Experimental testing of time dilation

Time dilation as predicted by special relativity is often verified by means of particle lifetime experiments.

A variety of experiments confirming this effect have been performed both in the atmosphere and in particle accelerators.

The probability that muons can reach the Earth depends on their half-life, which itself is modified by the relativistic corrections of two quantities: a) the mean lifetime of muons and b) the length between the upper and lower atmosphere (at Earth's surface).

is the travel time in the rest frame of the Earth by which the muons traverse the distance between those regions, and

is the mean proper lifetime of the muons:[3] In 1940 at Echo Lake (3240 m) and Denver in Colorado (1616 m), Bruno Rossi and D. B.

Rossi and Hall confirmed the formulas for relativistic momentum and time dilation in a qualitative manner.

[4][5][6][7] A much more precise experiment of this kind was conducted by David H. Frisch and Smith (1962) and documented by a film.

[8] They measured approximately 563 muons per hour in six runs on Mount Washington at 1917m above sea-level.

Assuming a mean lifetime of 2.2 μs, only 27 muons would reach this location if there were no time dilation.

However, approximately 412 muons per hour arrived in Cambridge, resulting in a time dilation factor of 8.8±0.8.

Frisch and Smith showed that this is in agreement with the predictions of special relativity: The time dilation factor for muons on Mount Washington traveling at 0.995 c to 0.9954 c is approximately 10.2.

Their kinetic energy and thus their velocity was diminished until they reached Cambridge to 0.9881 c and 0.9897 c due to the interaction with the atmosphere, reducing the dilation factor to 6.8.

So between the start (≈ 10.2) and the target (≈ 6.8) an average time dilation factor of 8.4±2 was determined by them, in agreement with the measured result within the margin of errors (see the above formulas and the image for computing the decay curves).

[9] Since then, many measurements of the mean lifetime of muons in the atmosphere and time dilation have been conducted in undergraduate experiments.

The clock hypothesis states that the extent of acceleration does not influence the value of time dilation.