High Energy Physics
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INTRODUCTION
In the conventional view, "stuff" is made of atoms. The atoms are made
of electrons, protons and neutrons. High Energy Physics deals with the question
of what the electrons, protons and neutrons are made of. It is called "high
energy" because experimentally one needs very high energy probes to try to take
these "elementary particles" apart.
This document is an overview of high energy physics at a non-technical
level. It is divided into four sections:
Some of the material presented is decidedly not traditional for an
overview of High Energy Physics.
Classically, we describe electron-electron scattering in terms of an electromagnetic field caused by one electron which causes a force on the second electron. The second electron similarly causes an electromagnetic field which causes a force on the first electron. Of course, we know that this field has a complementary particulate aspect, the photon.
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To the right we show a
spacetime diagram for electron-electron scattering in this particulate
view.
The electron on the left emits a photon, labeled , which is then absorbed by the electron on the right.
The fact that such a series of events causes both electrons to
change their state of motion is a pure quantum effect. According to Quantum
Mechanics, when two object exchange an object, a Quantum Exchange Force
exerts a force on both objects. When the object being exchanged is a photon,
the interaction is electromagnetic.
This diagram has two vertices, which are the points where
the electron worldlines have a kink and the photon worldline connects at the
kink. |
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Although the above is the simplest possible interaction between
two electrons exerting electromagnetic forces on each other, it is not the only
possible interaction. For example, to the right are two more possible
mechanisms. The upper figure shows the exchange of two photons, and the lower
one of three photons.
In the 1950's Richard Feynman and Julian Schwinger realised that
the total electromagnetic interaction between two electrons is just the sum of
all possible interactions. Each of the above spacetime diagrams represent some
Quantum Mechanical wave function amplitude, and to get the total amplitude just
add up all the terms.
The fact that there are an infinite number of diagrams, each of
increasing complexity, turns out not to be a problem, because the more vertices
in the diagram the smaller its contribution to the total wave
function. |
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This is very similar to the set of sums of numbers such as:
In fact, the mathematicians have shown that if the above sum is extended
to an infinite number of terms, the value of the sum converges to an irrational
number whose value is approximately 1.64493. Similarly, the infinite sum of
spacetime diagrams for electron-electron scattering converges to a finite
value.
Another example of an infinite sum of numbers equal to a finite value can be seen in a little Flash animation. It has a size of 12k, and will appear in a separate window. To access the animation click here.
The physical interpretation of this approach to electrodynamics is that
when a pair of electrons in some initial state scatters so they end up in some
final state, they get there via every possible path. Recall that the Quantum
Mechanical description involves the wave function or state function, which in
conventional interpretations represents some sort of partially unmanifested
level of reality; a good analogy is the Aristotelian concept of
potentia. Here the infinite number of diagrams connecting the initial
and final states become an infinite number of wave functions, each representing
a mechanism to get to the final state.
If you think again about the double slit experiment for electrons, when
we see the interference pattern we know that the wave function was non-zero at
both of the slits. Thus in some sense we can say that the electron got from the
electron gun to the observing screen by going through both slits. Both paths
from the gun to the screen have non-zero wave functions.
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Recall Feynman's theory of antimatter being regular matter going
backwards in time. Thus if we reverse the direction of the arrow heads, as
shown, the same Feynman diagram describes positron-positron scattering.
This shouldn't be a big surprise if you remember that two
negatively charged objects like electrons repel each other exactly like two
positively charged objects like positrons.
Further reflection may convince you that as a consequence, we need
not include arrowheads at all on the worldlines of objects represented in these
diagrams. Similarly we need not include a time axis. For example, the diagram
shown to the right is essentially identical to the first diagram we looked at
above if we take the first diagram and reverse the direction of the time axis
(and stand on our head to look at it!).
When we drop the arrowheads on the worldlines and drop the time
axis entirely, we call these spacetime diagrams Feynman
diagrams. |
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If we don't have to put arrow heads or time axes in Feynman diagrams,
then what about interpreting the above diagram as having time flow from left to
right? Then it is describing an electron-positron pair annihilating into a
photon, and the photon later creating an electron-positron pair. And in fact,
it is believed that this interpretation as well as all the other
interpretations of this diagram is correct also.
So, pair production and annihilation is described by exactly the same
mechanism as everyday electron-electron scattering.
Consider an electron interacting with all the other electrons in the
universe: it experiences forces caused by the other electrons and in turn
exerts forces on them. For the Feynman diagram describing the effect of the
other electrons, the "propagators", the worldlines of the photons, lie along
the light cones connecting the electron to other electrons which lie in the
past. Similarly, the electron causes electromagnetic forces on all other
charged bodies in the universe, and these propagators lie along the light cone
from the electron at the present to charged bodies at times in the future.
However, we have just argued that the direction of time is irrelevant in
these Feynman diagrams. Thus we can say that the forces exerted on the electron
have two causes: the interactions from the past the the interactions
from the future! Technically, these two causes are called the retarded
and advanced potentials respectively. Similarly, the electron exerts
forces on electrons in the past as well as the future.
Wheeler and Feynman commented in 1949:
"Generalizing, we conclude advanced and retarded interactions give a
description of nature logically as acceptable and physically as completely
deterministic as the Newtonian scheme of mechanics. In both forms of dynamics
the distinction between cause and effect is pointless. With deterministic
equations to describe the event, one can say: the stone hits the ground because
it was dropped from a height; equally well: the stone fell from a height
because it was going to hit the ground."
Reference: J.A. Wheeler and R.P. Feynman, Rev. Mod.
Phys. 21, (1949) 425.
Fred Hoyle and J.V. Narlikar have speculated that the direction of
time's arrow may be related to the expanding universe via Wheeler and Feynman's
acausal electrodynamics:
"We want to see how an arrow of time can emerge from this apparently
time-symmetrical description. If we consider each separate particle, we give
equal importance to advanced and retarded solutions. Where can the asymmetry
come from? The asymmetry would normally come in this case from the asymmetry of
the universe. The [light] cone in the future is different from that in the
past. The distribution of the particles, the density, and so forth, in the
future is in general different from the distribution in the past, and therefore
it is not unlikely that when we perform the summation [over particles] we may
find an asymmetry."
Reference: In T. Gold, ed., The Nature of Time
(Cornell, 1967), pg. 25-26.
So far in this section, we have been describing the use of Feynman
diagrams to describe the quantum aspect of the electromagnetic interaction.
Technically this description is called Quantum Electrodynamics, and
Feynman and Schwinger were awarded the Nobel Prize in Physics in 1964 for its
development. Quantum Electrodynamics is one of our most successful theories.
This is because the predictions that it makes can be experimentally tested to
10 or more significant figures, which is incredible precision and accuracy for
any experiment, and so far the predictions agree with the experiments.
If the photon is the intermediary for the quantum exchange force that we
call the electromagnetic interaction, what about the other interactions? Yukawa
asked himself exactly this question about the strong force that holds the
nucleus together in the 1930's. We know that, in contrast to the
electromagnetic force, the strong force is short range: when two, say, protons
get an appreciable distance away from each other the strong force becomes
negligible and the electromagnetic one dominates causing them to repel each
other. In 1935 Yukawa proposed that the particulate aspect of the strong field
was a new "elementary particle" and in order for it to produce a short range
interaction it must have a non-zero rest mass.
This strong force intermediary is now called the pi meson or
pion. It was discovered in 1947 in cosmic rays by Lattes using a cloud
chamber. Sometimes the intermediary of the strong force is given a more generic
name: a gluon.
If one tries to use the Feynman diagram approach to describing these
strong interactions, it turns out that the more vertices in the diagram the
larger the value. Thus, as opposed to quantum electrodynamics, the sums do not
converge to a finite value. This means that this approach to the strong
interactions is mathematically intractable.
It is believed that there are massive W and Z particles
which are responsible for the weak interaction.
Finally, people have proposed a graviton as the particulate
intermediary of the gravitational interaction. This is one of many attempts to
merge General Relativity and Quantum Mechanics. Sadly, as with all such
attempts, it has been a failure.
Many people believe that the field of "High Energy Physics" is the same
as the field of "Elementary Particle Physics." Note that this belief assumes
that there really are elementary particles in the universe: I think that this
prejudges the whole question.
The proton and neutron are examples of nucleons, the type of
particles found in the atomic nucleus. It turns out that there are hundreds of
different nucleons, all of which but the proton and neutron almost
instantaneously decay into a nucleon with less mass. The final stage in these
decays is the proton, which so far as we know is stable. A free neutron will
decay into a proton, but in stable nuclei it does not decay. The higher mass
nucleons are sometimes called resonances.
There are also hundreds of different kinds of mesons.
To produce these high-mass nucleons and mesons, just take a very high
energy electron beam such as can be produced by a super-strength electron gun
and bang the beam into a block of matter. All these objects come streaming out.
In the late 1960's new particles were discovered almost weekly. This approach
has been compared to taking a watch, busting it into bits with a hammer, and
then looking at the bits to try to figure out how the watch worked.
The remainder of this section on Elementary Particle Physics is divided
into some perhaps surprising sub-sections:
- The Quark Model
- Ancient Greek Atomism
- Platonic Classifications
- The Sankhya Hindus
- Conclusion
The Quark Model
If there are photons, electrons, nucleons and mesons, plus a few more
so-called elementary particles, it is natural to ask what they are made of.
The conventional answer is that photons and electrons are not made of
anything, that they really are elementary. The conventional answer is also that
mesons and nucleons are made of quarks. The quark model was proposed by
Gell-Mann and, independently, Zweig in 1963.
Originally there were three kinds of quarks, called up,
down, and strange, plus their corresponding anti-particles. Now
three more quarks are proposed, named charm, bottom, and
top. The names are the quarks are not intended to imply the nature of
the quarks or their properties. The magnitude of the electric charge of the
quarks is either 1/3 or 2/3 of the charge of the electron, and can be positive
or negative. The nucleons are made of three quarks, and the mesons are made of
a quark-antiquark pair.
All quarks are also believed to carry an additional property, called
color. There are three possible colors for quarks in this view.
The next logical question might be of what are the quarks made? So far,
the answer seems to be nothing: the quarks and the electrons are truly
elementary particles in this view. If a substructure to quarks is ever
discovered I propose calling those objects smitherons, whose plural is
of course smithereens!
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Immediately after the quark model was proposed, experimentalists
began looking for them. They looked in cosmic rays, nuclear decays, cyclotrons,
oysters (true!), basically everywhere they could think of. However, all the
attempts ended in failure. So finally, believers came to the conclusion that we
can't have an independent single quark, that they are "confined" inside the
nucleons and mesons.
A rough analogy involves magnets. As you may know, magnets have a
"North" and "South" pole. If we cut a magnet in half, as indicated to the
right, we end up with two little magnets, each with a North and South pole. We
have never observed a North or South magnetic pole separate from its opposite
pole. Thus if these magnetic monopoles exist, they too are confined.
We shall call quarks a type of parton, by which we mean
that they are a part of something else. So the quark model is an example of a
confined parton theory. |
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Recall that according to the quark model, the nucleons are made of
three quarks, while the mesons are made of quark-antiquark pairs. Thus, we can
represent nucleon-nucleon scattering via the strong interaction by a Feynman
diagram similar to that shown to the left. The worldlines are for the
quarks.
Analyzing strong interactions in this way is called Quantum
Chromodynamics. The similarity of the name to the wildly successful
Quantum Electrodynamics of Feynman and Schwinger is obvious, while the
'Chromo' part refers to the fact that quarks have color. Spiff name or not, in
my opinion so far the success of this approach has been
under-whelming. |
Ancient Greek Atomism
Democritus and Epicurus (4th - 5th century BCE) also believed that the
world was made of atoms. The theory is fully described by Lucretius in De
Rerum Natura.
The word atom means literally that which can not be divided.
Lucretius also used the word elementa to describe them; the word also
means the letters of the alphabet. This is sort of interesting since Needham in
his classic multi-volume study Science and Civilisation in China has
speculated that only cultures with alphabetic written languages develop
atomistic theories (Volume 4, pg. 13). We shall see in the next section, for
example, that the Chinese, who do not have an alphabetic written language,
analysed the world into five elements but those elements are definitely not
atoms.
Democritus describes an atomistic worldview in a famous statement:
"By convention sweet is sweet, by convention bitter is bitter, by
convention hot is hot, by convention cold is cold, by convention color is
color. But in reality there are atoms and the void. That is, objects of sense
are supposed to be real and it is customary to regard them as such, but in
truth they are not. Only the atoms and the void are real"
Lucretius' writing is pretty dense, but notice his discussion of
least parts:
"The first principles, then, are solid and simple; they consist of least
parts tightly compacted and compressed - not compounded by the coming together
of these parts, but rather enduring in everlasting simplicity; from them
nothing is permitted to be torn away or diminished, by nature which preserves
the seed of things."
In 1977, Julia H. Gaisser and T.K. Gaisser wrote that the least parts
that Lucretius writes about are a confined parton just as are the quarks. They
also suggested that the reason for the need for confined partons in atomistic
theories is that there is "an inherent conflict between the intuitive notion of
infinite divisibility and the idea of discrete fundamental atoms of matter."
(Reference: American Journal of Physics 45, (1977) 439.)
Platonic Classifications
Plato, of course, was not an atomist. He did, however, accept
Empedocles' notion that there are four fundamental elements: air, earth, fire
and water. He also knew that there are five and only five regular convex
polyhedra each of whose faces are all identical: the tetrahedron, cube,
octahedron, icosahedron and dodecahedron. In his one work on science,
Timaeus, Plato associated four of these polyhedra with the four
elements.
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Tetrahedron: four faces, fire
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Cube: six faces, earth
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Octahedron: 8 faces, air
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Icosahedron: 20 faces, water
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The fifth regular polyhedron, the 12 faced dodecahedron, "divinity
employed in the fabrication of the universe." |
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Plato used this scheme to explain how the elements "are able from
certain dissolutions into each other to become the sources of each other's
generation." He constructed the faces of the polyhedra from two types of right
triangles, isosceles and 30-60-90 degrees. However, even without taking the
faces apart into these triangles we see that:
2 air=2 octahedra=2 x 8=16 triangular faces.
1 fire=1 tetrahedron=1 x 4=4 triangular faces.
Thus, 2 air plus 1 fire=16 + 4=20 faces=1 icosahedron=1 water
Thus, we can do a Platonic form of chemistry.
However, consider the triangles that make up the faces. They are only
two dimensional, and thus can not be true bodies. As Plato wrote, "In the first
place, then, it is of course obvious to anybody that fire, earth, water, and
air are bodies; and all body has depth."
The triangles in this classification are clearly partons, and
since they are only two dimensional they can not exist separate from the thing
of which they are a part. Thus they too are a type of confined parton.
This system of Plato's had a profound effect on Heisenberg, who read
Timaeus as a young teenager.
The Sankhya Hindus
Hindu philosophy evolved an account of cosmic evolution, the Sankhya
system, that had both continuum and atomistic aspects. Although some of the
concepts can be traced back to the Upanishads and even the Rigveda, the oldest
Sankhya text now available is the Sankhyakarika, which probably dates
from the 5th century A.D.
The Sankhya idea was that there were five perceptible gross elements,
the bhutas:
- Ether (akasa) - ubiquitous, all-pervading, capable of vibration and
sound.
- Air (vayu) - light, cold, dry.
- Fire (tejas) - light, hot, dry, luminous.
- Water (apa) - liquid, cold wet.
- Earth (kshiti) - heavy, hard, dense.
The bhutas were composed of actual atoms, called paranus.
Initially, the universe was a formless undifferentiated invisible
ground, the prakriti. The prakriti was composed of a completely
homogenous mixture of three "reals" called the gunas:
- Essence (sattva) - makes something perceptible by the senses; serene,
calm, Vishnu.
- Energy (rajas) - active, fiery, Brahma.
- Mass (tamas) - inertial, dark, destructive - Shiva.
Then the God Purusa caused a disturbance in the equilibrium, and
initiated creation.
The connection from continuum, the prakriti, to the atom, the paranus,
was by the aggregation of the gunas into a type of parton called
tanmatras. The tanmatras then combined to form the atoms.
There were five types of tanmatras, and they corresponded to the five
senses:
- Vibration - Hearing
- Momentum - Touch
- Energy - Sight
- Viscous Attraction - Taste
- Cohesive Attraction - Smell
However, they tanmatras themselves were unobservable. Thus they too are
confined partons. S.S.S. Sastri comments, "The subtle elements [tanmatras] are
not cognisable by us with our limited faculties; their distinctions, thus, not
being perceived by us they are non-specific." (Reference: The Sankhyakarika
of Isvara Krsna (Univ. of Madras, 1973), pg. 80-81. See also
Sankhyakarika 34.)
Conclusion
According to Jung, when we observe more-or-less independent cultures
that have developed similar systems of analysis and/or symbolism, we are
probably seeing a reflection of a universal tendency of the human mind, an
archetype. One of Jung's favorite examples was the mandala, the
circular images that are drawn, painted, modelled or danced; often they contain
a quarternity or a multiple of four. The physicist Pauli proposed that our
basic mathematical intuitions are another example of an archetype.
When the Gaissers realised that ancient Greek atomism had confined
partons, as does modern Elementary Particle Physics, I realised that similar
analysis can be found in Plato and Sankhya Hinduism (Reference: American
Journal of Physics 46, (1978), pg 432.)
Thus, I am proposing that the modern quark model has an archetypal
aspect.
Although the quark model has been a success and many physicists believe
that quarks actually exist, there are at least two other competing systems of
analysis. In this section we discuss one of them, the bootstrap, and
will examine the other in the next section.
I shall argue that the bootstrap analysis, just as the quark model,
exists in many different contexts, and thus has an archetypal aspect. The
discussion has the following sub-sections:
- The Modern Bootstrap
- Buddhist Elements
- Chinese Elements
- Leibniz' Monadology
- Conclusion
The Modern Bootstrap
In the 1920's it was known that the neutron is unstable. If we have a
neutron that is not bound inside an atomic nucleus it will decay into a proton
and an electron; we now know that in the decay it also emits an antineutrino.
This naturally led people to speculate that the neutron was made of a proton
plus an electron.
In 1932 Anderson discovered the anti-electron, the positron. This
particle is identical to an electron except that it has a positive electric
charge instead of a negative charge. A document on antimatter is available
here.
This discovery particularly pleased Heisenberg. Now he could view the
proton as being made of a neutron and a positron. As he wrote, "The symmetry
between the proton and neutron was completely restored. This sounded like
Timaeus."
So the neutron is made of a proton, and the proton is made of a neutron.
This means that they are made of each other. This is the central idea of the
bootstrap: there are no elementary particles, but rather each "particle"
is just a reflection of all the other particles. It is called the bootstrap
because in this view if I have any one of the particles I can get to all the
other particles by lifting the particle by its own bootstraps.
The bootstrap idea is in opposition to the quark model. As Chew
remarked, "To a bootstrapper the identification of a seemingly fundamental
quark would constitute frustration." (Physics Today 23, (Oct. 1970),
23.)
Instead of trying to classify the elementary particles, this approach
concentrates on process, on the various nuclear reactions that can occur. It
envisions the universe in terms of an infinite dynamic matrix, the
Scattering Matrix, or S-Matrix. And each element of the S-matrix
describes a particular nuclear reaction, not a particular nuclear particle.
J.A. Wheeler began work on the S-matrix approach in the 1930's, and was
shortly joined by Heisenberg and others.
Chew comments "Carried to its logical extreme, the bootstrap conjecture
implies that the existence of consciousness, along with all other aspects of
nature, is necessary for self-consistency of the whole." (Science 161,
(1968), 762.)
Buddhist Elements
The Buddhists have a five element system of earth, water, air, fire, and
ether. Sometimes the ether is omitted, and at other times it is called
void. The elements are superficially the same as the Hindu ones, and
very similar to the ancient Greek classification of Empedocles. We also note an
echo of Plato reserving the fifth regular polyhedron, the dodecahedron, for the
fabrication of the universe in this fifth ether/void element.
This concept of void is crucial to Buddhist thought. For example, the
Heart Sutra states repeatedly:
"Form is emptiness, emptiness is form.
Likewise the feelings,
conceptions, impulses and consciousness."
The concept of void is also closely related to the development of the
number zero, which took hold thousands of years ago in Northern India/Southern
China. The number zero was adopted by the Arab mathematicians, who finally
carried it to Europe. In Europe, however, resistance to its use continued for
years. One thing that "carried the day" in Europe was that it is very very
difficult to do arithmetic such as long division in Roman numerals, or any
other representation without a placeholder like zero.
The following figure of the universe by Sengai (1750 - 1837) represents
the void as a zero and seems to echo the Platonic forms discussed above. In
"reading" the figure remember to go from right to left.
D.T. Suzuki comments on this figure:
"The circle represent the infinite, and the infinite is at the basis of
all beings. But the infinite in itself is formless. We humans endowed with
senses and intellect demand tangible forms. Hence the triangle. The triangle is
the beginning of all forms. Out of it first comes the square. The square is the
triangle doubled. This doubling process goes on infinitely." (Sengai the Zen
Master pg. 36.)
The Buddhist elements, however, are definitely not atoms. Rather they
stand for forces or momentary quanta of energy. We can call them
cooperators or cooperating forces. Thus, they are another example
of a bootstrap classification. As the Lankavatara Sutra states:
"Long and short and suchlike come to exist mutually conditioned;
not-to-be grows effective by to-be and to-be by not-to-be.
When things
are analyzed into atoms, there remains nothing to be discriminated as objects."
(D.T. Suzuki trans.)
In fact, the Buddhists provide my personal favorite image of the
bootstrap, called Indra's net of pearls:
"In the heaven of Indra, there is said to be a network of pearls, so
arranged that if you look at one you see all the others reflected in it. In the
same way, each object in the world is not merely itself but involves every
other object and in fact is everything else." (Avatamsaka
Sutra)
Chinese Elements
In the 4th century B.C. the Chinese were developing classifications that
seemed to be a rudimentary form of atomism. However, this was dropped in favor
of a system involving the five elements of wood, fire, earth, metal, and water.
The origins of these elements goes back at least to the Lu Shih Ch'un
Ch'iu of Tsou Yen (c. 350 - 270 B.C.).
The Shu Ching discusses the elements: "The nature of water is to
soak and descend; of fire to blaze and ascend; of wood to be crooked and to be
straight; of metal to obey and to change; while the virtue of earth is seen in
seed-sowing and in gathering." Needham comments: "Chinese thought here
characteristically avoided substance and clung to relation." (Science and
Civilisation in China, Volume 2, pg. 243.)
In fact the Chinese character for the elements, hsing
, also
means "go, move" and in ancient times was represented as a cross-roads
.
The point is that the Chinese element classification is yet another
bootstrap.
Leibniz' Monadology
Leibniz considered the world to be made of fundamental substances
called monads. However, as George Gale has realised, the
monads are yet another bootstrap:
"Leibniz constantly speaks of the monads as being in `mirroring'
relations. But what are the relata of the mirroring relations? Mirrors
mirroring other mirrors. Leibniz's monadic kingdom is a pure bootstrap
operation." (Journal of the History of Ideas 35, (1974) 339.)
Earlier we made reference to a physicist involved in the modern
bootstrap, J.A. Wheeler. He wrote "Not machinery but magic may be
the treasure that is waiting. Rather than Newtonian law it may resemble
more the logic of relationships that Leibniz envisaged." (in J.
Mehra, ed., The Physicist's Conception of Nature.) In fact,
the historical argument between Newton and Leibniz about atomism
some 300 years ago is mirrored in the modern disagreement between
the elementary particle physicists and the bootstrappers.
The fact that Leibniz' monads and the Chinese elements are both
bootstraps may not be coincidental or even archetypal. Leibniz'
philosophy was strong influenced by Chinese Neo-Confucian thought
brought back to Europe by Jesuit missionaries. To the right is the
frontispiece of a paper by Leibniz on Chinese philosophy, one of
the first such studies carried out in Europe:
Needham comments: "An unexpected vista thus opens before our eyes
- the possibility that while the philosophy of fortuitous concourse
of atoms, stemming from the society of European city-states, was
essential for the construction of modern science in its 19th century
form; the philosophy of organism essential for the construction
of modern science in its present and coming form stemmed from the
bureaucratic society of ancient and medieval China." (Science
and Civilisation in China, Volume 2, pg. 339.) |
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Conclusion
At present the vast majority of high energy physicists are elementary
particle physics. One major point of this section is that there is an
alternative view, held by physicist and non-physicist alike. Thus I tend to
cringe when I see statements like "There is no longer any doubt about the
existence of quarks." The quote is from a very popular introductory textbook
which I shall refrain from citing.
There is yet another relatively new approach to high energy physics that
also relates to theories of gravitation. It is called string theory,
and can be traced to 1970. It can be viewed as being consistent with
the emphasis on relationship and process that characterises the bootstrap.
Previously it had been somewhat of a cult,
but information on it that is accessible to a non-technical audience
is now beginning to appear. One nice but now somewhat dated resource
is Brian Greene, The
Elegant Universe (W.W. Norton, 1999).
On the web I am aware of two excellent sites.
- http://superstringtheory.com/index.html.
A wealth of information, presented in a well designed and well written site.
The site is dual track, with both Basic and Advanced discussions of many
topics. This site is also the source for the figures that appear below. If you
are reading the html version of this document on-line, those figures are
animations; the pdf version does not support animations.
- http://online.itp.ucsb.edu/online/plecture/witten/.
This page contains an audio presentation and copies of the accompanying
overheads for a one hour popular-level talk given by Edward Witten, professor
of physics at the Institute for Advanced Study in Princeton, N.J. The talk was
given by the Institute for Advanced Physics and the University of California at
Santa Barbara in January 1998.
The string theorists hope to solve a long-standing problem. We can
classify the world in terms of the interactions that can occur:
- Strong - responsible for holding the nucleus together.
- Weak - responsible for radioactive decay.
- Electromagnetic.
- Gravitation.
It used to be thought that the magnetic interaction and the electric
interaction were separate. They were unified by Faraday and Maxwell into the
electromagnetic interaction in the 19th century. Physicists would like to
continue unifying these interactions, and some progress has been made on
unifying the strong, weak, and electromagnetic forces. However, our best theory
of gravitation, Einstein's General Theory of Relativity, continues to stand
alone, resisting all attempts at unification.
We can state this situation in a slightly different way. We can describe
the strong, weak, and electromagnetic interactions using the Feynman diagrams
we saw above. It turns out that this is equivalent to saying that we can
describe the interactions using Quantum Mechanics. But no workable Feynman
diagrams for the gravitational interaction have been found; there is no
unification of Quantum Mechanics and the General Theory of Relativity.
In string theories, as in the bootstrap, there are no particles; there
are only strings. The vibrations of the strings is what we normally interpret
as the elementary particles. The different modes of vibration correspond to the
different particles.
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There are two basic types of string theories: those with
closed string loops that break into open strings, and those with closed string
loops that don't break into open strings |
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The reason why the elementary objects, electrons, photons, quarks, etc.,
appear to us to be point-particles instead of vibrating strings is that size of
the strings are much too small to be directly seen with current technology.
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It turns out that the dimensions of the strings is much greater
than the three spatial dimensions and one time dimension we are used to.
However, those extra dimensions are "folded up" inside the string, so are
unobservable. This is called "compactification."
Currently, the dimensionality of spacetime is believed to be 10 or
11, of which only 4 are normally observable: the three spatial dimensions and
the time dimension. |
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The Feynman diagrams used to describe three of the four elementary
interactions have one property which string theories do not: they describe all
fundamental interactions as occurring at a single point in space and time, the
vertices. One possible reason for the difficulty in unifying these
interactions with gravitation is that gravity acts at a distance, not at a
point. The figure to the right shows the equivalent of a Feynman diagram in a
string theory. String theorists hope that since this reaction is no longer
confined to a single point it may be possible to unify all four fundamental
interactions. |
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As mentioned above, in its early days string theory was somewhat of a cult.
In the past decade or so that situation has been totally reversed. If
a young graduate student is interested in questions such as what are the
ultimate constituents of the universe, or how does one build a theory
of gravity consistent with Quantum Mechanics, that person's chances of
getting a job are almost vanishingly small unless they are a string theorist.
So string theory now "rules" and other approaches to these fundamental
questions are being largely ignored.
This is despite the fact that there really is no such thing as String Theory.
What is usually called "String Theory" is actually a program to develop
such a theory. That program has been in operation since about 1970. Some
critics are now calling the program a failure. One such critic is Lee
Smolin of the Perimeter Institutute in Waterloo Ontario: a recent book
by him is The Trouble With Physics (Houghton Mifflin, 2007).
Author
This document was written in March 1999 by David M. Harrison, Department of Physics, University of Toronto, harrison@physics.utoronto.ca. This is version 1.13, date (m/d/y) 12/06/07.
This document is Copyright © 1999 - 2004 by David M. Harrison. The
four animated figures in the String Theories section are Copyright © 1998
Patricia Schwartz; the originals appear on the string theory web site cited
at the beginning of that section and are used by permission.
Some of the material in this document was originally published by David Harrison in The American Journal of Physics 46, 432 (1978).
