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| The Theory of Relativity (2)
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"Is motion relative? After some first thoughts you may be inclined to answer, 'Of course it is!'
Imagine a train moving north at 100 kilometers per hour. On the train a man walks south at
4 kilometers per hour. In what direction is he moving and at what speed? It is immediately
obvious that this question cannot be answered without choosing a frame of reference. Relative
to the train, the man moves south at 4 kilometers per hour. Relative to the ground, he moves
north at 100 - 4 = 96 kilometers per hour.
"Can we say that the man's 'ground speed (96 kilometers per hour) is his true, absolute speed?
No, because there are other, larger frames of reference. The earth itself is moving. It both rotates
and swings around the sun. The sun, with all its planets, speeds through the galaxy. The galaxy
rotates and moves relative to other galaxies. The galaxies in turn form galactic clusters that
move relative to each other. No one really knows how far this chain of motions can be carried.
There is no apparent way to chart the absolute motion of anything; that is to say, there is no
fixed, final frame of reference by which all motions can be measured. (Since that sentence
was written, a way has been found to measure the earth's quasi-absolute motion relative to
the black-body radiation that permeates our universe.) Motion and rest, like large and small,
slow and fast, up and down, left and right, seem to be completely relative. There is no way
to measure the motion of one object except by comparing it with the motion of some other
object.
"Alas, it is not so simple! If this were all there is to say about the relativity of motion, there
would have been no need for Albert Einstein to develop his theory of relativity. Physicists
would have had the theory all along!
"The reason it is not simple is this: there appear to be two very easy ways to detect absolute
motion. One method makes use of the speed of light; the other makes use of various inertial
effects that occur when a moving object alters its path or velocity. Einstein's special theory of
relativity deals with the first, his general theory of relativity with the second. The first method
that might serve as a clue to absolute motion is the method that makes use of the speed of
light.
"In the nineteenth century, before the time of Einstein, physicists thought of space as containing
a kind of fixed, invisible substance called the ether. Often it was called the 'luminiferous ether,'
meaning that it was the bearer of light waves. It filled the entire universe. It penetrated all material
substances. If all the air were pumped out of a glass bell jar, the jar would still be filled --filled
with ether. Otherwise, how could light travel through the vacuum? Light is a wave motion; there
had to be something there to transmit the waving. The ether itself, although it must vibrate,
seldom (if ever) would move with respect to material objects; rather, all objects would move
through it, like the movement of a sieve through water. The absolute motion of a star, planet,
or any object whatever was (so these early physicists were convinced) simply its motion with
respect to this motionless, invisible, etherial sea.
"But, you may ask, if the ether is an invisible, nonmaterial substance -- a substance that
cannot be seen, heard, felt, smelled or tasted -- how can the movement of, say, the earth
ever be measured with respect to it? The answer is simple. The measurement can be made
by comparing the earth's motion with the motion of a beam of light.
"To understand this, consider for a moment the nature of light. Actually, light is only the small
visible portion of a spectrum of electromagnetic radiation which includes radio waves, radar
waves, infrared light, ultraviolet light, and gamma rays. Everything said about light in this book
applies equally to any type of electromagnetic wave, but 'light' is a shorter term than
'electromagnetic wave,' so this term will be used throughout. Light is a wave motion. To think
of such a motion without thinking also of a material ether seemed to the early physicists as
preposterous as thinking about water waves without thinking of water.
"If a bullet is fired straight ahead from the front of a moving jet plane, the ground speed of the
bullet is faster than if it were fired from a gun held by someone on the ground. The ground
speed of the bullet fired from the plane is obtained by adding the speed of the plane to the
speed of the bullet. In the case of light, however, the velocity of a beam is not affected by the
speed of the object that sends out the beam. This was strongly indicated by experiments in
the late nineteenth and early twentieth centuries, and has since been amply confirmed,
especially by recent tests on the decay of neutral pi mesons. One famous test was made by
Russian astronomers in 1955, using light from opposite sides of the rotating sun. One edge
of our sun is always moving toward us, the other edge always moving away. It was found that
light from both edges travels to the earth with the same velocity. Similar tests had been made
decades earlier with light from revolving double stars. Regardless of the motion of its source,
the speed of light through empty space is always the same: about 299,800 kilometers
(186,300 miles) per second.
"Do you see how this fact provides a means by which a scientist (we will call him the observer)
could calculate his own absolute motion? If light travels through a fixed, stationary ether with a
certain speed, c, and if this velocity is independent of the velocity of its source, then the speed
of light can be used as a kind of yardstick for measuring the observer's absolute motion. An
observer moving in the same direction as a beam of light should find the beam passing him
with a speed less than c; an observer moving toward a beam of light should find the beam
approaching him with a velocity greater than c. In other words, measurements of the velocity of
a beam of light should vary, depending on the observer's motion relative to the beam. These
variations would indicate his true, absolute motion through the ether.
"Physicists often describe this situation in terms of what they call an 'ether wind.' To understand
just what they mean by this, consider again that moving train. We have seen how the speed of a
man walking through the train at 4 kilometers per hour is always the same relative to the train,
regardless of whether he walks toward the engine or toward the rear of the train. The same is
true of the speed of sound waves inside a closed car. Sound is a wave motion transmitted by
molecules of air. Because the air is carried along by the car, sound will travel north in the car
with the same velocity (relative to the car) with which it travels south.
"The situation alters if we move from the closed passenger car to an open flatcar. The air is
no longer trapped inside the car. If the train moves at 100 kilometers per hour, there will be
a wind of 100 kilometers per hour blowing back across the flatcar. Because of this wind, the
speed of sound moving from the back to the front of the car will be less than normal. The
speed of sound from front to back will be greater than normal.
"Physicists of the nineteenth century believed that the ether surely must behave like the air
that rushes over a moving flatcar. How could it be otherwise? If the ether is motionless, any
object moving through it would have to encounter an 'ether wind' blowing in the opposite
direction. Light is a wave motion in this fixed ether. The velocity of light, measured on a moving
object, would of course be influenced by such an ether wind.
"The earth is hurtling through space, on its trip around the sun, at a speed of about 30 kilometers
per second. This motion, the physicists reasoned, should create an ether wind of 30 kilometers
per second, blowing past the earth and through the spaces between its atoms. To measure
the absolute motion of the earth -- its motion with respect to the fixed ether -- all that would be
necessary would be to measure the speed of light as it travels back and forth in different directions
on the earth's surface. Because of the ether wind, light would surely move faster in one direction
than another. By comparing the various speeds of light as it is sent in different directions, it
should then be possible to calculate the absolute direction and velocity of the earth's motion
at any given instant. Such an experiment was first proposed in 1875, four years before Einstein
was born, by the great Scottish physicist James Clerk Maxwell. (The suggestion appears in
Maxwell's article on 'Ether' in the ninth edition of Encyclopaedia Britannica.)
"In 1881 Albert Abraham Michelson, then a young officer in the United States Navy, made
just such an experiment. Michelson had been born in Germany, of Polish parents, but his
father had taken him to America when he was two. After graduating from the U.S. Naval
Academy at Annapolis and serving two years at sea, he became a teacher of physics and
chemistry at the Academy. A leave of absence permitted him to study in Europe. It was at the
University of Berlin, in the laboratory of the famous German physicist Hermann von Helmholtz,
that young Michelson made his first attempt to detect an ether wind. To his great surprise, he
could find no difference in the speed with which light traveled back and forth in any direction
of the compass. It was as if a fish had discovered that it could swim in any direction through
the sea without being able to detect the motion of water past its body; as if a pilot flying in the
open cockpit of a plane could feel no wind against his face.
"A distinguished Austrian physicist named Ernst Mach had for some time been criticizing the
notion of absolute motion through the ether. He read Michelson's published report on the test
and decided at once that the concept of an ether had to be discarded. However, most physicists
refused to take this daring step. Michelson's apparatus had been crude. There was good reason
to think that a better-designed experiment, with more sensitive equipment, would show positive
results. Michelson himself thought so. He was disappointed in the 'failure' of his test, and eager
to try again.
"Michelson resigned his naval commission to become a professor of physics at the Case
School of Applied Science (now the Case Institute) in Cleveland, Ohio. At nearby Western
Reserve University, Edward Williams Morley was teaching chemistry. The two men became
good friends. 'Outwardly,' writes Bernard Jaffe in his book Michelson and the Speed of Light,
'the two scientists were a study in contrast. . . . Michelson was goodlooking and trim, always
immaculately turned out. Morley, who was casual in dress, to say the least, fit the stereotype
of the absent-minded professor. . . . He let his hair grow until it curled up on his shoulders,
and he wore a great bristling red mustache that straggled almost to his ears.'
"In 1887, in Morley's basement laboratory, the two scientists made a second, more careful
attempt to detect the elusive ether wind. Their experiment, which became known as the
Michelson-Morley experiment, marked one of the great turning points in modern physics.
"The apparatus was mounted on a square slab of stone about five feet on the side and more
than a foot thick. The slab floated on liquid mercury. This eliminated vibrations, kept the slab
horizontal, and permitted it to be rotated easily around a central pin. An arrangement of mirrors
on the slab sent a light beam in a certain direction; then the mirrors reflected the beam back
and forth in that same direction until it had made eight round trips. (This was done to make
the path as long as possible and still keep the equipment on a device that could be rotated
easily.) At the same time, the mirror arrangement sent a beam of light on eight round trips in
a direction at right angles to the first beam.
"The assumption was that when the slab was turned so that one beam traveled back and
forth parallel to the ether wind, this beam would make the trip in a longer time than it would
take the other beam to go the same distance across the wind. At first you might think the
reverse would be true. Consider the light that travels with and against the wind. Would not
the wind boost the speed by the same amount one way that it would retard the speed the
other way? If so, the boosts and drags would cancel each other, and the time for the total trip
would be the same as if there were no wind at all.
"It is true that the wind would increase the velocity of light in one direction by the same amount
that it would decrease the velocity in the other direction, but -- and this is the crucial point -- the
wind would retard the speed for a longer period of time. Calculation quickly shows that the
entire trip would take longer than if there were no wind. The wind would also have a retarding
effect on the beam that traveled across the wind at right angles. This is also easily calculated.
It turns out that this retarding effect is less than in the case of the beam traveling parallel to the
wind.
"There was little doubt, then, that if the earth moved through an immovable sea of ether, there
would be an ether wind, and if there were an ether wind, the Michelson-Morley apparatus would
detect it. In fact, both scientists were confident that they would not only find such a wind, but
they could also determine (by rotating the slab until there was a maximum difference in the
time it took light to make the two journeys) the exact direction, at any given moment, of the
earth's path through the ether.
"It should be pointed out that the Michelson-Morley apparatus did not measure the actual
velocities of each beam of light. The two beams, after making their respective back-and-forth
trips, were combined into a single beam which was viewed through a small telescope. The
apparatus would then be rotated slowly. Any alteration in the relative velocities of the two
beams would cause a shifting of an interference fringe pattern of alternate light and dark
bands.
"Again Michelson was astounded and disappointed. This time the astonishment was felt by
physicists all over the world. Regardless of how Michelson and Morley turned their apparatus,
they found no sign of an ether wind! Never before in the history of science had the negative
results of an experiment been so positive and so shattering. Michelson once more thought
his experiment a failure. He never dreamed that this 'failure' would make the experiment one
of the most successful, revolutionary experiments in the history of science.
"Later, Michelson and Morley repeated their test with even more accurate equipment. Other
physicists did the same. An extremely accurate test was made in 1960 by Charles H. Townes
of Columbia University. His apparatus, using a device called a maser (an 'atomic clock' based
on the vibrations of molecules), was so sensitive that he could have detected an ether wind
even if the earth moved at a mere one-thousandth of its actual speed. There was no trace of
such a wind.
"Physicists at first were so amazed by the negative results of the Michelson-Morley test that
they began inventing all sorts of explanations to save the ether-wind theory. Of course, if the
experiment had been performed a few centuries earlier, as G. J. Whitrow points out in his
book The Structure and Evolution of the Universe, a very simple explanation would immediately
have occurred to everyone: the earth doesn't move! This theory seemed unlikely. The best
explanation was a theory (much older than the first Michelson-Morley experiment) that the
ether is dragged along by the earth, like air inside a closed train. This was Michelson's own
guess. But other experiments, one by Michelson himself, ruled this out.
"The strangest explanation of all was put forth by an Irish physicist, George Francis FitzGerald.
Perhaps, he said, the ether wind puts pressure on a moving object, causing it to shrink a bit
in the direction of motion. To determine the length of a moving object, its length at rest must
be multiplied by the following simple formula, in which v² is the velocity of the object multiplied
by itself, c² the velocity of light multiplied by itself:
Study this formula and you will see that the amount of contraction is negligible at small
velocities, increases as the velocity increases, becomes great as the object's speed
approaches the speed of light. Thus, a spaceship shaped like a long cigar would, if it moved
with great speed, alter its shape to that of a short cigar. The speed of light is an unobtainable
limit; when this is reached the formula hecomes
which reduces to 0. Multiplying the length of the object by 0 results in 0. In other words, if an
object could attain the speed of light, it would have no length at all in the direction of its motion!
"FitzGerald's theory was put into elegant mathematical form by the Dutch physicist Hendrik
Antoon Lorentz, who had independently thought of the same explanation. (Later, Lorentz
became one of Einstein's closest friends, but at this time they did not know one another.)
The theory came to be known as the Lorentz-FitzGerald (or the FitzGerald-Lorentz) contraction
theory.
"It is easy to understand how the contraction theory would explain the failure of the Michelson-
Morley test. If the square slab and all the apparatus on it were contracted by a tiny amount in
the direction in which the ether wind was blowing, the light would have a shorter total distance
to travel. Even though the wind would have an overall drag effect on the beam's back-and-forth
journey, the shorter path would permit the beam to finish the trip in the same time that it would
take if there were no wind and no contraction. In other words, the contraction would be just
enough to keep the speed of light a constant, regardless of the direction in which the Michelson-
Morley apparatus is turned.
"Why, you may ask, couldn't this theory be tested simply by measuring the length of the apparatus
to see if it shortens in the direction of the earth's motion? The answer is that the ruler would
shorten also, in the same proportion. As a result, measurements would come out the same as
if there were no contraction. The contractions would apply to everything on the moving earth. The
situation is similar to Jules Henri Poincaré's thought experiment in which the cosmos suddenly
grows a thousand times larger, except that in the Lorentz-FitzGerald theory the change would be
in one direction only. Since the change applies to everything, there is no way to detect it. Within
certain limits (the limits are set by topology -- the study of properties that stay the same when an
object is deformed), shape itself is as relative as size. The contraction of the apparatus, as well
as the contraction of everything else on the earth, could be observed only by someone outside
the earth and not moving with it.
"Many writers on relativity have spoken of the Lorentz-FitzGerald contraction hypothesis as
ad hoc, a Latin phrase (it rhymes with sad sock) meaning formulated 'for this case alone,'
and incapable of being tested by any other experiment. This is not, as Adolf Grünbaum has
pointed out, strictly true. The contraction theory was ad hoc only in the sense that at the time
there was no way to test it. In principle it is not at all ad hoc. In fact, it was definitely ruled out
in 1932 by an important experiment called the Kennedy-Thorndike experiment.
"Roy J. Kennedy and Edward M. Thorndike, two American physicists, repeated the Michelson-
Morley test with this major difference: Instead of making the two arms of the apparatus as
equal in length as possible, they made the lengths as different as possible. The apparatus
was then rotated to see if there was any change in the difference between the times it took the
two light beams to make round trips in the two directions. According to the contraction theory,
this time difference would alter as the apparatus turned. It would be detected (as in Michelson's
test) by changes in the interference fringes when the two beams were recombined. No such
changes were observed. More accurate tests have been made in recent years by using a
Mössbauer source of light and a receiver mounted at opposite ends of a turntable which is
then rotated rapidly. All such tests have falsified the contraction theory.
"Although experiments of this sort could not be made in Lorentz's time, he realized that they
could be made in principle, and there were good reasons to suppose that like Michelson's
experiment, they would show negative results. To account for such probable results, Lorentz
made an important addition to his original theory. He introduced changes in time. Clocks, he
said, would be slowed down by an ether wind, and in just such a way as to make the velocity
of light always measure 299,800 kilometers per second.
"For one example of how this works out, suppose an attempt is made to measure the speed
of light from A to B along a straight path in the direction the earth is moving. Two clocks at A
are synchronized, then one clock is moved to B. A note is made of the time that a light beam
starts from A and the time (measured by the other clock) that the beam is received at B. Since
the light would be moving against the ether wind, its speed should be slowed down and the
time of the trip should be a little longer than it would be if the earth were at rest. Do you see the
flaw in this theory? The clock, in moving from A to B, also moves against the ether wind. This
slows the clock at B down a bit, so that it is running slightly behind the clock at A. Result: the
velocity of light still clocks at 299,800 kilometers per second.
"The same thing happens (Lorentz maintained) if the speed of light is measured in the reverse
direction, from B to A. Two clocks are synchronized at B, then one is taken to A. A light beam is
sent from B to A, moving with the ether wind. The beam's speed is boosted by the wind, therefore
the time taken by the light beam to make the trip should be a trifle less than if the earth were at
rest. However, in moving the clock from B to A, it also went with the wind. The reduction of
ether-wind pressure on the moving clock allowed the clock to gain a bit in time; therefore, when
the experiment is made, the clock at A is running a bit ahead of the clock at B. Result: the velocity
of light once again clocks at 299,800 kilometers per second.
"Lorentz's new theory not only accounted for the negative results of the Michelson-Morley
experiment; it also accounted for any conceivable experiment designed to detect changes in
the speed of light as a result of an ether wind. Its equations for variations in length and time
were worked out in such a way that every possible method of measuring the speed of light,
from any frame of reference, would always give the same result. It is easy to understand why
physicists were unhappy with this theory. It was ad hoc in the full sense of the word. It seemed
little more than a weird effort to patch up the rents that had developed in the ether theory.
There was no imaginable way either to confirm or refute it. Physicists found it hard to believe
that if there were an ether wind, nature would go to such curious, drastic, almost prankish
lengths to prevent it from being detected. Arthur Stanley Eddington, a distinguished British
astronomer who was one of Einstein's earliest admirers, described the situation aptly by
quoting the following lines from Lewis Carroll's song of the White Knight in Through the
Looking-Glass:
But I was thinking of a plan
To dye one's whiskers green,
And always use so large a fan
That they could not be seen.
"Lorentz's new theory, with its time as well as length changes, seemed almost as absurd as
the White Knight's plan. But try as they would, physicists were unable to think of a better plan.
"Einstein's special theory of relativity pointed to a bold, remarkable way out of this extraordinary
confusion."
-- Martin Gardner, The Relativity Explosion, 1976
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Posted by rallen2 on 2008-05-31 10:40:41 | Rating: | Views: 60
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