for Time Dilation
The previous chapter presented an argument that time-dilation between moving objects could
not occur. However a number of experiments have been conducted which appear to support the
Special Relativity (SR) principle of time dilation. Here is a clash between theory and
experiment that needs to be resolved. Good scientific principle tells us that theory must
always give way to experiment: either we must modify the theory to suit, or show that the
experiment is faulty.
Experiments in Time Dilation
A number of experiments exist which appear to support SR time dilation.
. Clocks on orbiting satellites move slower
. Atomic clocks on planes move slower
. Michelson-Morley experiment
. Muon particles decay more slowly while falling
There are other experiments also that are usually a variation of the above. I will discuss
each of these here.
Clocks on GPS satellites
Global Positioning System (GPS) satellites are used to help pinpoint a
location on Earth. The location finding method requires that a satellite transmit a time
signal to a GPS receiver which can then determine its distance from the satellite by
measuring the time that the signal took to reach the receiver. The satellites contain
accurate atomic clocks and it has been noticed that these clocks in orbit run at a
different rate than clocks on Earth. This could be a big problem for GPS because it means
that errors in calculated positions would grow steadily larger each day.
This timing difference is said to be due to a combination of the effects of SR, which
predicts that time should slow down at high speeds, and GR (General Relativity) which says
that time should move more quickly in the lower gravity of high altitudes. GR predicts it
should run faster by 45,900 nanoseconds (ns) a day, while SR predicts a slowdown of 7,200
ns. The net predicted result of SR and GR is that the satellites clock should run
faster by 38,700 ns a day, and this closely corresponds to what is measured .
To compensate for this expected dilation GPS engineers adjust the clock rate on the
satellites prior to their launch, slowing them down by a fixed amount of about 38,500
nanoseconds a day, and this solves the time calculation problem .
On the face of it, this looks like a good argument in support of both SR and GR.
Surprisingly however, it would not make any difference to GPS accuracy whether relativistic
effects were considered or not. The reason for this is explained in a separate chapter:
GPS, Relativity, and Pop-Science Mythology (<-- click to read)
Nevertheless, the fact that unadjusted GPS clocks run faster by an amount closely predicted
by Relativity theory is rather impressive and needs to be studied more closely. I will deal
further with this topic in a later chapter on General Relativity.
Atomic Clocks on Aeroplanes
Atomic clocks are the most accurate of clocks known to man. It has been
said that if an atomic clock, such as a caesium clock, were to be flown on an aeroplane,
those clocks should move at a different speed relative to those on Earth, and that the
slowdown could be attributable to differences both in GR, which predicts that the clocks
should go faster at lower gravity, and SR, which predicts that the clocks should move
slower due to the speed of the aeroplanes.
In 1971 Hafele & Keating (H&K) conducted tests to measure the effects of
relativity on caesium clocks on aeroplanes. The planes flew in east and west directions
along the equator, making a round-world trip to their starting point. H&K calculated
that, due to the combined effects of SR and GR, the different east/west travel times and
different altitudes, the eastward should loose 40 ns and the westward should gain 275 ns.
The measured results showed that the eastward lost 59 ns, while the atomic clock
transported westward gained 273 ns, compared to the stationary laboratory clocks.
Impressive stuff, yes? Perhaps not...
It later transpired that the published results were quite different from the original
measurements. H&K made a number of corrections to their data to average
out the errors between the clocks used, and the variations between the clocks moving in
similar directions were large enough to invalidate the overall measurements. A discussion
of the results is here . If the experiments were as flawed as this
article suggests then they cannot be used to prove or disprove time dilation.
The Michelson-Morley (M-M) experiment was performed in 1887 to
determine the existence of ‘luminiferous ether/aether’, which was the
medium believed to allow the propagation of light waves. The
experiment consisted of comparing the speed of light along different
directions by observing interference patterns in coherent beams
. The experiment proposed that if there was an aether,
then the speed of light should be different in differing directions,
because the Earth must be in constant motion against the aether as it
orbits the Sun, and this would change the speed of light in the
Early M-M results indicated that the speed of light appeared to be the
same in all directions, and this implied that there could be no aether
required for light’s propagation. Later experiments have
reproduced this with a great accuracy of 1 in 1016 .
According to SR proponents , this result proves that the speed of
light is the same for all observers (targets) and thus vindicates the
time dilation hypothesis.
But the experiment does not necessarily prove that. All the
components – mirrors and beam-splitters – are stationary relative to
the light source and each other. So it could be
equally argued the apparatus is showing the speed of light is constant
relative to its source.
To make an analogy, suppose a game of billiards was being played aboard
a moving train. As we know, the train’s velocity will be
added to the ball when hit in the same direction as the train is
moving, and subtracted when hit in the other. When hit across
the table, the ball’s tangential (sideways) velocity will be that of
the train and table, allowing it to directly hit the opposite
side. As a result the game plays in the same manner
regardless of the train’s constant speed. Now replace the
train with Earth, the ball with photons, the table edges with mirrors,
and you have something like an M-M interferometer.
All that aside, the M-M experiment contains a serious flaw because it
was done, not in a vacuum, but in air. Many scientists at the
time were dissatisfied with the experiment’s ‘null result’ and began a
debate about whether the Earth’s gravity was dragging an aether
along. Well regardless whether it is or not, the Earth is
certainly carrying an atmosphere with it, and our atmosphere is far
denser than any assumed aether. Now we know that light
travels through a refractive medium at a slower speed, and this speed
is measured/described relative to the medium. So aether or
not, a ‘null result’ should be expected.
The same limitation seems to be present in the follow-up experiments,
in that they were either done in air or some other medium. A
1930 repetition by George Joos had interferometer arms made of
quartz. This is worse because the refractive index of quartz
is far higher than air. In 1969 Shamir and Fox had them made
The most modern repeat is by Schiller’s team. There they used
super-cooled sapphire as the medium . Sapphire has a
refractive index of around 1.6 to 1.9, depending on wavelength (which
is not clear from the article). But regardless, the light
would be moving through it a fixed speed relative to that
medium. This makes the experiment pointless as far trying to
prove or disprove an aether.
Muons are sub-atomic particles generated when cosmic rays strike the upper
levels of our atmosphere. They have a half life of about 2.2 microseconds (µs) meaning
that every 2.2 µs, their population will reduce by half. By observing the concentration
of muons at both the top and bottom of a mountain, we can see what proportion of them have
decayed and compare this result with the predictions of SR. This can be done using special
counters that only count muons traveling within a certain speed range, say from 0.9950c
When an experiment was performed, the height difference was 1.9 km between top and bottom
of the mountain. Flying 1.9 km through the atmosphere at the above speed takes about 6.4
µs. Based on the stated half life, we should thus expect that only 13% of the original
concentration of muons should arrive. However, it is observed that about 82% of the muons
arrive below. This percentage corresponds to a half life of 22 µs, i.e. ten times greater
than the original. A factor of ten corresponds to what the LT would give for a speed of
This experiment has been repeated for different velocities and on many occasions (even by
students ) and presumably the measurement errors were well within
tolerance. So the experiment seems to properly validate SR.
Could there be another explanation for the lower decay rates? I believe so. There may be a
fundamental problem with the experiment in the form of an invalid assumption. The
reasoning is too deep to go into here but I discuss it in a later
Evaluating experimental data is difficult because it requires accepting
that the published results of the experimenters are correct and that their assumptions
were valid. On one hand there appears to be some misinterpretations of experimental
results (as with M-M) and fudging of figures (as with H&K). On the other hand, the
muon decay experiments appear convincing if no alternative explanation for the results can
A team of scientists might tomorrow announce that they have measured the time-dilation
between a moving and stationary clock and matched the SR prediction to ten significant
digits. If the results were accurate wed have to accept them. Yet we should also ask
this question: Why are the clocks labelled moving and
stationary, and not vice-versa? For there are supposedly no absolute
velocities in the universe.
 See reference  the clocks are set to run at
10.22999999543 MHz instead of 10.23 MHz. If left on earth, this would cause them to run
slower by 38,640 ns per day.
 http://www.cartesio-episteme.net/H&KPaper.htm or
 e.g. Hawking: A Brief History of Time, page 31
 http://physicsworld.com/cws/article/news/2009/sep/14/michelson-morley-experiment-is-best-yet ,
 http://www.motionmountain.net/download.html (volume II, page 45)