Einstein's Genius Club (2 page)

Political activism characterized the latter decades of Russell's life. Few left-wing causes escaped his energetic support: pacifism, Bolshevism, antifascism, anti-Stalinism, nuclear disarmament, de-colonization, the International War Crimes Tribunal. On the brink of war over the Cuban missile crisis, Kennedy and Khrushchev each received a telegram. (Kennedy's reaction, in private, was to call Russell a “son of a bitch.”) Even into his nineties, Russell did not flag. A letter transcribed and mailed on February 3, 1970, a day after Russell died, sent his greetings to representatives of South Vietnam's Provisional Revolutionary Government. A lifetime of writing on philosophy and politics won Russell the 1950 Nobel Prize in Literature.

As a logician, Gödel has no modern rival. Not since Aristotle, some say, have one man's theories so utterly transformed the field of logic. He was a quiet, remote, unworldly mathematician, given to eccentricities and belief in ghosts. With Einstein, he would make his daily trek to the Institute for Advanced Study in Princeton. Their friendship was famous. In Gödel, Einstein found his intellectual equal.

As a graduate student at the University of Vienna, Gödel sat in on meetings of the Vienna Circle, a highly influential group of philosophers dedicated to empiricism (the idea that knowledge is derived through experience) and logical analysis (held to be the proper method for solving problems in philosophy). Yet in 1931, Gödel proposed his
incompleteness theorems
, ending once and for all attempts to find a complete and consistent set of axioms for
all of mathematics. Russell's logicism and the Vienna Circle's logical analysis were dealt a fatal blow, insofar as they sought complete consistency within a system of logic.

Although Gödel contributed to mathematical and logical thought throughout his life, the incompleteness theorems and their metalogical system of notation known as
Gödel numbering
were his crowning achievements. Gödel left Vienna for Princeton in 1940 and never returned, gaining a professorship at the Institute for Advanced Studies in 1946 and publishing a tantalizing demonstration of time travel based on general relativity in 1949. He died in 1978 of starvation, so overcome by paranoia that he believed his food was being poisoned.

Few outside the world of physics know of Wolfgang Pauli. His fame rests on two discoveries: the
exclusion principle
and the
neutrino
. The former is an esoteric explanation of how electrons behave in the atom. The latter is a bit more fathomable among laypeople—the neutrino being first of many particles found to exist within the atom, beyond the electron, proton, and neutron.

Within the world of physics, however, Pauli is legendary. His exclusion principle is indispensable to our understanding of matter. In 1930, he postulated the existence of the neutrino, the confirmation of which came a year before Pauli's death. Equally important, though, was his centrality to quantum theory. In the 1920s, as the world entered a depression and headed toward world war, Pauli helped foment a revolution that overturned classical physics. Among his fellow revolutionaries were Niels Bohr (the “father” of quantum theory), Werner Heisenberg, Erwin Schrödinger (of “Schrödinger's cat” fame), Paul Dirac, Max Born, and Louis de Broglie.

So integral was Pauli to the development of quantum theory and quantum mechanics that he became known as the repository
of “conscience” within the movement. Personable, brash, painfully critical, intellectually honest, he was an inveterate collaborator and an indefatigable letter writer. He won the 1945 Nobel Prize in Physics for the exclusion principle. Having left Europe for the duration of the war, he returned to Switzerland in 1946 and headed the physics program at Zurich Polytechnic School (ETH) until his death.

Erudite and precocious, Oppenheimer left Harvard in 1925 with a degree in chemistry and sufficient background in physics to join the Cavendish Laboratory in Cambridge. At twenty-three, he was awarded a doctorate from the University of Göttingen, where he worked with such giants in quantum mechanics as Wolfgang Pauli and Max Born. Having gained respect from his European colleagues, he accepted a position at the University of California, Berkeley, in 1929.

Oppenheimer made no great discovery in physics. As an intellectual and administrative leader, he was second to none. Over the next decade, he mentored dozens of graduate students, dabbled in leftist politics, and favorably impressed the great Ernest Lawrence, who ran the Berkeley Radiation Laboratory. As the American bomb effort began taking shape, Oppenheimer rose from adviser to director of Los Alamos, the secret and central laboratory where the greatest minds in physics concocted the atomic bomb. At the first successful test of an atomic weapon, he later said, words from the
Bhagavad Gita
echoed in his mind: “I am become death, the destroyer of worlds.”

During and after the war, he was targeted by government security forces for his leftist politics. His support of an international approach to the uses of atomic fission and his opposition to the hydrogen bomb led to investigations by the House Un-American Activities Committee, and in 1954, his security clearance was
revoked. He continued to lecture and work on the fringes of power. From 1946 to 1965, he was director of the Institute for Advanced Study in Princeton. He won the Fermi Prize for Physics in 1963. He died in 1967, having never regained his security clearance.

Unlike his friend Pauli and his mentor Niels Bohr, Heisenberg tended to think in flashes of brilliance. In 1925, he took on the murky question of quantum mechanics. If we cannot see within an atom, he reasoned, let us use what we can observe, namely, how atoms emit and absorb light. From that thought came
quantum mechanics
. To calculate the movements of particles, Heisenberg stumbled into what became
matrix mechanics
. Meanwhile, Erwin Schrödinger countered with a less abstract explanation likening electrons to waves (
wave mechanics
). To reconcile the seemingly bizarre quantum world with the more familiar classical physics, Heisenberg came up with the
uncertainty principle
: It is possible to measure the location of an electron and the momentum of an electron, but never both simultaneously. For his work on quantum mechanics, he was awarded the Nobel Prize in 1932.

Heisenberg was a fervent nationalist. When the Nazis came to power, he continued his atomic work, participating at the highest levels in the German effort to harness fission. He traveled often to conferences and, on one famous occasion, to visit his old friend and teacher Bohr. That conversation became the subject of Michael Frayn's drama
Copenhagen
. At the end of the war, Heisenberg was interned along with nine other German scientists at Farm Hill in England, where from July through December 1945 their conversations were secretly recorded by British agents. From the end of the war until his death, Heisenberg labored to rebuild atomic physics in Germany.

Beta-decay
: radioactive decay, or the emission of a beta particle or electron from an atom

Black-body radiation
: thermal radiation (that is, heat radiating) from a closed system heated to a particular temperature

Born's probability interpretation
: a reconciliation of wave mechanics with quantum mechanics that explains waves as containing the probable location of an electron

Bose-Einstein statistics
: first proposed by S. N. Bose and championed by Einstein, these statistics explain the behavior of
bosons.

Bosons
: one of two general classes of elementary particles (along with
fermions
) determined by how they spin

Bright-line spectra
: the unique spectral lines formed when an element is heated and its atoms emit light; every atom has its own signature of bright lines.

Brownian motion
: in fluids, the seemingly random movements of tiny particles as they are struck by the molecules of the fluid; Einstein applied statistical mechanics to explain the movements.

Copenhagen interpretation
: under Niels Bohr, the most persuasive, complete framework for understanding quantum mechanics

Double-slit experiment
: a method for analyzing light by diffracting light beams through two slits and observing the resulting patterns on a screen

Exclusion principle
: Pauli's discovery, expressed as a law, that no two particles occupy the same space at the same time

Fermions
: see
Bosons

Field
: the extension of a physical quality throughout space (as the electromagnetic field); in classical or quantum physics, field theory describes the dynamics and effects within the field.

General Relativity
: Einstein's generalization of his theory of special relativity to include gravity. It reconceived Newton by showing that apples fall to the ground because the earth's mass curves the adjacent space-time, forcing apples to move in a special way, that is, towards the surface of the earth. It has proven extremely difficult to unify general relativity with quantum mechanics.
String theory
is currently the best hope.

Gödel numbering
: the assignment of numbers to mathematical symbols and formulas, to allow for mathematical statements about mathematics (that is, metamathematical statements)

Incompleteness theorems
: Gödel's demonstrations that in any formal system, there are statements that are true, but are not provable using the axioms of that system. The paper containing the theorems was entitled “On Formally Undecidable Propositions of
Principia Mathematica
and Related Systems,” a reference to the work by Russell and Whitehead.

Induction
: reasoning that begins with information from particular instances and leads to general propositions

Locality
: in classical physics, the idea that two objects in separate places are independent and cannot interact, a restriction seemingly disproved by recent experiments demonstrating quantum particles to be “entangled” no matter what the distance between them

Logicism
: an approach to philosophy in which mathematics is subsumed into logic

Matrix mechanics
: the first complete definition of the laws and properties of subatomic particles using matrices to describe their properties

Maxwell's equations
: four equations that describe electric and magnetic fields and their interaction with matter

Neutrino
: an extremely light particle, the existence of which was hypothesized by Pauli

Paradox
: in logic, reasoning that leads to contradiction, revealing false assumptions or faulty processes

Particle physics
: the study of the basic subatomic elements and the forces acting upon and among them

Photoelectric effect
: the emission of electrons when exposed to electromagnetic radiation and the subject of Einstein's first 1905 paper, in which he proposed that rather than waves, light was made of quanta (later called
photons
)

Photon
: the elementary particle that forms light

Planck's constant
: the ratio of a
photon
's energy to its frequency

Quantum mechanics
: a theory of subatomic systems that derives information about particles through an application of statistics, conceives of electrons and protons as both particle and wave in their behavior, and acknowledges uncertainty in measuring both movement and position simultaneously

Quantum physics
: the entire body of modern, postclassical physics incorporating
quantum mechanics
and treating both large and small scale forces

Russell's paradox
: a conundrum discovered by Russell in 1901. The problem occurs when, in attempting to account for and classify all sets, one imagines a “set of all sets that are not members of themselves.” A set can be a member of itself: Imagine the set of all objects that are not cars. Since the set of all noncars is not a car, it can be a member of itself. Now, we must move up a rung in abstraction, because set theory conceives of “sets of sets.” The set of all sets that are
members of themselves is, indeed, possible: e.g., the set of all sets of cars can be a member of itself. But the set of all sets that are
not
members of themselves is a paradox. Is it a member of itself? It must be, since it is a set that includes just that: sets that are not members of themselves; and yet it cannot be, since by being a member of the set of all sets that are not members of themselves, it would become a member of itself.