Myths of Physics: 1. Einstein's Speed Limit Is the Speed of Light

This is the first of some huffing and puffing I plan to do involving several common myths about physics, which are held by most people including some but not all physicists. The first involves the speed of light.

One of the axioms of Einstein's special theory of relatively is that the speed of light in a vacuum is equal to an absolute constant c that is independent of the motion of the source or observer of the light. The first common myth I wish to address is that c is a measurable quantity and that it is possible to disprove the special theory by measuring a different speed in different frames of reference.

Occasionally you will read in the media that some scientist has described some phenomenon showing that Einstein was wrong. Most recently, a paper published online by physicist J. D. Franson of the University of Maryland has caught attention. The paper was misinterpreted as implying the violation of Einsteins's axiom. The author made no such assertion. Rather he argued that light would slow down passing the sun more than the amount that had been calculated by Einstein. He proposed that this explains an anomaly in the time delays between the neutrinos and visible light detected from Supernova 1987a.

Franson's calculation is questionable, as are the data suggesting an anomaly. However, this is not the subject of this essay. Rather, I wish to clarify the physical meaning of the parameter c that appears in so many physics equations in order to dispel the myth that by measuring the speed of light more precisely we might disprove relativity.

Light does not always travel at the speed c. It generally moves slower than c in a medium. And, as Einstein showed, light also slows down in passing by the sun or through any other strong gravitational field. Franson is somewhat dubiously claiming that it slows down even more that Einstein said because of a quantum gravity effect that Einstein could not have known about. Even if Franson is correct, this has no consequence for the axioms of relativity.

Now, according to the special theory, particles with zero mass will move at the speed c. The photons that compose a beam of light seem to have zero mass to very high precision and so are usually assumed to move at the speed c. However, if the photon should someday be shown to have a very tiny, nonzero mass, it would move at a speed less than c that, like any other particle with mass, would depend on its energy. Furthermore, some quantum gravity proposals imply a speed other than c for massless photons.

The point is: "speed of light" is a misnomer for the quantity c. Light does not always travel at this speed, even in a vacuum. If you look into special relativity you will see that c is more precisely understood as "Einstein's speed limit." It is the speed beyond which no particle can be accelerated. The theory allows for particles to move faster than c, as long as they never move slower. These are called "tachyons" and, while theoretically possible, none have ever been observed.

For over a century now, thousands of experiments have been performed severely testing the special theory of relativity and, so far, it has withstood every test. These involved many kinds of phenomena, not just the speed of light. In 1983, by international agreement, Einstein's postulate was incorporated into the operational structure of physics by the redefinition of the very meaning of space. The distance between two points in space was defined as the time it takes a particle moving at Einstein's speed limit to go between those points.

Generally this is stated as "the time it takes light in a vacuum to go between those points," but we see that this is not exactly what the definition implies.

Like time, space is what you measure on a clock.

Earlier, in 1967, the basic unit of time, the second, had been redefined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine energy levels of the ground state of the Cesium-133 atom at rest at absolute zero. In 1983, the basic unit of distance in the Standard International system of units, the meter, was specified to be the distance traveled by a particle moving at Einstein's speed limit during 1/299,792,458 of a second. Again, I have restated the original, still official definition in a more precise form.

In short, the meter is no longer defined, as it once was--by a separate measurement--but rather by a measurement on the same atomic clock you use to measure time. This codified the fundamental assumption build into Einstein's model that time and space comprise interdependent parts of a single, four-dimensional spacetime manifold.

As a result, the value of the quantity c depends on what units you decide to use for distance and time. If you choose to measure time in seconds and distance in meters, then by definition c = 299,792,458 meters per second. If you choose to measure time in years and distance in light-years, then by definition c = 1 light-year per year. Again, c is not necessarily the speed of light or that of any other material substance.

You can go ahead and try to measure the speed of light in a vacuum if you like. If your measuring instruments are properly calibrated by an atomic clock, then you are going to get 299,792,458 meters per second every time. If you don't, then all this will prove is that your light beam did not travel at c, not that Einstein was wrong. Einstein could someday turn out to be wrong, because that's how science works. But that fact will not be discovered by measuring the speed of light.