experiments was to verify the time dilation effect, predicted by Larmor–Lorentz ether theory, due to motion through the ether using Einstein's suggestion that Doppler effect in canal rays would provide a suitable experiment. These experiments measured the Doppler shift of the radiation emitted from cathode rays, when viewed from directly in front and from directly behind. The high and low frequencies detected were not the classically predicted values:The high and low frequencies of the radiation from the moving sources were measured as:as deduced by Einstein from the Lorentz transformation, when the source is running slow by the Lorentz factor.
  • Hasselkamp, Mondry, and Scharmann measured the Doppler shift from a source moving at right angles to the line of sight. The most general relationship between frequencies of the radiation from the moving sources is given by:as deduced by Einstein. For this reduces to. This lower frequency from the moving source can be attributed to the time dilation effect and is often called the transverse Doppler effect and was predicted by relativity.
  • In 2010 time dilation was observed at speeds of less than 10 metres per second using optical atomic clocks connected by 75 metres of optical fiber.