Another assumption on the laws of physics made by the SI definition of the metre is that the theory of relativity is correct. It is a basic postulate of the theory of relativity that the speed of light is the same in all inertial frames. This can be broken down into two parts:
- The speed of light is independent of the motion of the observer.
- The speed of light does not vary with time or place.
To state that the speed of light is independent of the velocity of the observer is very counterintuitive. Some people even refuse to accept this as a logically consistent possibility, but in 1905 Einstein was able to show that it is perfectly consistent if you are prepared to give up assumptions about the absolute nature of space and time.
In 1879 it was thought that light must propagate through a medium in space, the ether, just as sound propagates through the air and other substances. The two scientists Michelson and Morley set up an experiment to attempt to detect the ether, by observing relative changes in the speed of light as Earth changed its direction of travel relative to the sun during the year. To their surprise, they failed to detect any change in the speed of light.
Fitzgerald then suggested that this might be because the experimental apparatus contracted as it passed through the ether, in such a way as to countermand the attempt to detect the change in velocity. Lorentz extended this idea to changes in the rates of clocks to ensure complete undetectability of the ether. Einstein then argued that those transformations should be understood as changes of space and time rather than of physical objects, and that the absoluteness of space and time introduced by Newton should be discarded. Just after that, the mathematician Minkowski showed that Einstein's theory of relativity could be understood in terms of a four dimensional non-euclidean geometry that considered space and time as one entity, ever after called spacetime.
The theory is not only mathematically consistent, it agrees with many direct experiments. The Michelson-Morley experiment was repeated with greater accuracy in the years that followed. In 1925 Dayton Miller announced that he had detected a change in the speed of light and was even awarded prizes for the discovery, but a 1950s appraisal of his work indicated that the most likely origin of his results lay with diurnal and seasonal variations in the temperature of his equipment.
Modern instruments could easily detect any ether drift if it existed. Earth moves around the Sun at a speed of about 30 km/s, so if velocities added vectorially as newtonian mechanics requires, the last 5 digits in the value of the speed of light now used in the SI definition of the metre would be meaningless. Today, high energy physicists at CERN in Geneva and Fermilab in Chicago routinely accelerate particles to within a whisker of the speed of light. Any dependence of the speed of light on inertial reference frames would have shown up long ago, unless it is very slight indeed. Their measurements are actually made in a non-inertial frame because gravity is present. But in the context of the measurements, this non-inertial frame is almost identical to a "uniformly accelerated frame" (this is actually the content of Einstein's Principle of Equivalence). And it turns out that a measurement of light's speed made in a uniformly accelerated frame directly by someone who is very close to the light will return the inertial value of c—although that observer must be close to the light to measure this value.
But what if we pursued the original theory of Fitzgerald and Lorentz, who proposed that the ether is there, but is undetectable because of physical changes in the lengths of material objects and the rates of clocks, rather than changes in space and time? For such a theory to be consistent with observation, the ether would need to be completely undetectable using clocks and rulers. Everything, including the observer, would have to contract and slow down by just the right amount. Such a theory could make exactly the same prediction in all experiments as the theory of relativity; but it would reduce the ether to essentially no more than a metaphysical construct unless there was some other way of detecting it—which no one has found. In the view of Einstein, such a construct would be an unnecessary complication, to be best eliminated from the theory.