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in a nearby wire or otherwise produce some kind of electric force on 
charged particles. He primarily wanted to see if magnetism could in-
duce 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 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 mag-
net, 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 intro-
duced. 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 be-
hind 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 
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question had been posed by Newton in terms of gravity, where he ear-
lier wondered how the Earth "knew" to respond as it did to the gravita-
tional pull of the Sun. How was the gravitational force conveyed from 
one body to another? To this, he gave his famous response "Hypotheses 
non jingo," "I frame no hypotheses," suggesting that he had worked out 
the force law of gravity and showed that his predictions matched obser-
vations, and that was good enough. Many of us physicists have subse-
quently used this defense when asked to 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: 
\17( 
\ 
7Th 
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 in-
tuitively understand both what would happen when another test charge 
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29 
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: 
\-17( 
71,\ 
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 
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in a way that would otherwise require solving the algebraic equations 
that describe electrical forces. What is most amazing about these pic-
tures is that they capture the mathematics exactly, not merely approxi-
mately. 
A similar pictorial view could be applied to magnets, and magnetic 
fields, reproducing the magnetic force law between magnets, experi-
mentally verified by Coulomb, or current-carrying wires, derived by 
Andth-Marie Ampere. (Up until Faraday, all the heavy lifting in discov-
ering the laws of electricity and magnetism was done by the French.) 
Using these mental crutches, we can then reexpress Faraday's dis-
covery 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 con-
version 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. Voila, 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 tech-
nology 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 more recent great experi-
mental physicist, Robert R. Wilson—who, at age twenty-nine, was head 
of the Research Division at Los Alamos, which developed the atomic 
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bomb during the Manhattan Project. Many years later he was the first 
director of the Fermi National Accelerator Laboratory in Batavia, Il-
linois. 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 interac-
tions of elementary particles. Asked if it contributed to national security 
(which would have easily justified 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 contribu-
tion 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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THROUGH A GLASS, LIGHTLY 
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 IS. 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 Mi-
chael 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 combina-
tion of primary colors that would reproduce for human perception all the 
visible colors contained in white light? Using a collection of colored spin-
ning 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 
33 
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fascinated with polarized light, which results from light waves whose elec-
tric and magnetic fields oscillate only in certain directions. He sandwiched 
blocks of gelatin between 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 use-
ful 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 loos" 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 in-
terrupted, but by the age of thirteen he had hit his stride at the pres-
tigious 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. 
After this precocious start, Maxwell thrived at university. He gradu-
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35 
ated 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 hav-
ing any energy left for research). Yet Maxwell nevertheless found time to 
solve a problem that was two centuries old: How could Saturn's rings re-
main 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 philoso-
phy. In what must surely go down in history as one of the dumbest aca-
demic 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 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 
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THE GREATEST STORY EVER TOLD-SO FAR 
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 Institu-
tion, 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 mag-
netism, 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 hy-
pothesized 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 on his 
greatest work, a complete theory of electricity and magnetism. 
To do this, Maxwell used Faraday's discovery as the key to revealing 
that the relationship between electricity and magnetism is symmetrical. 
Oersted's and Faraday's experiments had shown, simply, that a current 
of moving charges produces a magnetic field; and that a changing mag-
netic field (produced by moving a magnet or simply turning on a cur-
rent to produce a magnet) produces an electric field. 
Maxwell first expressed these results mathematically in 2861, but 
soon realized that his equations were incomplete. Magnetism appeared 
to be different from electricity. Moving charges create a magnetic field, 
but a magnetic field can create an electric field even without moving—
just by changing. As Faraday discovered, turning on a current, which 
produces a changing magnetic field as the current ramps up, produces 
an electric force that causes a current to flow in another nearby wire. 
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Maxwell recognized that to make a complete and consistent set of equa-
tions for electricity and magnetism he had to add an extra term to the equa-
tions, representing what he called a Misplacement current." He reasoned 
that moving charges, namely a current, produce a magnetic field, and mov-
ing charges represent one way to produce a changing electric field (since 
the field from each charge changes in space as the charge moves along). So, 
maybe, a changing electric field—one that gets stronger or weaker—in a 
region with no charges in motion, could produce a magnetic field. 
Maxwell envisioned that if he hooked up two parallel plates to op-
posite poles of a battery, each plate would get charged with an opposite 
charge as current flowed from the battery. This would produce a growing 
electric field between the plates and would also produce a magnetic field 
around the wires connected to the plates. For his equations to be com-
pletely consistent, Maxwell realized, the increasing electric field between 
the plates should also produce a magnetic field in that empty space be-
tween the plates. And that field would be the same as any magnetic field 
produced by a real current flowing through that space between the plates. 
So Maxwell altered his equations by adding a new term (displace-
ment current) to produce mathematical consistency. This term effec-
tively behaved like an imaginary current, flowing between the plates 
producing a changing electric field identical in magnitude to the actual 
changing electric field in the empty space between the plates. It also 
was the same as the magnetic field that a real current would produce 
if it flowed between the plates. Such a magnetic field does in fact arise 
when you perform the experiment with parallel plates, as undergradu-
ates demonstrate every day in physics laboratories around the world. 
Mathematical consistency and sound physical intuition generally 
pay off in physics. This subtle change in the equations may not seem like 
much, but its physical impact is profound. Once you remove real elec-
tric charges from the picture, it means that you can describe everything 
about electricity and magnetism entirely in terms of the hypothetical 
"fields" that Faraday had relied upon purely as a mental crutch. The con-
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THE GREATEST STORY EVER TOLD-SO FAR 
nections between electricity and magnetism can thus be simply stated: 
A changing electric field produces a magnetic field. A changing mag-
netic field produces an electric field. 
Suddenly the fields appear in the equations as real physical objects in 
their own right and not merely as a way to quantify the force between 
charges. Electricity and magnetism became inseparable. It is impossible 
to talk about electrical forces alone because, as I will shortly show, one 
person's electric force is another person's magnetic force, depending on 
the circumstances of the observer, and whether the field is changing in 
his frame of reference. 
We now refer to electromagnetism to describe these phenomena, for 
a good reason. After Maxwell, electricity and magnetism were no longer 
viewed as separate forces of nature. They were different manifestations 
of one and the same force. 
Maxwell published his complete set of equations in 1865 and later 
simplified them in his textbook of 1873. These would become famous as 
the four Maxwell's Equations, which (admittedly rewritten in modern 
mathematical language) adorn the T-shirts of physics undergraduates 
around the world today. We can thus label 1873 as establishing the sec-
ond great unification in physics, the first being Newton's recognition 
that the same force governed the motion of celestial bodies as governed 
falling apples on Earth. Begun with Oersted's and Faraday's experimen-
tal discoveries, this towering achievement of the human intellect was 
completed by Maxwell, a mild-mannered young theoretical physicist 
from Scotland, exiled to England by the vicissitudes of academia. 
Gaining a new perspective on the cosmos is always—or should be—
immensely satisfying. But science adds an additional and powerful ben-
efit. New understanding also breeds tangible and testable consequences, 
and often immediately. 
So it was with Maxwell's unification, which now made Faraday's hy-
pothetical fields literally as real as the nose on your face. Literally, be-
cause it turns out you couldn't see the nose on your face without them. 
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Maxwell's genius didn't end just with codifying the principles of elec-
tromagnetism in elegant mathematical form. He used the mathematics 
to unravel the hidden nature of that most fundamental of all physical 
quantities—which had eluded the great natural philosophers from Plato 
to Newton. The most observable thing in nature: light. 
Consider the following thought experiment. Take an electrically 
charged object and jiggle it up and down. What happens as you do this? 
Well, an electric field surrounds the charge, and when you move the 
charge, the position of the field lines changes. But, according to Max-
well, this changing electric field will produce a magnetic field, which 
will point in and out of the paper as shown below: 
0 
(-; 
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Here the field line pointing into the paper has a cross (the back of an 
arrow), and that pointing out of the paper has a dot (the tip of an arrow). 
This field will flip direction as the charge changes the direction of its 
motion from upward to downward. 
But we should not stop there. If I keep jiggling the charged object, 
the electric field will keep changing, and so will the induced magnetic 
field. But a changing magnetic field will produce an electric field. Thus 
there are new induced electric field lines, which point vertically, chang-
ing from up to down as the magnetic field reverses its sign. I display the 
electric field line to the right only for lack of space, but the mirror image 
will be induced on the left-hand side. 
0 
<— • 
—> X 
0 
<— • 
—> X 
But that changing electric field will in turn produce a changing mag-
netic field, which would exist farther out to the right and left of the 
diagram, and so on. 
Jiggling a charge produces a succession of disturbances in both elec-
tric and magnetic fields that propagate outward, with the change in 
each field acting as a source for the other, due to the rules of electro-
magnetism as Maxwell defined them. We can extend the picture shown 
above to a 3-D image that captures the full nature of the changing as 
shown below: 
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41 
E 
We see a wave of electric and magnetic disturbances, namely an 
electromagnetic wave moving outward, with electric and magnetic 
fields oscillating in space, and time, and with the two fields oscillating 
in directions that are perpendicular to each other and also the direction 
of the wave. 
Even before Maxwell had written down the final form of his equa-
tions, he showed that oscillating charges would produce an electromag-
netic wave. But he did something far more significant. He calculated the 
speed of that wave, in a beautiful and simple calculation that is probably 
my favorite derivation to show undergraduates. Here it is: 
We can quantify the strength of an electric force by measuring its 
magnitude between two charges whose magnitude we already know. 
The force is proportional to the product of the charges. Let's call the 
constant of proportionality A. 
Similarly we can quantify the strength of the magnetic force be-
tween two electromagnets, each with a current of known magnitude. 
This force is proportional to the product of the currents. Let's call the 
constant of proportionality in this case B. 
Maxwell showed that the speed of an electromagnetic disturbance 
that emanates from an oscillating charge can be rendered precisely in 
terms of the measured strength of electricity and the measured strength 
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of magnetism, which are determined by measuring the constants A and 
B in the laboratory. When he used the data then available for the mea-
sured strength of electricity and the measured strength of magnetism 
and plugged in the numbers, he derived: 
Speed of electromagnetic waves Fac 311,000,000 meters per second 
A famous story claims that when Albert Einstein finished his Gen-
eral Theory of Relativity and compared its predictions for the orbit of 
Mercury to the measured numbers, he had heart palpitations. One can 
only imagine, then, the excitement that Maxwell must have had when 
he performed his calculation. For this number, which may seem arbi-
trary, was well known to him as the speed of light. In 1849, the French 
physicist Fizeau had measured the speed of light, an extremely difficult 
measurement back then, and had obtained: 
Speed of light 
313,000,000 meters per second 
Given the accuracy available at the time, these two numbers are 
identical. (We now know this number far more precisely as 299,792,458 
meters per second, which is a key part of the modern definition of the 
meter.) 
In his typical understated tone, Maxwell noted in 1862, when he first 
performed the calculation, We can scarcely avoid the conclusion that 
light consists in the transverse undulations of the same medium which 
is the cause of electric and magnetic phenomena." 
In other words, light is an electromagnetic wave. 
Two years later, when he finally wrote his classic paper on electro-
magnetism, he added somewhat more confidently, "Light is an elec-
tromagnetic disturbance propagated through the field according to 
electromagnetic laws? 
With these words, Maxwell appeared to have finally put to rest the 
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43 
two-thousand-year-old mystery regarding the nature and origin of light. 
His result came, as great insights often do, as an unintended by-product 
of other fundamental investigations. In this case, it was a by-product of 
one of the most important theoretical advances in history, the unifica-
tion of electricity and magnetism into a single beautiful mathematical 
theory. 
Before Maxwell, the chief source of wisdom came from a faith in divin-
ity via Genesis. Even Newton relied upon this source for understanding 
the origin of light. After 1862, however, everything changed. 
James Clerk Maxwell was deeply religious, and like Newton before 
him, his faith sometimes led him to make strange assertions about na-
ture. Nevertheless, like the mythical character Prometheus before him, 
who stole fire from the gods and gave it to humans to use as a tool 
to forever change their civilization, so too Maxwell stole fire from the 
Judeo-Christian God's first words and forever changed their meaning. 
Since 1873, generations of physics students have proudly proclaimed: 
"Maxwell wrote down his four equations and said, Let there be lights" 
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Chapter 4 
THERE, AND BACK AGAIN 
He set the earth on its foundations; it can never 
be moved. 
-PSALMS 104:5 
Wen Galileo Galilei was being tried in 1633 for heresy 
for "holding as true the false doctrine taught by some that the Sun is the 
center of the world," he allegedly muttered under his breath in front of 
his Church inquisitors, And yet it moves:' With these words, his revo-
lutionary nature once again sprang forth, in spite of his having been 
forced to publicly adhere to the archaic position that the Earth was fixed. 
While the Vatican eventually capitulated on Earth's motion, the poor 
God of the Psalms never got the news. This is somewhat perplexing 
since, as Galileo showed a year before the trial, a state of absolute rest is 
impossible to verify experimentally. Any experiment that you perform 
at rest, such as throwing a ball up in the air and catching it, will have an 
identical result if performed while moving at a constant speed, as, say, 
might happen while riding on an airplane in the absence of turbulence. 
No experiment you can perform on the plane, if its windows are closed, 
will tell you whether the plane is moving or standing still. 
While Galileo started the ball rolling, both literally and metaphori-
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cally, in 1632, it took another 273 years to fully lay to rest this issue (issues, 
unlike objects, can be laid to rest). It would take Albert Einstein to do so. 
Einstein was not a revolutionary in the same sense as Galileo, if by this 
term one describes those who tear down the dictates of the authorities who 
came before, as Galileo had for Aristotle. Einstein did just the opposite. He 
knew that rules that had been established on the basis of experiment could 
not easily be tossed aside, and it was a mark of his genius that he didn't. 
This is so important I want to repeat it for the benefit of those people 
who write to me every week or so telling me that they have discovered a 
new theory that demonstrates everything we now think we know about 
the universe is wrong—and using Einstein as their exemplar to justify 
this possibility. Not only is your theory wrong, but you are doing Ein-
stein a huge disservice: rules that have been established on the basis of 
experiment cannot easily be tossed aside. 
• 
• 
• 
Albert Einstein was born in 1879, the same year that James Clerk Maxwell 
died. It is tempting to suggest that their combined brilliance was too 
much for one simple planet to house at the same time. But it was just a 
coincidence, albeit a fortuitous one. If Maxwell hadn't preceded him, Ein-
stein couldn't have been Einstein. He came from the first generation of 
young scientists who grew up wrestling with the new knowledge about 
light and electromagnetism that Faraday and Maxwell had generated. 
This was the true forefront of physics for young Turks such as Einstein 
near the end of the nineteenth century. Light was on everyone's mind. 
Even as a teenager, Einstein was astute enough to realize that Max-
well's beautiful results regarding the existence of electromagnetic waves 
presented a fundamental problem: they were inconsistent with the 
equally beautiful and well-established results of Galileo regarding the 
basic properties of motion, produced three centuries earlier. 
Even before his epic battle with the Catholic Church over the motion of 
Earth, Galileo had argued that no experiment exists that can be performed 
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