Lawrence Krauss - The Greatest Story Ever Told--So Far
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others imagined at the time. In hindsight the answer may seem
almost obvious, just as the little clues that reveal the murderer in
Agatha Christie stories are clear after the solution. But, as in her
mysteries, we also find lots of red herrings, and these blind alleys
make the eventual resolution even more surprising.
We can empathize with the confusion in particle physics at the
time. New accelerators were coming online, and every time a new
collision-energy threshold was reached, new strongly interacting
cousins of neutrons and protons were produced. The process
seemed as if it would be endless. This embarrassment of riches
meant that both theorists and experimentalists were driven to focus
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on the mystery of the strong nuclear force, which seemed to be
where the biggest challenge to existing theory lay.
A potentially infinite number of elementary particles with
everhigher masses seemed to characterize the microscopic world.
But this was incompatible with all the ideas of quantum field theory
—the successful framework that had so beautifully provided an
understanding of the relativistic quantum behavior of electrons and
photons.
Berkeley physicist Geoffrey Chew led the development of a
popular, influential program to address this problem. Chew gave up
the idea that any truly fundamental particles exist and also gave up
on any microscopic quantum theory that involved pointlike particles
and the quantum fields associated with them. Instead, he assumed
that all of the observed strongly interacting particles were not
pointlike, but complicated, bound states of other particles. In this
sense, there could be no reduction to primary fundamental objects.
In this Zen-like picture, appropriate to Berkeley in the 1960s, all
particles were thought to be made up of other particles—the so-
called bootstrap model, in which no elementary particles were
primary or special. So this approach was also called nuclear
democracy.
While this approach captivated many physicists who had given up
on quantum field theory as a tool to describe any interactions other
than the simple ones between electrons and photons, a few scientists
were sufficiently impressed by the success of quantum
electrodynamics to try to mimic it in a theory of the strong nuclear
force—or strong interaction, as it has become known—along the
lines earlier advocated by Yang and Mills.
One of these physicists, J. J. Sakurai, published a paper in 1960
rather ambitiously titled “Theory of Strong Interactions.” Sakurai
took the Yang-Mills suggestion seriously and tried to explore
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precisely which photonlike particles might convey a strong force
between protons and neutrons and the other newly observed
particles. Because the strong interaction was short-range—spanning
just the size of the nucleus at best—it seemed the particles required
to convey the force would be massive, which was incompatible with
any exact gauge symmetry. But otherwise, they would have many
properties similar to the photon’s, having spin 1, or a so-called
vector spin. The new predicted particles were thus dubbed massive
vector mesons. They would couple to various currents of strongly
interacting particles similar to the way photons couple to currents of
electrically charged particles.
Particles with the general properties of the vector mesons
predicted by Sakurai were discovered experimentally over the next
two years, and the idea that they might somehow yield the secret of
the strong interaction was exploited to try to make sense of the
otherwise complex interactions between nucleons and other
particles.
In response to this notion that some kind of Yang-Mills symmetry
might be behind the strong interaction, Murray Gell-Mann
developed an elegant symmetry scheme he labeled in a Zen-like
fashion the Eightfold Way. It not only allowed a classification of
eight different vector mesons, but also predicted the existence of
thus-far-unobserved strongly interacting particles. The idea that
these newly proposed symmetries of nature might help bring order
to what otherwise seemed a hopeless menagerie of elementary
particles was so exciting that, when his predicted particle was
subsequently discovered, it led to a Nobel Prize for Gell-Mann.
But Gell-Mann is remembered most often for a more
fundamental idea. He, and independently George Zweig, introduced
what Gell-Mann called quarks—a word borrowed from James Joyce’s
Finnegans Wake—which would physically help explain the symmetry
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properties of his Eightfold Way. If quarks, which Gell-Mann viewed
simply as a nice mathematical accounting tool (just as Faraday had
earlier viewed his proposal of electric and magnetic fields), were
imagined to comprise all strongly interacting particles such as
protons and neutrons, the symmetry and properties of the known
particles could be predicted. Once again, the smell of a grand
synthesis that would unify diverse particles and forces into a
coherent whole appeared to be in the air.
I cannot stress how significant the quark hypothesis was. While
Gell-Mann did not advocate that his quarks were real physical
particles inside protons and neutrons, his categorization scheme
meant that symmetry considerations might ultimately determine the
nature not only of the strong interaction, but of all fundamental
particles in nature.
However, while one sort of symmetry might govern the structure
of matter, the possibility that this symmetry might be extended to
some kind of Yang-Mills gauge symmetry that would govern the
forces between particles seemed no closer. The nagging problem of
the observed masses of the vector mesons meant that they could not
truly reflect any underlying gauge symmetry of the strong interaction
in a way that could unambiguously determine its form and
potentially ensure that it made quantum-mechanical sense. Any
Yang-Mills extension of quantum electrodynamics required the new
photonlike particles to be massless. Period.
Faced with this apparent impasse, an unexpected wake-up call
from superconductivity provided another, more subtle, and
ultimately more profound, possibility.
The first person to stir the embers was a theorist who worked
directly in the field of condensed matter physics associated with
superconductivity in materials. Philip Anderson, at Princeton, later a
Nobel laureate for other work, suggested that one of the most
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fundamental, ubiquitous phenomena in superconductors might be
worth exploring in the context of particle physics.
One of the most dramatic demonstrations one can perform with
superconductors,
especially
the
new
high-temperature
superconductors that allow superconductivity to become manifest at
liquid-nitrogen temperatures, is to levitate a magnet above the
superconductor as shown below:
Creative Commons/Photograph by Mai-Linh Doan
This is possible for a reason discovered in an experiment in 1933
by Walther Meissner and colleagues, explained by theorists Fritz and
Heinz London two years later, which goes by the name the Meissner
effect.
As Faraday and Maxwell discovered sixty years earlier, electric
charges respond in different ways to magnetic and electric fields. In
particular, Faraday discovered that a changing magnetic field can
cause a current to flow in a distant wire. Equally important, but
which I didn’t emphasize earlier, is that the resulting current will
flow in a way that produces a new magnetic field in a direction that
counters the changing external magnetic field. Thus, if the external
field is decreasing, the current generated will produce a magnetic
field that counters that decrease. If it is increasing, the current
generated will be in an opposite direction, producing a magnetic
field that works to counter that increase.
You may have noticed that when you are talking on your cell
phone and get in certain elevators, particularly ones in which the
outer part of the elevator cage is encased in metal, when the door
closes your call gets dropped. This is an example of something called
ͤ͜͞
a Faraday cage. Since the phone signal is being received as an
electromagnetic wave, the metal shields you from the outside signal
because currents flow in the metal in a way that counters the
changing electric and magnetic fields in the signal, diminishing its
strength inside the elevator.
If you had a perfect conductor, with no resistance, the charges in
the metal could essentially cancel any effects of the outside changing
electromagnetic field. No signal of these changing fields—i.e., no
telephone signal—would remain to be detected inside the elevator.
Moreover, a perfect conductor will also shield out the effects of any
constant external electric field, since the charges can realign in the
superconductor in response to any field and completely cancel it out.
But the Meissner effect goes beyond this. In a superconductor, all
magnetic fields—even constant magnetic fields such as those due to
the magnet above—cannot penetrate into the superconductor. This
is because, when you slowly bring a magnet in closer from a large
distance, the superconductor generates a current to counter the
changing magnetic field that increases as the magnet approaches.
But since the material is superconducting, the current continues to
flow and does not stop if you stop moving the magnet. Then as you
bring the magnet in closer, a larger current flows to counter the new
increase. And so on. Thus, because electric currents can flow
without dissipation in a superconductor, not only are electric fields
shielded, but so are magnetic fields. This is why magnets levitate
above superconductors. The currents in the superconductor expel
the magnetic field due to the external magnet, and this repels the
magnet just as if another magnet were at the surface of the
superconductor with north pole facing north pole or south pole
facing south pole.
The London brothers, who first attempted to explain the
Meissner effect, derived an equation describing this phenomenon
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inside a superconductor. The result was suggestive. Each different
type of superconductor would create a unique characteristic length
scale below the surface of the superconductor—determined by the
microscopic nature of the supercurrents that are created to
compensate any external field—and any external magnetic field
would be canceled on this length scale. This is called the London
penetration depth. The depth is different for different
superconductors and depends on their detailed microphysics in a
way the brothers couldn’t determine since they didn’t have a
microscopic theory of superconductivity at the time.
Nevertheless, the presence of a penetration depth is striking
because it implies that the electromagnetic field behaves differently
inside a superconductor—it is no longer long-range. But if
electromagnetic fields become short-range inside the surface, then
the carrier of electromagnetic forces must behave differently. The
net effect? The photon behaves as if it has mass inside the
superconductor.
In superconductors, virtual photons—and the electric and
magnetic fields they mediate—can only propagate below the surface
through a distance comparable to the London penetration depth,
just as would be the case if electromagnetism inside the
superconductor resulted from the exchange of massive—not
massless—photons.
Now imagine what it would be like to live inside a
superconductor. To you, electromagnetism would be a short-range
force, photons would be massive, and all the familiar physics that we
associate with electromagnetism as a long-range force would
disappear.
I want to emphasize how remarkable this is. No experiment you
could perform within the superconductor, as long as it remained
superconducting, would reveal that photons are massless in the
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outside world. If you were Plato’s philosopher inside such a
superconductor, you would have to intuit an incredible amount
about the outside world before you could infer that a mysterious and
invisible phenomenon was the cause of an illusion. It might take
several thousand years of thinking and experiment before you or
your descendants could guess the nature of the reality underlying the
shadow world in which you live, or before you could build a device
with enough energy to break apart Cooper pairs and melt the
superconducting state, restoring electromagnetism to its normal
form, and revealing the photon to be massless.
In retrospect, we physicists might have expected, just on the
grounds of symmetry, and without considering the Meissner effect
directly, that photons should behave as massive particles inside a
superconductor. The Cooper-pair condensate, being made of
electron pairs, has a net electric charge. This breaks the gauge
symmetry of electromagnetism because in this background any
positive charges one adds to the material will behave differently
from negative charges added to the material. So now there is a real
distinction between positive and negative. But recall that the
masslessness of photons is a sign that the electromagnetic field is
long-range, and the long-range nature of the electromagnetic field
reflects that it allows local variations in the definition of electric
charge in one place to not affect the physics globally throughout the
material. But if gauge invariance is gone, then local variations in the
definition of electric charge will have a real physical effect, so there
can be no such long-range field that cancels out such variations. One
way to get rid of a long-range field is to make the photon massive.
Now the $64
,000 question: Could something like this happen in
the world in which we find ourselves living? Could the masses of
heavy photonlike particles arise because we are actually living in
something akin to a cosmic superconductor? This was the
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fascinating question that Anderson raised, at least by analogy with
regular superconductors.
Before we can answer this question, we need to understand a
technical bit of wizardry that allows the generation of mass for a
photon in a superconductor.
Recall that in an electromagnetic wave the electric (E) and
magnetic (B) fields oscillate back and forth in directions that are
perpendicular to the direction of the wave, as shown:
Since there are two perpendicular directions, one could draw an
electromagnetic wave in two ways. The wave could look like that
shown above, or one could interchange the E and B fields. This
reflects that electromagnetic waves have two degrees of freedom,
which are called two different polarizations.
This arises from the gauge invariance of electromagnetism, or
equivalently from the masslessness of photons. If, however, photons
had a mass, then not only would gauge invariance be broken, but a
third possibility can arise. The electric and magnetic fields could
oscillate along the direction of motion, instead of just oscillating
perpendicular to this direction. (Since the photons will no longer be
traveling at the speed of light, oscillations along the direction of
motion of the particles become possible.)
But this means that the corresponding massive photons would
have three degrees of freedom, not just two. How can photons pick
up this extra degree of freedom in superconductors?
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Anderson explored this issue in superconductors, and its
resolution is intimately related to a fact that I described earlier. In
the absence of electromagnetic interactions in a superconductor, it’s
possible to produce slight spatial variations in the Cooper-pair
condensate that would have arbitrarily small energy cost because
Cooper pairs would not interact with each other. However, when
electromagnetism is taken into account, those low-energy modes
(which would destroy superconductivity) disappear precisely because
of the interactions of the charges in the condensate with the
electromagnetic field. That interaction causes photons in the