Experimental Evidence
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. They are:

. 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 satellite’s clock should run faster by 38,700 ns a day, and this closely corresponds to what is measured [1].

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 [2].

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 [3]. If the experiments were as flawed as this article suggests then they cannot be used to prove or disprove time dilation.

Michelson-Morley experiment

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 [4].  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 carrying medium.

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 [6].  According to SR proponents [5], 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 of plexiglass.

The most modern repeat is by Schiller’s team.  There they used super-cooled sapphire as the medium [6].  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.

Muon decay

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 to 0.9954c.

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 0.995c [7].

This experiment has been repeated for different velocities and on many occasions (even by students [8]) 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 chapter.

Conclusion

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 be found.

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 we’d 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.”

[1]  http://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System
[2]  See reference [1] – 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.
[3]  http://www.cartesio-episteme.net/H&KPaper.htm or http://astrojan.hostei.com/hafele.htm
[4]  http://en.wikipedia.org/wiki/Michelson-Morley_experiment
[5]  e.g. Hawking: A Brief History of Time, page 31
[6]  http://physicsworld.com/cws/article/news/2009/sep/14/michelson-morley-experiment-is-best-yet , http://arxiv.org/pdf/physics/0305117v1.pdf
[7]  http://www.motionmountain.net/download.html (volume II, page 45)
[8]  http://cerncourier.com/main/article/46/4/18