A Theory Of Everything?
Page 5
FIELD THEORY IN HIGHER DIMENSIONS
To see how higher dimensions helps to unify the laws of nature,
physicists use the mathematical device called "field theory." For
example, the magnetic field of a bar magnet resembles a spider's web
which fills up all of space. To describe the magnetic field, we
introduce the field, a series of numbers defined at each point in space
which describes the intensity and direction of the force at that point.
James Clerk Maxwell, in the last century, proved that the
electro-magnetic force can be described by four numbers at each point in
four dimensional space-time (labeled by A _ 1, A _ 2 , A _ 3 , A _ 4 ).
These four numbers, in turn, obey a set of equations (called Maxwell's
field equations).
For the gravitational force, Einstein showed that the field requires a
total of 10 numbers at each point in four dimensions. These 10 numbers
can be assembled into the array shown in fig. 3. (Since g _ 12 = g _ 21
, only 10 of the 16 numbers contained within the array are independent.)
The gravitational field, in turn, obey Einstein's field equations.
The key idea of Theodore Kaluza in the 1920s was to write down a five
dimensional theory of gravity. In five dimensions, the gravitational
field has 15 independent numbers, which can be arranged in a five
dimensional array (see fig.4). Kaluza then re-defined the 5th column and
row of the gravitation al field to be the electromagnetic field of
Maxwell. The truly miraculous feature of this construction is that the
five dimensional theory of gravity reduces down precisely to Einstein's
original theory of gravity plus Maxwell's theory of light. In other
words, by adding the fifth dimension, we have trivially unified light
with gravity. In other words, light is now viewed as vibrations in the
fifth dimension. In five dimensions, there is "enough room" to unify
both gravity and light.
This trick is easily extended. For example, if we generalize the theory
to N dimensions, then the N dimensional gravitational field can be
split-up into the following pieces (see fig. 5). Now, out pops a
generalization of the electromagnetic field, called the "Yang-Mills
field," which is known to describe the nuclear forces. The nuclear
forces, therefore, may be viewed as vibrations of higher dimensional
space. Simply put, by adding more dimensions, we are able to describe
more forces.
Similarly, by adding higher dimensions and further embellishing this
approach (with something called "supersymmetry), we can explain the
entire particle "zoo" that has been discovered over the past thirty
years, with bizarre names like quarks, neutrinos, muons, gluons, etc.
Although the mathematics required to extend the idea of Kaluza has
reached truly breathtaking heights, startling even professional
mathematicians, the basic idea behind unification remains surprisingly
simple: the forces of nature can be viewed as vibrations in higher
dimensional space.
WHAT HAPPENED BEFORE THE BIG BANG?
One advantage to having a theory of all forces is that we may be able to
resolve some of the thorniest, long-standing questions in physics, such
as the origin of the universe, and the existence of "wormholes" and even
time machines.
The 10 dimensional superstring theory, for example, gives us a
compelling explanation of the origin of the Big Bang, the cosmic
explosion which took place 15 to 20 billion years ago, which sent the
stars and galaxies hurling in all directions. In this theory, the
universe originally started as a perfect 10 dimensional universe with
nothing in it. In the beginning, the universe was completely empty.
However, this 10 dimensional universe was not stable. The original 10
dimensional space-time finally "cracked" into two pieces, a four and a
six dimensional universe. The universe made the "quantum leap" to
another universe in which six of the 10 dimensions collapsed and curled
up into a tiny ball, allowingexplanation of the origin of the Big Bang,
the cosmic explosion which took place 15 to 20 billion years ago, which
sent the stars and galaxies hurling in all directions. In this theory,
the universe originally started as a perfect 10 dimensional universe.
This explains the origin of the Big Bang. The cur rent expansion of the
universe, which we can measure with our instruments, is a rather minor
aftershock of a more cataclysmic collapse: the breaking of a 10
dimensional universe into a four and six dimensional universe.
In principle, this also explains why we cannot measure the six
dimensional universe, because it has shrunk down to a size much smaller
than an atom. Thus, no earth-bound experiment can measure the six
dimensional universe because it has curled up into a ball too small to
be analyzed by even our most powerful instruments. (This will be
disappointing to those who would like to visit these higher dimensions
in their lifetimes. These higher dimensions are much too small to
enter.)
TIME MACHINES?
Another longstanding puzzle concerns parallel universes and time travel.
According to Einstein's theory of gravity, space-time can be visualized
as a fabric which is stretched and distorted by the presence of matter
and energy. The gravitational field of a black hole, for example, can be
visualized as a funnel, with a dead, collapsed star at the very center
(see fig. 6). Anyone unfortunate enough to get too close to the funnel
inexorably falls into it and is crushed to death.
One puzzle, however, is that, according to Einstein's equations, the
funnel of a black hole necessarily connects our universe with a parallel
universe. Furthermore, if the funnel connects our universe with itself,
then we have a "worm hole" (see fig. 7). These anomalies did not bother
Einstein because it was thought that travel through the neck of the
funnel, called the "Einstein-Rosen bridge," would be impossible (since
anyone falling into the black hole would be killed).
However, over the years physicists like Roy Kerr as well as Kip Thorne
at the Calif. Institute of Technology have found new solutions of
Einstein's equations in which the gravitational field does not become
infinite at the center, i.e. in principle, a rocket ship could travel
through the Einstein- Rosen bridge to an alternate universe (or a
distant part of our own universe) without being ripped apart by intense
gravitational fields. (This wormhole is, in fact, the mathematical
representation of Alice's Looking Glass.)
Even more intriguing, these wormholes can be viewed as time machines.
Since the two ends of the wormhole can connect two time eras, Thorne and
his colleagues have calculated the conditions necessary to enter the
wormhole in one time era and exit the other side at another time era.
(Thorne is undaunted by the fact that the energy necessary to open an
Einstein-Rosen bridge exceeds that of a star, and is hence beyond the
reach of present-day technology. But to Thorne, this is just a small
detail for the engineers of some sufficiently advanced civilization in
outer space!)
Thorne even gives a crude idea of what a time machine might look like
when built. (Imagine, however, the chaos that could erupt if time
machines were as common as cars. History books could never be written.
Thousands of meddlers would constantly be going back in time to
eliminate the ancestors of their enemies, to change the outcome of World
War I and II, to save John Kennedy's and Abraham Lincoln's life, etc.
"History" as we know it would become impossible, throwing professional
historians out of work. With every turn of a time machine's dial,
history would be changing like sands being blown by the wind.)
Other physicists, however, like Steven Hawking, are dubious about time
travel. They argue that quantum effects (such as intense radiation
fields at the funnel) may close the Einstein-Rosen bridge. Hawking even
advanced an experimental "proof" that time machines are not possible
(i.e. if they existed, we would have been visited by tourists from the
future).
This controversy has recently generated a flurry of papers in the
physics literature. The essential problem is that although Einstein's
equations for gravity allow for time travel, they also break down when
approaching the black hole, and quantum effects, such as radiation, take
over. But to calculate if these quantum corrections are intense enough
to close the Einstein-Rosen bridge, one necessarily needs a unified
field theory which includes both Einstein's theory of gravity as well as
the quantum theory of radiation. So there is hope that soon these
questions may be answered once and for all by a unified field theory.
Both sides of the controversy over time travel acknowledge that
ultimately this question will be resolved by the Theory of Everything.
RECREATING CREATION
Although the 10 dimensional superstring theory has been called the most
fascinating discovery in theoretical physics in the past decades, its
critics have focused on its weakest point, that it is almost impossible
to test. The energy at which the four fundamental forces merge into a
single, unified force occurs at the fabulous "Planck energy," which is a
billion billion times greater than the energy found in a proton.
Even if all the nations of the earth were to band together and
single-mindedly build the biggest atom smasher in all history, it would
still not be enough to test the theory. Because of this, some physicists
have scoffed at the idea that superstring theory can even be considered
a legitimate "theory." Nobel laureate Sheldon Glashow, for example, has
compared the superstring theory to the former Pres. Reagan's Star Wars
program (because it is untestable and drains the best scientific
talent).
The reason why the theory cannot be tested is rather simple. The Theory
of Everything is necessarily a theory of Creation, that is, it must
explain everything from the origin of the Big Bang down to the lilies of
the field. Its full power is manifested at the instant of the Big Bang,
where all its symmetries were intact. To test this theory, therefore,
means recreating Creation on the earth, which is impossible with
present-day technology. (This criticism applies, in fact, to any theory
of Creation. The philosopher David Hume, for example, believed that a
scientific theory of Creation was philosophically impossible. This was
because the foundation of science depends on reproducibility, and
Creation is one event which can never be reproduced in the laboratory.)
Although this is discouraging, a piece of the puzzle may be supplied by
the Superconducting Supercollider (SSC), which, if built, will be the
world's largest atom smasher. The SSC (which is likely to be cancelled
by Congress) is designed to accelerate protons to a staggering energy of
tens of trillions of electron volts. When these sub-atomic particles
slam into each other at these fantastic energies within the SSC,
temperatures which have not been seen since the instant of Creation will
be generated. That is why it is sometimes called a "window on Creation."
Costing /8-10 billion, the SSC consists of a ring of powerful magnets
stretched out in a tube over 50 miles long. In fact, one could easily
fit the Washington Beltway, which surrounds Washington D.C., inside the
SSC.
If and when it is built, physicists hope that the SSC will find some
exotic sub-atomic particles in order to complete our present-day
understanding of the four forces. However, there is also the small
chance that physicists might discover "super- symmetric" particles,
which may be remnants of the original superstring theory. In other
words, although the superstring theory cannot be tested directly by the
SSC, one hopes to find resonances from the superstring theory among the
debris created by smashing protons together at energies not found since
the Big Bang.
WE ARE NOT SMART ENOUGH
Superstring physicists, however, are not bothered by these criticisms.
To them, the fundamental problem is theoretical, not practical. The true
problem is to solve the theory completely, and then compare it with
present-day experimental data. The problem, therefore, is not in
building ever larger atom smashers; the problem is being clever enough
to solve the theory.
Edward Witten of the Institute for Advanced Study, impressed by the vast
new areas of mathematics opened up by the superstring theory, has said
that the superstring theory represents "21th century physics that fell
accidentally into the 20th century." This is because the theory was
discovered by accident. By the normal progression of science, we
theoretical physicists might not have discovered the theory for another
century.
The superstring theory may very well be 21st century physics, but the
bottleneck is that 21st century mathematics has not yet been discovered.
That is the fundamental problem: at present, millions of solutions to
these equations have been discovered, but no one is smart enough to
determine how to select the correct one. In other words, although the
string equations are perfectly well-defined and have millions of
solutions, no one is capable at present of determining which is the
unique solution. If we could only sharpen our analytical skills and
develop even more powerful mathematical tools, perhaps we could solve
for the unique solution and settle the controversy.
Ironically, the superstring equations stand before us in perfectly
well-defined form, yet we are too primitive to understand why they work
so well and too dim witted to determine its unique solution.
Imagine a child gazing at a TV set. The images and stories conveyed on
the screen are easily understood by the child, who can easily change the
channels and manipulate the settings on the TV Yet the electronic
wizardry inside the TV set is beyond the child's ken. We physicists are
like this child, gazing in wonder at the mathematical sophistication and
elegance of the superstring equations and awed by its power. However,
like this child, we do not understand why the theory works.
Sheila Na Gig
Send e-mail to mapona@yahoo.com
Copyright © 1999 Sheila Na Gig.
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