The notion that the world of our experience is a similar accident
of our particular circumstances rather than a direct reflection of
underlying 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
different from our right hands even though electromagnetism—the
force that governs the building of large biological structures such as
our bodies—doesn’t distinguish between left and right.
Two other examples I know of, both presented by distinguished
physicists, also help illuminate spontaneous symmetry breaking in
different ways that might be useful. Abdus Salam, who won a Nobel
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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 symmetry 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
describe 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 cylindrical 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
characteristics 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 transition, 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
science 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 liquefy helium, at just four degrees above absolute zero.
For this experimental 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 astonishment 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 completely
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 interaction.) 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, electrons can actually bind to other electrons. This happens
in the material 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
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around the first electron. Pairs of electrons can bind together, with
the glue, if you wish, being the positively charged field caused by the
attraction of the first electron on the lattice of positive charges
associated with the atoms in the material.
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 discovered 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
mercury (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 individual photons all behave
coherently in the same state. For this reason particles with integral
spin such as photons are called bosons, to distinguish 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,
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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,
&nb
sp; sometimes macroscopic, object, but in this case acting via the rules
of quantum mechanics, rather than classical mechanics.
As a result, a Bose-Einstein condensate can have exotic
properties, the way laser light can behave very differently from
normal light coming from flashlights. Since a Bose-Einstein
condensate is a huge amalgamation of what would otherwise be
individual noninteracting particles, now tied together into a single
quantum state, creating such a condensate 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 Cornell, another
feat that was deemed worthy of a Nobel Prize.
What makes the possibility of such a condensation inside bulk
materials 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 ½ 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
concert, and since both of them have spin ½, the combined object
has integral (2 × ½) spin. Voilà, 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
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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 current 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 condensate of particles. It would again be like
trying to move a truck by throwing popcorn at it. Quantum
mechanically the result is similar. In this case we would say that to
change the configuration of the condensate would require the whole
condensate of particles to shift by a large fixed amount to a new
quantum state that differs in energy from the state it is in. But no
such energy is available from the thermal bath at low temperature.
Alternatively, we might wonder if the collision could break apart two
electrons from a Cooper pair in the condensate—sort of like
knocking off the rearview mirror when a truck collides with a post.
But at low temperatures everything is moving too slowly for that to
happen. So the current flows unimpeded. The Borg would say,
resistance is futile. But in this case resistance is simply nonexistent. A
current, once initiated, will flow forever, even if the battery initially
attached to the wire is removed.
This was the Bardeen-Cooper-Schrieffer (BCS) theory of
superconductivity, a remarkable piece of work, which ultimately
explained all of the experimental properties of superconductors such
as mercury. These new properties signal that the ground state of the
system has changed from what it had been before it became a
͜͜͞
superconductor, and like ice crystals on a window, these new
properties
reflect
spontaneous
symmetry
breaking.
In
superconductors the breaking of symmetry is not as visually obvious
as it is in the ice crystals on a windowpane, but it is there, under the
surface.
Mathematically, the signature of this symmetry breaking is that
suddenly, once the condensate of Cooper pairs forms, a large
minimum energy is now required to change the configuration of the
whole material. The condensate acts like a macroscopic object with
some large mass. The generation of such a “mass gap” (as it is called
—expressed as the minimum energy it takes to break the system out
of its superconducting state) is a hallmark of the symmetry-breaking
transition that produces a superconductor.
You might be wondering what all of this, as interesting as it might
be, has to do with the story we have been focusing on, namely
understanding the fundamental forces of nature. With the benefit of
hindsight, the connection will be clear. However, in the tangled and
confused world of particle physics in the 1950s and ’60s the road to
enlightenment was not so direct.
In 1956, Yoichiro Nambu, who had recently moved to the
University of Chicago, heard a seminar by Robert Schrieffer on what
would become the BCS theory of superconductivity, and it left a
deep impression on him. He, like most others interested in particle
physics at the time, had been wrestling with how the familiar
particles that make up atomic nuclei—protons and neutrons—fit
within the particle zoo and the jungle of interactions associated with
their production and decay.
Nambu, like others, was struck by the almost identical masses of
the proton and the neutron. It seemed to him, as it had to Yang and
Mills, that some underlying principle in nature must produce such a
result. Nambu, however, speculated that the example of
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superconductivity might provide a vital clue—in particular the
appearance of a new characteristic energy scale associated with the
excitation energy required to break apart the Cooper-pair
condensate.
For three years Nambu explored how to adapt this idea to
symmetry breaking in particle physics. He proposed a model by
which a similar condensate of some fields that might exist in nature
and the minimum energy to create excitations out of this condensate
state could be characteristic of the large mass/energy associated with
protons and neutrons.
Independently, he and the physicist Jeffrey Goldstone discovered
that a hallmark of such symmetry breaking would be the existence of
other massless particles, now called Nambu-Goldstone (NG) bosons,
whose interactions with other matter would also reflect the nature of
the symmetry breaking. An analogy of sorts can be made here to a
more familiar system such as an ice crystal. Such a system
spontaneously breaks the symmetry under spatial translation
because moving in one direction things look very different from
when moving in another direction. But in such a crystal, tiny
vibr
ations of individual atoms in the crystal about their resting
positions are possible. These vibrational modes—called phonons, as
I have mentioned—can store arbitrarily small amounts of energy. In
the quantum world of particle physics, these modes would be
reflected as Nambu-Goldstone massless particles, because where the
equivalence between energy and mass is manifest, excitations that
carry little or no energy correspond to massless particles.
And, lo and behold, the pions discovered by Powell closely fit the
bill. They are not exactly massless, but they are much lighter than all
other strongly interacting particles. Their interactions with other
particles have the characteristics one would expect of NG bosons,
which might exist if some symmetry-breaking phenomenon existed
͜͞͞
in nature with a scale of excitation energy that might correspond to
the mass/energy scale of protons and neutrons.
But, in spite of the importance of Nambu’s work, he and almost
all of his colleagues in the field overlooked a related but much
deeper consequence of the spontaneous symmetry breaking in the
theory of superconductivity that later provided the key to unlock the
true mystery of the strong and weak nuclear forces. Nambu’s focus
on symmetry breaking was inspired, but the analogies that he and
others drew to superconductivity were incomplete.
It seems that we are much closer to the physicists on that ice
crystal on the windowpane than we ever imagined. But just as one
might imagine would be the case for those physicists, this myopia
was not immediately obvious to the physics community.
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C h a p t e r 1 5
L I V I N G
I N S I D E
A
S U P E R C O N D U C T O R
Everyone lies to their neighbor; they flatter with their lips but
harbor deception in their hearts.
—PSALMS 12:2
The mistakes of the past may seem obvious with the benefit
of hindsight, but remember that objects viewed in the rearview
mirror are often closer than they appear. It is easy to castigate our
predecessors for what they missed, but what is confusing to us today
may be obvious to our descendants. When working on the edge, we
travel a path often shrouded in fog.
The analogy to superconductivity first exploited by Nambu is
useful, but largely for reasons very different from what Nambu and
Lawrence Krauss - The Greatest Story Ever Told--So Far Page 21
