Beyond the God Particle (32 page)

Dirac's idea was a straightforward extension of Pauli's exclusion principle: He hypothesized that
the vacuum itself is completely filled with electrons
,
occupying all of the negative energy states
. And, if all of the negative energy levels in the whole universe are already filled, then positive-energy electrons, such as in atoms, could not drop down into these quantum states—they would be
excluded
from doing so by the Pauli exclusion principle. The seats in the whole vacuum are all sold out! The vacuum is now stable because it is already filled up with negative-energy electrons.
⁸

Dirac thought that this was the fix, but he soon realized that it was not the end of the story. It was now theoretically possible to “excite” the vacuum. This means that physicists could arrange a collision in which they could kick a negative-energy electron out of the vacuum, much like a fisherman
pulls a deep-sea fish into his boat. Dirac realized that this process would leave behind a
hole in the vacuum
. The hole, however, would represent the
absence of a negative-energy electron
. This means that the hole
actually would have a positive energy
. However, the hole would also represent the
absence of a negative electrically charged electron
, and hence the hole would be a
positively charged particle
(see
figure 9.33
).

FIGURE 9.32. Dirac Sea.
The “Dirac sea,” picture of the vacuum. All of the allowed negative energy levels for fermions, predicted by Dirac's equation where relativity is combined with quantum theory, are filled. The Pauli exclusion principle forbids any more electrons in these levels, so the vacuum is “stable.” The vacuum is like an inert element, e.g., neon, where all orbitals are filled, so neon becomes chemically inactive.

FIGURE 9.33. Antiparticle as Hole in Dirac Sea.
Dirac's sea leads to the prediction that a negative-energy electron can be “ejected out of the vacuum,” e.g., by the nearby collision. The hole left in the vacuum is the absence of a
negative-energy
,
negatively charged
electron, and therefore appears as a
positive-energy, positively charged
particle with identical mass to the electron. Dirac thus predicted the
positron
, and the phenomenon of “electron–positron pair creation.” The positron was discovered experimentally a few years later by Carl Anderson. The phenomenon of antimatter is now well established and a standard phenomenon in particle physics—the Tevatron discovered the top quark by pair producing top and anti-top quarks in this way.

Dirac predicted the existence of something bizarre:
Antimatter.
Every particle species in nature has a corresponding antiparticle. We call the antiparticle of the electron the
positron
. The positron is the “absence” of a negatively charged electron, a hole, in the vacuum, and is therefore a positively charged particle with positive energy but is otherwise indistinguishable from the electron, with the same mass and the same (though opposite) spin. The laws of special relativity require that the hole in the vacuum, which is the
absence of negative
energy (note the double negative!), must have a positive energy of exactly E = +mc
²
, where
m
is
exactly
the
same as the
electron
mass. Positrons were predicted by Dirac, and they must exist if both quantum theory and special relativity are true.

Positrons were subsequently discovered in an experiment in 1933 by Carl Anderson.
⁹
They are the positively charged beta rays that are seen in radioactivity. Antimatter will annihilate matter when the two collide, as the positive-energy electron jumps back into the hole in the vacuum. The annihilation produces a lot of energy (at rest, electron–positron annihilation would release E = 2mc
²
by direct conversion of all the rest-mass energy of the two particles into gamma rays). Antimatter can easily be produced by particle accelerators.

Antimatter is a useful commodity and is already “paying rent.” The positrons naturally generated from radioactive disintegration have found a use in positron-emission tomography (PET) scanners, a form of medical imaging. It is estimated that the cash-flow generated by this one activity, again a by-product of pure and basic research, is larger than the cost of funding all of the science of particle physics today. It is unclear if the future utility of synthesized antimatter will expand to warp-drive starship engines or compact super-energy storage devices, but eventually it will likely find many more practical applications—and yes, we're sure that one day the government will tax it.

Corresponding to
every
particle there is an antiparticle in nature. Corresponding to protons we have antiprotons, to neutrons we have antineutrons, to top quarks we have anti-top quarks. When we made top quarks in the good ol’ days at the Fermilab Tevatron—now a staple of the CERN LHC—we made them in pairs: top plus anti-top. We literally go fishing and pull the negative-energy top quark out of the deep depths of the vacuum. This leaves behind a top quark hole (the anti-top quark), and we see the pair,
top quark and anti-top quark, produced in our detectors. Particle physicists are simply metaphorical fishermen on the great Dirac sea.

BETA DECAY: THE SIMPLEST WEAK INTERACTION

The simplest example of the weak interaction is the
beta-decay
reaction that occurs with a single
neutron
, one of the particles found in the atomic nucleus, causing it to decay in about 11 minutes when it is floating about freely in space:

n
⁰
→
p
⁺
+
e
^–
+
(missing energy)

Beta decay is observed throughout many atomic nuclei, and it always involves this basic reaction. But beta decay posed a new problem: what is the “missing energy”? From countless observations, the electron and proton energies in the final state of the decay process always added up to something less than the original neutron energy. There thus appeared to be
a missing amount of energy
in the decay of a neutron. Essentially all beta decays of nuclei are a variation on this process, where the neutron is typically bound within the nucleus, and all revealed the mysterious “missing energy.”
¹⁰

Niels Bohr, one of the founding fathers of quantum mechanics, attempted to explain this phenomenon with the radical hypothesis that energy conservation, by which the initial energy is always equal to the final energy in any physical process, has only a limited validity in the world. Bohr proposed that the beta-decay processes were exhibiting, for the first time, a true violation of this time-honored and vaulted conservation law. Bohr, a brilliant and creative thinker, had already seen in the early part of the twentieth century that our detailed understanding of energy was significantly modified by the new rules of quantum mechanics, and he thought that perhaps beta decay was an indicator of deeper novelties and surprises yet to come.

Wolfgang Pauli, the brash and brilliant theoretical physicist who had developed his exclusion principle to explain how atoms with many electrons are built, could not accept Bohr's idea. The principle of the conservation of energy up to this point had proven valid in all domains of physics. It seemed unnatural to Pauli that the violations would show up
only in beta-decay
reactions, where it is apparently seen to be a very large effect, and yet it doesn't show up elsewhere. Wouldn't any violation of this fundamental law of physics be universal, felt by all forces in nature, and not just be a property of beta decay? Bohr's proposal made no sense to Pauli.

In 1930, Pauli therefore did something quite radical by the intellectual standards of his day: he postulated the existence of a new and unseen elementary particle that was also produced, together with the proton and the electron, in the beta-decay reaction. This new particle must carry no electric charge and would therefore escape the decay region totally unobserved, and it would maintain the validity of the conservation law of energy, provided it had a very tiny mass. In other words, physicists could now compute the missing energy required to maintain the conservation law in any beta-decay reaction, and this would be the exact energy carried off by the new particle.

Pauli announced his new particle in a letter written on December 4, 1930, in a response to an invitation to attend a conference on radioactivity, which he declined.

Dear Radioactive Ladies and Gentlemen,
     As the bearer of these lines, to whom I graciously ask you to listen, will explain to you in more detail, how because of the “wrong” statistics of the N and Li
⁶
nuclei and the continuous beta spectrum, I have hit upon a desperate remedy to save the…the law of conservation of energy. Namely, the possibility that there could exist…electrically neutral particles, that I wish to call [neutrinos], which have spin 1/2 and obey the exclusion principle…and in any event [have masses] not larger than 0.01 proton masses. The continuous beta spectrum would then become understandable by the assumption that in beta decay a (neutrino) is emitted in addition to the electron such that the sum of the energies of the neutron and the electron is constant…
     I agree that my remedy could seem incredible because one should have seen these (neutrinos) much earlier if they really exist. But only the one who dare can win and the difficult situation, due to the continuous structure of the beta spectrum, is lighted by a remark of my honoured predecessor, Mr Debye, who told me recently in Bruxelles: “Oh, It's well better not to think about this at all, like new taxes.” From now on, every solution to the issue must be discussed. Thus, dear radioactive people, look and judge.
     Unfortunately, I cannot appear in Tubingen personally since I am indispensable here in Zurich because of a ball on the night of 6/7 December. With my best regards to you, and also to Mr Back.
     Your humble servant,
     W. Pauli
¹¹

The process of beta decay with Pauli's neutrino thus looks like this:

The new particle, n, is the
neutrino
(with a “bar” over the symbol, it becomes the conventional symbol for antiparticle, or
antineutrino
).
¹²
Therefore, when the neutron decays in free space, it produces a proton, an electron, and an (anti)neutrino. In our modern parlance, the electron is always produced together with the anti-electron-neutrino in a beta decay. The sums of the final energies of all of the three final particles will be exactly the same as the initial energy (mc
²
) of the original parent neutron. Notice also that the neutrino, with zero electric charge, allows the beta-decay reaction to satisfy
the law of conservation of electric charge
. The zero electric charge of the neutrino means that it can't be easily detected—it lacks the “handle” of electric charge that we could otherwise “grab onto” through electromagnetic fields in our particle detectors.