Is there any practical proof of time dilation on atomic particles?
Yes there is, and you don't even need an expensive cyclotron to get the particles up to speed. In nature, subatomic muons are created by cosmic ray interaction with the upper atmosphere. At rest, muons disintegrate in about 2 x 10-6 seconds and should not have time to reach the Earth's surface given there speed and travel distance. Because they move at close to the speed of light, however, time dilation extends their life span as seen from Earth so they can be observed at the surface before they disintegrate.
As counter-intuitive as it may seem to our non-relativistic experience, time dilation experiments of all kinds have been performed and Einstein's predictions have (thus far, at least) always been confirmed within the margin of experimental error.
Paul Walorski, B.A., Part-time Physics/Astronomy Instructor
Yes. One very good example of this is Cosmic Ray Muons.
When scientists created muons in the lab (aside: a muon is very similar to an electron except it has a much greater mass) at rest, they found that the average lifetime of a muon was around 2.2 microseconds before it decayed into an electron, muon neutrino and an anti-electron neutrino.
Muons are often created when Cosmic Rays collide with the atmosphere. These muons typically have high velocities around 99.98% of the speed of light. Using classical mechanics it should be virtually impossible for any muons to be detected at all on the surface of the Earth. However, muons are detected at the surface and the activity cannot be attributed to just the odd few muons that have a slightly longer lifetime or greater energy. However, if we apply time dilation to the cosmic ray muons which have a lifetime of 2.2 microseconds at rest in an inertial reference frame travelling towards earth at 99.98% of the speed of light we find that this resolves the problem and we get around the observed activity.
This problem can also be tackled by saying that in the muon's rest frame the Earth's atmosphere appears length contracted, thus allowing a certain percentage of muons to arrive at the Earth's surface.
Martin Archer, None, Physics Student, Imperial College, London, UK
Pion experiments at CERN have measured time dilation effects. Pions are produced in high energy collisions of nucleons. They are unstable and decay into a muon and a neutrino.
Not taking into account time dilation pions would travel about 7.6 meters before decaying.
Taking into account time dilation a pion of energy 4.5 GeV would travel about 250 meters before decaying.
CERN has measured a mean distance of 250 meters before the pions decay.
Other evidence comes form the study of cosmic-ray muons. A muons if not taking into account time dilation would travel 0.66 km on average before decaying. As cosmic ray muons are created at about 60 km, this implies that almost no muons should reach sea level.
This is not so, a significant fraction do reach sea level. Taking in to account time dilation accounts for the experimental findings. muons with total energy 3 GeV (as detected at sea level) travel about 20 km on average before decaying.
These experiments and others give us confidence in the Lorentz transformations and special relativity.
Andrew James Bruce, Physics graduate, UK
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