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Chapter 13 
ENDLESS FORMS MOST 
BEAUTIFUL: SYMMETRY 
STRIKES BACK 
Now faith is the substance of things hoped for, 
the evidence of things not seen. 
-HEBREWS 11:1 
Borrowing from Pauli, we can say Mother Nature is a weak 
left-hander. With the shocking realization that nature distinguishes left 
from right, physics itself took a strange left turn down a road with no 
familiar guideposts. The beautiful order of the periodic table governing 
phenomena on atomic scales gave way to the mystery of the nucleus and 
the inscrutable nature of the forces that governed it. 
Gone were the seemingly simple days of light, motion, electromag-
netism, gravity, and quantum mechanics. The spectacularly successful 
theory of quantum electrodynamics, which had previously occupied the 
forefront of physics, seemed to be replaced by a confusing world of ex-
otic phenomena associated with the other two newly discovered weak 
and strong nuclear forces that governed the heart of matter. Their ef-
fects and properties could not easily be isolated, despite that one force 
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was thousands of times stronger than the other. The world of funda-
mental particles appeared to be ever more complicated, and the situa-
tion was getting more confusing with each passing year. 
If the discovery of parity violation created shadows of confusion by 
demonstrating that nature had completely unexpected preferences, the 
first rays of light arose from the realization that other nuclear quantities, 
which on the surface seemed quite different, might, when viewed from 
a fundamental perspective, be not so different at all. 
Perhaps the most important discovery in nuclear physics was that pro-
tons and neutrons could convert into each other, as Yukawa had specu-
lated years earlier. This was the basis of the emerging understanding of 
the weak interaction. But most physicists felt that it was also the key to 
understanding the strong force that appeared to hold nuclei together. 
Two years before his revolutionary work with T.-D. Lee, exposing 
the demise of the sacred left-right symmetry of nature, C.-N. Yang had 
concentrated his efforts on trying to understand how a different type of 
symmetry, borrowed from quantum electrodynamics, might reveal an 
otherwise hidden beauty inside the nucleus. Perhaps, as Galileo discov-
ered regarding the basis of motion, the most obvious things we observe 
about nature are also the things that most effectively mask its funda-
mental properties. 
What had slowly become clear, not only from the progress in under-
standing neutron decay and other weak effects in nuclei, but also from 
looking at strong nuclear collisions, was that the obvious distinction be-
tween protons and neutrons—the proton is charged and the neutron is 
neutral—might, as far as the underlying physics governing the nucleus 
is concerned, be irrelevant. Or at least as irrelevant as the apparent dis-
tinction between a falling feather and a falling rock is to our under-
standing of the underlying physics of gravity and falling objects. 
First off, the weak force could convert protons into neutrons. More 
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important, when one examined the rates of other, stronger nuclear re-
actions involving proton or neutron collisions, replacing neutrons by 
protons and vice versa didn't significantly change the results. 
In 1932, the year the neutron was discovered, Heisenberg had sug-
gested that the neutron and proton might be just two states of the same 
particle, and he invented a parameter he called isotopic spin to distinguish 
them. After all, their masses are almost the same, and light-stable nuclei 
contain equal numbers of them. Following this, and after the recognition 
by the distinguished nuclear physicists Benedict Cassen, Edward Con-
don, Gregory Breit, and Eugene Feenberg that nuclear reactions seemed 
to be largely blind to distinguishing protons and neutrons, the brilliant 
mathematical physicist Eugene Wigner suggested that isotopic spin was 
"conserved" in nuclear reactions—implying an underlying symmetry 
governing the nuclear forces between protons and neutrons. (Wigner 
had earlier developed rules demonstrating how symmetries in atomic 
systems ultimately allowed a complete classification of atomic states and 
the transitions between them, for which he later won the Nobel Prize.) 
Earlier, when discussing electromagnetism, I noted that the net 
electric charge doesn't change during electromagnetic interactions—
i.e., electric charge is conserved—because of an underlying symmetry 
between positive and negative charges. The underlying connection be-
tween conservation laws and symmetries is far broader and far deeper 
than this one example. The deep and unexpected relationship between 
conservation laws and symmetries of nature has been the single most 
important guiding principle in physics in the past century. 
In spite of its importance, the precise mathematical relationship be-
tween conservation laws and symmetries was only made explicit in 1915 
by the remarkable German mathematician Emmy Noether. Sadly, al-
though she was one of the most important mathematicians in the early 
twentieth century, Noether worked without an official position or pay 
for much of her career. 
Noether had two strikes against her. First, she was a woman, which 
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made obtaining education and employment during her early career dif-
ficult, and second, she was Jewish, which ultimately ended her academic 
career in Germany and resulted in her exile to the United States shortly 
before she died. She managed to attend the University of Erlangen as one 
of 2 female students out of 986, but even then she was only allowed to 
audit classes after receiving special permission from individual profes-
sors. Nevertheless, she passed the graduation exam and later studied at 
the famed University of Gottingen for a short period before returning to 
Erlangen to complete her PhD thesis. After working for seven years at 
Erlangen as an instructor without pay, she was invited in 1915 to return 
to Gottingen by the famed mathematician David Hilbert. Historians and 
philosophers among the faculty, however, blocked her appointment. As 
one member protested, "What will our soldiers think when they return 
to the university and find that they are required to learn at the feet of a 
woman?" In a retort that eternally reinforced my admiration for Hilbert, 
beyond that for his remarkable talent as a mathematician, he replied, 1 
do not see that the sex of the candidate is an argument against her ad-
mission as a Privatdozent. After all, we are a university, not a bathhouse." 
Hilbert was overruled, however, and while Noether spent the next 
seventeen years teaching at Gottingen, she was not paid until 1923, and 
in spite of her remarkable contributions to many areas of mathemat-
ics—so many and so deep that she is often considered one of the great 
mathematicians of the twentieth century—she was never promoted to 
the position of professor. 
Nevertheless, in 1915, shortly after arriving at Gottingen, she proved 
a theorem that is now known as Noether's theorem, which all graduate 
students in physics learn, or should learn, if they are to call themselves 
physicists. 
Returning once again to electromagnetism, the relationship between the 
arbitrary distinction between positive and negative (had Benjamin Frank-
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lin had a better understanding of nature when he defined positive charge, 
electrons would today probably be labeled as having positive, not negative, 
charge) and the conservation of electric charge—namely, that the total 
charge in a system before and after any physical reaction doesn't change—
is not at all obvious. It is in fact a consequence of Noether's theorem, which 
states that for every fundamental symmetry of nature—namely for every 
transformation under which the laws of nature appear unchanged—some 
associated physical quantity is conserved. In other words, some physical 
quantity doesn't change over time as physical systems evolve. Thus: 
• The conservation of electric charge reflects that the laws of nature 
don't change if the sign of all electric charges is changed. 
• The conservation of energy reflects that the laws of nature don't 
change with time. 
• The conservation of momentum reflects that the laws of nature don't 
change from place to place. 
• The conservation of angular momentum reflects that the laws of na-
ture don't depend on which direction a system is rotated. 
Hence, the claimed conservation of isotopic spin in nuclear reactions 
is a reflection of the experimentally verified claim that nuclear interac-
tions remain roughly the same if all protons are changed into neutrons 
and vice versa. It is reflected as well in the world of our experience, in 
that for light elements, at least, the number of protons and neutrons in 
the nucleus is roughly the same. 
In 1954, Yang, and his collaborator at the time, Robert Mills, went one 
important step further, once again thinking about light. Electromagne-
tism and quantum electrodynamics do not just have the simple symme-
try that tells us that there is no fundamental difference between negative 
charge and positive charge, and that the label is arbitrary. As I described 
at length earlier, a much more subtle symmetry is at work as well, one that 
ultimately determines the complete form of electrodynamics. 
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Gauge symmetry in electromagnetism tells us that we can change 
the definition of positive and negative charge locally without changing 
the physics, as long as there is a field, in this case the electromagnetic 
field, that can account for any such local alterations to ensure that the 
long-range forces between charges are independent of this relabeling. 
The consequence of this in quantum electrodynamics is the existence 
of a massless particle, the photon, which is the quantum of the electro-
magnetic field, and which conveys the force between distant particles. 
In this sense, that gauge invariance is a symmetry of nature ensures 
that electromagnetism has precisely the form it has. The interactions 
between charged particles and light are prescribed by this symmetry. 
Yang and Mills then asked what would happen if one extended the 
symmetry that implies that we could interchange neutrons and protons 
everywhere without changing the physics, into a symmetry that allows 
us to change what we label as "neutron" and "proton" differently from 
place to place. Clearly by analogy with quantum electrodynamics, some 
new field would be required to account for and neutralize the effect of 
these arbitrarily varying labels from place to place. If this field is a quan-
tum field, then could the particles associated with this field somehow 
play a role in, or even completely determine, the nature of the nuclear 
forces between protons and neutrons? 
These were fascinating questions, and to their credit Yang and Mills 
didn't merely ask them, they tried to determine the answers by explor-
ing specifically what the mathematical implications of such a new type 
of gauge symmetry associated with isotopic spin conservation would be. 
It became clear immediately that things would get much more com-
plicated. In quantum electrodynamics, merely switching the sign of 
charges between electrons and positrons does not change the magnitude 
of the net charge on each particle. However, relabeling the particles in 
the nucleus replaces a neutral neutron with a positively charged proton. 
Therefore whatever new field must be introduced in order to cancel out 
the effect of such a local transformation so that the underlying physics is 
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unchanged must itself be charged. But if the field is itself charged, then, 
unlike photons—which, being neutral, don't themselves interact directly 
with other photons—this new field would also have to interact with itself. 
Introducing the need for a new charged generalization of the elec-
tromagnetic field makes the mathematics governing the theory much 
more complex. In the first place, to account for all such isotopic spin 
transformations one would need not just one such field but three fields, 
one positively charged, one negatively charged, and one neutral. This 
means that a single field at each point in space, like the electromagnetic 
field in QED, which points in a certain direction in space with a certain 
magnitude (and is called a vector field in physics for this reason), is not 
sufficient. The electric field must be replaced by a field described by a 
mathematical object called a matrix—not to be confused with anything 
having to do with Keanu Reeves. 
Yang and Mills explored the mathematics behind this new and more 
complex type of gauge symmetry, which today we call either a non-
abelian gauge symmetry—arising from a particular mathematical prop-
erty of matrices that makes multiplying them different from multiplying 
numbers—or, in deference to Yang and Mills, a Yang-Mills symmetry. 
Yang and Mills's article appears at first glance to be an abstract—or 
purely speculative—mathematical exploration of the implications of a 
guess about the possible form of a new interaction, motivated by the ob-
servation of gauge symmetry in electromagnetism. Nevertheless, it was 
not an exercise in pure mathematics. The paper tried to explore possible 
observable consequences of the hypothesis to see if it might relate to the 
real world. Unfortunately the mathematics was sufficiently complicated 
such that the possible observable signatures were not so obvious. 
One thing was clear, however. If the new "gauge fields" were to ac-
count for and thus cancel out the effects of separate isotopic spin 
transformations made in distant locations, the fields would have to be 
massless. This is equivalent to saying that only because photons are 
massless can the force they transmit between particles be arbitrarily 
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long-range. To return to my chessboard analogy, you need a single rule-
book to tell you how to properly move over the entire board if I have pre-
viously changed the colors of the board randomly from place to place. 
But having massive gauge fields, which cannot be exchanged over arbi-
trarily long distances, is equivalent to having a rulebook that tells you 
how to compensate for changing colors only on nearby squares around 
your starting point. But this would not allow you to move pieces across 
the board to distant locations. 
In short, a gauge symmetry such as that in electromagnetism, or in 
the more esoteric Yang-Mills proposal, only works if the new fields re-
quired by the symmetry are massless. Amid all the mathematical com-
plexity, this one fact is inviolate. 
But we have observed in nature no long-range forces involving the 
exchange of massless particles other than electromagnetism and grav-
ity. Nuclear interactions are short-range—they only apply over the size 
of the nucleus. 
This obvious problem was not lost on Yang and Mills, who recog-
nized it and, frankly, punted. They proposed that somehow their new 
particles could become massive when they interacted with the nucleus. 
When they tried to estimate masses from first principles, they found 
the theory was too mathematically complicated to allow them to make 
reasonable estimates. All they knew was that empirically the mass of the 
new gauge particles would have to be greater than that of pions in order 
to have avoided detection in then-existing experiments. 
Such a willingness to throw their hands in the air might have seemed 
either lazy or unprofessional, but Yang and Mills knew, as Yukawa had 
known before them, that no one had been able to write down a sensible 
quantum field theory of a particle like the photon, but one that, unlike 
the photon, had a mass. So it didn't seem worthwhile at the time to try 
to solve all the problems of quantum field theory at once. Instead, with 
less irreverence than Jonathan Swift, they merely presented their paper 
as a modest proposal, to spur the imagination of their colleagues. 
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Wolfgang Pauli, however, would have none of it. While he had thought 
of some related ideas a year earlier, he had discarded them. Moreover, he 
felt that all this talk about quantum uncertainties in estimating masses 
was a red herring. If there was to be a new gauge symmetry in nature as-
sociated with isotopic spin and governing nuclear forces, the new Yang-
Mills particles, like the photon, would have to be massless. 
For these reasons, among others, the Yang-Mills paper made far less 
of a stir at the time than the later Yang and Lee opus. To most physicists 
it was an interesting curiosity at best, and the discovery of parity viola-
tion seemed much more exciting. 
But not to Julian Schwinger, who was no ordinary physicist. A child 
prodigy who had graduated from university by the age of eighteen, he 
received his PhD by the age of twenty-one. Perhaps no two physicists 
could have been as different as he and Richard Feynman, who shared 
the Nobel Prize in 196s for their separate but equivalent work devel-
oping the theory of quantum electrodynamics. Schwinger was refined, 
formal, and brilliant. Feynman was brilliant, casual, and certainly not 
refined. Feynman relied often on intuition and guesswork, building on 
prodigious mathematical skill and experience. Schwinger's mathemati-
cal skill was every bit Feynman's equal, but Schwinger worked in an 
orderly fashion, manipulating complicated mathematical expressions 
with an ease not possible for ordinary mortals. He joked about Feynman 
diagrams, which Feynman had developed to make what had previously 
been perilously laborious calculations in quantum field theory manage-
able, saying, "Like the silicon chips of more recent years, the Feynman 
diagram was bringing computation to the masses." Both of them shared 
one characteristic, however. They marched to the beat of a different 
drummer... in opposite directions. 
Schwinger took the Yang-Mills idea seriously. The mathematical 
beauty must have appealed to him. In 3.9s7, the same year that parity 
violation was discovered, Schwinger made a bold and seemingly highly 
unlikely suggestion that the weak interaction responsible for the decay 
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of neutrons into protons, electrons, and neutrinos might benefit from 
the possibility of Yang-Mills fields, but in a new and remarkable way. 
He proposed that the observed gauge symmetry of electromagnetism 
might simply be one part of a larger gauge symmetry in which new 
gauge particles might mediate the weak interaction that caused neu-
trons to decay. 
An obvious objection to this kind of unification is that the weak 
interaction is far weaker than electromagnetism. Schwinger had an 
answer for this. If somehow the new gauge particles were very heavy, 
almost one hundred times heavier than protons and neutrons, then the 
interaction they might mediate would be of much shorter range than 
even the size of a nucleus, or even a single proton or neutron. In this 
case, one could work out that the probability that this interaction would 
cause a neutron to decay would be small. Thus, if the range of the weak 
interaction was small, these new fields, the strength of whose intrinsic 
coupling to electrons and protons on small scales could be comparable 
to the strength of electromagnetism, could nevertheless, on the scale of 
nuclei and larger, appear to be much, much weaker. 
Put more bluntly, Schwinger proposed the outrageous idea that 
electromagnetism and the weak interaction were part of a single Yang-
Mills theory, in spite of the remarkable and obvious differences between 
them. He thought that perhaps the photon could be the neutral member 
of a Yang-Mills-type set of three gauge particles required by treating 
isotopic spin as a gauge symmetry, with the charged versions convey-
ing the weak interaction and being responsible for mediating the decay 
of neutrons. Why the charged particles would have a huge mass while 
the photon was massless, he had no idea. But, as I have often said, lack 
of understanding is neither evidence for God, nor evidence that one is 
necessarily wrong. It just is evidence of lack of understanding. 
Schwinger was not only a brilliant physicist but a brilliant teacher 
and mentor. While Feynman had few successful students, probably be-
cause none of them could keep up with him, Schwinger seemed to have 
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a knack for guiding brilliant PhD students. In his life he supervised more 
than seventy PhDs, and four of his students later won the Nobel Prize. 
Schwinger was sufficiently interested in relating the weak interac-
tion to electromagnetism that he encouraged one of his dozen graduate 
students at Harvard at the time to explore the issue. Sheldon Glashow 
graduated in 1958 with a thesis on the subject and continued to explore 
the issue for the next few years as a National Science Foundation post-
doctoral researcher in Copenhagen. In his Nobel lecture twenty years 
later, Glashow indicated that he and Schwinger had planned to write a 
manuscript on the subject after Glashow graduated, but one of them 
lost the first draft of the manuscript, and they never got back to it. 
Glashow was no clone of Schwinger's. Refined and brilliant, yes, but 
also brash, playful, and boisterous, Glashow did research that was not 
characterized by mathematical acrobatics, but rather by a keen focus on 
physical puzzles and exploring new possible symmetries of nature that 
might resolve them. 
When I was a young graduate student in physics at MIT, I was ini-
tially drawn to deep mathematical questions in physics and had written 
my admissions essay for my PhD application on just this subject. Within 
a few years I found myself depressed by the nature of the mathematical 
investigations I was pursuing. I met Glashow at a summer school for 
PhD students in Scotland and became friends with both him and his 
family—a friendship that continued to blossom when we later became 
colleagues at Harvard. The year after we met, he spent a sabbatical year 
at MIT. During this important time for me, when I was considering 
alternatives, he said to me, "There's physics, and there's formalism, and 
you have to know the difference." Implicit in this advice was the sugges-
tion that I should pursue physics. When I saw the fun he was having, it 
became easier to consider joining in. 
I soon realized that for me to make progress in physics I needed to 
work on questions driven primarily by physical issues, not ones driven 
primarily by mathematical issue. The only way I could do that would 
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be to keep in touch with ongoing experiments—and new experimental 
results. By watching Shelly and how he did physics, I realized that he 
had an uncanny ability to know which experiments were interesting, 
and which results might be significant or might point toward some-
thing new. Part of this was undoubtedly innate, but part was based on 
a lifetime of keeping in touch with what was happening on the ground. 
Physics is an empirical science, and we lose touch with that at our peril. 
In Copenhagen, Glashow realized that if he wanted to properly im-
plement Schwinger's proposal to connect the weak interaction with the 
electromagnetic interaction, then simply making the photon be the neu-
tral member of a triplet of gauge particles, with the charged members 
becoming massive by some as yet unknown miracle, wouldn't fly. This 
couldn't explain the proper nature of the weak interaction, in particular 
the strange fact that the weak interaction seemed to apply only to left-
handed electrons (and neutrinos), whereas electromagnetic interactions 
don't depend on whether the electrons are left- or right-handed. 
The only solution to this problem would be if another neutral gauge 
particle existed—in addition to the photon—which itself coupled to 
only left-handed particles. But clearly the new neutral particle would 
also have to be heavy since the interactions it mediated would have to 
be weak as well. 
Glashow's ideas were reported to the physics community by Murray 
Gell-Mann at the 1960 Rochester meeting, as Gell-Mann had by then 
recruited Glashow to Caltech to work in Gell-Mann's group. Glashow's 
paper on the subject, submitted in 1960, appeared in 1961 in print. Yet, 
no sudden stampede occurred in response. 
After all, two fundamental problems remained with Glashow's pro-
posal. The first was the long-familiar problem of how one could have the 
different masses of the particles needed to convey the different forces, 
when gauge symmetries required all the gauge particles to be massless. 
Glashow simply stated in the introduction of his paper, following in a long 
line of such hubris, "It is a stumbling block we must overlook." 
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The second problem was more subtle, but from an experimental per-
spective equally severe. Neutron decay, pion decay, and muon decay, if 
they were indeed mediated by some new particles conveying the weak 
force, all appeared to require only the exchange of new charged par-
ticles. No weak interaction had been observed that would require the 
exchange of a new neutral particle. If such a new neutral particle did 
exist, calculations at the time suggested it would allow the other known 
heavier mesons that decayed into two or three pions (and were respon-
sible for the original confusion that led to the discovery of parity viola-
tion) to decay much more rapidly than they were observed to decay. 
For these reasons, Glashow's proposal drifted into the background 
as physicists became entranced with the new particle zoo that was 
emerging out of accelerators, and the concomitant opportunity for new 
discoveries. Yet several of the key theoretical ingredients needed to 
complete a revolution in fundamental physics were in place, but it was 
far from obvious at the time. That within slightly more than a decade 
after Glashow's paper was published all of the known forces in nature 
save gravity would be unveiled and understood would have seemed like 
pure fantasy at the time. 
And symmetry would be the key. 
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Chapter 14 
COLD, STARK REALITY: 
BREAKING BAD OR BEAUTIFUL? 
From whose womb has come the ice? And the frost 
of heaven, who has given it birth? 
-JOB 38:29 
It is easy to pity the poor protagonists in Plato's cave, who 
may understand everything there is to know about the shadows on the 
wall, except that they are shadows. But appearances can be deceiving. 
What if the world around us is just a similar shadow of reality? 
Imagine, for example, that you wake up one cold winter morning and 
look out your window, and the view is completely obscured by beautiful 
ice crystals, forming strange patterns on the glass. It might look like this: 
blidOgf aril by Hokin AM:v.2 
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The beauty of the image is striking at least in part because of the re-
markable order on small scales lurking within the obvious randomness 
on large scales. Ice crystals have grown gorgeous treelike patterns, start-
ing in random directions and bumping into each other at odd angles. 
The dichotomy between small-scale order and large-scale randomness 
suggests that the universe would look very different to tiny physicists or 
mathematicians confined to live on the spine of one of the ice crystals 
in the image. 
One direction in space, corresponding to the direction along the 
spine of the ice crystal, would be special. The natural world would ap-
pear to be oriented around that axis. Moreover, given the crystal lattice 
structure, electric forces along the spine would appear to be quite dif-
ferent from the forces perpendicular to it: the forces would behave as if 
they were different forces. 
If the physicist or mathematician living on the crystal was clever, or, 
like the mathematician in Plato's cave, lucky enough to leave the crystal, 
it would soon become clear that the special direction that governed the 
physics of the world they were used to was an illusion. They would find, 
or surmise, that other crystals could point in many other directions. 
Ultimately if they could observe the window from the outside on large 
enough scales, the underlying symmetry of nature under rotations in 
all directions, reflected in the growth of the crystals in all directions, 
would become manifest. 
The notion that the world of our experience is a similar accident of 
our particular circumstances rather than a direct reflection of underly-
ing realities has become central to modern physics. We even give it a 
fancy name: spontaneous symmetry breaking. 
I mentioned one sort of spontaneous symmetry breaking earlier 
when discussing parity, or left-right symmetry. Our left hands look dif-
ferent from our right hands even though electromagnetism—the force 
that governs the building of large biological structures such as our bod-
ies—doesn't distinguish between left and right. 
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Two other examples I know of, both presented by distinguished 
physicists, also help illuminate spontaneous symmetry breaking in dif-
ferent ways that might be useful. Abdus Salam, who won a Nobel Prize 
in 1979 for work that depended crucially on this phenomenon, described 
a situation that is familiar to all of us: sitting down with a group of 
people at a round dining table set for, say, eight people. When you sit 
down, it may not be obvious which wineglass is yours and which is your 
neighbor's—the one on the right or the one on the left. But regardless of 
the laws of etiquette, which dictate it should be on your right, once the 
first person picks up her glass, everyone else at the table has only one 
option if everyone is to get a drink. Even though the underlying symme-
try of the table is manifest, the symmetry gets broken when a direction 
is chosen for the wineglasses. 
Yoichiro Nambu, another Nobelist who was the first physicist to de-
scribe spontaneous symmetry breaking in particle physics, gave another 
example that I will adapt here. Take a rod, or even a drinking straw, hold 
it up with one end on a table, and press down on the top end of the rod. 
Ultimately the rod will bend. It could bend in any direction, and if you 
try the experiment several times, you may find it bending in different 
directions each time. Before you press down, the rod has complete cy-
lindrical symmetry. Afterward, one direction among many possibilities 
has been chosen, not determined by the underlying physics of the rod 
but by the accident of the particular way you press on the rod each time. 
The symmetry has been broken spontaneously. 
If we now return to the world of the frozen window, the character-
istics of materials can change as we cool systems down. Water freezes, 
gases liquefy, and so on. In physics, such a change is called a phase tran-
sition, and as the window example demonstrates, whenever a system 
undergoes a phase transition, it is not unusual to find that symmetries 
associated with one phase will disappear in the other phase. Before the 
ice froze into the crystals on the window, the water droplets wouldn't 
have been so ordered, for example. 
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One of the most astonishing phase transitions ever witnessed in sci-
ence was first observed by the Dutch physicist Kamerlingh Onnes on 
April 8, 1911. Onnes had—remarkably—been able to cool materials to 
temperatures never before achieved, and he was the first person to liq-
uefy helium, at just four degrees above absolute zero. For this experi-
mental prowess he was later awarded a Nobel Prize. On April 8, when 
cooling a mercury wire down to 4.2 degrees above absolute zero in a 
liquid helium bath and measuring its electrical resistance, to his aston-
ishment he discovered that the resistance suddenly dropped to zero. 
Currents could flow in the wire indefinitely once they began, even after 
any battery that started the flow was removed. Demonstrating that his 
talent for public relations was as astute as his experimental talents, he 
coined the term superconductivity to describe this remarkable and com-
pletely unexpected result. 
Superconductivity was so unexpected and strange that it would take 
almost fifty years after the discovery of quantum mechanics, on which it 
depends, before a fascinating physics explanation was developed by the 
team of John Bardeen, Leon Cooper, and Robert Schrieffer, in 1957. (That 
was same year that parity violation was observed, and that Schwinger 
proposed a model to try to unify the weak and electromagnetic interac-
tion.) Their work was a tour de force, built on a succession of insights 
made over several decades of work. Ultimately the explanation relies on 
an unexpected phenomenon that can only occur in certain materials. 
In empty space, electrons repel other electrons because like charges 
repel each other. However, in certain materials, as they are cooled, elec-
trons can actually bind to other electrons. This happens in the mate-
rial because a free electron tends to attract around it positively charged 
ions. If the temperature is extremely low, then another electron can be 
attracted to the positively charged field around the first electron. Pairs 
of electrons can bind together, with the glue, if you wish, being the posi-
tively charged field caused by the attraction of the first electron on the 
lattice of positive charges associated with the atoms in the material. 
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Since the nuclei of atoms are heavy and pinned in place by relatively 
strong atomic forces, the first electron slightly distorts the lattice of 
nearby atoms, moving some of the atoms slightly closer to the electron 
than they would otherwise be. Distortions of the lattice in general cause 
vibrations, or sound waves, in the material. In the quantum world these 
vibrations are quantized and are called phonons. Leon Cooper discov-
ered that these phonons can bind pairs of electrons, as I have described 
above, so these are called Cooper pairs. 
The true magic of quantum mechanics occurs next. When mer-
cury (or any of several other materials) is cooled below a certain point, 
a phase transition occurs and all the Cooper pairs suddenly coalesce 
into a single quantum state. This phenomenon, called Bose-Einstein 
condensation, occurs because unlike fermions, particles with integral 
quantum mechanical spin, such as photons, or even particles with zero 
spin, instead prefer to all be in the same state. This was proposed first 
by the Indian physicist Satyendra Nath Bose and later elaborated upon 
by Einstein. Once again light played a crucial role, as Bose's analysis 
involved the statistics of photons, and Bose-Einstein condensation is 
intimately related to the physics governing lasers, in which many indi-
vidual photons all behave coherently in the same state. For this reason 
particles with integral spin such as photons are called bosons, to distin-
guish them from fermions. 
In a gas or a solid at room temperature, normally so many collisions 
occur between particles that their individual states are changing rapidly 
and any collective behavior is impossible. However, a gas of bosons can 
coalesce at a low enough temperature into a Bose-Einstein condensate, 
in which the individual particles identities disappear. The whole system 
behaves like a single, sometimes macroscopic, object, but in this case 
acting via the rules of quantum mechanics, rather than classical me-
chanics. 
As a result, a Bose-Einstein condensate can have exotic properties, 
the way laser light can behave very differently from normal light coming 
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THE GREATEST STORY EVER TOLD-SO FAR 
from flashlights. Since a Bose-Einstein condensate is a huge amalga-
mation of what would otherwise be individual noninteracting particles, 
now tied together into a single quantum state, creating such a conden-
sate required exotic and special atomic physics experiments. The first 
direct observation of such a condensation from a gas of particles did not 
take place until 1995, by the US physicists Carl Wieman and Eric Cor-
nell, another feat that was deemed worthy of a Nobel Prize. 
What makes the possibility of such a condensation inside bulk ma-
terials such as mercury so strange is that the fundamental particles 
initially involved are electrons—which not only normally repel other 
electrons, but in addition have spin 1/2 and, as fermions, have precisely 
the opposite behavior of bosons, as I described above. 
But when the Cooper pairs form, the two electrons each act in con-
cert, and since both of them have spin 1/2, the combined object has 
integral (2 x 54) spin. Voile, a new kind of boson is created. The lowest-
energy state of the system, to which it relaxes at low temperature, is a 
condensate of Cooper pairs—all condensed into a single state. When 
that happens, the properties of the material change completely. 
Before the condensate forms, when a voltage is applied to a wire, 
individual electrons begin to move to form an electric current. As they 
bump into atoms along the way, they dissipate energy, producing an 
electrical resistance that we are all familiar with, and heating up the 
wire. Once the condensate forms, however, the individual electrons and 
even each Cooper pair no longer have any individual identity. Like the 
Borg in Star Trek, they have assimilated into a collective. When a cur-
rent is applied, the whole condensate moves as one entity. 
Now, if the condensate were to bounce off an individual atom, the 
trajectory of the whole condensate would change. But this would take 
a lot of energy, much more than would have been required to redirect 
the flow of an individual electron. Classically we can think of the result 
as follows: at low temperatures, not enough heat energy is available in 
the random jittering of atoms to cause a change of motion of the bulk 
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