Michael Fowler Physics
Dept., U.
As we shall soon see, attempts to measure the speed of light played an important part in the development of the theory of special relativity, and, indeed, the speed of light is central to the theory.
The first recorded discussion of the speed of light (I think) is in Aristotle, where he quotes Empedocles as saying the light from the sun must take some time to reach the earth, but Aristotle himself apparently disagrees, and even Descartes thought that light traveled instantaneously. Galileo, unfairly as usual, in Two New Sciences (page 42) has Simplicio stating the Aristotelian position,
SIMP. Everyday experience shows that the propagation of light is instantaneous; for when we see a piece of artillery fired at great distance, the flash reaches our eyes without lapse of time; but the sound reaches the ear only after a noticeable interval.
Of course, Galileo points out that in fact nothing about the speed of light can be deduced from this observation, except that light moves faster than sound. He then goes on to suggest a possible way to measure the speed of light. The idea is to have two people far away from each other, with covered lanterns. One uncovers his lantern, then the other immediately uncovers his on seeing the light from the first. This routine is to be practiced with the two close together, so they will get used to the reaction times involved, then they are to do it two or three miles apart, or even further using telescopes, to see if the time interval is perceptibly lengthened. Galileo claims he actually tried the experiment at distances less than a mile, and couldn’t detect a time lag. From this one can certainly deduce that light travels at least ten times faster than sound.
The first real measurement of the speed of light came about half a century later, in 1676, by a Danish astronomer, Ole Römer, working at the Paris Observatory. He had made a systematic study of Io, one of the moons of Jupiter, which was eclipsed by Jupiter at regular intervals, as Io went around Jupiter in a circular orbit at a steady rate. Actually, Römer found, for several months the eclipses lagged more and more behind the expected time, until they were running about eight minutes late, then they began to pick up again, and in fact after about six months were running eight minutes early. The cycle then repeated itself. Römer realized the significance of the time involved-just over one year. This time period had nothing to do with Io, but was the time between successive closest approaches of earth in its orbit to Jupiter. The eclipses were furthest behind the predicted times when the earth was furthest from Jupiter.
The natural explanation was that the light from Io (actually reflected sunlight, of course) took time to reach the earth, and took the longest time when the earth was furthest away. From his observations, Römer concluded that light took about twenty-two minutes to cross the earth’s orbit. This was something of an overestimate, and a few years later Newton wrote in the Principia (Book I, section XIV): “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 (NOTE: I think this means at finite speed) and requires about seven or eight minutes to travel from the sun to the earth.” This is essentially the correct value.
Of course, to find the speed of light it was also necessary to know the distance from the earth to the sun. During the 1670’s, attempts were made to measure the parallax of Mars, that is, how far it shifted against the background of distant stars when viewed simultaneously from two different places on earth at the same time. This (very slight) shift could be used to find the distance of Mars from earth, and hence the distance to the sun, since all relative distances in the solar system had been established by observation and geometrical analysis. According to Crowe (Modern Theories of the Universe, Dover, 1994, page 30), they concluded that the distance to the sun was between 40 and 90 million miles. Measurements presumably converged on the correct value of about 93 million miles soon after that, because it appears Römer (or perhaps Huygens, using Römer’s data a short time later) used the correct value for the distance, since the speed of light was calculated to be 125,000 miles per second, about three-quarters of the correct value of 186,300 miles per second. This error is fully accounted for by taking the time light needs to cross the earth’s orbit to be twenty-two minutes (as Römer did) instead of the correct value of sixteen minutes.
The next substantial improvement in measuring the speed of light took place
in 1728, in
The problem is, all these astronomical techniques do not have the appeal of
Galileo’s idea of two guys with lanterns. It would be reassuring to measure the
speed of a beam of light between two points on the ground, rather than making
somewhat indirect deductions based on apparent slight variations in the
positions of stars. We can see,
though, that if the two lanterns are ten miles apart, the time lag is of order
one-ten thousandth of a second, and it is difficult to see how to arrange that.
This technical problem was solved
in
Albert Michelson was born in 1852 in
Shortly after graduation, Michelson was ordered aboard the USS Monongahela,
a sailing ship, for a voyage through the Caribbean and down to
[SALV.] Shut yourself up with some friend in the largest room below decks of some large ship and there procure gnats, flies, and other such small winged creatures. Also get a great tub full of water and within it put certain fishes; let also a certain bottle be hung up, which drop by drop lets forth its water into another narrow-necked bottle placed underneath. Then, the ship lying still, observe how those small winged animals fly with like velocity towards all parts of the room; how the fish swim indifferently towards all sides; and how the distilling drops all fall into the bottle placed underneath. And casting anything toward your friend, you need not throw it with more force one way than another, provided the distances be equal; and leaping with your legs together, you will reach as far one way as another. Having observed all these particulars, though no man doubts that, so long as the vessel stands still, they ought to take place in this manner, make the ship move with what velocity you please, so long as the motion is uniform and not fluctuating this way and that. You will not be able to discern the least alteration in all the forenamed effects, nor can you gather by any of them whether the ship moves or stands still. ...in throwing something to your friend you do not need to throw harder if he is towards the front of the ship from you... the drops from the upper bottle still fall into the lower bottle even though the ship may have moved many feet while the drop is in the air ... Of this correspondence of effects the cause is that the ship’s motion is common to all the things contained in it and to the air also; I mean if those things be shut up in the room; but in case those things were above the deck in the open air, and not obliged to follow the course of the ship, differences would be observed, ... smoke would stay behind... .
[SAGR.] Though it did not occur to me to try any of this out when I was at sea, I am sure you are right. I remember being in my cabin wondering a hundred times whether the ship was moving or not, and sometimes I imagined it to be moving one way when in fact it was moving the other way. I am therefore satisfied that no experiment that can be done in a closed cabin can determine the speed or direction of motion of a ship in steady motion.
I have paraphrased this last remark somewhat to clarify it. This conclusion of Galileo’s, that everything looks the same in a closed room moving at a steady speed as it does in a closed room at rest, is called The Principle of Galilean Relativity. We shall be coming back to it.
On returning to
At work, lecture demonstrations had just been introduced at
The next lecture is on the Michelson-Morley experiment to detect the aether.
Text Copyright © Michael Fowler 1996 except where otherwise noted.