Why we believe in Special Relativity:
|pre 1905 results||optical experiments of Arago, Fizeau, Bradley, Airy with moving bodies|
|Tests of Postulates||round-trip tests of speed of light||Michelson-Morley expt and derivatives|
|one-way tests||lasers, masers and Mossbauer effect|
|independence of speed of light||Alvager et al, Brecher (on motion of source), Schaefer (on energy)|
|limit on photon rest mass||Goldhaber & Nieto, Davis et al|
|tests on Lorentz invariance||Trouton-Noble expt and others|
|Test on time dilation etc||Particle lifetimes||muon lifetimes, Bailey et al|
|Doppler formulae||Ives and Stillwell, McGowan et al|
|Twin paradox||Hafele & Keating|
|Relativistic kinematics||limiting velocity is c||Brown et al, Glashow & Coleman, Stodolsky (neutrinos)|
|variation of mass with velocity||Particle accelerators + special tests|
|E=mc2||Element transformations, astrophysics|
I certainly support the bottom line that no repeatable and generally accepted experimental result is in disagreement with special relativity.
One of the most dramatic predictions of Special Relativity is time dilation. Time dilation implies that clocks in a frame moving with respect to you appear to run slow. You and I are never likely to be moving at near the speed of light but many elementary particles can hardly help themselves from doing so.
Mu-mesons, or muons as they are called these days, are elementary particles bearing some similarity to massive electrons. They are created by collisions induced in particle accelerators and by the same process in cosmic ray showers when particles called π-mesons decay. Muons are among the particles that travel from several km high in the atmosphere to the surface of the earth. The fact that they reach the Earth at all is very curious indeed. But reach the earth they do, as you can hear in this radiation detector that records the natural background radiation in which life on earth evolves. About 1 in 8 of these clicks is caused by muons.
Muons have a short half-life of 2.197 μs. This means 2.197 μs before they have a 50% chance of spontaneously decaying into an electron or positron (depending on their charge) and neutrinos. A bunch of muons travelling at 0.99 times the speed of light (0.99c) will only go 650 m before half of them have decayed. In the atmosphere, muons are created in a shower at a typical height of 10 km and will need 15.3 half-lives of time to reach the ground, more if they are coming at an angle. Let's suppose there are 15 rows in this lecture theatre and I were to give a sum of money to the back row and ask each row to take out half the money you get and pass the rest forward. How much would I have to give to the back row to ensure that I received at least 1 p at the front? The answer is about £327. After 15 rows each taking out half, very little of the original is left. The same should happen to the muons travelling earthwards. It doesn’t, as this Geiger counter testifies.
Special Relativity explains why. For muons travelling at 0.99c, the time dilation factor is about 7. (γ = 7.09, to be exact). Their half-life observed in our ground frame of reference is longer by a factor of 7.09 and hence according to relativity the time needed for muons to reach the ground is not 15.3 half lives but only 15.3/7.09 = 2.18 half-lives. If there are only 2 rows dividing the £327 before I get it instead of 15, I’m not going to get just 1p but about £82, or 8,000 times as much.
The original experiment was done by Rossi & Hall in 1941 who measured muon fluxes not 10 km high but at the top of Mt Washington in New England, about 2 km high, and at the base of the mountain. The effect is less for a height difference of only 2 km but for their muon speeds of 0.994c, relativistically the reduction should have been only a factor of 1.26 whereas without time dilation the reduction would be a factor of 8.5. Rossi and Hall’s figures were consistent with the relativitistic prediction. The experiment has since been repeated by others with convincing results.
|frame of muon||frame of ground|
|distance||0.219 km||2 km||2 km|
|time||0.734 μs||6.71 μs||6.71 μs|
In 1979 Bailey et al at a CERN accelerator reported a similar experiment with CERN generated muons of speeds 0.9994c, trapped in a particle accelerator, that were observed in the lab to have 29.3 times the muon rest lifetime, completely consistent with time dilation.
One of the consequential results in relativity is that no bodies can travel at a faster speed than the speed of light. Nobel prize winner Sheldon Glashow and collaborator Sidney Coleman showed in 1997 that the argument could be taken further. The mere existence of very high energy cosmic ray photons reaching the Earth is strong proof, without any extra experiment, of the existence of an upper limit of the speed of light c for material bodies. Their argument is that photons decay by pair production into electrons and positrons at a rate that can be calculated from particle physics. If the upper limit to the speed of electrons differed from c by a small amount, then high-energy photons (~20 Tev) would decay in nanoseconds and never travel any significant distance from their point of creation. The detection of these particles on Earth sets a tight bound of an upper limit to the speed of matter being within 1.5×10-15 of c.
Another implication of special relativity is the famous twin paradox in which one twin who travels away and returns finds the other twin who has remained behind has aged more than the travelling twin has.
The Hafele and Keating Experiment in 1971 described how 4 Caesium beam clocks, which are highly accurate clocks stable to about 1 part in 1013, were sent on a global round trip on commercial airliners. The time these clocks gained or lost was compared with a master clock that stayed at the US Naval Observatory, who carried out the experiments. A difference in elapsed time measured by the moving clocks was expected both because of the time dilation of Special Relativity and because of a gravitational effect of General Relativity due to the difference in height of the surface clock and the aircraft clock of about 9 km. The time differences were nanoseconds, but Cs beam clocks can accurately measure such small differences.
|Predicted:||Time difference in ns|
The results are shown in the table for the difference in elapsed times for the aircraft clocks and the surface clocks. They were in complete agreement with Einstein’s predictions. Subsequent repetitions of this experiment in more recent times with better clocks making different trips have confirmed the results.
I’m sure the Navy weren’t testing Einstein’s theory just to show solidarity with modern physics. The GPS system was creation of the US military, based upon highly accurate clocks orbiting the world in satellites. Corrections have to be included for both Special Relativistic effects and for General Relativistic gravitational effects. Without these corrections the system would not produced the accuracy it does, by a long way. Light travels 1 m in about 3 ns so to get 1 m accuracy, and the military system can do better, the clocks and timing corrections need to be correct to this level of accuracy.
Would you bet your life on Special Relativity being true? Anyone who relies on GPS in bad weather may be doing just that. Probably thousands of aircraft passengers and crew do so every day.
The inter-convertability of energy and mass is now part of the woodwork of modern physics, so much so that no-one is devising special tests to see if it is true. Commercial nuclear reactors work because of the mass loss when uranium fissions into lighter elements. The amount of energy produced is that expected from E = mc2. I doubt if anyone weighs the products before and after to the nearest microgram. More quantitative is the so-called Standard Model of the Sun, which predicts how much energy is produced by fusion processes taking place within the Sun. This model has the reality check with the energy actually produced, the rate of consumption of the hydrogen from which the Sun is made, and so on. Much stronger, standard astrophysics explain how stars differing widely from the Sun evolve and has to be consistent with the population of stars actually observed.
Even our local hospital PET scanner shows E = mc2 in action when positrons emitted by the radio-isotope injected in to the patient decay into radiation when they meet an electron from a nearby atom.
In my young days, which was well after 1905, we
were taught about the conservation of mass. Ex nihilo de nihil fecit,
“from nothing, nothing can be made” was the justification. Einstein didn’t
say that something could be created from nothing but he did say that the
mass of an object depended on the speed it was travelling and hence the
energy it had. He gave the precise dependence by the term called
that keeps coming up in Special Relativity. This concept has been tested again and again in pretty well every particle accelerator that has been built.
Particle accelerators are a multi-billion pound international industry these days. In the Daresbury accelerator that is used by academics at Aberdeen, including myself, electrons are accelerated to an energy of 2 Gev. They have some 4000 times the electron rest mass. Accelerators are designed and built to exquisite tolerances based upon special relativity. They need to be. If the mass effect were not taken precisely into account in the roughly circular accelerator then the beam would very quickly crash in to the wall of the accelerator. To keep the beam circulating for hours, which is what happens, you need to know very precisely its mass. Einstein relationship is what is needed and it works precisely. CERN’s LHC accelerator, due to come on line in 2007, will accelerate protons to 7 TeV, giving them about 7000 times their rest mass.
When James Clerk Maxwell predicted the existence
of electromagnetic waves there was an extraordinary feature of his
prediction whose full implication wasn’t fully appreciated at the time.
Maxwell’s equations included a fixed constant
c = (ε0μ0)-½
for the speed of the electromagnetic waves, the speed of light. In everyday life, speeds aren’t fixed constants. They depend on how you, the observer move. Imagine you are the police standing on the roadside clocking my car coming towards you at 60 mph. Alternatively, imagine in a second scenario that you are in a police car coming towards me in my vehicle at 60 mph. You would expect your radar gun now to read the closing speed between us of 120 mph. There isn’t one constant that describes my speed. Maxwell’s speed of light must therefore be the speed in one particular frame of reference, which contemporary physicists called the aether. Michelson set himself the task of measuring the speed of the aether v, as Graham has explained.
Einstein was aware of the result of the Michelson-Morley experiment, and was aware that this experiment found v was zero within experimental error. The Michelson-Morley experiment underpins a central assumption in relativity. It is one of the classic experiments of physics.
Michelson hit upon an ingenious way of measuring the speed of the invisible ether. His problem was that the speed of light is about 300,000 km s-1 and whatever our speed was relative to the invisible ether it should be at least 30 km s-1, due to the orbital speed of the Earth around the Sun, as Bradley had demonstrated. To detect this Michelson needed to measure the speed of light to an accuracy of about 10 km s-1. This accuracy was beyond the scope of technology in the 1880s, when he was considering the issue. Michelson was the best optical experimenter of his generation. He had a stroke of genius. He realised that he just needed to measure the difference in the speed of light in the direction of the aether and at right angles to the aether. This could be done by a ‘round trip’ experiment in a device with two light paths at right angles to each other. He invented such a device, now called a Michelson interferometer. I have one here. It turns out to be an enormously versatile instrument with a huge number of uses.
The bottom line of the experiment is to rotate the equipment smoothly round and if the speed of light is different in different directions the comparison times between light travelling along the two arms will change. Comparison fringes seen in the equipment will shift with the rotation. Michelson found no shift at all. You can see these fringes if you look at the TV monitor here. The apparatus is pretty delicate and can easily detect changes in the length of either arm of 1 micron. The limit on Michelson’s sensitivity was ~15 km per second.
The result was that no velocity could be found. The experiment has been repeated on many occasions with variant and improved equipment. It is not that easy an experiment to do. The strong consensus of results is that no aether can be detected.
I’m showing as a final slide a table that made an impression on me when I first saw it many years ago. It lists 13 key experiments that have a testing relevance to Special Relativity in the columns, and the predictions of 6 alternative theories to Special Relativity in the rows. The red boxes mark the places where the experimental results disagree with the predictions of the theory. Only Special Relativity is in agreement with all testing experiments.
|Light Propagation experiments||Experiments from other fields|
|aether attached to ponderable bodies||D||D||A||A||A||A||A||D||N||N||N||A||N|
|emission theories||original source||A||A||A||A||A||D||D||N||N||D||N||N||N|
A: the theory agrees with experimental
D: the theory disagrees with experimental results
N: the theory is not applicable to the experiment
1: Aberration, 2: Fizeau convection
coefficient; 3: Michelson-Morley; 4: Kennedy-Thorndike; 5: Moving sources
and mirrors; 6: De Sitter spectroscopic binaries; 7: Michelson-Morley, using
8: Variation of mass with velocity; 9: General Mass-Energy equivalence; 10: Radiation from moving charges; 11: Muon decay at high velocity; 12: Trouton-Noble; 13: Unipolar induction, using moving magnet.
Special Relativity is built into the framework of modern physics. Its results are used all the time and areas of physics that use these results work very well. Although some of the results of Special Relativity are counter-intuitive, in hindsight what Einstein did now seems natural. He realised that the incompatibility between Newtonian Mechanics and Electricity & Magnetism should and could be resolved by re-writing the old mechanics and not the new Electricity & Magnetism. In the past this re-write has seemed a bit like a princess climbing into the bed of an elephant and saying “this bed isn’t right for the both of us. You’ll have to move”. Einstein successfully moved the elephant and 100 years of subsequent experiment has proved it was the right thing to do.