Relativistic time dilation is the observation that the measured time interval between two events appears to have a minimum value in the inertial system in which the measuring clock is at rest. The measurement of time in relativity (special and general) is an operation that depends strongly on the kinematic and/or gravitational conditions under which the observer performs it.

Time dilation is a consequence of Lorentz transformations and is a relativistic phenomenon in which the measurement of the duration of an event changes depending on whether the reference system from which the measurement is made is at rest or in motion.

For example, μ particles, or muons, found in particle swarms produced by cosmic ray impacts in the atmosphere, hit the Earth’s surface at speeds very close to the speed of light after a flight time on the order of 200 microseconds. Muons are unstable particles that spontaneously decay in the laboratory in as little as 2 microseconds. Their increased average lifetime in atmospheric swarms is justified by the time dilation predicted by special relativity for moving observers.

Time dilation phenomena also occur in general relativity. In this theory, the Einstein effect consists of a redshift manifested by the electromagnetic radiation emitted by celestial bodies with large gravitational fields (gravitational redshift). In the vicinity of the Sun, this shift reaches 0.01 Å, which corresponds in frequency – and therefore on the local time scale – to a time dilation of 2×10^{-6} seconds per second. However, the time dilation would increase to 15 times larger values if the star were a compact white dwarf with a very strong surface intensity of the gravitational field, such as Sirius B. Finally, at the “event surface” surrounding a black hole, the time course would be completely zero (infinitely large dilation).

## Experimental proof of time dilation

Experimental proof of time dilation did not occur until 1972, when atomic clocks became available.

The physicists Hafele and Keating synchronized two atomic clocks that were carried in two different airplanes, leaving one on the ground. One plane traveled east (the speed of the plane added to the speed of the Earth), the other west (the speed of the plane subtracted from the speed of the Earth). On their return, both clocks reported a delay of a few nanoseconds, in perfect agreement with relativistic predictions.

It took a full 70 years to experimentally prove what Einstein had discovered; in fact, it was necessary to wait for technology to reach a level of accuracy that could detect the very small variations in time that occur at the speeds we can achieve on Earth, which are much slower than the speed of light.