Re: Syncronized atomic clocks

From: Sam Wormley (swormley1_at_mchsi.com)
Date: 06/10/04 

Date: Thu, 10 Jun 2004 15:02:59 GMT

The Ghost In The Machine wrote:
>
> In sci.physics, Sam Wormley
> <swormley1@mchsi.com>
> >
> > Whoa Ghost--The speed of light is constant!
> > http://scienceworld.wolfram.com/physics/SpeedofLight.html
>
> That's the theory, yes...I agree with it in general but
> would be curious as to how one can verify that c in deep
> space is the same as c on the Earth. (Presumably one can
> locate a binary star on the edge of a dust cloud, perhaps.)
>

Ref: http://www.phys.virginia.edu/classes/109N/lectures/spedlite.html

The Speed of Light

Michael Fowler

Physics Dept., U. Va.

Index of Lectures and Overview of the Course Link to Previous Lecture

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, 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.

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
Carribean 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.

Index of Lectures and Overview of the Course

Text Copyright © Michael Fowler 1996 except where otherwise noted.

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