Infinite in All Directions

I chose the title, "Infinite in All Directions", from a book by
Freeman Dyson. I feel that this title is particularly pertinent, since
it reminds us of the scale of the observed universe around us. Our
known universe extends from the microscopic to the macroscopic. On the
microscopic end, we have probed what lies deep within matter. The
smallest distances that we have probed, directly or indirectly, are
about twenty four orders of magnitude smaller than us i.e. one trillionth
of a trillionth of a meter. On the macroscopic end, we are surrounded
by an immense universe of galaxies, stars, planets, gas, dust and many
as yet undiscovered objects. The observable universe is roughly ten
billion light years across or a trillion trillion meters. Our physical
size, of the order of a meter, stands in the center of this enormous
range of sizes. I like to think about it as follows: To an elementary particle, we are as large comparatively, as the universe is to us! In this immense scheme of things, the largest and the smallest come together, very much like a snake biting its own tail. The study of matter at the smallest scale
gives us clues about the origins and the structure of the universe at
the biggest scale, and the field of particle physics deals directly
with this. This connectedness of the universe has been a source of
deep mystery and fascination for me, and I would like to share some of
the joy of being a particle physicist with the esteemed visitors to
Chowk. As we begin this journey, I will first focus on the
microscopic and go through some of the major things that we know
today about the nature of matter at its smallest. Subsequently, I will
start looking at the macroscopic picture.

Introduction


If the whole enterprise of particle physics is distilled into its
essence, it will boil down to two questions: What are the building
blocks of matter and how do they interact with each other to give us
the universe that we see around us? Undoubtedly, these questions
have been with us ever since the dawn of humanity. They have been
tackled by the most inquisitive of minds through the centuries. This
process, begun by the philosophers of the ancient world, has
progressively grown over the centuries, resulting in an ever
sophisticated understanding of the world around us. That refined
understanding translates into an increased ability of man to tap the
potential of nature. Today, the eyes of man, peer deep into the heart
of matter, and understand it at a level unprecedented ever before in
human history. At last it seems that the answers to the two questions
may finally be at hand. If that is so, then truly we are living in an
era of immense importance to the human civilization. A fundamental
understanding of the universe is as important a milestone in human
history as the development of language was for our ancestors.

Though we may feel we are at an important threshold, we must temper
our optimism. The very continued existence of these questions today is
a constant reminder of the incredible beauty and subtlety of nature
and its ability to puzzle and bemuse us. Many times in the past,
people have stood at a potential threshold of a glimpse into the 'mind
of God' only to be outwitted by nature. Will that be the case with us?
Only time will tell.

Whereas the philosophers of yesterday were content with coming up with
a mental model of the world around them, today, we understand that
theory merely comprises one half of the quest for
understanding. The other vital ingredient is
experimentation. Hand in hand, theory and experiment, form a
dynamic duo that guide us in unknown territory. Where one is blind,
the other sees. This process, termed The Scientific Method, is
the basic epistemological tool at our disposal in our
quest. Admittedly, it is not perfect, but it is the best tool
currently at our disposal.

All the knowledge gained over the preceding centuries, has been
condensed into certain basic principles, that dictate the behavior of
the universe around us. These principles underlie the edifice of
modern physics. Modern theories of physics rest on two key principles:
Relativity and Quantum Mechanics.

The first principle, Relativity, formulated by Einstein in 1905,
states that nothing can travel at a velocity greater than the velocity
of light. Therefore, it forbids an instantaneous transmission
of the effects of forces from one body to another. Instead, particles
interact with each other over large distances by interacting with
fields that are created by them, and these fields propogate at
the velocity of light. For example, a body that is electrically
charged, produces an electric field around it, and another body which
is situated some distance away from the first body, interacts with
that electric field, and experiences a force. If one were to deposit a
charge on the first body at a particular time, then the second body
would not experience the effect of the electric field instantaneously,
but after the amount of time taken by the field to cover the
separation between the two bodies.

The second principle, quantum mechanics, states that the way to view
these fields is to view them as exchanges of particles, which are the
quanta or the constituents of those fields. In the quantum mechanical
picture, therefore, every time a body is charged, it produces a lot of
particles called photons around it. These photons are then
exchanged between the two bodies and therefore they experience a
force. The combination of these two key principles leads to the
concept of a Quantum Field Theory, where now the field
generated by a body is interpreted as a collection of an infinite
number of particles, corresponding to the different modes of vibration
of the field, that contain and transmit the energy carried by the
field. Of course, particles that comprise the field of another
particle, can in turn generate their own fields. Thus the picture of
the matter around us breaks down into visualizing basic constituents
or particles of matter that interact with each other through the
exchange of other particles.

All particles in nature can be divided into two classes:
Fermions and Bosons. These two kinds of particles are
classified according to the amount of a property called spin
possessed by them. Fermions are intensely individualistic -no two
fermions with exactly the same properties will be found close to each
other. They always try to maximize their distance from other fermions
who are exactly like them. Bosons, on the other hand, are intensely
gregarious. They seek other bosons that share exactly the same
properties as them, and try to clump together into groups of particles
with exactly the same properties.

It turns out that this stark difference in the properties of these two
kinds of particles is essential to constitute matter and to allow it
to interact with itself. We said that we view matter as basic
constituents or particles of matter that interact with each other
through the exchange of other particles. To put it more concretely,
the particles that are exchanged and form a field are always
bosons. Whereas the particles that exchange those bosons are usually
fermions, though they can also be other bosons. Thus, fermions are
the building bricks of matter, and bosons are the mortar that binds it
together.

The bricks of matter are of two varieties: quarks and
leptons. Three quarks, for example, bind together in different
ways to form what we call protons and neutrons. Protons, neutrons and
electrons form atoms. Atoms bind in different ways to form molecules
and these in turn form every thing that we see today, including
ourselves.

As the bosons are the mortar of matter, or the agents that transmit
forces from quarks and leptons to each other, the different kinds of
fundamental bosons in nature depends on the number of fundamental
forces in nature. We experience four fundamental forces of nature and
thus expect four basic categories of fundamental bosons.

The first fundamental force is the Gravitational force, which we
directly experience everyday. However, gravity is the weakest of the
four forces. It is so weak that it has a negligible effect on the
physics of elementary particles. Therefore, most theories of particle
physics ignore the effects of gravity. The second force is the
familiar force of electricity and magnetism or
Electromagnetism. Although we tend to think of electricity and
magnetism as two different phenomena, in reality they are the same,
since electric fields and electrically charged particles can produce
magnetic fields and vice versa. The Electromagnetic force is the
principal agent the keeps the atoms and the molecules together, and
accounts for everything from the hardness or softness of different
materials to the light that we see. The third force is called the Weak
nuclear force. It is the force that causes radioactivity and
transmutation of one kind of element into another. Some other
manifestations of this force are the processes that power the sun and
the intense energy release during a nuclear explosion. Calling this
force "Weak" is actually misleading. It is in reality a little bit
stronger than the Electromagnetic force, however its effects are not
as readily observed since the universe today is a lot colder than the
ambient temperatures at which its effects become comparable to those
of the Electromagnetic force. And finally, the fourth force is called
the Strong Nuclear force, which causes the quarks to bind together to
form protons and neutrons, despite intense electromagnetic repulsion
between like charges. The strong nuclear force is by far the
strongest of the four forces and is responsible for the stability of
the matter that we see around us.

Each force acts on a particular "charge" or property carried by
matter. The Gravitational force, for example, depends on the mass of
the two particles, and decreases as the distance between them
grows. The Electromagnetic force is proportional to the familiar
electric charge of the interacting bodies and also decreases in
intensity with growing distance between charges. The charges for the
other two forces are not so obvious as we do not experience those
forces directly in our everyday life. The charge for the Weak nuclear
force is called Weak Isospin, whereas the charge for the Strong
nuclear force is called Color (which is not the same color that we see
everyday). All quarks experience the Strong force as well as the
Electromagnetic force, and hence carry the color charge in addition to
the normal electric charge. Whereas an electric charge can be either
positive or negative, the color charge can take one of six values,
conventionally called red, anti-red, blue, anti-blue, green and
anti-green. The Strong force has the peculiar property that it grows
stronger as the distance between two particles carrying the color
charge increases, unlike other forces. However, before we move
further, we should see how modern physics treats the concept of a
force.

We understand today that forces arise from underlying
Symmetries of nature. There is an intimate connection between
the different laws of conservation in physics (like the conservation
of energy and the conservation of momentum) and the underlying
symmetries of matter. Symmetries are transformations of matter, like
moving it from one point to another, or rotating it in some way, that
leave the equations of motion for that system unchanged. Every
symmetry is related to the conservation of a quantity. For example,
suppose we have a system of particles, and the equations of motion of
that system do not change when we move it from one point to another in
space, then the system is said to possess a translational symmetry and
the linear momentum of that system is conserved. Similarly, if we
rotate a system of particles and their equations of motion have the
same form as before then the system possesses a rotational symmetry
and the angular momentum of that system is conserved. Forces arise
whenever a symmetry is broken or has to be restored. When for example,
the linear momentum of a system is not conserved, then there has to be
a force that is causing the system to accelerate or decelerate. The
concept of symmetries is very important in physics, and we can break
down the different symmetries of physics into two broad categories:
global symmetries and local symmetries.

Suppose we have a collection of particles, and we move each and every
one of them, en masse, from one point to another. If the equations of
motion of the system do not change by doing so, we say that the system
has a global symmetry under translation from one point to another. One
the other hand, if we were to move each and every particle
individually, independently of all others, and still not see a
difference, then we would say that the system has a local symmetry
under translation. Clearly, a principle that requires the presence of
local symmetries in a physical theory is more stringent than one which
requires a global symmetry. When we require that the equations of
motion in a quantum field theory of charged particles possess a
special kind of local symmetry, also called a gauge symmetry,
we see that the Electromagnetic force arises naturally to preserve
that condition. Thus, the Electromagnetic force is a manifestation
of an underlying gauge symmetry of matter. A requirement of local
gauge symmetries, i.e. that are true locally at each and every point
in space and time, give rise to what are called gauge forces. The
familiar Electromagnetic force, as well as the Weak and Strong Nuclear
forces are all examples of such gauge forces.

At this point we can ask ourselves the following question: Why are
there four different forces in nature, and not just one? The
distinction between different forces may be artificial, just as the
distinction between the electric and the magnetic forces, as seen by
us, is artificial. The first known unification of forces was done by
James Clerk Maxwell, when by writing down the equations that bear his
name today, he showed that the electric and the magnetic forces were
in actuality just one Electromagnetic force. In 1915 Albert Einstein
formulated the General Theory of Relativity, which described
gravitational phenomena. Next he tried to unify his theory of
gravitation with the theory of electromagnetism. In that endeavour
however he was not successful. But simply by asking the question of a
unification of forces, he defined a path that has attracted the most
eminent physicists of this century. In 1970's, Abdus Salam and Steven
Weinberg, working independently, unified two more forces, the Weak
Nuclear force and the Electromagnetic force, and showed that they were
the manifestations of one fundamental force called the
Electroweak force. The saga continues, as physicists search for
a Grand Unified Theory that unifies all forces, and describes
all matter at a fundamental level. The closest experimentally
verifiable candidate that we have today is called the Standard
Model. It provides a description of the Strong and the Electroweak
force, and classifies matter in a manner reminiscent of the periodic
table of Mendeleev. The history of the Standard Model is very
interesting and merits a brief tour.

A Brief History of the Standard Model


The discovery of radioactivity, and in particular, the discovery of
beta decay, or the decay of a neutron into a proton and an electron,
led to the realization that we were seeing the manifestation of a new
fundamental force, the Weak nuclear force. It was observed that
apparently, in beta decay, momentum was not being conserved. This was
a most unsettling situation, and was explained by Wolfgang Pauli by
postulating the existence of a new particle, called the neutrino (or a
little neutron), that interacted extremely weakly with matter, and was
therefore not observed as an end product of the decay of a
neutron. Admittedly, at that moment, there was no other justification
for the concept of the neutrino, except to conserve the sacred
principle of conservation of momentum. However, assuming the existence
of the neutrino, immediately solved the problem of beta decay, and led
to a successful empirical model of the weak interactions by Enrico
Fermi. It was, however, far from a fundamental description.

During this time, as the list of observed particles was growing,
physicists were beginning to understand some of the properties of
these particles. Many important advances were made in theoretical
aspects of quantum field theory. Paul Dirac, a physicist of the
caliber of Newton, Maxwell and Einstein, did seminal work in
formulating a modern theory of quantum fields and predicted the
presence of antimatter in 1930's. His and the work of others was taken
up by a new crop of extremely talented physicists. With stalwarts
like Freeman Dyson, Richard Feynman, Siichiro Tomonaga and Julian
Schwinger working on them, a successful quantum field theory of
electromagnetism was formulated. Called Quantum Electrodynamics, or
QED, it was the most successful theory ever -its predictions agreed
with experiments to an incredible 12 decimal places! In the process,
however, the physicists ran across a snag. QED had a propensity to
give infinite answers. To a physicist, this was not a problem per se,
because, after all one was dealing with a quantum version of a vacuum,
which includes the effect of an infinite number of photons and other
quanta of the field. The trick was to figure out a consistent method
to remove these infinities to get answers that could be cross-checked
with experiments. One after another, the different infinities in the
theory were understood, and separated from the physical answers of
QED. This scheme of removing the infinities is called
Renormalization and a physical theory in which infinities can
be handled in a consistent way is said to be a renormalizable
theory. Ever since, renormalizability has become one of the basic
requirements of any consistent physical theory. With an understanding
of renormalization, it was quickly realized that the theory of weak
interactions formulated by Fermi was not renormalizable, and hence
could not be a fundamental theory.

Around that time another breakthrough happened in physics. In physics,
we often take for granted that if we switch a particle with its mirror
image, the equations of motion of the two will be identical. That is,
if we compare the decay distributions of a particle and its
anti-particle, they should be exactly the same. In other words, for
the purpose of physics, a left-handed world and a right-handed world
were exactly the same. In 1956, C. N. Yang and T. D. Lee argued that
there was no evidence that weak interactions actually obeyed this
rule. Few months later C. S. Wu experimentally verified the postulate
of Yang and Lee, and they went on to win the Nobel prize in physics
for it. The discovery of the breakdown of mirror image symmetry, or
parity violation in the weak interactions had far reaching effects. It
showed that there was a force that could absolutely distinguish
between left and right, and to date forms one of the outstanding
puzzles of physics.

By that time physicists had discovered a plethora of particles, and
there did not appear to be any fundamental description of them. There
was no apparent order in a seemingly ever increasing number of
particles -nothing like the equivalent of a periodic table of
Mendeleev that classified elements in different groups existed for
these particles. It was realized by Gell-Mann and Zweig, that the
proliferation of particles could be understood if one considered them
to be different combinations of more fundamental particles called
quarks. This also led to the realization that there had to be a new
fundamental force, the Strong Nuclear force, that bound those quarks
together despite their intense electromagnetic repulsion. A further
analysis of the observed particles revealed that these quarks must
carry a new kind of charge, color. It was realized that nature
abhorred the presence of isolated color charges, and that all of the
observed particles in nature were those combinations of quarks such
that no residual color charge remained. This is so since only by
having no residual color charge can the observed particles be free
from the Strong Force and travel freely. These breakthroughs instantly
brought order to apparent disorder. Now, instead of hundreds of
particles, one could consider them to be different combinations of
quarks. Although the quarks could not be observed directly (since they
carried the color charge), experiments could search for them
indirectly.

The first direct evidence for quarks was seen in the famous Deep
Inelastic Scattering experiment by Friedman, Kendall and Taylor in
1969. They bombarded protons with highly energetic electrons, and in
the process discovered that the electrons were behaving as if they
were colliding not with something the size of a proton, but something
much smaller contained within the proton. To put it another way, they
showed that protons were not solid, but were constituted of more
fundamental particles whose properties matched those expected for the
quarks. In a way they had repeated the celebrated experiment of
Rutherford almost a century ago which had led to the discovery of the
nucleas within an atom. Except this time they were looking at
something that was billions of time smaller.

With the evidence in place for the existence of quarks, and the
presence of QED, the natural question arose whether quantum field
theories could be constructed for the Strong and the Weak Nuclear
forces. In the case of the Strong force, a successful quantum field
theory was built based upon QED. Called Quantum Chromodynamics (QCD),
it was very similar to QED, except that it used a color charge instead
of an electric charge, and made appropriate adjustments to the
interactions of the particles. QCD modelled the interaction between
particles carrying the color charge through the exchange of
gluons that are the bosons for the Strong Nuclear force. Unlike
QED, which just has one photon, there are eight gluons. QCD was
renormalizable in many regions of interest to physicists, and
therefore a successful candidate for a physical theory. It turned out,
however, that the Weak Nuclear force was not tackled that easily.

As I described earlier, quantum field theories view the interactions
between different particles in terms of exchange of certain other
particles. In QED, the interaction between two electrons is viewed in
terms of an exchange of photons. An equivalent approach to the weak
interactions was to view them as an exchange of another boson, which
unlike the photon had to be massive to account for the observed
weakness of the interaction. At this level, QED and a quantum theory
of weak interactions appeared to be very similar in form. There was
however no way to make that boson massive, without destroying the
renormalizability of the theory of weak interactions. In addition, one
needed to identify the equivalent of an electric charge for the Weak
interactions.

The mass problem was eventually solved by drawing upon the properties
of matter when it undergoes phase transitions just like water changing
from a solid phase (ice) to liquid or from liquid to gas
(steam). J. Goldstone and Y. Nambu introduced a concept of a
'spontaneous' breakdown of symmetry, which was later extended by
P. Higgs to quantum field theories. The concept of Spontaneous
Symmetry Breaking (SSB) can be illustrated by a simple
example. Suppose you stand a knitting needle on a table and press down
on its other end. When you are not pressing down hard, the knitting
needle will stay straight. However, once you press hard, the needle
will buckle. If you took a thousand different needles and repeated the
experiment, you will find that each needle buckles in a different
direction. The reason is that energetically any given direction of
buckling is not preferred, or that is to say that there exists a
complete symmetry in the possible ways the needle could
buckle. However, in the real world, the needle has to buckle in a
particular direction, and whenever it does so, it chooses one
particular direction out of many equally possible ones. This is
Spontaneous Symmetry Breaking. It was discovered that if an equivalent
of SSB happened with regards to a global symmetry of a physical
theory, then new massless particles were produced. Salam, and
independently Steven Weinberg realized that SSB, when applied to
certain gauge theories gave rise to massive bosons, just the kind that
were required to formulate the gauge theory of Weak interactions.

In 1967, Salam and Weinberg, arranged the known quarks and leptons in
pairs, according to the Weak Isospin carried by each of them, which
they identified as the charge of the Weak interactions. Now we know
that there are six kinds of fundamental leptons, the electron, the
muon, the tau, the electron neutrino, the muon neutrino and the tau
neutrino. Similarly, there are six kinds of quarks, up, down, charm,
strange, top and bottom. The electrons, for example are paired with
electron neutrinos, the muons with muon neutrinos etc. The quarks with
arranged into pairs: (up, down), (charm, strange) and (top,bottom). In
addition a new particle was postulated, called the Higgs boson, that
causes SSB and gives mass to the bosons of Weak interactions. The
theory that they formulated, treated the electromagnetic and weak
interactions on equal footing, and after SSB gave rise to the correct
decay rates and reactions observed in particle physics. This unified
theory of weak and electromagnetic interactions was named the
Electroweak theory. The Electroweak theory predicted the presence of a
new kind of a weak interaction called the neutral current reaction. In
addition it predicted the masses of the electrically charged (called
W+ and W-) and neutral weak bosons (called Z) that constituted the
bosons for the Weak Nuclear force. In 1971 G. t'Hooft proved that the
Electroweak theory was renormalizable, and the interest in it
soared. A few years later, neutral current reactions were discovered
vindicating the Electroweak theory. In 1979, A. Salam, S. Weinberg and
S. Glashow were awarded the Nobel prize in physics for their work.

The initial quark model had only hypothesized the existence of three
quarks, called up, down and strange. Glashow,
along with others, predicted the existence of another quark, called
the charm, based upon the observed rates of decay of certain
particles. In 1974, Samuel Ting and Burton Richter discovered the
J-Psi particle, which was later interpreted to be composed of two
charmed quarks. In the same year, a new lepton was discovered by Perl
and his associates and was named the tau. The tau was a heavier
equivalent of the electron and the muon. In 1977, the bottom
quark was discovered, and its existence was taken as a proof of the
existence of the top quark. However, the top quark was not discovered
until almost two decades later.

The weak bosons were surprisingly massive, about 80 to 90 times
heavier than a proton. At the moment there was no experimental
facility where they could be produced. A large proton and anti-proton
collider came on line in CERN in Geneva in early eighties, and in 1983
the charged weak bosons (W+ and W-) were observed directly for the
first time, with exactly the mass predicted by the Electroweak
theory. Shortly afterwards, the Z bosons were also directly observed
and found to be in complete agreement with the predictions of the
Electroweak theory.

Today, in laboratories like Fermilab and CERN, millions of these
bosons have been produced, and studied in excruciating
detail. Fermilab, which houses the most powerful particle accelerator
in the world, the Tevatron, discovered the top quark in 1995, and in
doing so completed the last of the three pairings of the quarks. The
top quark itself is about twice as massive as the weak bosons
themselves, and the origin of its large mass is an extermely important
question of physics. So far, the Electroweak theory, along with its
counterpart for the Strong interactions, QCD, have been found to be
extremely successful in describing the world of elementary
particles. Both of these theories comprise the Standard Model of
particle physics. However, how robust is the Standard Model?

Beyond the Standard Model


Although most physicists would swear by it, the Standard Model is by
no means the end of this saga. Through years of careful
experimentation and developments in theoretical physics, we are
already seeing its limitations. On the experimental front, the Higgs
boson, which is required for the Electroweak theory, has not yet been
seen. Though technically it is not a problem with the Electroweak
theory per se because it could be beyond the reach of our current
machines, it does pose what is now considered to be the biggest
question in particle physics: Where is the Higgs boson? The Standard
Model itself, however, successfully withstood the tests of experiment
until recently. In the summer of this year (1998), the Super
Kamiokande experiment in Japan announced that they had definitely
observed a phenomenon known as neutrino oscillations. This phenomenon
refers to a process where a muon-type neutrino changes into an
electron-type neutrino and back. Practically speaking, this translates
into the fact that neutrinos must possess a definite mass. This is in
complete contradiction to the assumption of Standard Model that the
neutrinos should be massless. While technically the modification of
the Standard Model is not difficult, it poses deep questions about the
limitations of the model itself. On the theoretical front, there are
several arguments that are unsettling. First, if one calculates the
reaction rates for certain physical processes, one still finds
infinite answers. As I mentioned earlier, these infinities can be
consistently thrown away, or renormalized, but in the case of the
Standard Model, they pose certain important concerns about the
consequences of the procedure, which are not very aesthetic
mathematically. Furthermore, the Standard Model is highly artificial
in its construction, it assumes many parameters in its construction,
and does not provide a more fundamental explanation about why the
fundamental particles of nature should be the way they are. In
addition, it does not provide any description of that ubiquitous force
of nature we are so familiar with, i.e. gravity. All of these concerns
point to the fact that the Standard Model is merely a good-enough
explanation, and not a fundamental explanation of the workings of
matter. Clearly, physicists have to explore what lies beyond the
Standard Model.

Fortunately, people have been hard at work over the last few decades.

(To be continued ...)