Dinah Simone Bouma
WRIT-340
Ramsey
Revised 11.29.2011
Nothing Really Matters: the Journey of Antimatter from Science to Fiction
In the movie Star Trek: First Contact, the starship Enterprise uses a matter/antimatter
reactor to power its warp drive, which enables it to travel faster than light. This
superluminal travel leads to the initiation of the first contact with the Vulcans. In Dan
Brown’s popular novel Angels and Demons, an antimatter bomb is stolen from the
European Laboratory for Particle Physics and concealed beneath the Vatican. While
Vulcans, superluminal speeds, and antimatter bombs will remain the stuff of science
fiction, antimatter itself has become a common observation in particle physics
experiments. Elementary particle theory states that each particle has its own
“antiparticle”, which has the same mass as the original particle but opposite charge and
magnetic moment. When a matter particle at rest collides with its conjugate antiparticle,
also at rest, they annihilate each other and produce a pair of highly energetic photons,
which travel in opposite directions from the point of annihilation.
The existence of antimatter was first postulated in 1928 by the great physicist Paul A. M.
Dirac as part of his relativistic formulation of the quantum theory of the electron [1]. He
arrived at the familiar result for the total relativistic energy 𝐸 2 = (𝑝𝑐)2 + (𝑚0 𝑐 2 )2 ,
which states that the square of the total energy of this electron is the sum of the squares of
its kinetic energy 𝑝𝑐 and its rest energy 𝑚𝑒 𝑐 2 , where 𝑚𝑒 is the electron rest mass. The
rest energy term may be recognized as Einstein’s famous formula for mass-energy
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equivalence. To determine the total energy of an electron, Dirac took the square root of
both
sides
of
the
relativistic
energy
equation
to
obtain
𝐸 = ±√(𝑝𝑐)2 + (𝑚0 𝑐 2 )2
That is to say, special relativity implies that any particle with a nonzero rest mass can
have negative energies. Rather than discarding the negative energy on the grounds that it
is unphysical, though, Dirac chose to pursue its consequences in the particular case of the
electron. He suggested that, if electrons can exist at negative energy levels, then an
electron at a positive energy level should be able to transition to a negative energy level
by emitting a photon of sufficiently high energy. Electrons are known to emit photons as
they transition from a positive energy to a lower positive energy, but no photon of a
sufficiently high energy to indicate a transition to a negative energy level has ever been
observed. Dirac resolved this apparent inconsistency by postulating that the vacuum
consisted of a “sea” of electrons occupying the negative energy levels. This theory
predicted that one of these electrons in negative energy levels could be excited by an
energetic photon to a positive energy level, leaving a “hole” in the “sea” of negative
energy electrons. It turns out that this “hole” behaves like a particle having the same mass
as the electron but opposite charge, and positive energy [2]. A particle with the same
mass as the electron but opposite charge meets the description for the electron’s
antiparticle. A simple algebraic consequence of Dirac’s relativistic quantum theory, then,
predicted the existence of the anti-electron, and its discovery would provide some
confirmation for Dirac’s theory [3].
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This discovery occurred in 1933, when the physicist Carl D. Anderson was studying
cosmic rays in his cloud chamber at the Mount Wilson Observatory in Southern
California. Cosmic rays are what physicists call the radiation consisting of photons,
electrons, and a whole zoo of other particles coming from the rest of the universe.
Anderson’s cloud chamber consisted of some vapor enclosed in a sealed, transparent
container. Upon passing through this container, charged particles ionize the vapor and
leave a visible track in the container, which can be captured using ordinary photography.
In order to discern the mass-to-charge ratio of particles passing through the cloud
chamber, the change in direction suffered by charged particles in a magnetic field is
exploited by applying a field through the chamber perpendicular to the anticipated
direction of travel of the particles. This field will result in negatively charged particles
curving in one direction, and positively charged particles curving in the opposite
direction in the cloud chamber. However, since the acceleration of a particle with charge
𝑞 ,
mass 𝑚 ,
and
velocity 𝑣⃗
𝑎⃗ =
in
a
magnetic
⃗⃗
field 𝐵
is
given
by
𝑞
⃗⃗
𝑣⃗ × 𝐵
𝑚
we can determine only the ratio of charge to mass from a particle’s track in a cloud
chamber. To obtain more information about the particles, Anderson inserted lead plates
into his cloud chamber. He knew that heavier particles will be slowed down more than
lighter particles by passing through lead, since they will experience greater interactions
with the atoms in the lead.
As he studied 1300 photographs of particle tracks through his cloud chamber, Anderson
discovered fifteen tracks displaying unusual behavior: they moved rapidly, not curving
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very much below the lead plate, and then curved more after passing through the lead plate
and consequently slowing down (see Fig.1). The direction of the curvature of the track
indicated that the particle was positively charged, but the particle appeared to still move
too quickly after passing through the lead plate for it to be a proton. Anderson was able to
conclude that the charge on the mystery particle was less than twice that on the electron,
and that the mystery particle’s pass was less than 20 times that of the electron [4] (for
comparison, the mass of the proton is approximately
1,800 times that of the electron). To his best
interpretation, this particle was practically an electron,
but it had the opposite charge: it was the electron’s
antiparticle, predicted by Dirac five years prior.
Anderson called this particle the “positive electron”,
FIGURE 1. Anderson’s new
particle moves rapidly below
the lead plate, as can be seen by
the large radius of curvature. It
is slowed by the plate but still
moves too rapidly to be a
proton.
and contracted this name to “positron”, which is the
name retained by the electron’s antiparticle today.
As
the
twentieth
century
progressed,
further
Source: www.thenakedscientists.com.
antiparticles were discovered. In 1955, physicists
Emilio Segrè and Owen Chamberlain discovered the antiproton at Lawrence Berkeley
National Laboratory by accelerating protons and smashing them into a target. Such
particle accelerators, which accelerate readily available particles such as protons and
electrons to high energies with the intent of smashing them together to see what will
come out, became key to discovering and producing a plethora of new matter particles as
well as their antimatter conjugates. In 1995, physicists at the European Laboratory for
Particle Physics (CERN) successfully bound a positron into an orbit around an
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antiproton, creating the first antihydrogen atom [5]. Evidently, since antimatter
annihilates on contact with matter, the scientists cannot store antimatter in an ordinary
container. Charged antimatter particles can be confined using an appropriate arrangement
of electric and magnetic fields, due to the motion of charges in these fields. Neutral
antimatter particles, such as antihydrogen atoms, are harder to handle as they pass right
through electric and magnetic fields. However, neutral particles still have a magnetic
moment, which can be exploited to contain them in a magnetic field whose strength
varies in a very particular way in space. In 1995, the scientists at CERN were able to
contain antihydrogen for approximately a sixth of a second before it ran into matter,
which resulted in the annihilation of the positron with an electron and the annihilation of
the antiproton with a proton. By April of 2011, physicists at the same institution had
modified their containment mechanism for neutral antiparticles and managed to contain
antihydrogen for a celebrated fifteen minutes [6].
Of course, this containment mechanism was developed over ten years after popular
culture caught wind of antimatter from Dan Brown’s thriller Angels and Demons. In this
novel, several grams of antimatter in their battery-powered magnetic trap are stolen from
CERN, and hidden in a catacomb beneath the Vatican City. The antagonist places a
camera on the antimatter canister such that the protagonist can see the clock ticking as the
battery on the containment system runs down, threatening to release huge quantities of
energy as the antimatter annihilates with the matter in the walls of the container. To begin
with, even the 2011 capture of antihydrogen contained only about 300 atoms, which is a
fraction of a gram of antimatter. Upon annihilating with matter, a harmless 45 nanojoules
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of energy would have been released. To put this in perspective, the energy of a mosquito
in flight is about 160 nanojoules. Furthermore, the preceding calculation assumed that all
the mass contained the annihilating matter and antimatter would have been converted into
energy. While this is the case when positrons and electrons annihilate, the annihilation of
protons and antiprotons is slightly more complex. Instead of creating a pair of highly
energetic photons like the positron and electron, the proton and antiproton can actually
create other unstable particles when they annihilate [7]. These unstable particles will
decay until they reach stable particles, which are generally electrons or other particles
that will carry off some of the energy of the annihilation (see Fig. 2). Thus, antihydrogen
will make a less than ideal bomb, since we are struggling to control when it would
explode, and since, when it does explode, we are not even guaranteed that all the energy
we expect to see released will actually be released. Even if scientists attempted to make a
positron bomb, which would guarantee that the rest energy would be released as highly
energetic photons, they would need about a billion billion billion positrons to create a
bomb as devastating as the atomic bomb dropped on Hiroshima in 1945. In addition to
the containment troubles arising from the repulsion of like charges, such a huge number
positrons would be prohibitively expensive to create, both monetarily and energetically.
Figure 2. The decay of a quark and an
antiquark, the constituents of protons and
antiprotons respectively. While some energy
is released, products are mostly particles.
Source: particleadventure.org.
The limitations of using antimatter as a bomb also apply to the idea of using antimatter as
a fuel. The production of a billionth of a gram of antimatter, according to CERN, costs a
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few hundred million dollars [8]. Even if scientists could contain antihydrogen
indefinitely, as the Enterprise does to fuel the matter/antimatter reactor for the warp drive
in Star Trek, it would still not be a perfect source of energy due to the variety of decay
products created in the annihilation of protons with antiprotons. Since energy is
conserved, we will never get more energy out of annihilating antimatter with matter than
the rest energies of those particles and, with current techniques of antimatter creation,
many times the rest energy of an antimatter particle goes into creating that particle. On a
broader scale, therefore, antimatter would be an enormously inefficient fuel.
As science broadens our understanding of the properties and behavior of antimatter, it
remains to be shown whether science fiction will embrace the science of antimatter or
whether scientific advances will tickle the imagination of science fiction to greater fancy.
It is unlikely that uses of antimatter from the realm of science fiction will venture into the
realm of science fact; however, Dirac, Anderson, and their contemporaries left science
with no dearth of unanswered questions springing from the existence of antimatter.
Physicists still desire to trap anti-atoms for longer time periods to study their interactions.
They wish to synthesize heavier anti-atoms (the heaviest that has been created to date was
anti-helium). One of the single most profound questions facing physics today springs
from the existence of antimatter: if equal amounts of matter and antimatter existed at the
time of the Big Bang, how did humanity wind up in a universe made of matter? Now,
there’s a question that really matters.
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Works Cited
[1] P. A. M. Dirac, “The Quantum Theory of the Electron,” Proc. Roy. Soc. London A,
vol. 117, pp. 610-624, Jan. 1928.
[2] R. Eisberg and R. Resnick, “Pair Production and Pair Annihilation,” in Quantum
Physics of Atoms, Molecules, Nuclei, and Particles, 2nd ed.: John Wiley & Sons, 1985,
ch. 2, sec. 2-7, pp. 43-47.
[3] R. N. Cahn and G. Goldhaber, “The Atom Completed and a New Particle,” in The
Experimental Foundations of Particle Physics, 1st ed. New York: Press Synd. Univ.
Cambridge, 1989, ch. 1, pp. 1-7.
[4] C. D. Anderson, “The Positive Electron,” Physical Review, vol. 41, pp. 491-494, Mar.
1933.
[5]
D.
Manglunki,
The
Antimatter
Factory
[Online].
Available:
http://livefromcern.web.cern.ch/livefromcern/antimatter/factory/AM-factory00.html.
[6] CERN Press Office, CERN experiment traps antimatter atoms for 1000 seconds
[Online].
Available:
http://press.web.cern.ch/press/pressreleases/Releases2011/PR05.11E.html.
[7] Lawrence Berkeley National Laboratory, The Particle Adventure: Top Production
[Online]. Available: http://particleadventure.org/top_pro.html.
[8] A. de Rújula and R. Landua, Antimatter Questions and Answers [Online]. Available:
http://livefromcern.web.cern.ch/livefromcern/antimatter/FAQ.html.