drives almost every device we use.
Two years after Davy’s death in 1829, and six years after Faraday
had become director of the laboratory of the Royal Institution, he
made the discovery that cemented his reputation as perhaps the
greatest experimental physicist of the nineteenth century—magnetic
induction. Since 1824, he had tried to see if magnetism could alter
the current flowing in a nearby wire or otherwise produce some kind
of electric force on charged particles. He primarily wanted to see if
magnetism could induce electricity, just as Oersted had shown that
electricity, and electric currents in particular, could produce
magnetism.
On October 28, 1831, Faraday recorded in his laboratory
notebook a remarkable observation. While closing the switch to turn
on a current in a wire wound around an iron ring to magnetize the
iron, he noticed a current flow momentarily in another wire
wrapped around the same iron ring. Clearly the mere presence of a
nearby magnet could not cause an electric current to flow in a wire
—but turning the magnet on or off could. Subsequently he showed
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that the same effect occurred if he moved a magnet near a wire. As
the magnet came closer or moved away, a current would flow in the
wire. Just as a moving charge created a magnet, somehow a moving
magnet—or a magnet of changing strength—created an electric
force in the nearby wire and produced a current.
If the profound theoretical implication of this simple and
surprising result is not immediately apparent, you can be forgiven,
because the implication is subtle, and it took the greatest theoretical
mind of the nineteenth century to unravel it.
To properly frame it, we need a concept that Faraday himself
introduced. Faraday had little formal schooling and was largely self-
taught and thus was never comfortable with mathematics. In
another probably apocryphal story, Faraday boasted of using a
mathematical equation only one time in all of his publications.
Certainly, he never described the important discovery of magnetic
induction in mathematical terms.
Because of his lack of comfort with formal mathematics, Faraday
was forced to think in pictures to gain intuition about the physics
behind his observations. As a result he invented an idea that forms
the cornerstone of all modern physics theory and resolved a
conundrum that had puzzled Newton until the end of his days.
Faraday asked himself, How does one electric charge “know” how
to respond to the presence of another, distant electric charge? The
same question had been posed by Newton in terms of gravity, where
he earlier wondered how the Earth “knew” to respond as it did to the
gravitational pull of the Sun. How was the gravitational force
conveyed from one body to another? To this, he gave his famous
response “Hypotheses non fingo,” “I frame no hypotheses,” suggesting
that he had worked out the force law of gravity and showed that his
predictions matched observations, and that was good enough. Many
of us physicists have subsequently used this defense when asked to
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explain various strange physics results—especially in quantum
mechanics, where the mathematics works, but the physical picture
often seems crazy.
Faraday imagined that each electric charge would be surrounded
by an electric “field,” which he could picture in his head. He saw the
field as a bunch of lines emanating radially outward from the charge.
The field lines would have arrows on them, pointing outward if the
charge was positive, and inward if it was negative:
He further imagined that the number of field lines increased as
the magnitude of the charge increased:
The utility of this mental picture was that Faraday could now
intuitively understand both what would happen when another test
charge was put near the first charge and why. (Whenever I use the
colloquial why, I mean “how.”) The test charge would feel the “field”
of the first charge wherever the second charge was located, with the
strength of the force being proportional to the number of field lines
in the region, and the direction of the force being along the direction
of the field lines. Thus, for example, the test charge in question
would be pushed outward in the direction shown:
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One can do more than this with Faraday’s pictures. Imagine
placing two charges near each other. Since field lines begin at a
positive charge and end on a negative charge and can never cross, it
is almost intuitive that the field lines in between two positive charges
should appear to repel each other and be pushed apart, whereas
between a positive and a negative charge they should connect
together:
Once again, if a test charge is placed anywhere near these two
charges, it would feel a force in the direction of the field lines, with a
strength proportional to the number of field lines in that region.
Faraday thus pictured the nature of electric forces between
particles in a way that would otherwise require solving the algebraic
equations that describe electrical forces. What is most amazing
about these pictures is that they capture the mathematics exactly,
not merely approximately.
A similar pictorial view could be applied to magnets, and
magnetic fields, reproducing the magnetic force law between
magnets, experimentally verified by Coulomb, or current-carrying
wires, derived by André-Marie Ampere. (Up until Faraday, all the
heavy lifting in discovering the laws of electricity and magnetism
was done by the French.)
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Using these mental crutches, we can then reexpress Faraday’s
discovery of magnetic induction as follows: an increase or decrease
in the number of magnetic field lines going through a loop of wire
will cause a current to flow in the wire.
Faraday recognized quickly that his discovery would allow the
conversion of mechanical power into electrical power. If a loop of
wire was attached to a blade that was made to rotate by, say, a flow
of water, such as a waterwheel, and the whole thing was surrounded
by a magnet, then as the blade turned the number of magnetic field
lines going through the wire would continuously change, and a
current would continuously be generated in the wire. Voilà, Niagara
Falls, hydroelectricity, and the modern world!
This alone might be good enough to cement Faraday’s reputation
as the greatest experimental physicist of the nineteenth century. But
technology wasn’t what motivated Faraday, which is why he stands
so tall in my estimation; it was his deep sense of wonder and his
eagerness to share his discoveries as broadly as possible that I admire
most. I am convinced that he would agree that the chief benefit of
science lies in its impact in changing our fundamental understanding
of our place in the cosmos. And ultimately, this is what he did.
I cannot help but be reminded of another mo
re recent great
experimental physicist, Robert R. Wilson—who, at age twenty-nine,
was head of the Research Division at Los Alamos, which developed
the atomic bomb during the Manhattan Project. Many years later he
was the first director of the Fermi National Accelerator Laboratory
in Batavia, Illinois. When Fermilab was being built, in 1969 Wilson
was summoned before Congress to defend the expenditure of
significant funds on this exotic new accelerator, which was to study
the fundamental interactions of elementary particles. Asked if it
contributed to national security (which would have easily justified
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the expenditure in the eyes of the congressional committee
members), he bravely said no. Rather:
It only has to do with the respect with which we regard one
another, the dignity of men, our love of culture. . . . It has to do
with, are we good painters, good sculptors, great poets? I mean all
the things that we really venerate and honor in our country and
are patriotic about. In that sense, this new knowledge has all to do
with honor and country, but it has nothing to do directly with
defending our country except to help make it worth defending.
Faraday’s discoveries allowed us to power and create our
civilization, to light up our cities and our streets, and to run our
electric devices. It is hard to imagine any discovery that is more
deeply ingrained in the workings of modern society. But more
deeply, what makes his contribution to our story so remarkable is
that he discovered a missing piece of the puzzle that changed the
way we think about virtually everything in the physical world today,
starting with light itself. If Newton was the last of the magicians,
Faraday was the last of the modern scientists to live in the dark,
regarding light. After his work, the key to uncovering the true nature
of our main window on the world lay in the open waiting for the
right person to find it.
• • •
Within a decade, a young Scottish theoretical physicist, down on his
luck, took the next step.
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C h a p t e r 3
T H R O U G H
A
G L A S S,
L I G H T LY
Nothing is too wonderful to be true, if it be consistent with the
laws of nature; and in such things as these, experiment is the
best test of such consistency.
—FARADAY, LABORATORY JOURNAL ENTRY #10,040 (MARCH 18,
1849)
The greatest theoretical physicist of the nineteenth century,
James Clerk Maxwell, whom Einstein would later compare to
Newton for his impact on physics, was coincidentally born in the
same year that Michael Faraday made his great experimental
discovery of induction.
Like Newton, Maxwell also began his scientific career fascinated
by color and light. Newton had explored the spectrum of visible
colors into which white light splits when traversing a prism, but
Maxwell, while still a student, investigated the reverse question:
What is the minimal combination of primary colors that would
reproduce for human perception all the visible colors contained in
white light? Using a collection of colored spinning tops, he
demonstrated that essentially all colors we perceive can result from
mixtures of red, green, and blue—a fact familiar to anyone who has
plugged RGB cables into a color television. Maxwell used this
realization to produce the world’s first, rudimentary color
photograph. Later he became fascinated with polarized light, which
results from light waves whose electric and magnetic fields oscillate
only in certain directions. He sandwiched blocks of gelatin between
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polarizing prisms and shined light through them. If the two prisms
allowed only light to pass that was polarized in different
perpendicular directions, then if one was placed behind the other, no
light would make it through. However, if stresses were present in the
gelatin, then the light could have its axis of polarization rotated as it
passed through the material, so that some light might then make it
through the second prism. By searching for such fringes of light
passing through the second prism, Maxwell could explore for
stresses in the material. This has become a useful tool today for
exploring possible material stresses in complex structures.
Even these ingenious experiments do not adequately represent
the power of Maxwell’s voracious intellect or his mathematical
ability, which were both manifest at a remarkably early age.
Tragically, Maxwell died at the age of forty-eight and had precious
little time to accomplish all that he did. His inquisitive nature was
reflected in a passage his mother added to a letter from his father to
his sister-in-law when Maxwell was only three:
He is a very happy man, and has improved much since the
weather got moderate; he has great work with doors, locks, keys,
etc., and “show me how it doos” is ever out of his mouth. He also
investigates the hidden course of streams and bell-wires, the way
the water gets from the pond through the wall.
After his mother’s untimely death (of stomach cancer, to which
Maxwell would later succumb at the same age), his education was
interrupted, but by the age of thirteen he had hit his stride at the
prestigious Edinburgh Academy, where he won the prize for
mathematics, and also for English and poetry. He then published his
first scientific paper—concerning the properties of mathematical
curves—which was presented at the Royal Society of Edinburgh
when he was only fourteen.
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After this precocious start, Maxwell thrived at university. He
graduated from Cambridge, becoming a fellow of the college within
a year after graduation, which was far sooner than average for most
graduates. He left shortly thereafter and returned to his native
Scotland to take up a chair in natural philosophy in Aberdeen.
At only twenty-five, he was head of a department and teaching
fifteen hours a week plus an extra free lecture for a nearby college for
working men (something that would be unheard of for a chaired
professor today, and something that I find difficult to imagine doing
myself and still having any energy left for research). Yet Maxwell
nevertheless found time to solve a problem that was two centuries
old: How could Saturn’s rings remain stable? He concluded that the
rings must be made of small particles, which garnered him a major
prize that had been set up to encourage an answer to this question.
His theory was confirmed more than a hundred years later when
Voyager provided the first close-up view of the planet.
You would think that, after his remarkable output, he would have
been able to remain secure in his professorship. However, in 1860,
the same year that he was awarded the Royal Society’s prestigious
Rumford Medal for his work on color, the college where he lectured
merged with another college and had no room for two professors of
>
natural philosophy. In what must surely go down in history as one of
the dumbest academic decisions ever made (and that is a tough list
to top), Maxwell was unceremoniously laid off. He tried to get a
chair in Edinburgh, but again the position was given to another
candidate. Finally, he found a position down south, at King’s College,
London.
One might expect Maxwell to have been depressed or
disconsolate because of these developments, but if he was, his work
reflected no signs of it. The next five years at King’s were the most
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productive period in his life. During this time he changed the world
—four times.
The first three contributions were the development of the first
light-fast color photograph; the development of the theory of how
particles in a gas behave (which helped establish the foundations of
the field now known as statistical mechanics—essential for
understanding the properties of matter and radiation); and finally his
development of “dimensional analysis,” which is perhaps the tool
most frequently used by modern physicists to establish deep
relationships between physical quantities. I just used it last year, for
example, with my colleague Frank Wilczek, to demonstrate a
fundamental property of gravity relevant to understanding the
creation of our universe.
Each contribution on its own would have firmly established
Maxwell among the greatest physicists of his day. However, his
fourth contribution ultimately changed everything, including our
notions of space and time.
During his period at King’s, Maxwell frequented the Royal
Institution, where he came in contact with Michael Faraday, who
was forty years older but still inspirational. Perhaps these meetings
encouraged Maxwell to return his focus to the exciting
developments in electricity and magnetism, a subject he had begun
to investigate five years earlier. Maxwell used his considerable
mathematical talents to describe and understand the phenomena
explored by Faraday. He began by putting Faraday’s hypothesized
lines of force on a firmer mathematical footing, which allowed him
to explore in more depth Faraday’s discovery of induction. Over the
dozen years between 1861 and 1873, Maxwell put the final touches
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