The Speed of Light
Michael Fowler, UVa Physics
Department
Early Ideas about Light Propagation
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 practised 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.
Measuring the Speed of Light with Jupiter’s Moons
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, but then
they began to pick up again. In
September 1676,he correctly predicted that an eclipse on November 9 would be 10
minutes behind schedule. This was
indeed the case, to the surprise of his skeptical colleagues at the Royal
Observatory in Paris. Two weeks later, he told them what was
happening: as the Earth and Jupiter moved in their orbits, the distance between
them varied. 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. When the Earth was furthest from
Jupiter, there was an extra distance for light to travel equal to the diameter
of the Earth’s orbit compared with the point of closest approach. The observed eclipses were furthest
behind the predicted times when the earth was furthest from Jupiter.
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.
Starlight and Rain
The next substantial improvement in measuring the speed of light took place
in 1728, in England. An astronomer James Bradley, sailing on
the Thames with some friends, noticed that the little pennant on top of the
mast changed position each time the boat put about, even though the wind was
steady. He thought of the boat as
the earth in orbit, the wind as starlight coming from some distant star, and
reasoned that the apparent direction the starlight was “blowing” in
would depend on the way the earth was moving. Another possible analogy is to imagine
the starlight as a steady downpour of rain on a windless day, and to think of
yourself as walking around a circular path at a steady pace. The apparent direction of the incoming
rain will not be vertically downwards—more will hit your front than your
back. In fact, if the rain is
falling at, say, 15 mph, and you are walking at 3 mph, to you as observer the
rain will be coming down at a slant so that it has a vertical speed of 15 mph,
and a horizontal speed towards you of 3 mph. Whether it is slanting down from the
north or east or whatever at any given time depends on where you are on the
circular path at that moment. Bradley
reasoned that the apparent direction of incoming starlight must vary in just
this way, but the angular change would be a lot less dramatic. The earth’s speed in orbit is
about 18 miles per second, he knew from Römer’s work that light went
at about 10,000 times that speed. That
meant that the angular variation in apparent incoming direction of starlight
was about the magnitude of the small angle in a right-angled triangle with one
side 10,000 times longer than the other, about one two-hundredth of a degree. Notice this would have been just at the
limits of Tycho’s measurements, but the advent of the telescope, and
general improvements in engineering, meant this small angle was quite
accurately measurable by Bradley’s time, and he found the velocity of
light to be 185,000 miles per second, with an accuracy of about one percent.
Fast Flickering Lanterns
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 France
about 1850 by two rivals, Fizeau and Foucault, using slightly different
techniques. In Fizeau’s
apparatus, a beam of light shone between the teeth of a rapidly rotating
toothed wheel, so the “lantern” was constantly being covered and
uncovered. Instead of a second
lantern far away, Fizeau simply had a mirror, reflecting the beam back, where
it passed a second time between the teeth of the wheel. The idea was, the blip of light that
went out through one gap between teeth would only make it back through the same
gap if the teeth had not had time to move over significantly during the round
trip time to the far away mirror. It
was not difficult to make a wheel with a hundred teeth, and to rotate it
hundreds of times a second, so the time for a tooth to move over could be
arranged to be a fraction of one ten thousandth of a second. The method worked. Foucault’s method was based on the
same general idea, but instead of a toothed wheel, he shone the beam on to a
rotating mirror. At one point in
the mirror’s rotation, the reflected beam fell on a distant mirror, which
reflected it right back to the rotating mirror, which meanwhile had turned
through a small angle. After this
second reflection from the rotating mirror, the position of the beam was
carefully measured. This made it
possible to figure out how far the mirror had turned during the time it took
the light to make the round trip to the distant mirror, and since the rate of
rotation of the mirror was known, the speed of light could be figured out. These techniques gave the speed of light
with an accuracy of about 1,000 miles per second.
Albert Abraham Michelson
Albert Michelson was born in 1852 in Strzelno,
Poland. His father Samuel was a Jewish merchant,
not a very safe thing to be at the time.
Purges of Jews were frequent in the neighboring towns and villages. They decided to leave town. Albert’s fourth birthday was
celebrated in Murphy’s Camp, Calaveras
County, about fifty miles south east
of Sacramento,
a place where five million dollars worth of gold dust was taken from one four
acre lot. Samuel prospered selling
supplies to the miners. When the
gold ran out, the Michelsons moved to Virginia City,
Nevada, on the Comstock
lode, a silver mining town.
Albert went to high school in San
Francisco.
In 1869, his father spotted an announcement in the local paper that
Congressman Fitch would be appointing a candidate to the Naval
Academy in Annapolis, and inviting applications. Albert applied but did not get the
appointment, which went instead to the son of a civil war veteran. However, Albert knew that President
Grant would also be appointing ten candidates himself, so he went east on the
just opened continental railroad to try his luck. Unknown to Michelson, Congressman Fitch
wrote directly to Grant on his behalf, saying this would really help get the
Nevada Jews into the Republican party.
This argument proved persuasive.
In fact, by the time Michelson met with Grant, all ten scholarships had
been awarded, but the President somehow came up with another one. Of the incoming class of ninety-two,
four years later twenty-nine graduated.
Michelson placed first in optics, but twenty-fifth in seamanship. The Superintendent of the Academy, Rear
Admiral Worden, who had commanded the Monitor
in its victory over the Merrimac,
told Michelson: “If in the future you’d give less attention to
those scientific things and more to your naval gunnery, there might come a time
when you would know enough to be of some service to your country.”
Sailing the Silent
Seas: Galilean Relativity
Shortly after graduation, Michelson was ordered aboard the USS Monongahela,
a sailing ship, for a voyage through the Carribean and down to Rio. According
to the biography of Michelson written by his daughter (The Master of Light,
by Dorothy Michelson Livingston, Chicago, 1973) he thought a lot as the ship
glided across the quiet Caribbean about
whether one could decide in a closed room inside the ship whether or not the
vessel was moving. In fact, his
daughter quotes a famous passage from Galileo on just this point:
[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.
Michelson Measures the Speed of Light
On returning to Annapolis from the cruise,
Michelson was commissioned Ensign, and in 1875 became an instructor in physics
and chemistry at the Naval
Academy, under Lieutenant
Commander William Sampson. Michelson
met Mrs. Sampson’s niece, Margaret Heminway, daughter of a very
successful Wall Street tycoon, who had built himself a granite castle in New Rochelle, NY. Michelson married Margaret in an
Episcopal service in New Rochelle
in 1877.
At work, lecture demonstrations had just been introduced at Annapolis. Sampson suggested that it would be a
good demonstration to measure the speed of light by Foucault’s method. Michelson soon realized, on putting
together the apparatus, that he could redesign it for much greater accuracy,
but that would need money well beyond that available in the teaching
demonstration budget. He went and
talked with his father in law, who agreed to put up $2,000. Instead of Foucault’s 60 feet to
the far mirror, Michelson had about 2,000 feet along the bank of the Severn, a distance he measured to one tenth of an inch. He invested in very high quality lenses
and mirrors to focus and reflect the beam.
His final result was 186,355 miles per second, with possible error of 30
miles per second or so. This was
twenty times more accurate than Foucault, made the New York Times, and
Michelson was famous while still in his twenties. In fact, this was accepted as the most
accurate measurement of the speed of light for the next forty years, at which
point Michelson measured it again.
The next lecture is on the Michelson-Morley
experiment to detect the aether.