Hiding in the Mirror (3 page)

By the time that Faraday introduced these ideas
in print, he was a wellestablished scientific figure, so his
colleagues certainly took note of them. However, his descriptions
were sufficiently vague that it is fair to say that most others were
not convinced by them. For the case to become truly compelling it
would require a physicist whose talents as a theorist were a match
for those of Faraday as an experimentalist. Fortunately, such a
theoretician had just moved to England at around the time Faraday
was proposing his ideas. The nineteenth century was full of
towering mathematical geniuses, a number of whom pushed forward the
frontiers of accepted knowledge, such as Newtonian mechanics. James
Clerk Maxwell, however, in his short lifetime, left a legacy that
is unmatched by any of them. He not only originated what is now the
modern theory of gases, and the basis for the theory of statistical
mechanics, which Boltzmann, Einstein, and Gibbs would later place
firmly at the center of modern physics, but also completed the
theoretical formulation of electromagnetism, the model prototype
for the theories of all the known forces in nature. So complete and
beautiful was his formulation that his equations for
electrodynamics, now called “Maxwell’s Equations,” are emblazoned
on the T-shirts of physics students and teachers throughout the
world, who rely on them for much of what they do on a daily basis
(the equations, not the T-shirts).

All these were conceived by a man who, before
he died at the tender age of forty-eight, established the
reputation of the Cavendish Laboratory at Cambridge, whose first
director he was, as the major experimental physics laboratory in
the world. Born and raised in Scotland, Maxwell did not have an
auspicious youth. A private tutor who had been employed to teach
him was not optimistic, reporting that he was a slow learner. Later
Maxwell got the nickname “Dafty” from his schoolmates. By his teens
he began to show mathematical promise, and studied at Edinburgh
University and then Cambridge, where he ultimately received a
fellowship. Nevertheless, he longed for his native Scotland and
returned to Aberdeen to teach.

His treatment there, however, does not suggest
that he gave any indication that he would eventually become known
as perhaps the greatest theoretical physicist of the century. When
Marischal College, where he was professor of natural philosophy,
was merged with King’s College to form Aberdeen University, two
professorships were merged into one, and his post was given to the
professor at King’s, forcing Maxwell to seek another position. He
applied for the professorship at Edinburgh University, which had
become vacant, but it was given to one of his friends and former
classmates instead. Maxwell was once again driven back down to
England, where he accepted a post at King’s College London, which
he occupied until he was ultimately offered his position as
Cavendish Professor at Cambridge. While in London, Maxwell got to
know Faraday, for whom he had immense respect. Both physicists
thought in terms of physical pictures, although Maxwell’s
mathematical talent was sufficient to allow him to translate his
ideas into precise mathematical formulations. In 1856, while still
in studying in Cambridge, Maxwell wrote a lengthy paper entitled
“On Faraday’s Lines of Force,” in which he attempted to put
Faraday’s idea on a solid mathematical footing. This was the first
step in his attempts to determine and formulate the laws of
electrodynamics in a mathematically consistent fashion, which would
culminate in his
Treatise on Electricity and
Magnetism
(1873). By the time his work was completed, he had
taken the geometric crutch of Faraday—the electric and magnetic
lines of force, and the “fields” they represented—and turned them
into entities as real as you or I.

As it was originally discovered, through the
experiments of Oersted, Faraday, and their colleagues, the theory
of electromagnetism was framed completely in terms of measurable
physical entities (charges, currents, and magnets) and how they
interact with one another. By trying to picture how these
interactions operated, Faraday imagined space as full of electric
and magnetic fields. Who would have guessed that the fields
themselves could produce physical effects even if there were no
charges, currents, or magnets nearby to respond to them? It would
be disingenuous to say that the answer was as clear as the nose on
your face, except that it is: The nose on your face
is
clear precisely because of these fields. It is
these very fields that allow you to see.

Let’s recap the rules of electromagnetism up
until Maxwell. Oersted had discovered that currents (i.e.,
moving
charges) could produce a force on
magnets. Ampère had shown that these currents were in themselves
magnets. Faraday discovered that changing the strength of a magnet
put near a charge could produce a force on the charge.

What concerned Maxwell (as it had Faraday) was
trying to find a unified understanding of these effects. What
happened in the empty space between charges and magnets that could
convey these forces? Both scientists, as they flailed about trying
to understand the nature of the electromagnetic interaction,
imagined this empty space as being filled with a remarkable amount
of paraphernalia (invisible vortices, ball bearings, etc.) that
might implement the action of Faraday’s imaginary field lines.
Ultimately Maxwell realized that the magnetic and electric fields
that Faraday envisaged throughout space might have a reality beyond
their mere mathematical convenience, even if Maxwell himself
probably still personally retained a physical picture of some
“fluid” medium that permeated space, like the classical aether of
Aristotle, with currents flowing within it. But the mathematical
discovery that Maxwell made that changed everything was simply the
following: One could frame the laws of electromagnetism in terms of
these electric and magnetic fields as fundamentals and not derived
quantities. If moving charges would produce an everchanging
electric field and also a constant magnetic field, then perhaps the
observation about currents and magnets could instead be framed as
this: Changing electric fields can produce magnetic fields. And the
observation about forces on charges being produced by moving
magnets (which would produce changing magnetic fields) could be
rephrased: Changing magnetic fields produce electric fields. This
subtle revision, with the fields taking center stage, could only
truly have physical meaning if, in empty space, devoid of charges
and currents, a measurable magnetic field could be produced purely
by a changing electric field, and vice versa. Again, Maxwell led the
way by showing that the mathematical description of
electromagnetism was not consistent unless this
phenomenon—occurring in empty space without physical changes and
currents—could also occur, and he described precisely an experiment
that would demonstrate just this effect.

But the biggest prediction—one of my favorite
ones in all of physics—was yet to come. If I take a charge and move
it, the electric field around it changes. That changing electric
field in turn produces a changing magnetic field. But that changing
magnetic field in turn produces a changing electric field. And so on,
and so on, and before you know it an “electromagnetic disturbance”
will propagate out into space. Maxwell could use the equations of
electromagnetism he had derived to calculate the velocity of this
disturbance in terms of two fundamental constants in nature: the
strength of the electric force between charged particles, and the
strength of the magnetic force between magnets. When he did this
calculation, he found that this disturbance would have the
character of a wave, like a water wave, with crests and troughs not
of water, but of the fields itself. Moreover, the speed that he
calculated for this “electromagnetic wave” was familiar. It turned
out to be the speed of light. This suggested, and it was later
confirmed by experiments, that light itself might be waves of
electromagnetic fields.

Maxwell’s remarkable proposal—that light itself
is an electromagnetic wave—occurred a full decade before Edwin
Abbott wrote
Flatland,
and it would be over
twenty more years before a young physicist working as a patent
clerk in Switzerland would realize the full implication of this
insight. Nevertheless, nature was competing with the literary
imagination. Within less than seventy-five years of the discovery of
the electromagnetic phenomena that power our modern civilization
today, Faraday’s imaginary crutches had become real, and they would
ultimately force us to change the way we conceive of such
fundamental concepts as space and time.

We have no direct intuition
about the equality of two time intervals.
People who believe they have this intuition are the
dupes of an illusion.

—Henri Poincaré,
La Mesure
du Temps

T
he eighth edition of
the
Encyclopedia Britannica
appeared in
1878, just a year before James Clerk Maxwell’s untimely demise. In
that edition Maxwell penned an article entitled “Ether,” in which
he sardonically commented, “Space has been filled three or four
times over with ethers.” His critique was based on the fact that
scientists had, over the years, proposed separate, distinguishable,
but invisible media permeating all space, in which either light,
heat, electricity, or magnetism might be conveyed. Maxwell felt
that one of his great contributions, by demonstrating that light
was an electromagnetic wave, was to reduce all of these separate
“ethers” to a single medium, in which such waves might propagate.
Maxwell was so convinced that such a medium must exist that he
actually set out to measure its effect on the propagation of light
rays from the moons of Jupiter when the gas giant eclipses them, as
seen from Earth, when our planet is moving at different speeds
relative to Jupiter. In 1879 he wrote a letter acknowledging the
receipt of data on Jupiter and its moons from the Nautical Almanac
Office in Washington, D.C.

Maxwell reasoned that if one measured the
apparent velocity of light at different times relative to Earth by
measuring the time it took light to traverse the distance from
Jupiter to Earth when Earth was moving in different directions in
its orbit through the fixed ether in which the light rays presumably
propagated, one could measure Earth’s motion relative to this
ether. Whether Maxwell had sufficient time to adequately analyze the
Nautical Almanac data before his death, or whether the data was
good enough to even discern such a possible effect in principle, is
now immaterial. The truth is, his proposal was doomed to fail, for
reasons even he probably never imagined.

The first empirical evidence that the velocity
of light did not obey the expected dependence on Earth’s motion
appeared less than two years after Maxwell’s letter to Washington,
in an experiment performed by the man who would eventually become
America’s first Nobel laureate in science, Albert A. Michelson.
Michelson was on leave from the navy at the time, doing what all
good would-be scientists living in the United States who wanted to
get ahead then did—namely, spending time in the superior
laboratories in Europe. In this case, he chose to work in
Helmholtz’s laboratory in Berlin. Michelson, an experimental
genius, had designed an apparatus that could detect a far smaller
effect caused by the Earth’s motion through the ether than Maxwell
had proposed looking for. Instead of relying on data from
observations of the Jovian system, Michelson could compare the
round-trip travel time of two light rays traveling at the earth’s
surface in different directions with respect to the earth’s motion
around the sun—and thus also, presumably, with respect to the ether
background. (Light rays traveling through the ether would
presumably travel more slowly relative to the earth if they were
battling an “aether headwind” as opposed to being propelled along
by it, just as a golf ball hit into a headwind will travel more
slowly, and hence cover less distance, than a ball hit into a
tailwind. As a result, the round-trip travel time of a light ray
should depend on its direction of motion relative to an ether
headwind.) Even though the predicted effect of the earth’s motion
through the ether was minute, Michelson’s apparatus should have
been able to discern it, but in 1881 he reported that his attempt
to do so was unsuccessful. He was unequivocal in his conclusion:
“The result of the hypothesis of a stationary aether is thus shown
to be incorrect, and the necessary conclusion follows that the
hypothesis is erroneous.”

It is remarkable how willing Michelson was to
throw out centuries of accepted wisdom on the basis of a single
experiment, but while he was supremely confident in his results, the
rest of the world was not. The eminent Dutch physicist Hendrik
Lorentz, who was one of the few who seemed to even consider
Michelson’s data seriously, uncovered an error in Maxwell’s
theoretical analysis and thus distrusted the rest of the work. Both
he and the eminent British physicist Lord Rayleigh urged Michelson
to repeat the experiment with higher accuracy.

Thus it was that in 1887 Michelson, who had
moved to Case School of Applied Science in Cleveland, teamed with
chemist Edward Morley, from nearby Western Reserve University—a
collaboration that presaged the merger eighty years later of Case
and Western Reserve into my home institution, Case Western Reserve
University—to perform one of the most celebrated experiments in
modern physics.

The Michelson-Morley experiment definitively
established that the velocity of light as measured on Earth was
independent of a light ray’s direction relative to the earth’s
motion around the sun. While Michelson jumped to the conclusion
that this implied the ether did not exist (ultimately the correct
conclusion), it is, in fact, not the only logical possibility.
Rather, the results could have implied that for some reason the
ether may have affected the measurement of light’s velocity in ways
that no one had yet understood. Indeed, Lorentz’s first question
following the experiment, in a letter to Rayleigh, was whether
there could be some error in the dynamic theory of electromagnetism
that might explain the Michelson-Morley data. Lorentz continued to
think deeply about this paradox, and in 1892 he argued that there
was only one way he had come up with to reconcile their findings
with commonsense notions about what should happen for observers
moving with respect to each other. They would measure precisely the
same round-trip travel time for light rays going in different
directions with respect to the earth’s motion through a stationary
ether if, somehow, lengths along the direction of motion with
respect to the ether were foreshortened.

What Lorentz was in effect arguing was that the
only way light rays would be measured to take the same time for
round-trip travels independent of whether or not they were fighting
an ether headwind would be if somehow lengths were also shortened
along the direction of motion as the earth moved against any such
headwinds. Since the distance the light ray traveled is calculated
by its velocity multiplied by the time it travels, shortening the
distance would cancel what would otherwise have been an extra
travel time due to the slowing of light in these directions. It was
not so radical an idea to imagine that dynamic electromagnetic
effects could cause lengths to so change. After all, if light is an
electromagnetic phenomenon, and electric and magnetic forces are
conveyed via the medium of the ether, then perhaps the electrically
charged particles that make up the constituents of all atoms could
be affected by their interactions with the ether as they pushed
through it in a way that would move the atoms closer together. (In
fact, the Irish physicist George Fitzgerald made precisely this
argument in 1889, to derive precisely the same result, although it
was unknown to Lorentz in 1892.)

Over the next twelve years Lorentz continued to
think about the nature of electromagnetism in this context, and
also about the mathematical properties of the theory that might
determine what different observers moving with respect to each
other would measure. In the process he made an observation that is
implicit in Maxwell’s equations but that had never been explicitly
described. In 1895 he demonstrated that a moving charged particle
would experience a force in a background magnetic field, because
moving charges produce magnetic fields, and are therefore magnets
and so must also experience forces due to other magnets.

I have always felt that it is precisely this
revelation that carries the key to understanding why it was
electromagnetism, and not some other force, that led Einstein to
cause us to rethink our ideas of space, time, and motion.
Ultimately, what the “Lorentz force,” as it has become known, tells
us is that what one observer measures as uniquely an electric
force, another observer can measure as a magnetic force.

Think about it this way. If you are at rest
with respect to some charged particle, and you observe it to move,
you know it must have experienced a force, because things do not
suddenly start moving without a force having acted on them. But the
only force that a charged particle at rest can respond to is an
electric force. Now, instead, imagine that you are moving at a
constant velocity away from the charged particle. Relative to you
the particle is moving backward, away from you. The laws of
electromagnetism say that in your reference frame this moving
charge must produce a magnetic field. If such a particle is then
suddenly deflected in its path, you can measure this deflection and
infer that the cause of this deflection was due to an external
magnetic field acting on this current.

Thus, one person’s electricity can be another
person’s magnetism. That is really the beauty of Maxwell’s theory
of electromagnetism. It demonstrated that electricity and magnetism
are not only related, they are identical—merely different sides of
the same coin. Different observers would measure the same
phenomena, and ascribe them to either magnetic or electric effects,
depending upon their state of motion. Since it is motion that
relates electric and magnetic fields, it is perhaps not so
surprising that light, an electromagnetic phenomenon, would cause
us to rethink the nature of motion itself. Albert Einstein was only
five years old when the Michelson-Morley experiment was performed,
but over the next eighteen years, while Lorentz, Fitzgerald,
Rayleigh, and other well-known physicists were puzzling over the
null results of Michelson and Morley, Einstein came to realize that
the real problem was not reconciling Maxwell’s theory with the
MichelsonMorley finding (which he would later often claim not even
to have known about at the time), but rather reconciling Maxwell’s
theory with the understanding of space and time that had prevailed
in physics since the days of Galileo.

Again, with hindsight, the problem can be
simply stated. One of Maxwell’s greatest discoveries was that if
light was an electromagnetic wave, one could calculate its speed
from first principles, using solely quantities that could be
measured in any laboratory associated with the strength of electric
and magnetic forces.

But there is a fundamental, hidden problem with
this result. It had long been recognized—indeed, since the time of
Galileo and later Newton—that the laws of motion as measured by an
observer moving at a constant velocity (say, a person on a train or
plane) are the same as for an observer standing still. Think about
throwing a ball in the air or playing catch. If you are on a plane
or train that is moving in a straight line, and you throw a ball up
in the air, you will see exactly the same thing that you would see
if you threw the ball while standing still. This is to say, you
won’t feel as if you are moving. If the windows are covered, and
there are no bumps, and the engines are not making any noise, there
is, in fact, really no way to know if you are moving or standing
still.

Galileo first recognized this fact about motion
and codified it, stating that there is no way to distinguish between
observers at rest and observers in constant motion. That principle
is literally the foundation on which all of our understanding of
modern physics was based. We now call this “Galilean
relativity.”

However, as Einstein realized from his teenage
years onward, there is a problem reconciling Galilean relativity
with Maxwell’s discovery about light. For, if the speed of light
can be calculated from fundamental constants that can be measured
in a laboratory, and if observers in laboratories moving at a
constant velocity with respect to each other should observe the
same results as observers in laboratories at rest, then this would
imply something remarkable. Since all such observers should measure
the same fundamental constants of nature, in terms of which they
could each calculate the speed of light rays that they would
measure in their laboratories, then all observers, regardless of
their state of motion with respect to an ether background, should
measure the same speed of light. This result is, of course,
precisely what the Michelson-Morley experiment seemed to
demonstrate, but it also leads to a paradox if light is a wave in
an ether. It is like saying that, if you are driving a car along a
river, the waves moving in the water would appear to move along
relative to you at the same speed that they would be measured to
move relative to someone sitting on the shore. That is silly,
because if your car is moving along at the same speed as the waves,
they will be stationary with respect to you, but not to an observer
on the shore.

This is so counterintuitive that it perhaps
explains why the best physics minds in the world spent much of the
two decades after the Michelson-Morley experiment trying to find a
way to dynamically change the predictions of Maxwell’s theory in
different ways to accommodate it, rather than accepting that the
theory in fact required this result. Einstein, on the other hand,
accepted this implication of Maxwell’s theory at face value,
because the theory perfectly described all other measured aspects
of electromagnetism. Instead, he recognized that to accommodate it
one would have to revise other aspects of our understanding of the
world.

The first person to suggest that one must begin
to think along these lines was not Albert Einstein, but the famous
French mathematical physicist, Jules Henri Poincaré. A leading
scientific intellect who had a philosophical bent as well, Poincaré
realized as early as 1898 that we might have to alter basic notions
regarding the objective meaning of various concepts of space and
time to account for the fact that the occurrence of events at
distant points could only be relayed to us after a finite time. It
was in this context that he uttered the words quoted at the
beginning of this chapter.