about doing this in an urban area, Fermi was confident enough to
convince the leader of the project to allow him to build it at the
University of Chicago. On December 2, 1942, the reactor went
critical, and Chicago survived.
Two and a half years later, Fermi was on hand in New Mexico to
observe the first nuclear explosion, the Trinity test. Typical of Fermi,
while the others stood in awe and horror, he conducted an
impromptu experiment to estimate the bomb’s strength by dropping
several strips of paper when the blast wave came by, to see how far
they were carried.
Fermi’s constant experimental approach to physics is one of the
reasons I cherish his memory. He always found a simple, easy way to
reach the correct answer. Even though he had great mathematical
skill, he disliked complication, and he realized that he could get an
approximate answer that was “good enough” in a short time, while
getting the exact answer might take months or years. He refined his
abilities and helped his students do so by inventing what we now call
Fermi Problems, which he is also said to have assigned at lunchtime
each day to the team working for him. My favorite problem, which I
always assign to my introductory-physics students, is “How many
piano tuners are there in Chicago?” Try it. If you get between one
hundred and five hundred, you did well.
Fermi won the Nobel Prize for his experimental work, but his
theoretical legacy for physics may be far greater. True to form, the
“theory” he proposed in his famously rejected paper on neutron
decay was remarkably simple, yet it did the job. It wasn’t a full theory
at all, and at the time it would have been premature to develop one.
Instead he made the simplest possible assumption. He imagined
some new kind of interaction between particles that took place at a
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single point. The four particles were a neutron, a proton, an electron,
and the new particle Pauli and Fermi named the neutrino.
The starting point of Fermi’s thinking involved light, as did
almost all of modern physics, and in this case the modern quantum
theory of light interacting with matter. Recall that Feynman
developed a pictorial framework to think about fundamental
processes in space and time, when he argued that antimatter should
exist. The space-time picture of an electron emitting a photon is
reproduced here, but with the electron replaced by a proton, p:
Fermi imagined the decay of a neutron in a similar fashion, but
instead of the neutron emitting a photon and remaining the same
particle, the neutron, n, would emit a pair of particles—an electron,
e, and a neutrino, ν, and would be converted into a proton, p:
In electromagnetism the strength of the interaction between
charged particles and photons (determining the probability of
emitting a photon at the point shown in the first figure on the
previous page) is proportional to the charge of the particle. Since the
charge is what allows particles to interact, or “couple” to the
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electromagnetic field, we call the magnitude of the fundamental
quantum of charge—the charge on a single electron or proton—the
“coupling constant” of electromagnetism.
In Fermi’s interaction the numerical quantity that appears at the
interaction point in the figure where a neutron converts into a
proton determines the probability of such a conversion. The value of
this quantity is determined by experiment, and we now call it the
Fermi constant. Relative to electromagnetism, the numerical value of
this quantity is small because the neutron takes a long time to decay
—compared, for example, to the rate at which electromagnetic
transitions take place in atoms. As a result, Fermi’s interaction,
describing a new force in nature, became known as the weak
interaction.
One of the things that made Fermi’s proposal so remarkable was
that it was the first time in physics that anyone had proposed that
particles other than photons could be spontaneously created in the
quantum world. (In this case the electron and the neutrino are
created at the same time as the neutron converts into a proton.) This
both inspired and became the prototype for much of the subsequent
exploration of the quantum character of the fundamental forces in
nature.
Moreover, it didn’t just make postdictions about nature. It made
predictions precisely because a single mathematical form for the
interaction that caused neutron decay could also predict a host of
other phenomena, which were later observed.
Even more important, this interaction, with precisely the same
strength, governs similar decays of other particles in nature. For
example, in 1936 Carl Anderson, the discoverer of the positron,
discovered another new particle in cosmic rays—the first of what
would be so many that particle physicists would wonder whether the
progression would ever end. When informed of this discovery, the
͟͝͠
atomic physicist and later Nobel laureate I. I. Rabi is said to have
exclaimed, “Who ordered that?”
We now know that this particle, called the muon and
characterized by the Greek letter µ, is essentially an exact copy of the
electron, only about two hundred times heavier. Because it is
heavier, it can decay, emitting an electron and a neutrino in an
interaction that looks identical to neutron decay, except the muon
converts into another type of neutrino (called the muon neutrino)
instead of a proton. Remarkably, if we use the same Fermi constant
for the strength of this interaction, we derive exactly the right
lifetime for the muon.
Clearly a new fundamental force is at work here, universal in
nature, with some similarities to electromagnetism, and some
important differences. First, the interaction is much weaker. Second,
unlike electromagnetism, the interaction appears to operate over
only a small range—in Fermi’s model at a single point. Neutrons
don’t turn into protons in one place and cause electrons to turn into
neutrinos somewhere else, whereas the interaction between
electrons and photons allows electrons to exchange virtual photons
and be repelled by each other even at a great distance. Third, the
interaction changes one type of particle into another.
Electromagnetism involves the creation and absorption of photons
—the quanta of light—but the charged particles that interact with
them preserve their identity before and after the interaction. Gravity
too is long-range, and when a ball falls toward the Earth, it remains a
ball. But the weak interaction causes neutrons to decay into protons,
muons into neutrinos, and so on.
Clearly something about the weak interaction is different, but you
may wonder if it is worth worrying about. Neutron decay is
interesting, but happily the properties of nuclei protect us from it so
that stable atoms can exist. Thus it seems to have little impact on
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͠͠
everyday lives. Unlike gravity and electromagnetism, we don’t sense
it. If the weak interaction were of little other importance, then its
anomalous nature could be easily overlooked.
However, the weak interaction, at least as much as gravity and
electromagnetism, is directly responsible for our existence. In 1939,
Hans Bethe, who would soon help lead the effort to build the atomic
bomb, realized that the interactions that broke apart heavy nuclei as
the source of the explosive power of the bomb could, under different
circumstances, be utilized to build larger nuclei from smaller nuclei.
This could release even more energy than was released in the A-
bomb.
Up until that time the energy source of the Sun was a mystery. It
was well established that the temperature in the solar core could not
exceed a few tens of millions of degrees—which may seem extreme,
but the energies available to the colliding nuclei at those
temperatures had already been achieved in the lab. Moreover, the
Sun could not involve simple burning, like a candle.
It had been established as early as the eighteenth century that an
object with the mass of the Sun could only burn with its observed
brightness for perhaps ten thousand years if it were just something
like a burning lump of coal. While that meshed nicely with Bishop
Ussher’s estimates for the age of the universe as inferred from the
Bible’s tale of creation, geologists and biologists had already
established by the mid-nineteenth century that Earth itself was far
older. With no apparent new energy source, the longevity and
brightness of the Sun was inexplicable.
Enter Hans Bethe. Another of the incredibly talented and prolific
theoretical physicists coming out of Germany in the first half of the
twentieth century, Bethe was also another doctoral student of
Arnold Sommerfeld’s and also went on to win the Nobel Prize.
Bethe began his career in chemistry because the introductory physics
͝͠͡
instruction at his university was poor—a common problem. (I also
dropped physics in my first year for the same reason, but happily the
physics department at my university let me take a more advanced
course the following year.) Bethe switched to physics before moving
on to graduate studies and emigrated to the United States to escape
the Nazis.
A consummate physicist, Bethe could work through detailed
calculations to solve a wide variety of problems on the blackboard,
beginning at the upper left of the board and ending at the lower right
with almost no erasures. Bethe strongly influenced Richard
Feynman, who used to marvel at Bethe’s patient methodological
approach to problems. Feynman himself often jumped from the
beginning of a problem to the end and worked out the steps in
between afterward. Bethe’s solid technical prowess and Feynman’s
brilliant insights combined well when they both worked at Los
Alamos on the atomic bomb. They would go down the hallway with
Feynman loudly countering the patient but persistent Bethe, and
their colleagues labeled them “the Battleship and the Torpedo Boat.”
Bethe was legendary when I was a young physicist because even
into his nineties he was still writing important physics articles. He
was also happy to talk to anyone about physics. When I gave a
visiting lecture at Cornell—where Bethe spent most of his
professional career—I felt immensely honored when he walked into
my office to ask me questions and then listened intently to me, as if I
actually had something to offer him.
He was also physically robust. A physicist friend of mine told me
of a time he too visited Cornell. One weekend he decided to be
ambitious and climb one of the many steep hiking trails near the
campus. He was proud of himself for huffing and puffing his way
almost to the top until he spied Bethe, then in his late eighties,
happily making his way down the trail from the summit.
͢͝͠
While I always liked and admired Bethe, in researching material
for this book I found two additional happy personal connections that
were satisfying enough for me to relate them here. First, I found out
that I am in a sense his intellectual grandson, as my undergraduate
physics honors thesis adviser, M. K. Sundaresan, was one of his
doctoral students. Second, I discovered that Bethe, who had little
patience for grand claims made of fundamental results that were
carried out without any real motivation or evidence, once wrote a
hoax paper while a postdoc poking fun at a paper he deemed
ridiculous by the famous physicist Sir Arthur Stanley Eddington.
Eddington claimed to “derive” a fundamental constant of
electromagnetism using some fundamental principles, but Bethe
correctly viewed the claim as nothing other than misguided
numerology. Learning this made me feel better about a hoax paper I
wrote when I was an assistant professor at Yale, responding to what I
thought was an inappropriate paper, published in a distinguished
physics journal, that claimed to discover a new force in nature
(which indeed later turned out to be false). At the time that Bethe
wrote his paper, the physics world took itself a little more seriously,
and Bethe and his colleagues were forced to issue an apology. By the
time I wrote mine, the only negative reaction I got was from my
department chair, who was worried that the Physical Review might
actually publish my article.
When he was in his early thirties, Bethe had already established
himself as a master physicist with his name attached to a host of
results, from the Bethe formula, describing the passage of charged
particles through matter, to the Bethe ansatz, a method to obtain
exact solutions for certain quantum problems in many-body physics.
A series of reviews he cowrote on the state of the nascent field of
nuclear physics in 1936 remained authoritative for some time and
became known as Bethe’s Bible. (Unlike the conventional Bible, it
ͣ͝͠
made testable predictions, and it was eventually replaced as scientific
progress was made.)
In 1938, Bethe was induced to attend a conference on “stellar
energy generation,” though at that time astrophysics was not his
chief interest. By the end of the meeting, he had worked out the
nuclear processes by which four individual protons (the nuclei of
hydrogen atoms) eventually “fuse”—as a result of Fermi’s weak
interaction—to form the nucleus of helium, containing two protons
and two neutrons. This fusion releases about a million times more
energy per atom than is released when coal burns. This allows the
Sun to last a million times longer than previous estimates would
have permitted, or about 10 billion years instead of ten thousand
years. Bethe later showed that other nuclear reactions help power
the Sun, including a set that converts carbon to nitrogen and oxygen
—the so-called CNO cycle.
The secret of the Sun—the ultimate birth of
light in our solar
system—had been unveiled. Bethe won the Nobel Prize in 1967, and
almost forty years after that, experiments on neutrinos coming from
the Sun confirmed Bethe’s predictions. Neutrinos were the key
experimental observable that allowed such confirmation. This is
because the whole chain begins with a reaction in which two
protons collide, and via the weak interaction one of them converts
into a neutron, allowing the two to fuse into the nucleus of heavy
hydrogen, called deuterium, and release a neutrino and a positron.
The positron later interacts in the Sun, but neutrinos, which interact
only via the weak interaction, travel right out of the Sun, to Earth
and beyond.
Every second of every day, more than 400,000 billion of these
neutrinos are passing through your body. Their interaction strength
is so weak that they could traverse on average through ten thousand
light-years of solid lead before interacting, so most of them travel
ͤ͝͠
right through you, and Earth, without anyone’s noticing. But if not
for the weak interaction, they would not be produced, the Sun
wouldn’t shine, and none of us would be here to care.
So the weak interaction, although extremely weak, nevertheless is
largely responsible for our existence. Which is one of the reasons
why, when the Fermi interaction, developed to characterize it, and
the neutrinos first predicted by it, turned out to both defy common
sense, physicists had to stand up and take notice. And they were
driven to change our notions of reality itself.
ͥ͝͠
P a r t Tw o
E X O D U S
͜͝͡
C h a p t e r 1 1
D E S P E R AT E
T I M E S
A N D
D E S P E R AT E M E A S U R E S
To every thing there is a season, and a time for every purpose.
—ECCLESIASTES 3:1
The rapid succession of events during the 1930s, from the
discovery of the neutron to probing the nature of neutron decay, as
well as the discovery of the neutrino and the consequent discovery of
a new and universal short-range weak force in nature, left physicists
more confused than inspired. The brilliant march that had led to the
unification of electricity and magnetism, and the unification of
Lawrence Krauss - The Greatest Story Ever Told--So Far Page 15
