Hiding in the Mirror (13 page)

More important, however, was the fact that
while Klein’s explanation for why the fifth dimension was hidden was
ingenious, it was also clearly incomplete. Namely, why would the
fourth spatial dimension curl up in a circle while the other three
spatial dimensions did not? Compounding this issue was the residual
problem of that one extra quantity related to the five-dimensional
metric that Kaluza, and later Klein, continued to ignore. It was
recognized clearly by the 1940s that this extra quantity would
affect the nature of gravity, so that the residual theory in four
dimensions would no longer precisely be described by general
relativity. Finally, and most important of all, perhaps, was the
fact that the world of physics was continuing to undergo
revolutionary changes. Starting in 1930, with the discovery of the
neutron, the subatomic world began to become far more complex and
interesting. In short order, antimatter was discovered, as was a
then new force in nature, now known as the weak force, responsible
for radioactive decays. Any unification of merely gravity and
electromagnetism would thus fall far short of a complete
description of nature. Consequently, the majority of the physics
community—rightly, I would argue—began to concentrate on trying to
understand this host of new experimental phenomena, and left
speculations about unobserved extra dimensions aside. It would take
almost half a century before events would once again drive
physicists to reconsider the possibility of a new hidden universe
lying just out of sight.

The theoretical
possibilities in a given case are relatively few and
rela
tively simple. . . . Considering these
tells us what is possible but does
not tell
us what reality is.

—Albert Einstein

A
s exciting as the
possibility of hidden extra dimensions may have seemed in 1926,
within a decade the direct experimental evidence for new phenomena
in three dimensions had succeeded in redirecting the imagination of
the physics community toward somewhat less esoteric pursuits, or at
least more experimentally accessible ones. The half-century
following 1930 was one of the most productive periods in the
history of physics in terms of changing our picture of the
fundamental nature of matter and energy in the universe. This may
seem a surprising claim, given the fact that the two greatest
single developments in the field in the twentieth century—the
development of general relativity, and the discovery of the laws of
quantum mechanics—had both been essentially completed by this time.
Nevertheless if the theoretical advances made during the first three
decades of the century revealed a hidden nature to space and time,
the experimental work conducted over the next fifty years revealed a
hidden universe of exotic particles and forces. This is not to say
that stunning theoretical strides were not made. They were, and I
will describe them. But in contrast with general relativity and
even quantum mechanics, these developments derived directly from
unexpected experimental evidence based on new technologies that
opened important new windows on the universe. And each time a new
window on the universe has been opened, surprises have inevitably
followed.

In the last years of the 1920s the capstone
achievement in the theoretical development of quantum mechanics had
been the work of Paul Dirac, who discovered an equation describing
the quantum mechanical behavior of an electron in a way that was,
for the first time, completely consistent with the principles of
special relativity.

One of the remarkable predictions of Dirac’s
equation was that there were always two different independent
solutions that satisfied the equation, which described the behavior
of electrons of a certain energy. One of these described a
negatively charged particle, the electron, and one described a
particle with equal mass but opposite—meaning positive—charge. When
this prediction first appeared, it caused some embarrassment,
because while there was one known particle in nature with equal and
opposite charge to the electron—namely, the proton—it had a mass
almost two thousand times larger than that of the electron. At first
Dirac thought that the positive particle that showed up in his
equation might somehow represent the proton. But this
interpretation clearly could not hold up under detailed scrutiny.
At one point, in desperation, he appealed to another sort of hidden
universe: He proposed that perhaps there were other, as of yet
unobserved, places in the universe where positives and negatives
were reversed.

Nevertheless, this embarrassing situation
turned triumphant when, in the summer of 1932, the second great
discovery of the post-1930 era was made. The experimental physicist
Carl Anderson, while examining the tracks left by particles in
cosmic rays, the high-energy particles that bombard the earth from
space every moment of every day, discovered the tracks of a
particle that appeared to have a mass identical to that of the
electron, but a positive charge.

The technique he used was quite
straightforward. As I have described, Oersted discovered in the
nineteenth century that a charged particle will experience a force
if it is moving through a magnetic field. The effect of this force
will be to cause its trajectory to bend. If it is positively
charged, it will bend one way, and if negatively charged, the
other. Anderson used a device called a cloud chamber to observe the
tracks of incoming cosmic rays. This device causes charged
particles to leave a cloudlike track, much like that trailed by
airplanes in the sky. By placing the chamber in a large magnetic
field, Anderson could determine the charge of the incoming particles
by observing the direction in which their trajectories curved.
Particles such as protons will indeed curve in the opposite
direction to electrons, but, because the former are two thousand
times heavier, a proton tends to have far greater inertia, which
means its path will tend to bend far less in a magnetic field of a
fixed strength than that of a high-energy electron. In one of the
photographs of his chamber, taken every fifteen seconds over the
course of many days, Anderson saw a track whose curvature was
identical to that of the high-energy electrons he was seeing, but
the direction of its curvature was opposite. The positron, as it is
now known, had been discovered!

Dirac’s theory was vindicated, and Dirac
stated, regarding his own timidity in believing in the existence of
positrons, “My equation was smarter than I was!” . One of the
related striking predictions of Dirac’s theory was that relativity
implied that all charged elementary particles should have
“antiparticles” (as they have become known): particles with
identical mass and opposite electric charge. Moreover, electrons
and their antiparticles—indeed all particles and their
antiparticles—should be able to annihilate each other, producing
pure electromagnetic radiation as an end product. Anderson was able
to show that the reverse process also occurs: Very energetic
electromagnetic radiation, called a gamma ray, could convert into
electron–positron pairs as it traversed matter. The annihilation of
these particles and antiparticles back into gamma rays was also
observed. The fact that particles and antiparticles could be
created in pairs from pure energy (i.e., radiation) completely
changed our thinking about matter. This was the most obvious
vindication of Einstein’s famous relation
E
=
mc
²
. Even more importantly,
perhaps, it has forever changed our thinking about empty space. The
reason stems from that other crown jewel of quantum mechanics, the
Heisenberg uncertainty principle. As I have mentioned, the
uncertainty principle states that there are certain combinations of
physically observable quantities that cannot be measured at the
same time with a combined accuracy better than some amount fixed by
the laws of nature, not by an experimental apparatus. The most
famous such combination involves the position of a particle and its
momentum, both of which cannot be measured at exactly the same
time. The more accurately you can determine a particle’s position,
for example, the less accurately you can measure in precisely which
direction it is moving. A less-known combination involves energy
and time. Here, the uncertainty principle tells us that the longer
we measure something, the more accurately we can determine its
total energy. Since all measurements take merely a finite time,
however, there is always a residual uncertainty in the value of the
energy that can be measured in any system. Now, as Faraday and
Maxwell told us, if an electron is moving through space it can act
as the source of electromagnetic radiation. But what if some of
this electromagnetic radiation were to spontaneously convert into
an electron–positron pair? Classically we would say that this is
impossible, because the electron and positron together weigh twice
as much as the original electron, so unless the original electron
is moving so fast that its total energy is more that three times
its rest mass energy, it is impossible to end up with three
particles after starting with one. But we don’t live in a classical
universe. Quantum mechanics is, as I like to say, just like the
White House: As long as no one can measure what is going on,
anything goes! In this case, the uncertainty principle tells us
that during some time interval that is short enough so that the
energy uncertainty is large enough—larger, say, than twice the rest
mass of the electron—we cannot say how many particles exist within
a region we may be measuring.

There is a finite probability that there might
be, for some short period, two extra particles present. For
example, an electron–positron pair could spontaneously appear for a
short time, and then these particles could annihilate, leaving just
the original system. As long as the particle–antiparticle pair
exists for a time short enough so that the uncertainty principle
indicates that we cannot measure the violation of energy
conservation implied by their brief presence, the laws of quantum
mechanics and relativity together suggest that such a configuration
is allowed. This represents another complete revision in our
fundamental understanding of the nature of space. According to this
new picture, empty space is not empty at all, but involves a
boiling, bubbling brew of these particle–antiparticle pairs popping
in and out of nothingness. Here is yet another hidden universe
lying just beyond our perception, and one that ultimately played a
key role in motivating physicists to consider the possibility of
yet more radical revisions in our picture of space and time. Before
jumping on the virtual particle bandwagon, one might wonder whether
suggesting particle–antiparticle pairs popping in and out of the
vacuum is really any different than fantasizing about psychics
popping in and out of extra dimensions in order to untie knotted
ropes and recover objects inside of boxes. In cooking, the proof is
in the tasting. In physics, it is in the testing.

How can we test for the existence of
unobservable particles? We do it just as we might work to uncover
evidence of a crime we did not witness directly: by looking for
indirect evidence. And so it turns out that while one cannot
measure virtual particles directly, one can nevertheless measure
their effect on processes we can both calculate and measure. Niels
Bohr’s first great success in his emerging quantum mechanics was to
correctly predict the spectrum of light emitted by hydrogen gas
when it is heated. During this process, an electron can jump
between discrete allowed orbits about a proton by absorbing or
radiating electromagnetic waves that we can observe as visible
light. The fixed nature of the frequencies/colors emitted by
hydrogen was a mystery until Bohr proposed that electrons were
somehow confined to such orbits. It was the great success of
Schrödinger and Heisenberg that they presented a self-consistent
mechanics that allowed a precise calculation of these energy levels
in hydrogen that agreed well with the measured frequencies of
radiation emitted by hydrogen atoms. However, as measurements
became more and more precise, a tiny discrepancy between the
predicted energy levels and the levels inferred from observation
emerged. In other areas of science, such a small discrepancy might
have been ignored. But such was the precision afforded by the new
merging of quantum mechanics, relativity, and electromagnetism—a
theory that became known as “quantum electrodynamics”—that this
experimental anomaly presented a major challenge for theoretical
physicists. Shortly after World War II the physicists who had
otherwise been occupied with developing the atomic bomb returned to
their fundamental investigations of nature. At one of the most
famous meetings in twentiethcentury physics, held on Shelter Island
off Long Island in New York, a group of young turks demonstrated
that a proper accounting of the effects of virtual particles could
yield the critical missing component that could resolve the
aforementioned shift in energy levels between theory and
experiment. This shift was by then known as the Lamb shift, after
the experimentalist Willis Lamb, who first discovered it.

At the time the different mathematical methods
used to calculate these effects were diverse, complex, and almost
mysterious, representing the similarly diverse approaches to
physics of the scientists involved, from the formal and
prodigiously brilliant Julian Schwinger, to the informal and
sometimes irreverent genius Richard Feynman, and independently by
the quiet Sin-Itiro Tomonaga, all of whom would later share the
Nobel Prize for their efforts. Nevertheless, with hindsight and
after a “translation” paper published by the equally brilliant
Freeman Dyson, it became clear that the different approaches all
reflected the same underlying physical reality. The central point of
all these approaches was that it is incorrect to calculate the
orbit of an electron around a proton as if these were the only two
particles present. For if virtual particle–antiparticle pairs can
spontaneously appear for short periods out of nothing, then the
electric field experienced by the orbiting electrons must be
affected by these virtual particles. Working independently, Feynman
and Schwinger used this technique to calculate the values of the
energy shifts. Their method is now known as QED—an acronym for
quantum electrodynamics—and its agreement with the empirically
observed values is better than one part in a million, a result that
remains the best-measured prediction in all of science. With the
recognition that empty space was anything but empty, a manifest
need arose to try to explicitly understand what processes take
place on the smallest scales that can be imagined, and in turn
understand how these processes might affect the nature of physical
reality on more familiar scales. As we shall see, this program
would set into motion a simmering set of internal conflicts in
physics that would ultimately drive theorists to new extremes of
speculation.

Alert readers will note that I referred to the
discovery of antiparticles as the “second great discovery” in the
post-1930 era. The first occurred about four months earlier, in
February 1932, although its origins date back to the dawn of the
modern era. In 1896 the French physicist Henri Becquerel found that
certain substances, such as uranium, spontaneously emit a strange
new sort of radiation. Mystified, he called this radiation U-rays,
although his contemporaries called them Becquerel rays. Ultimately
it was shown that there were actually three different kinds of
radiation given off by radioactive substances, which Lord
Rutherford later creatively labeled alpha, beta, and gamma
rays.