The Speed of Light

1: History

The approximate speed of light was already  known to us back in the time of Isaac Newton. Astronomers were able to use the rotation of planets and their moons as an incredibly precise system of "clockwork", and the precision of these measurements was so exact that they could identify the changes in apparent timings caused by light taking longer to reach us from more distant parts of the solar system. The critical measurement was that of the eclipse of the moons of Jupiter -- Roemer noted that the eclipses were seen slightly earlier when Jupiter was nearer to us, and slightly later when the planet was further away. 

Newton's quoted estimates in Opticks of light taking seven or eight minutes to reach us from the Sun, along with an estimated distance of the Sun of seventy million miles, would have given an estimated speed of light of 150,000-160,000 miles per second. More modern values of a bit over eight minutes (~500 seconds) and just over 93 million miles give us a speed of around 186,000 miles per second, so the old figures weren't that far off. [1] [2] 

James Maxwell's work on electricity and magnetism in the mid-Nineteenth Century then led to a prediction of the existence of electromagnetic waves that just happened to propagate at the same speed as light. Maxwell argued that light was an electromagnetic wave, and that visible light consisted of electromagnetic radiation whose wavelengths happened to be in a suitable range for human eyes to be able to detect it.

Maxwell's work suggested that the speed of light should be constant, but didn't tell us exactly what sort of lightspeed constancy ought to be  involved.

2: "Global" lightspeed constancy, and special relativity

G. F.Fitzgerald and H.A. Lorentz pointed out, around the turn of the Twentieth Century, that if lightspeed was absolutely fixed with respect to a background frame, but observers moving with respect to that background frame contracted (and perhaps time-dilated) in a particular way, then it'd be impossible for them to use round-trip measurements of the speed of light to work out whether they were "moving" or "stationary". [3] 

Einstein then took this system of "Lorentzian electrodynamics" and rederived it in more minimal form to produce his special theory of relativity [4]. If we said that light was globally constant for all inertial observers, then the effects associated with Lorentz's "special factor" would absorb the disagreements that we'd otherwise expect between these observers, over whose frame was the "real" frame for the propagation of light. Although it seemed impossible for the same lightbeam to have the same totally-constant speed in everybody's different frames, special relativity's redefinitions of distances and times created a system in which this could work. [5]  

If a lightbeam links two agreed events, special relativity says that two differently-moving observers can disagree as to the distance that they believe the lightbeam "really" traveled and the amount of time that it "really" took to do it, but the combination of those two things, modified by the appropriate Lorentz factors, would combine to produce the same nominal value for the speed of the lightbeam for both observers. For this system to work, we need the lightbeam to travel in a simple way that isn't disturbed by the motion of any nearby objects ... we say that the geometry of spacetime, as defined by lightbeams, is "flat" for all observers with simple inertial motion. 

3: "Local" lightspeed constancy, and general relativity

When Einstein wanted to extend the principle of relativity to deal with all forms of motion, he immediately ran into a problem. Gravity bends lightbeams, and a lightbeam that seems straight and constant for an inertial observer can appear to mark out a variable-speed curved path for an accelerating observer. So special relativity's concept of lightspeed constancy didn't work in a more ambitious theory that also had to be able to deal with accelerations and gravitational effects. Gravity didn't just appear to alter light-distances, it mangled clockrates too [6], so for two different observers drifting in deep space in different gravitational environments, their different rates of timeflow could lead them to assign different speeds to the same lightbeam. These effects also cause a lightbeam to take longer to cross a more "gravitationally-dense" region than one in which the background gravitational field intensity is weaker ("Shapiro effect"). [7]

Under general relativity, the user can respond to these variations by deciding to define distances and times locally. It's no longer necessary for us to apply the earlier SR idea that lightspeed has to be globally constant across the region, it turns out that Nature is happy to violate that rule, as long as lightspeed is still locally constant. So if an observer is drifting in a strong-gravity region where gravitational time dilation is causing their clocks to run at half the speed that we'd otherwise expect, then the same slowing effect should make light move across the region at half the usual speed as well. Someone far outside the region might argue that light is appearing to cross the region more slowly than usual, but to a local observer, whose local references are warped by the same degree as the propagation of light, the speed of adjacent light seems to be exactly right. If it seems to have a different speed somewhere else, well, that's someone else's problem.

4: Combining descriptions

It could now be argued that since we had learnt that only local c-constancy was necessary (and that SR's "law" of the propagation of light wasn't a law after all), perhaps the geometrical basis of the earlier and more restricted"special" theory wasn't valid. Einstein preempted this argument by designing his general theory to reduce to the special theory over small regions of spacetime. He then argued that the special theory wasn't invalidated by general relativity, but instead lived on within it as a limiting case. [8] 

Towards the end of his life, Einstein wrote that he no longer considered the decision to construct general relativity as a two-stage model, with "curvature" arguments built on top of a flat-spacetime "SR" foundation, as justifiable. It had been the best that could be achieved at the time, but with the benefit of hindsight it didn't deem to be defensible. [9] Quite what Einstein may have meant by this, what the alternative might have been, and what the implications might be of having a general theory that didn't have a forced reduction to special relativity, still seem to be unresolved questions. [10]  

References:

1. I. Newton, Principia, Book I (based on the 1729 Motte translation from the original Latin)
   " For it is now certain from the phenomena of Jupiter's satellites, confirmed by the observations of different astronomers, that light is propagated in succession, and requires about seven or eight minutes to travel from the sun to the earth.  ... ... Therefore because of the analogy there is between the propagation of rays of light and the motion of bodies, I thought it not amiss to add the following Propositions for optical uses; not at all considering the nature of the rays of light, or inquiring whether they are bodies or not; but only determining the curves of bodies which are extremely like the curves of the rays. " 

2. I. Newton, Opticks, Definitions II, and Query 21" ... But by an argument taken from the equations of the times of the eclipses of Jupiter's satellites it seems that light is propagated in time, spending in its passage from the Sun to us about seven minutes of time ... And therefore I have chosen to define rays and refractions in such general terms as may agree to light in both cases. "
   " Light moves from the Sun to us in about seven or eight minutes of time, which distance is about 70,000,000 English miles, supposing the horizontal parallax of the Sun to be about 12 ' '  "

3. H. A. Lorentz, "Electromagnetic Phenomena in a System moving with any Velocity less than that of Light", Proc. Acad Sci Amsterdam 6 1904[on "aether drift" results]: " The first example of this kind is Michelson's well-known interference-experiment, the negative result of which has led Fitzgerald and myself to the conclusion that the dimensions of solid bodies are slightly altered by their motion through the aether. "

4. A. Einstein, "On the Electrodynamics of Moving Bodies" ("Zur Elektrodynamik bewegter Körper"), Annalen der Physik 17 1905" If we imagine the electric charges to be invariably coupled to small rigid bodies (ions, electrons), these equations are the electromagnetic basis of the Lorentzian electrodynamics and optics of moving bodies. "

5. A. Einstein, Relativity, the Special and the General Theory section 7, "The apparent incompatibility of the Law of Propagation of Light with the Principle of Relativity"" At this juncture the theory of relativity entered the arena. As a result of an analysis of the physical conceptions of time and space, it became evident that in reality there is not the least incompatibility between the principle of relativity and the law of propagation of light, and that by systematically holding fast to both these laws a logically rigid theory could be arrived at. This theory has been called the special theory of relativity ... "

6. A. Einstein, "On the influence of Gravitation on the Propagation of Light" ("Über den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes") Annalen der Physik 35 1911" The principle of the constancy of the velocity of light holds good according to this theory in a different form from that which usually underlies the ordinary theory of relativity. "

7. For a good discussion of the Shapiro effect, see: Clifford Will, Was Einstein Right, ch.6: "The time delay of light: better late than never", pp 108-134

8. A. Einstein, Relativity, the Special and the General Theory section 22, "A few inferences from the General Principle of Relativity"" ... according to the general principle of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case ... ... No fairer destiny could be allotted to any physical theory, than that it should of itself point out the way to the introduction of a more comprehensive theory, in which it lives on as a limiting case. "

9. A. Einstein, Scientific American, April 1950
   " I do not see any reason to assume that ... the principle of general relativity is restricted to gravitation and that the rest of physics can be dealt with separately on the basis of special relativity ... I do not think that such an attitude, although historically understandable, can be objectively justified ... In other words, I do not believe that it is justifiable to ask: what would physics look like without gravitation? "

10. E. Baird, Relativity in curved spacetime (2007), section 12, "What's wrong with General relativity?" 
    " Almost all of the problems and potential problems that we've identified here with Einstein's general theory seem to be consequences of the theory's incorporation of special relativity, and its assumption that the relationships of SR have to apply as a limiting case of the theory. ..."

all original material copyright © Eric Baird 2007/2008