- Muon Experiment
- Muons enter the atmosphere (about 10km) at a velocity of 0.98c
and have at rest lifetime of 1.56 * 10-6
seconds. To travel 10 km at 0.98c, this will take
34 * 10-6 seconds, which is about 21.8 half-lives.
From this, it would appear that 2-21.8 of
the original population would be left, or about 0.3 out of every million
muons that enter that atmosphere.
However, this is not what is experimentally observed, and instead it
is several orders of magnitude grater. The number is closer to
50,000 muons out of a million that make it. So what is happening?
From the ground point of view, it appears that the muon's clock
is time dilated and running much slower by a factor of 5. When
translated to actual time, only 4.36 half-lives have passed for
the muon to move 10km. Thus instead we get
2-4.36 which is 0.049, or about 49,000
out of every million muons.
Realize that to the muon's point of view, time has not slowed down,
but rather the distance has been shortened by a factor of 5. Thus,
to move this distance it only takes 6.8 * 10-6
seconds, which happens to be 4.36 half-lives.
This experiment was
first conducted in 1941 by B. Rossi and D.B Hall. Since then, this
has also been demonstrated with muons in particle accelerators.
- Hafele and Keating Experiment
"During October, 1971, four cesium atomic beam clocks were flown on
regularly scheduled commercial jet flights around the world twice, once
eastward and once westward, to test Einstein's theory of relativity
with macroscopic clocks. From the actual flight paths of each trip,
the theory predicted that the flying clocks, compared with reference
clocks at the U.S. Naval Observatory, should have lost
40+/-23 nanoseconds during the eastward trip and should have
gained 275+/-21 nanoseconds during the westward trip
... Relative to the atomic time scale of the
U.S. Naval Observatory, the flying clocks lost 59+/-10 nanoseconds
during the eastward trip and gained 273+/-7 nanosecond during the
westward trip, where the errors are the corresponding
standard deviations. These results provide an unambiguous empirical
resolution of the famous clock "paradox" with macroscopic clocks."
J.C. Hafele and R. E. Keating, Science 177, 166 (1972)
Predicted -40 +/- 23ns +275 +/- 21ns
Measured -59 +/- 10ns +273 +/- 7ns
In this, several forms of time dilation occur:
The sum of these moves to the predicted values:
Gravitational +144 +/- 14ns +179 +/- 18ns
Kinematic -184 +/- 18ns + 96 +/- 10ns
Predicted - 40 +/- 23ns +275 +/- 21ns
The Gravitational component is associated with the altitude above
the earth. This plays a large role in GPS signals (and was not
initially corrected for resulting in large cumulative errors - it has
Kinematic time shift is the 'classic' one that we are more or less
familiar with. As an object moves faster, its clock slows down
with respect to the rest frame.
- Atomic Fine Structure
- With quantum theory came the prediction of the energy levels of
a hydrogen atom. Attempts were made to explain the actual structure
of the hydrogen spectral lines, an error was discovered that was off
by a factor of two. The solution to this error turned out to be that
time dilation must be used for the calculation of the frequency.
- Kaivola Time Dilation Experiment
- In 1985 time dilation was again measured with a double photon
experiment conducted by Kaviola. In this experiment, a beam of neon
atoms moving at 0.004c was excited by two lasers from opposite
directions. The absorption frequency which were observed were shifted
by the Doppler effect and time dilation. When the two directions were
measured, the Doppler shift was canceled out leaving only time dilation
which was measured by examining the beat frequency between the two
tuneable lasers. The experiment confirmed the expected time dilation
Kaivola, M., et al., Phys. Rev. Lett. 54, 255 (1985).