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"We go about our daily lives
understanding almost nothing of the world. We give little thought to
the machinery that generates the sunlight that makes life possible,
to the gravity that glues us to an Earth that would otherwise send
us spinning off into space, or to the atoms of which we are made and
on whose stability we fundamentally depend. Except for children (who
don't know enough not to ask the important questions), few of us
spend much time wondering why nature is the way it is;
where the
cosmos came from, or whether it was always here; if time will one
day flow backward and effects precede causes; or whether there are
ultimate limits to what humans can know."
Carl Sagan
From an introduction to "A Brief History of Time"
by Stephen Hawking
The overall framework of the big bang theory came out of solutions
to Einstein's general relativity field equations and remains
unchanged, but various details of the theory are still being
modified today. Einstein himself initially believed that the
universe was static. When his equations seemed to imply that the
universe was expanding or contracting, Einstein added a constant
term to cancel out the expansion or contraction of the universe.
When the expansion of the universe was later discovered, Einstein
stated that introducing this "cosmological constant" had
been a mistake. After Einstein's work of 1917, several scientists,
including the abbé Georges Lemaître in Belgium, Willem de Sitter
in Holland, and Alexander Friedmann in Russia, succeeded in finding
solutions to Einstein's field equations. The universes described by
the different solutions varied. De Sitter's model had no matter in
it. This model is actually not a bad approximation since the average
density of the universe is extremely low. Lemaître's universe
expanded from a "primeval atom." Friedmann's universe also
expanded from a very dense clump of matter, but did not involve the
cosmological constant. These models explained how the universe
behaved shortly after its creation, but there was still no
satisfactory explanation for the beginning of the universe.
In the 1940s George Gamow was joined by his students Ralph Alpher
and Robert Herman in working out details of Friedmann's solutions to
Einstein's theory. They expanded on Gamow's idea that the universe
expanded from a primordial state of matter called ylem consisting of
protons, neutrons, and electrons in a sea of radiation. They
theorized the universe was very hot at the time of the big bang (the
point at which the universe explosively expanded from its primordial
state), since elements heavier than hydrogen can be formed only at a
high temperature. Alpher and Hermann predicted that radiation from
the big bang should still exist. Cosmic background radiation roughly
corresponding to the temperature predicted by Gamow's team was
detected in the 1960s, further supporting the big bang theory,
though the work of Alpher, Herman, and Gamow had been forgotten.
The big bang theory seeks to explain what happened at or soon after
the beginning of the universe. Scientists can now model the universe
back to 10-43 seconds after the big bang. For the time before that
moment, the classical theory of gravity is no longer adequate.
Scientists are searching for a theory that merges quantum mechanics
and gravity, but have not found one yet. Many scientists have hope
that string theory will tie together gravity and quantum mechanics
and help scientists explore further back in time.
Because scientists cannot look back in time beyond that early
epoch, the actual big bang is hidden from them. There is no way at
present to detect the origin of the universe. Further, the big bang
theory does not explain what existed before the big bang. It may be
that time itself began at the big bang, so that it makes no sense to
discuss what happened "before" the big bang.
According to the big bang theory, the universe expanded rapidly
in its first microseconds. A single force existed at the beginning
of the universe, and as the universe expanded and cooled, this force
separated into those we know today: gravity, electromagnetism, the
strong nuclear force, and the weak nuclear force. A theory called
the electroweak theory now provides a unified explanation of
electromagnetism and the weak nuclear force theory. Physicists are now searching for a grand unification
theory to also incorporate the strong nuclear force. String theory
seeks to incorporate the force of gravity with the other three
forces.
One widely accepted version of big bang theory includes the idea
of inflation. In this model, the universe expanded much more rapidly
at first, to about 1050 times its original size in the first
10-32
second, then slowed its expansion. The theory was advanced in the
1980s by American cosmologist Alan Guth and elaborated upon by
American astronomer Paul Steinhardt, Russian American scientist
Andrei Linde, and British astronomer Andreas Albrecht. The
inflationary universe theory solves a
number of problems of cosmology. For example, it shows that the
universe now appears close to the type of flat space described by
the laws of Euclid's geometry: We see only a tiny region of the
original universe, similar to the way we do not notice the curvature
of the earth because we see only a small part of it. The
inflationary universe also shows why the universe appears so
homogeneous. If the universe we observe was inflated from some
small, original region, it is not surprising that it appears
uniform.
Once the expansion of the initial inflationary era ended, the
universe continued to expand more slowly. The inflationary model
predicts that the universe is on the boundary between being open and
closed. If the universe is open, it will keep expanding forever,
even though the rate of expansion will gradually slow. If the
universe is closed, the expansion of the universe will eventually
stop and the universe will begin contracting until it collapses.
Whether the universe is open or closed depends on the density, or
concentration of mass, in the universe. If the universe is dense
enough, it is closed.
The universe cooled as it expanded. After about one second, protons
formed. In the following few minutes—often referred to as the
"first three minutes," combinations of protons and
neutrons formed the isotope of hydrogen known as deuterium as well
as some of the other light elements, principally helium, as well as
some lithium, beryllium, and boron. The study of the distribution of
deuterium, helium, and the other light elements is now a major field
of research. The uniformity of the helium abundance around the
universe supports the big bang theory and the abundance of deuterium
can be used to estimate the density of matter in the universe.
From about 300,000 to about 1 million years after the big bang,
the universe cooled to about 3000° C (about 5000° F) and protons
and electrons combined to make hydrogen atoms. Hydrogen atoms can
only absorb and emit specific colors, or wavelengths, of light. The
formation of atoms allowed many other wavelengths of light,
wavelengths that had been interfering with the free electrons, to
travel much farther than before. This change set free radiation that
we can detect today. After billions of years of cooling, this cosmic
background radiation is at about 3° K (-270° C/-454° F).The
cosmic background radiation was first detected and identified in
1965 by American astrophysicists Arno Penzias and Robert Wilson.
The National Aeronautics and Space Administration's Cosmic
Background Explorer (COBE) spacecraft mapped the cosmic background
radiation between 1989 and 1993. It verified that the distribution
of intensity of the background radiation precisely matched that of
matter that emits radiation because of its temperature, as predicted
for the big bang theory. It also showed that the cosmic background
radiation is not uniform, that it varies slightly. These variations
are thought to be the seeds from which galaxies and other structures
in the universe grew.
Refining the Theory
Evidence indicates that the matter that scientists detect in the
universe is only a small fraction of all the matter that exists. For
example, observations of the speeds with which individual galaxies
move within clusters of galaxies show that there must be a great
deal of unseen matter exerting gravitational forces to keep the
clusters from flying apart.
Cosmologists now think that much of the universe - perhaps 99
percent - is dark matter, or matter that has gravity but that we
cannot see or otherwise detect. Theorized kinds of dark matter
include cold dark matter, with slowly moving (cold) massive
particles. No such particles have yet been detected, though
astronomers have given them names like Weakly Interacting Massive
Particles (WIMPs). Other cold dark matter could be nonradiating
stars or planets, which are known as MACHOs (Massive Compact Halo
Objects). An alternative model includes hot dark matter, where hot
implies that the particles are moving very fast. The fundamental
particles known as neutrinos are the prime example of hot dark
matter. If the inflationary version of big bang theory is correct,
then the amount of dark matter that exists is just enough to bring
the universe to the boundary between open and closed.
Scientists develop theoretical models to show how the universe's
structures, such as clusters of galaxies, have formed. Their models
invoke hot dark matter, cold dark matter, or a mixture of the two.
This unseen matter would have provided the gravitational force
needed to hold large structures such as clusters of galaxies
together. The theories continue to match the observations, though
there is no consensus on the type or types of dark matter that must
be included. Supercomputers are important for making such models.
Astronomers are making new observations that are
interpreted within the framework of the big bang theory. Scientists
have not found any major problems with the big bang theory, but the
theory is being constantly adjusted to match the observed universe.
Contributed By:
Jay M. Pasachoff, A.B., A.M., Ph.D.
Field Memorial Professor of Astronomy and Director of the Hopkins
Observatory, Williams College.
Author of
Astronomy: From the Earth
to the Universe, 6th ed.;
Field Guide to the Stars and Planets, 4th
ed.;
Fire in the Sky; and
Nearest Star: The Exciting Science of Our
Sun.
HOW TO CITE THIS ARTICLE
"Big Bang Theory," Microsoft® Encarta® Online
Encyclopedia 2002
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Theory of Everything
The following Section is based on:
- A Theory of Everything? Published in Mysteries of Life and the
Universe, edited by William Shore, Harcourt Brace Jovanovich, 1992.
-
Black Hole, Wormholes, and the 10th Dimension. Published in the
Sunday London Times, Literary Supplement 1994.
-
What Happened Before the Big Bang? Published in the London Daily
Telegraph. 1995.
-
Hyperspace: A Scientific Odyssey Through the 10th Dimension. Published
in Thesis Magazine. The Physics of Time Travel Reprinted from the PBS-TV Web
Page.
-
Hyperspace and the Theory of Everything Reprinted from the PBS-TV
Web Page.
-
M-theory: Mother of All Superstrings? Reprinted from Jan. 1997
issue of New Scientist magazine.
-
Before the Big Bang Reprinted from April 1996 issue of Astronomy
Magazine.
A THEORY OF EVERYTHING?
By Dr. Michio Kaku Prof. of Theoretical Physics City College of New York
When I was a child of 8, I heard a story that will stay with me for the rest
of my life. I remember my school teachers telling us about a great scientist who
had just died. They talked about him with great reverence, calling him one of
the greatest scientists in all history. They said that very few people could
understand his ideas, but that his discoveries changed the entire world and
everything around us.
But what most intrigued me about this man was that he died before he could
complete his greatest discovery. They said he spent years on this theory, but he
died with his unfinished papers still sitting on his desk. I was fascinated by
the story. To a child, this was a great mystery. What was his unfinished work?
What problem could possibly be that difficult and that important that such a
great scientist would dedicate years of his life in its pursuit? Curious, I
decided to learn all I could about Albert Einstein and his unfinished theory.
Some of the happiest moments of my childhood were spent quietly reading every
book I could find about this great man and his theories. When I exhausted the
books in our local library, I began to scour libraries and bookstores across the
city and state eagerly searching for more clues. I soon learned that this story
was far more exciting than any murder mystery and more important than anything I
could ever imagine. I decided that I would try to get t o the root of this
mystery, even if I had to become a theoretical physicist to do it.
Gradually, I began to appreciate the magnitude of his unfinished quest. I
learned that Einstein had three great theories. His first two theories, the
special and the general theory of relativity, led to the development of the
atomic bomb and the present-day theory of black holes and the Big Bang. These
two theories by themselves earned him the reputation as the greatest scientist
since Isaac Newton. However, Einstein was not satisfied. The third theory, which
he called the Unified Field Theory, was to have been his crowning achievement.
It was to be the Theory of the Universe, the Holy Grail of physics, the theory
which finally unified all physical laws into one simple framework. It was to be
the ultimate goal of all physics, the theory to end all theories.
Sadly, it consumed Einstein for the last 30 years of his life; he spent many
lonely years in a frustrating pursuit of the greatest theory of all time. But he
wasn't alone; I also learned that some of the greatest minds of the twentieth
century, such Werner Heisenberg and Wolfgang Pauli, also struggled with this
problem and ultimately gave up.
Given the fruitless search that has stumped the world's Nobel Prize winners for
half a century, most physicists agree that the Theory of Everything must be a
radical departure from everything that has been tried before. For example, Niels
Bohr, founder of the modern atomic theory, once listened to Pauli's explanation
of his version of the unified field theory. Bohr finally stood up and said,
"We are all agreed that your theory is absolutely crazy. But what divides
us is whether your theory is crazy enough."
Today, however, after decades of false starts and frustrating dead ends, many of
the world's leading physicists think that they have finally found the theory
"crazy enough" to be the Unified Field Theory. Scores of physicists in
the world's major research laboratories now believe we have at last found the
Theory of Everything.
The theory which has generated so much excitement is called the superstring
theory. Nearly every science publication in the world has featured major stories
on the superstring theory, interviewing some of its pioneers, such as John
Schwarz, Michael Green, and Yoichiro Nambu. (Discover magazine even featured it
twice on its cover.) My book, Beyond Einstein: the Cosmic Search for the Theory
of the Universe, was the first attempt to explain this fabulous theory to the
lay audience.
Naturally, any theory which claims to have solved the most intimate secrets of
the universe will be the center of intense controversy. Even Nobel Prize winners
have engaged in heated discussions about the validity of the superstring theory.
In fact, we are witnessing the liveliest debate in theoretical physics in
decades over this theory.
To understand the power of the superstring theory and why it is heralded as the
theory of the universe (and to understand the delicious controversy that it has
stirred up), it is necessary to understand that there are four forces which
control everything in the known universe, and that the superstring theory gives
us the first (and only) description which can unite all four forces into a
single framework.
The Four Fundamental Forces Over 2,000 years ago, the ancient Greeks thought
that all matter in the universe could be reduced down to four elements: air,
water, earth, and fire. Today, after centuries of research, we know that these
substances are actually composites; they, in turn, are made of smaller atoms and
sub-atomic particles, held together by just four and only four fundamental
forces.
These four forces are: Gravity is the force which keeps our feet anchored to the
spinning earth and binds the solar system and the galaxies together. If tsolar
system and the galaxies together. If the force of gravity could somehow be
turned off, we would be immediately flung into outer space at l,000 miles per
hour. Furthermore, without gravity holding the sun together, it would explode in
a catastrophic burst of energy. Without gravity, the earth and the planets would
spin out into freezing deep space, and the galaxies would fly apart.
Electro-magnetism is the force which lights up our cities and energizes our
household appliances. The electronic revolution, which has given us the light
bulb, TV, the telephone, computers, radio, radar, microwaves, light bulbs, and
dishwashers, is a byproduct of the electro-magnetic force. Without this force,
our civilization would be wrenched several hundred years into the past, into a
primitive world lit by candlelight and campfires.
The strong nuclear force is the force which powers the sun. Without the nuclear
force, the stars would flicker out and the heavens would go dark. Without the
sun, all life on earth would perish as the oceans turned to solid ice. The
nuclear force not only makes life on earth possible, it is also the devastating
force unleashed by a hydrogen bomb, which can be compared to a piece of the sun
brought down to earth.
The weak force is the force responsible for radioactive decay. The weak force is
harnessed in modern hospitals in the form of radioactive tracers used in nuclear
medicine. For example, the dramatic color pictures of the living brain as it
thinks and experiences emotions are made possible by the decay of radioactive
sugar in the brain.
It is no exaggeration to say that the mastery of each of these four fundamental
forces has changed every aspect of human civilization. For example, when Newton
tried to solve his theory of gravitation, he was forced to develop a new
mathematics and formulate his celebrated laws of motion. These laws of
mechanics, in turn, helped to usher in the Industrial Revolution, which has
lifted humanity from uncounted millennia of backbreaking labor and misery.
Furthermore, the mastery of the electromagnetic force by James Maxwell in the
1860s has revolutionized our way of life. Whenever there is a power blackout, we
are forced to live our lives much like our forebears in the last century. Today,
over half of the world's industrial wealth is now connected, in some way or
other, to the electromagnetic force. Modern civilization without the
electromagnetic force is unthinkable.
Similarly, when the nuclear force was unleashed with the atomic bomb, human
history, for the first time, faced a new and frightening set of choices,
including the total annihilation of all life on earth. With the nuclear force,
we could finally understand the enormous engine that lies within the sun and the
stars, but we could also glimpse for the first time the end of humanity itself.
Thus, whenever scientists unraveled the secrets of one of the four fundamental
forces, it irrevocably altered the course of modern civilization. In some sense,
some of the greatest breakthroughs in the history of the sciences can be traced
back to the gradual understanding of these four fundamental forces. Some have
said that the progress of the last 2,000 years of science can be summarized by
the mastery of these four fundamental forces.
Given the importance of these four fundamental forces, the next question is: can
they be united into one super force? Are they but the manifestations of a deeper
reality?
Two Great Theories At present there are two physical frameworks which have
partially explained the mysterious features of these four fundamental forces.
Remarkably, these two formalisms, the quantum theory and general relativity,
allow us to explain the sum total of all physical knowledge at the fundamental
level. Without exception. The laws of physics and chemistry, which can fill
entire libraries with technical journals and books, can in principle be derived
from these two fundamental theories, making them the most successful physical
theories of all time, withstanding the test of thousands of experiments and
challenges.
Ironically, these two fundamental frameworks are diametrically opposite to each
other. The quantum theory, for example, is the theory of the microcosm, with
unparalleled success at describing the sub-atomic world. The theory of
relativity, by contrast, is a theory of the macrocosmic world, the world of
galaxies, super clusters, black holes, and Creation itself.
The quantum theory explains three of the four forces (the weak, strong, and
electro-magnetic forces) by postulating the exchange of tiny packets of energy,
called "quanta." When a flashlight is turned on, for example, it emits
trillions upon trillion of photons, or the quanta of light. Everything from
lasers to radar waves can be described by postulating that they are caused by
the movement of these tiny photons of energy. Likewise, the weak force is
governed by the exchange of subatomic particles called W-bosons. The strong
nuclear force, in turn, binds the proton together by the exchange of
"gluons."
However, the quantum theory stands in sharp contrast to Einstein's general
relativity, which postulates an entirely different physical picture to explain
the force of gravity.
Imagine, for the moment, dropping a heavy shot put on a large bed spread. The
shot put will, of course, sink deeply into the bed spread. Now imagine shooting
a small marble across the bed. Since the bed is warped, the marble will execute
a curved path. However, for a person viewing the marble from a great distance,
it will appear that the shot put is exerting an invisible "force" on
the marble, forcing it to move in a curved path. In other words, we can now
replace the clumsy concept of a "force" with the more elegant bending
of space itself. We now have an entirely new definition of a "force."
It is nothing but the byproduct of the warping of space.
In the same way that a marble moves on a curved bed sheet, the earth moves
around the sun in a curved path because space-time itself is curved. In this new
picture, gravity is not a "force" but a byproduct of the warping of
space-time. In some sense, gravity does not exist; what moves the planets and
stars is the distortion of space and time.
However, the problem which has stubbornly resisted solution for 50 years is that
these two frameworks do not resemble each other in any way. The quantum theory
reduces "forces" to the exchange of discrete packet of energy or
quanta, while Einstein's theory of gravity, by contrast, explains the cosmic
forces holding the galaxies together by postulating the smooth deformation of
the fabric of space-time. This is the root of the problem, that the quantum
theory and general relativity have two different physical pictures (packets of
energy versus smooth space-time continuums) and different mathematics to
describe them.
All attempts by the greatest minds of the twentieth century at merging the
quantum theory with the theory of gravity have failed. Unquestionably, the
greatest problem of the century facing physicists today is the unification of
these two physical frameworks into one theory.
This sad state of affairs can be compared to Mother Nature having two hands,
neither of which communicate with the other. Nothing could be more awkward or
pathetic than to see someone whose left hand acted in total ignorance of the
right hand.
Superstrings Today, however, many physicists think that we have finally solved
this long-standing problem. This theory, which is certainly "crazy
enough" to be correct, has astounded the world's physics community. But it
has also raised a storm of controversy, with Nobel Prize winners adamantly
sitting on opposite sides of the fence. This is the superstring theory, which
postulates that all matter and energy can be reduced to tiny strings of energy
vibrating in a 10 dimensional universe.
Edward Witten of the Institute for Advanced Study at Princeton, who some claim
is the successor to Einstein, has said that superstring theory will dominate the
world of physics for the next 50 years, in the same way that the quantum theory
has dominated physics for the last 50 years.
As Einstein once said, all great physical theories can be represented by simple
pictures. Similarly, superstring theory can be explained visually. Imagine a
violin string, for example. Everyone knows that the notes A,B,C, etc. played on
a violin string are not fundamental. The note A is no more fundamental than the
note B. What is fundamental, of course, is the violin string itself. By studying
the vibrations or harmonics that can exist on a violin string, one can calculate
the infinite number of possible frequencies that can exist.
Similarly, the superstring can also vibrate in different frequencies. Each
frequency, in turn, corresponds to a sub-atomic particle, or a
"quanta." This explains why there appear to be an infinite number of
particles. According to this theory, our bodies, which are made of sub-atomic
particles, can be described by the resonances of trillions upon trillions of
tiny strings.
In summary, the "notes" of the superstring are the subatomic
particles, the "harmonies" of the superstring are the laws of physics,
and the "universe" can be compared to a symphony of vibrating
superstrings.
As the string vibrates, however, it causes the surrounding space-time continuum
to warp around it. Miraculously enough, a detailed calculation shows that the
superstring forces the space-time continuum to be distorted exactly as Einstein
originally predicted. Thus, we now have a harmonious description which merges
the theory of quanta with the theory of space-time continuum.
10 Dimensional Hyperspace The superstring theory represents perhaps the most
radical departure from ordinary physics in decades. But its most controversial
prediction is that the universe originally began in 10 dimensions. To its
supporters, the prediction of a 10 dimensional universe has been a conceptual
tour de force, introducing a startling, breath-taking mathematics into the world
of physics. To the critics, however, the introduction of 10 dimensional
hyperspace borders on science fiction.
To understand these higher dimensions, we remember that it takes three number to
locate every object in the universe, from the tip of your nose to the ends of
the universe.
For example, if you want to meet some friends for lunch in Manhattan, you say
that you will meet them at the building at the corner of 42nd and 5th Ave, on
the 37th floor. It takes two numbers to locate your position on a map, and one
number to specify the distance above the map. It thus takes three numbers to
specify the location of your lunch.
However, the existence of the fourth spatial dimension has been a lively area of
debate since the time of the Greeks, who dismissed the possibility of a fourth
dimension. Ptolemy, in fact, even gave a "proof" that higher
dimensions could not exist. Ptolemy reasoned that only three straight lines can
be drawn which are mutually perpendicular to each other (for example, the three
perpendicular lines making up a corner of a room.) Since a fourth straight line
cannot be drawn which is mutually perpendicular to the other three axes, Ergo!,
the fourth dimension cannot exist.
What Ptolemy actually proved was that it is impossible for us humans to
visualize the fourth dimension. Although computers routinely manipulate
equations in N-dimensional space, we humans are incapable of visualizing spatial
dimensions beyond three.
The reason for this unfortunate accident has to do with biology, rather than
physics. Human evolution put a premium on being able to visualize objects moving
in three dimensions. There was a selection pressure placed on humans who could
dodge lunging saber tooth tigers or hurl a spear at a charging mammoth.
Since tigers do not attack us in the fourth dimension, there simply was no
advantage in developing a brain with the ability to visualize objects moving in
four dimensions.
From a mathematical point of view, however, adding higher dimensions is a
distinct advantage: it allows us to describe more and more forces. There is more
"room" in higher dimensions to insert the electromagnetic force into
the gravitational force. (In this picture, light becomes a vibration in the
fourth dimension.) In other words, adding more dimensions to a theory always
allows us to unify more laws of physics.
A simple analogy may help. The ancients were once puzzled by the weather. Why
does it get colder as we go north? Why do the winds blow to the West? What is
the origin of the seasons? To the ancients, these were mysteries that could not
be solved. From their limited perspective, the ancients could never find the
solution to these mysteries.
The key to these puzzles, of course, is to leap into the third dimension, to go
up into outer space, to see that the earth is actually a sphere rotating around
a tilted axis. In one stroke, these mysteries of the weather become transparent.
The seasons, the winds, the temperature patterns, etc. all become obvious once
we leap into the third dimension.
Likewise, the superstring is able to accommodate a large number of forces
because it has more "room" in its equations to do so.
What Happened Before the Big Bang? One of the nagging problems of Einstein's old
theory of gravity was that it did not explain the origin of the Big Bang. It did
not give us a clue as to what happened before the Big Bang. The 10 dimensional
superstring theory, however, gives us a compelling explanation of the origin of
the Big Bang. According to the superstring theory, the universe originally
started as a perfect 10 dimensional universe with nothing in it.
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 curled up into a tiny ball,
allowing the remaining four dimensional universe to inflate at enormous rates.
The four dimensional universe (our world) expanded rapidly, eventually creating
the Big Bang, while the six dimensional universe wrapped itself into a ball and
collapsed down to infinitesimal size. This explains the origin of the Big Bang,
which is now viewed as 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, it also explains why we cannot measure the six dimensional
universe, because it has shrunk down to a size smaller than an atom. Thus, no
earth-bound experiment can measure the six dimension.
Recreating Creation Although the superstring theory has been called the most
sensational 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 necessarily
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 on the earth, therefore, means
to recreate Creation on the earth, which is impossible with present-day
technology.
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 - Biggest Experiment of All Time These questions about unifying the
fundamental forces are not academic, because the largest scientific machine ever
built, the SSC, may be built to test some of these ideas about the instant of
Creation. (Although the SSC was originally approved by the Reagan
administration, the project, because of its enormous cost, is still
touch-and-go, depending every year on Congressional funding.) The SSC is
projected to accelerate protons to a staggering energy of tens of trillions of
electron volts. When these subatomic particles slam into each other at these
fantastic energies, the SSC will create temperatures which have not been seen
since the instant of Creation (although it is still too weak to fully test the
superstring theory). That is why it is sometimes called a "window on
Creation."
The SSC is projected to cost over $8 billion (which is large compared to the
science budget, but insignificant compared to the Pentagon budget). By every
measure, it will be a colossal machine. It will consist of a ring of powerful
magnets stretched out in a tube over 50 miles in diameter. In fact, one could
easily fit the Washington Beltway, which surrounds Washington D.C., inside the
SSC. Inside this gigantic tube, protons will be accelerated to unimaginable
energies.
At present, it is scheduled to be finished near the turn of the century in
Texas, near the city of Austin. When completed, it will employ thousands of
physicists and engineers and cost millions of dollars to operate.
At the very least, physicists hope that the SSC will find some exotic sub-atomic
particles, such as the "Higgs boson" and the "top quark," in
order to complete our present-day understanding of the quantum theory. However,
there is also the small chance that physicists might discover "supersymmetric"
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.
Parable of the Gemstone To understand the intense controversy surrounding
superstring theory, think of the following parable. Imagine that, at the
beginning of time, there was once a beautiful, glittering gemstone. Its perfect
symmetries and harmonies were a sight to behold. However, it possessed a tiny
flaw and became unstable, eventually exploding into thousands of tiny pieces.
Imagine that the fragments of the gemstone rained down on a flat,
two-dimensional world, called Flatland, where there lived a mythical race of
beings called Flatlanders.
These Flatlanders were intrigued by the beauty of the fragments, which could be
found scattered all over Flatland. The scientists of Flatland postulated that
these fragments must have come from a crystal of unimaginable beauty that
shattered in a titanic Big Bang. They then decided to embark upon a noble quest,
to reassemble all these pieces of the gemstone.
After 2,000 years of labor by the finest minds of Flatland, they were finally
able to fit many, but certainly not all, of the fragments together into two
chunks. The first chunk was called the "quantum," and the second chunk
was called "relativity."
Although they Flatlanders were rightfully proud of their progress, they were
dismayed to find that these two chunks did not fit together. For half a century,
the Flatlanders maneuvered these two chunks in all possible ways, and they still
did not fit.
Finally, some of the younger, more rebellious scientists suggested a heretical
solution: perhaps these two chunks could fit together if they were moved in the
third dimension.
This immediately set off the greatest scientific controversy in years. The older
scientists scoffed at this idea, because they didn't believe in the unseen third
dimension. "What you can't measure doesn't exist," they declared.
Furthermore, even if the third dimension existed, one could calculate that the
energy necessary to move the pieces up off Flatland would exceed all the energy
available in Flatland. Thus, it was an untestable theory, the critics shouted.
However, the younger scientists were undaunted. Using pure mathematics, they
could show that these two chunks fit together if they were rotated and moved in
the third dimension. The younger scientists claimed that the problem was
therefore theoretical, rather than experimental. If one could completely solve
the equations of the third dimension, then one could, in principle, fit these
two chunks completely together and resolve the problem once and for all.
We Are Not Smart Enough
That is also the conclusion of today's superstring enthusiasts, that 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 gigantic atom smashers; the problem
is being clever enough to solve the theory.
Edward Witten, 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 superstring theory was discovered almost 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
has been that 21st century mathematics has not yet been discovered. In other
words, although the string equations are perfectly well-defined, no one is smart
enough to solve them.
This situation is not entirely new to the history of physics. When Newton first
discovered the universal law of gravitation at the age of 23, he was unable to
solve his equation because the mathematics of the 17th century was too
primitive. He then labored over the next 20 years to develop a new mathematical
formalism (calculus) which was powerful enough to solve his universal law of
gravitation.
Similarly, the fundamental problem facing the superstring theory is theoretical.
If we could only sharpen our analytical skills and develop more powerful
mathematical tools, like Newton before us, perhaps we could solve the theory and
end 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 solve them. The search for the theory of the universe is perhaps
finally entering its last phase, awaiting the birth of a new mathematics
powerful enough to solve it.
Imagine a child gazing at a TV set. The images and stories conveyed on the
screen are easily understood by the child, 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 superstring theory works.
In conclusion, perhaps some of the readers will be inspired by this story to
read every book in their libraries about the superstring theory. Perhaps some of
the young readers of this article will be the ones to complete this quest for
the Theory of the Universe, begun so many years ago by Einstein.
Dr. Kaku is author of Beyond Einstein (Bantam) and the forthcoming book,
Hyperspace, upon which this article is based.
BLACK HOLES, WORMHOLES, AND THE 10Th DIMENSION
Dr. Kaku is professor of theoretical physics at the City Univ. of New York
and author of Hyperspace: A Scientific Odyssey Through Parallel Universe, Time
Warps, and the 10th Dimension (Oxford Univ. Press).
Last June, astronomers were toasting each other with champagne glasses in
laboratories around the world, savoring their latest discovery. The repaired $2
billion Hubble Space Telescope, once the laughing stock of the scientific
community, had snared its most elusive prize: a black hole.
But the discovery of the Holy Grail of astrophysics may also rekindle a long
simmering debate within the physics community. What lies on the other side of a
black hole? If someone foolishly fell into a black hole, will they be crushed by
its immense gravity, as most physicists believe, or will they be propelled into
a parallel universe or emerge in another time era?
To solve this complex question, physicists are opening up one of the most
bizarre and ttantalizing chapters in modern physics. They have to navigate a
minefield of potentially explosive theories, such as the possibility of
"wormholes," "white holes," time machines, and even the 10th
dimension!
This controversy may well validate J.B.S. Haldane's wry observation that the
universe is "not only queerer than we sup- pose, it is queerer than we can
suppose."
This delicious controversy, which delights theoretical physicists but boggles
the mind of mere mortals, is the subject of my recent book, Hyperspace.
BLACK HOLES: COLLAPSED STARS
A black hole, simply put, is a massive, dead star whose gravity is so intense
than even light cannot escape, hence its name. By definition, it can't be seen,
so NASA scientists focused instead on the tiny core of the galaxy M87, a super
massive "cosmic engine" 50 million light years from earth.
Astronomers then showed that the core of M87 consisted of a ferocious, swirling
maelstrom of superhot hydrogen gas spinning at l.2 million miles per hour. To
keep this spinning disk of gas from violently flying apart in all directions,
there had to be a colossal mass concentrated at its center, weighing as much as
2 to 3 billion suns! An object with that staggering mass would be massive enough
to prevent light from escaping. Ergo, a black hole.
THE EINSTEIN-ROSEN BRIDGE
But this also revives an ongoing controversy surrounding black holes. The
best description of a spinning black hole was given in 1963 by the New Zealand
mathematician Roy Kerr, using Einstein's equations of gravity. But there is a
quirky feature to his solution. It predicts that if one fell into a black hole,
one might be sucked down a tunnel (called the "Einstein-Rosen bridge")
and shot out a "white hole" in a parallel universe!
Kerr showed that a spinning black hole would collapse not into a point, but to a
"ring of fire." Because the ring was spinning rapidly, centrifugal
forces would keep it from collapsing. Remarkably, a space probe fired directly
through the ring would not be crushed into oblivion, but might actually emerge
unscratched on the other side of the Einstein-Rosen bridge, in a parallel
universe. This "wormhole" may connect two parallel universes, or even
distant parts of the same universe.
THROUGH THE LOOKING GLASS
The simplest way to visualize a Kerr wormhole is to think of Alice's Looking
Glass. Anyone walking through the Looking Glass would be transported instantly
into Wonderland, a world where animals talked in riddles and common sense wasn't
so common.
The rim of the Looking Glass corresponds to the Kerr ring. Anyone walking
through the Kerr ring might be transported to the other side of the universe or
even the past. Like two Siamese twins joined at the hip, we now have two
universes joined via the Looking Glass.
Some physicists have wondered whether black holes or worm- holes might someday
be used as shortcuts to another sector of our universe, or even as a time
machine to the distant past (making possible the swashbuckling exploits in Star
Wars). However, we caution that there are skeptics. The critics concede that
hundreds of wormhole solutions have now been found to Einstein's equations, and
hence they cannot be lightly dismissed as the ravings of crack pots. But they
point out that wormholes might be unstable, or that intense radiation and
sub-atomic forces surrounding the entrance to the wormhole would kill anyone who
dared to enter.
Spirited debates have erupted between physicists concerning these wormholes.
Unfortunately, this controversy cannot be re- solved, because Einstein's
equations break down at the center of black holes or wormholes, where radiation
and sub-atomic forces might be ferocious enough to collapse the entrance. The
problem is Einstein's theory only works for gravity, not the quantum forces
which govern radiation and sub-atomic particles. What is needed is a theory
which embraces both the quantum theory of radiation and gravity simultaneously.
In a word, to solve the problem of quantum black holes, we need a "theory
of everything!"
A THEORY OF EVERYTHING?
One of the crowning achievements of 20th century science is that all the laws
of physics, at a fundamental level, can be summarized by just two formalisms:
(1) Einstein's theory of gravity, which gives us a cosmic description of the
very large, i.e. galaxies, black holes and the Big Bang, and (2) the quantum
theory, which gives us a microscopic description of the very small, i.e. the
microcosm of sub-atomic particles and radiation.
But the supreme irony, and surely one of Nature's cosmic jokes, is that they
look bewilderingly different; even the world's greatest physicists, including
Einstein and Heisenberg, have failed to unify these into one. The two theories
use different mathematics and different physical principles to describe the
universe in their respective domains, the cosmic and the microscopic.
Fortunately, we now have a candidate for this theory. (In fact, it is the only
candidate. Scores of rival proposals have all been shown to be inconsistent.)
It's called "superstring theory," and almost effortlessly unites
gravity with a theory of radiation, which is required to solve the problem of
quantum wormholes.
The superstring theory can explain the mysterious quantum laws of sub-atomic
physics by postulating that sub-atomic particles are really just resonances or
vibrations of a tiny string. The vibrations of a violin string correspond to
musical notes; likewise the vibrations of a superstring correspond to the
particles found in nature. The universe is then a symphony of vibrating strings.
An added bonus is that, as a string moves in time, it warps the fabric of space
around it, producing black holes, wormholes, and other exotic solutions of
Einstein's equations. Thus, in one stroke, the superstring theory unites both
the theory of Einstein and quantum physics into one coherent, compelling
picture.
A 10 DIMENSIONAL UNIVERSE
The curious feature of superstrings, however, is that they can only vibrate
in 10 dimensions. This is, in fact, one of the reasons why it can unify the
known forces of the universe: in 10 dimensions there is "more room" to
accommodate both Einstein's theory of gravity as well as sub-atomic physics. In
some sense, previous attempts at unifying the forces of nature failed because a
standard four dimensional theory is "too small" to jam all the forces
into one mathematical framework. To visualize higher dimensions, consider a
Japanese tea garden, where carp spend their entire lives swimming on the bottom
of a shallow pond. The carp are only vaguely aware of a world beyond the
surface. To a carp "scientist," the universe only consists of two
dimensions, length and width. There is no such thing as "height." In
fact, they are incapable of imagining a third dimension beyond the pond. The
word "up" has no meaning for them. (Imagine their distress if we were
to suddenly lift them out of their two dimensional universe into
"hyperspace," i.e. our world!)
However, if it rains, then the surface of their pond becomes rippled. Although
the third dimension is beyond their comprehension, they can clearly see the
waves traveling on the pond's surface. Likewise, although we earthlings cannot
"see" these higher dimensions, we can see their ripples when they
vibrate. According to this theory, "light" is nothing but vibrations
rippling along the 5th dimension. By adding higher dimensions, we can easily
accommodate more and more forces, including the nuclear forces. In a nutshell:
the more dimensions we have, the more forces we can accommodate.
One persistent criticism of this theory, however, is that we do not see these
higher dimensions in the laboratory. At present, every event in the universe,
from the tiniest sub-atomic decay to exploding galaxies, can be described by 4
numbers (length, width, depth, and time), not 10 numbers. To answer this
criticism, many physicists believe (but cannot yet prove) that the universe at
the instant of the Big Bang was in fact fully 10 dimensional. Only after the
instant of creation did 6 of the 10 dimensions "curled up" into a ball
too tiny to observe. In a real sense, this theory is really a theory of
creation, when the full power of 10 dimensional space-time was manifest.
21St CENTURY PHYSICS
Not surprisingly, the mathematics of the 10th dimensional superstring is
breathtakingly beautiful as well as brutally complex, and has sent shock waves
through the mathematics community. Entirely new areas of mathematics have been
opened up by this theory. Unfortunately, at present no one is smart enough to
solve the problem of a quantum black hole. As Edward Witten of the Institute for
Advanced Study at Princeton has claimed, "String theory is 21st century
physics that fell accidentally into the 20th century. However, since the stakes
are so high, that hasn't stopped teams of enterprising physicists from trying to
solve superstring theory. Already, over 5,000 papers have been written on the
subject. As Nobel laureate Steve Weinberg said, "how can anyone expect that
many of the brightest young theorists would not work on it?"
Progress has been slow but steady. Last year, a significant breakthrough was
announced. Several groups of physicists independently announced that string
theory can completely solve the problem of a quantum black hole. (However, the
calculation was so fiendishly difficult it could only be performed in two, not
10, dimensions.)
So that's where we stand today. Many physicists now feel that it's only a matter
of time before some enterprising physicist completely cracks this ticklish
problem. The equations, although difficult, are well-defined. So until then,
it's still a bit premature to buy tickets to the nearest wormhole to visit the
next galaxy or hunt dinosaurs!
WHAT HAPPENED BEFORE THE BIG BANG?
Einstein's theory of gravity, which gives us the Big Bang theory and black
holes, was subjected to the most stringent test yet and passed with flying
colors. In the October '95 issue of Physics Today, astronomers from Harvard,
MIT, and the Haystack Observatory proudly announced that they had confirmed
Einstein's theory to within an astonishing .04% accuracy by measuring the
bending of radio waves from the quasar 3C279 near the edge of the visible
universe.
But there is some irony in this announcement. Each success only highlights a
yawning gap. Even as scientists hail ever more accurate tests of Einstein's
theory of warped space, Einstein himself knew that his theory broke down at the
instant of the Big Bang. The theory had feet of clay.
Relativity was worthless, he realized, when it came to answering the most
embarrassing cosmic question in all of science:
What happened before the Big
Bang?
Ask any cosmologist this question, and they will throw up their hands,
roll their eyes, and lament, "This may be forever beyond the reach of
science. We just don't know." Until now, that is.
A remarkable consensus has been developing recently around what is called
"quantum cosmology," where scientists believe that a merger of the
quantum theory and Einstein's relativity may resolve these sticky theological
questions. Theoretical physicists are rushing in where the angels fear to tread!
In particular, an appealing but starting new picture is emerging in quantum
cosmology which may be able to synthesize some of the great mythologies of
creation.
There are two dominant religious mythologies.
According to Judeo-Christian
belief, the universe had a definite beginning. This is the Genesis hypothesis,
where the universe was hatched from a Cosmic Egg. However, according to the
Hindu-Buddhist belief in Nirvana, the universe is timeless; it never had a
beginning, nor will it have an end.
Quantum cosmology proposes a beautiful synthesis of these seemingly hostile
viewpoints. In the beginning was Nothing. No space, no matter or energy. But
according to the quantum principle, even Nothing was unstable. Nothing began to
decay; i.e. it began to "boil," with billions of tiny bubbles forming
and expanding rapidly. Each bubble became an expanding universe.
If this is true, then our universe is actually part of a much larger "multiverse"
of parallel universes, which is truly timeless, like Nirvana.
As Nobel laureate Steve Weinberg has said, "An important implication is
that there wasn't a beginning; that there were increasingly large Big Bangs, so
that the [multiverse] goes on forever - one doesn't have to grapple with the
question of it before the Bang. The [multiverse] has just been here all along. I
find that a very satisfying picture."
Universes can literally spring into existence as a quantum fluctuation of
Nothing. (This is because the positive energy found in matter is balanced
against the negative energy of gravity, so the total energy of a bubble is zero.
Thus, it takes no net energy to create a new universe.)
As Alan Guth, originator of the inflationary theory, once said, "It's often
said there is no such thing as a free lunch. But the universe itself may be a
free lunch."
Andre Linde of Stanford has said, "If my colleagues and I are right, we may
soon be saying good-bye to the idea that our universe was a single fireball
created in the Big Bang."
Although this picture is appealing, it also raises more questions. Can life
exist on these parallel universes? Stephen Hawking is doubtful; he believes that
our universe may co-exist with other universes, but our universe is special. The
probability of forming these other bubbles is vanishingly small.
On the other hand, Weinberg believes most of these parallel universes are
probably dead. To have stable DNA molecules, the proton must be stable for at
least 3 billion years. In these dead universes, the protons might have decayed
into a sea of electrons and neutrinos.
Our universe may be one of the few compatible with life. This would, in fact,
answer the age-old question of why the physical constants of the universe fall
in a narrow band compatible with the formation of life. If the charge of the
electron, the gravitational constant, etc. were changed slightly, then life
would have been impossible. This is called the Anthropic Principle. As Freeman
Dyson of Princeton said, "It's as if the universe knew we were
coming." The strong version of this states that this proves the existence
of God or an all-powerful deity.
But according to quantum cosmology, perhaps there are millions of dead
universes. It was an accident, therefore, that our universe had conditions
compatible with the formation of stable DNA molecules.
This leaves open the possibility, however, that there are parallel universes out
there which are almost identical to ours, except for some fateful incident.
Perhaps King George III did not lose the Colonies in one such universe.
However, I can calculate the probability that one day you might be walking down
the street, only to fall into hole in space and enter a parallel universe. You
would have to wait longer than the lifetime of the universe for such a cosmic
event to happen. So I guess the United States is safe for the present!
As J.B.S. Haldane once said, "the universe is not only queerer than we
suppose, it is queerer than we can suppose."
Dr. Michio Kaku is Prof. of theoretical physics at the City University of New York
and author of Hyperspace: a Scientific Odyssey through the 10th Dimension
(Oxford Univ. Press).
HYPERSPACE: A SCIENTIFIC ODYSSEY THROUGH THE TENTH
DIMENSION
Dr. Michio Kaku is professor of theoretical physics at the CUNY Graduate
Center and CCNY. This article is adapted from his next book, Hyperspace: A
Scientific Odyssey through Parallel Universes, Time Warps, and the 10th
Dimension (Oxford). He is the author of Introduction to Superstrings (Springer-Verlag).
Do higher dimensions exist? Are there unseen worlds just beyond our reach,
beyond the normal laws of physics?
Although higher dimensions have historically been the exclusive realm of
charlatans, mystics, and science fiction writers, many serious theoretical
physicists now believe that higher dimensions not only exist, but may also
explain some of the deepest secrets of nature. Although we stress that there is
at present no experimental evidence for higher dimensions, in principle they may
solve the ultimate problem in physics: the final unification of all physical
knowledge at the fundamental level.
My own fascination with higher dimensions began early in childhood. One of my
happiest childhood memories was crouching next to the pond at the famed Japanese
Tea Garden in San Francisco, mesmerized by the brilliantly colored carp swimming
slowly beneath the water lilies. In these quiet moments, I would ask myself a
silly question that a only child might ask: how would the carp in that pond view
the world around them?
Spending their entire lives at the bottom of the pond, the carp would believe
that their "universe" consisted of the water and the lilies; they
would only be dimly aware that an alien world could exist just above the
surface. My world was beyond their comprehension. I was intrigued that I could
sit only a few inches from the carp, yet we were separated by an immense chasm.
I concluded that if there were any "scientists" among the carp, they
would scoff at any fish who proposed that a parallel world could exist just
above the lilies. An unseen world beyond the pond made no scientific sense.
Once I imagined what would happen if I reached down and suddenly grabbed one of
the carp "scientists" out of the pond. I wondered, how would this
appear to the carp?
The startled carp "scientist" would tell a truly amazing story, being
somehow lifted out of the universe (the pond) and hurled into a mysterious
nether world, another dimension with blinding lights and strange-shaped objects
that no carp had ever seen before. The strangest of all was the massive creature
responsible for this outrage, who did not resemble a fish in the slightest.
Shockingly, it had no fins whatsoever, but nevertheless could move without them.
Obviously, the familiar laws of physics no longer applied in this nether world!
THE THEORY OF EVERYTHING
Sometimes I believe that we are like the carp living contently on the bottom
of that pond; we live our lives blissfully ignorant of other worlds that might
co-exist with us, laughing at any suggestion of parallel universes.
All this has changed rather dramatically in the past few years. The theory of
higher dimensional space may now become the central piece in unlocking the
origin of the universe. At the center of this conceptual revolution is the idea
that our familiar three dimensional universe is "too small" to
describe the myriad forces governing our universe.
To describe our physical world, with its almost infinite variety of forms,
requires entire libraries overflowing with mountains of technical journals and
stacks of obscure, learned books. The ultimate goal of physics, some believe, is
to have a single equation or expression from which this colossal volume of
information can be derived from first principles.
Today, many physicists believe that we have found the "unified field
theory" which eluded Einstein for the last thirty years of his life.
Although the theory of higher dimensional space has not been verified (and, we
shall see, would be prohibitively expensive to prove experimentally), almost
5,000 papers, at last count, have been published in the physics literature
concerning higher dimensional theories, beginning with the pioneering papers of
Theodore Kaluza and Oskar Klein in the 1920's and 30s, to the supergravity
theory of the 1970s, and finally to the superstring theory of the 1980s and 90s.
In fact, the superstring theory, which postulates that matter consists of tiny
strings vibrating in hyperspace, predicts the precise number of dimensions of
space and time: 10. (See xxxx issue of Thesis.)
WHY CAN'T WE SEE THE FOURTH DIMENSION?
To understand these higher dimensions, we remember that it takes three
numbers to locate every object in the universe, from the tip of your nose to the
ends of the world. For example, if you want to meet some friends in Manhattan,
you tell them to meet you at the building at the corner of 42nd street and 5th
avenue, on the 37th floor. It takes two numbers to locate your position on a
map, and one number to specify the distance above the map. It thus takes three
numbers to specify the location of your lunch. (If we meet our friends at noon,
then it takes four numbers to specify the space and time of the meeting.)
However, try as we may, it is impossible for our brains to visualize the fourth
spatial dimension. Computers, of course, have no problem working in N
dimensional space, but spatial dimensions beyond three simply cannot be
conceptualized by our feeble brains. (The reason for this unfortunate accident
has to do with biology, rather than physics. Human evolution put a premium on
being able to visualize objects moving in three dimensions. There was a
selection pressure placed on humans who could dodge lunging saber tooth tigers
or hurl a spear at a charging mammoth. Since tigers do not attack us in the
fourth spatial dimension, there simply was no advantage in developing a brain
with the ability to visualize objects moving in four dimensions.)
MEETING A HIGHER DIMENSIONAL BEING
To understand some of the mind-bending features of higher dimensions, imagine
a two-dimensional world, called Flat land (after Edwin A. Abbott's celebrated
novel) that resembles a world existing on a flat table-top.
If one of the Flatlanders becomes lost, we can quickly scan all of Flatland,
peering directly inside houses, buildings, and even concealed places. If one of
the Flatlanders becomes sick, we can reach directly into their insides and per
form surgery, without ever cutting their skin. If one of the Flatlanders is
incarcerated in jail (which is a circle enclosing the Flatlander) we can simply
peel the person off from Flatland into the third dimension and place the
Flatlander back somewhere else.
If we become more ambitious and stick our fingers and arms through Flatland, the
Flatlanders would only see circles of flesh that hover around them, constantly
changing shape and merging into other circles. And lastly, if we fling a
FlatlFlatlanders would only see circles of flesh that hover around them,
constantly changing shape and merging into other circles. And lastly, if we
fling a Flatlander into our three dimensional world, the Flatlander can only
Now imagine that we are "three dimensional Flatlanders" being visited
by a higher dimensional being. If we became lost, a higher dimensional being
could scan our entire universe all at once, peering directly into the most
tightly sealed hiding places. If we became sick, a higher dimensional being
could reach into our insides and perform surgery without ever cutting our skin.
If we were in a maximum-security, escape-proof jail, a higher dimensional being
could simply "yank" us into a higher dimension and redeposit us back
somewhere else. If higher dimensional beings stick their "fingers"
into our universe, they would appear to us to be blobs of flesh which float
above us and constantly merge and split apart. And lastly, if we are flung into
hyperspace, we would see a collection of spheres, blobs, and polyhedra which
suddenly appear, constantly change shape and color, and then mysteriously
disappear.
Higher dimensional people, therefore, would have powers similar to a god: they
could walk through walls, disappear and reappear at will, reach into the
strongest steel vaults, and see through buildings. They would be omniscient and
omnipotent. Not surprisingly, speculation about higher dimensions has sparked
enormous literary and artistic interest over the last hundred years.
MYSTICS AND MATHEMATICIANS
Fyodor Dostoyevsky, in The Brothers Karamazov, had his protagonist Ivan
Karamazov speculate on the existence of higher dimensions and non-Euclidean
geometries during a discussion on the existence of God. In H. G. Wells' The
Invisible Man, the source of invisibility was his ability to manipulate the
fourth dimension. Oscar Wilde even refers to the fourth dimension in his play
The Canterville Ghost as the homeworld for ghosts.
The fourth dimension also appears in the literary works of Marcel Proust and
Joseph Conrad; it inspired some of the musical works of Alexander Scriabin,
Edgar Varege, and George Antheil. It fascinated such diverse personalities as
the psychologist William James, literary figure Gertrude Stein, and
revolutionary socialist Vladimir Lenin.
Lenin even waged a polemic on the N-th dimension with philosopher Ernst Mach in
his Materialism and Empirio-Criticism. Lenin praised Mach, who "has raised
the very important and useful question of a space of n-dimensions as a
conceivable space," but then took him to task by insisting that the Tsar
could only be overthrown in the third dimension.
Artists have been particularly interested in the fourth dimension because of the
possibilities of discovering new laws of perspective. In the Middle Ages,
religious art was distinctive for its deliberate lack of perspective. Serfs,
peasants, and kings were depicted as if they were flat, much the way children
draw people. Since God was omnipotent and could therefore see all parts of our
world equally, art had to reflect His point of view, so the world was painted
two-dimensionally.
Renaissance art was a revolt against this flat God- centered perspective.
Sweeping landscapes and realistic, three dimensional people were painted from
the point of view of a person's eye, with the lines of perspective vanishing
into the horizon. Renaissance art reflected the way the human eye viewed the
world, from the singular point of view of the observer. In other words,
Renaissance art discovered the third dimension.
With the beginning of the machine age and capitalism, the artistic world
revolted against the cold materialism that seemed to dominate industrial
society. To the Cubists, positivism was a straitjacket that confined us to what
could be measured in the laboratory, suppressing the fruits of our imagination.
They asked: Why must art be clinically "realistic?" This Cubist
"revolt against perspective" seized the fourth dimension because it
touched the third dimension from all possible perspectives. Simply put, Cubist
art embraced the fourth dimension.
Picasso's paintings are a splendid example, showing a clear rejection of three
dimensional perspective, with women's faces viewed simultaneously from several
angles. Instead of a single point-of-view, Picasso's paintings show multiple
perspectives, as if they were painted by a being from the fourth dimension, able
to see all perspectives simultaneously.
As art historian Linda Henderson has written, "the fourth dimension and
non-Euclidean geometry emerge as among the most important themes unifying much
of modern art and theory."
UNIFYING THE FOUR FORCES
Historically, physicists dismissed the theory of higher dimensions because
they could never be measured, nor did they have any particular use. But to
understand how adding higher dimensions can, in fact, simplify physical
problems, consider the following example. To the ancient Egyptians, the weather
was a complete mystery. What caused the seasons? Why did it get warmer as they
traveled south? The weather was impossible to explain from the limited vantage
point of the ancient Egyptians, to whom the earth appeared flat, like a
two-dimensional plane.
But now imagine sending the Egyptians in a rocket into outer space, where they
can see the earth as simple and whole in its orbit around the sun. Suddenly, the
answers to these questions become obvious. From outer space, it is clear that
the see the earth as simple and whole in its orbit around the sun. Suddenly, the
answers to these questions become obvious. From outer space, it is clear that
the earth tilts about 23 degrees on its axis in its orbit around the sun.
Because of this tilt, the northern hemisphere receives much less sunlight during
one part of its orbit than during another part. Hence we have winter and summer.
In summary, the rather obscure laws of the weather are easy to understand once
we view the earth from space. Thus, the solution to the problem is to go up into
space, into the third dimension. Facts that were impossible to understand in a
flat world suddenly become obvious when viewing a unified picture of a three
dimensional earth.
THE FOUR FUNDAMENTAL FORCES
Similarly, the current excitement over higher dimensions is that they may
hold the key to the unification of all known forces. The culmination of 2,000
years of painstaking observation is the realization that that our universe is
governed by four fundamental forces. These four forces, in turn, may be unified
in higher dimensional space. Light, for example, may be viewed simply as
vibrations in the fifth dimension. The other forces of nature may be viewed as
vibrations in increasingly higher dimensions.
At first glance, however, the four fundamental forces seem to bear no
resemblance to each other. They are:
Gravity is the force which keeps our feet anchored to the spinning earth and
binds the solar system and the galaxies together. Without gravity, we would be
immediately flung into outer space at l,000 miles per hour. Furthermore, without
gravity holding the sun together, it would explode in a catastrophic burst of
energy.
Electro-magnetism is the force which lights up our cities and energizes our
household appliances. The electronic revolution, which has given us the light
bulb, TV, the telephone, computers, radio, radar, microwaves, light bulbs, and
dishwashers, is a byproduct of the electro-magnetic force.
The strong nuclear force is the force which powers the sun. Without the nuclear
force, the stars would flicker out and the heavens woulforce, the stars would
flicker out and the heavens would go dark. The nuclear force not only makes life
on earth possible, it is also the devastating force unleashed by a hydrogen
bomb.
The weak force is the force responsible for radio active decay involving
electrons. The weak force is harnessed in modern hospitals in the form of
radioactive tracers used in nuclear medicine. The weak force also wrecked havoc
at Chernobyl.
Historically, whenever scientists unraveled the secrets of one of the four
fundamental forces, this irrevocably altered the course of modern civilization,
from the mastery of mechanics and Newtonian physics in the 1700s, to the
harnessing of the electro-magnetism in the 1800s, and finally to the unlocking
of the nuclear force in the 1900s. In some sense, some of the greatest
breakthroughs in the history of science can be traced back to the gradual
understanding of these four fundamental forces. Some have even claimed that the
progress of the last 2,000 years of science can be understood as the successive
mastery of these four fundamental forces.
Given the importance of these four fundamental forces, the next question is: can
they be united into one super force? Are they but the manifestations of a deeper
reality?
Given the fruitless search that has stumped the world's Nobel Prize winners for
half a century, most physicists agree that the Theory of Everything must be a
radical departure from everything that has been tried before. For example, Niels
Bohr, founder of the modern atomic theory, once listened to Wolf gang Pauli's
explanation of his version of the unified field theory. In frustration, Bohr
finally stood up and said, "We are all agreed that your theory is
absolutely crazy. But what divides us is whether your theory is crazy
enough."
Today, however, after decades of false starts and frustrating dead ends, many of
the world's leading physicists think that they have finally found the theory
"crazy enough" to be the unified field theory. There is widespread
belief (although certainly not unanimous by any means) in the world's major re
search laboratories that we have at last found the Theory of Everything.
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. 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. 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.
PARABLE OF THE GEMSTONE
To understand the intense controversy surrounding superstring theory, think
of the following parable. Imagine that, at the beginning of time, there was once
a beautiful, glittering gemstone. Its perfect symmetries and harmonies were a
sight to behold. However, it possessed a tiny flaw and became unstable,
eventually exploding into thousands of tiny pieces. Imagine that the fragments
of the gemstone then rained down on Flatland.
These Flatlanders were intrigued by the beauty of the fragments, which could be
found scattered all over their world. The scientists of Flatland concluded that
these fragments must have come from a single crystal of unimaginable beauty that
shattered in a titanic Big Bang. They then decided to embark upon a noble quest,
to reassemble all these pieces of the gemstone.
After 2,000 years of labor by the finest minds of Flatland, they were finally
able to fit only a few of the fragments together. Many Flatlanders began to
think that these pieces could never be reassembled. Finally, some of the
younger, more rebellious scientists suggested a heretical solution: perhaps
these chunks could fit together if they were moved "up" in the third
dimension.
This immediately set off the greatest scientific controversy in years. The older
scientists scorned at this idea, because they didn't believe in the unseen third
dimension. "What you can't measure doesn't exist," they declared.
Furthermore, even if the third dimension existed, one could calculate that the
energy necessary to move the pieces up off Flatland would exceed all the energy
available in Flatland. Thus, it was an untestable theory, the critics shouted,
and hence not a theory at all.
However, the younger scientists were undaunted. Using pure mathematics, they
could show that every one of these pieces fit together perfectly if they were
assembled in the unseen third dimension. The younger scientists claimed that the
problem was therefore theoretical, rather than experimental, even if it can
never be tested.
And so the controversy rages, both in Flatland as well as in our own three
dimensional world.
"THE MIND OF GOD"
In conclusion, the theory of higher dimensions has set off perhaps the most
delicious, lively debate in theoretical physics in generations. Although the
existence of these higher dimensions cannot be verified by any experiment on
this planet, it has already sparked an avalanche of papers in the leading
research institutes around the world. Although the mathematics required to find
the unique solution has soared to dizzying heights, physicists around the world
are confident that the unique solution will eventually be found.
Nobel laureate Steven Weinberg, in his book Dreams of a Final Theory, holds out
for the exciting possibility of attaining the Final Theory. He writes, "How
strange it would be if the final theory were to be discovered in our lifetimes!
The discovery of the final laws of nature will mark a discontinuity in human
intellectual history, the sharpest that has occurred since the beginning of
modern science in the seventeenth century."
Cosmologist Steven Hawking, who closes his book A Brief History of Time on this
theory, has written, "...if we do discover a complete theory, it should in
time be understandable in broad principle by everyone, not just a few
scientists. Then we shall all, philosophers, scientists, and just ordinary
people, be able to take part in the discussion of the question of why it is that
we and the universe exist. If we find the answer to that, it would be the
ultimate triumph of human reason - for then we would know the mind of God."
Perhaps one day one of the readers of this article may gaze into a pond and
notice the carp swimming on the bottom, beneath the lilies. Perhaps the reader
will be inspired to investigate the theory of higher dimensions and complete the
quest for the Theory of the Universe.
THE PHYSICS OF TIME TRAVEL
In H.G. Wells' novel, The Time Machine, our protagonist jumped into a special
chair with blinking lights, spun a few dials, and found himself catapulted
several hundred thousand years into the future, where England has long
disappeared and is now inhabited by strange creatures called the Morlocks and
Eloi.
That may have made great fiction, but physicists have always scoffed at the idea
of time travel, considering it to be the realm of cranks, mystics, and
charlatans, and with good reason. However, rather remarkable advances in quantum
gravity are reviv- ing the theory; it has now become fair game for theoretical
physicists writing in the pages of Physical Review magazine.
One stubborn problem with time travel is that it is riddled with several types
of paradoxes. For example, there is the para- dox of the man with no parents,
i.e. what happens when you go back in time and kill your parents before you are
born? Question: if your parents died before you were born, then how could you
have been born to kill them in the first place?
There is also the paradox of the man with no past. For example, let's say that a
young inventor is trying futilely to build a time machine in his garage.
Suddenly, an elderly man appears from nowhere and gives the youth the secret of
building a time machine. The young man then becomes enormously rich playing the
stock market, race tracks, and sporting events because he knows the future.
Then, as an old man, he decides to make his final trip back to the past and give
the secret of time travel to his youthful self. Question: where did the idea of
the time machine come from?
There is also the paradox of the man who is own mother. (My apologies to
Heinlein.) "Jane" is left at an orphanage as a foundling. When
"Jane" is a teenager, she falls in love with a drifter, who abandons
her but leaves her pregnant. Then disaster strikes. She almost dies giving birth
to a baby girl, who is then mysteriously kidnapped. The doctors find that Jane
is bleeding badly, but, oddly enough, has both sex organs. So, to save her life,
the doctors convert "Jane" to "Jim."
"Jim" subsequently becomes a roaring drunk, until he meets a friendly
bartender (actually a time traveler in disguise) who wisks "Jim" back
way into the past. "Jim" meets a beautiful teenage girl, accidentally
gets her pregnant with a baby girl. Out of guilt, he kidnaps the baby girl and
drops her off at the orphanage. Later, "Jim" joins the time travelers
corps, leads a distinguished life, and has one last dream: to disguise himself
as a bartender to meet a certain drunk named "Jim" in the past.
Question: who is "Jane's" mother, father, brother, sister, grand-
father, grandmother, and grandchild?
Not surprisingly, time travel has always been considered impossible. After all,
Newton believed that time was like an arrow; once fired, it soared in a
straight, undeviating line. One second on the earth was one second on Mars.
Clocks scattered throughout the universe beat at the same rate.
Einstein gave us a much more radical picture. According to Einstein, time was
more like a river, which meandered around stars and galaxies, speeding up and
slowing down as it passed around mas- sive bodies. One second on the earth was
Not one second on Mars. Clocks scattered throughout the universe beat to their
own dis- tant drummer.
However, before Einstein died, he was faced with an embar- rassing problem.
Einstein's neighbor at Princeton, Kurt Goedel, perhaps the greatest mathematical
logician of the past 500 years, found a new solution to Einstein's own equations
which allowed for time travel!
The "river of time" now had whirlpools in which time could wrap itself
into a circle. Goedel's solution was quite ingenious: it postulated a universe
filled with a rotating fluid. Anyone walking along the direction of rotation
would find themselves back at the starting point, but backwards in time!
In his memoirs, Einstein wrote that he was disturbed that his equations
contained solutions that allowed for time travel. But he finally concluded: the
universe does not rotate, it ex- pands (i.e. as in the Big Bang theory) and
hence Goedel's solu- tion could be thrown out for "physical reasons."
(Apparently, if the Big Bang was rotating, then time travel would be possible
throughout the universe!)
Then in 1963, Roy Kerr, a New Zealand mathematician, found a solution of
Einstein's equations for a rotating black hole, which had bizarre properties.
The black hole would not collapse to a point (as previously thought) but into a
spinning ring (of neu- trons). The ring would be circulating so rapidly that
centrifugal force would keep the ring from collapsing under gravity.
The ring, in turn, acts like the Looking Glass of Alice. Anyone walking through
the ring would not die, but could pass through the ring into an alternate
universe.
Since then, hundreds of other "wormhole" solutions have been found to
Einstein's equations. These wormholes connect not only two regions of space
(hence the name) but also two regions of time as well. In principle, they can be
used as time machines.
Recently, attempts to add the quantum theory to gravity (and hence create a
"theory of everything") have given us some insight into the paradox
problem. In the quantum theory, we can have multiple states of any object. For
example, an electron can exist simultaneously in different orbits (a fact which
is responsible for giving us the laws of chemistry). Similarly, Schrodinger's
famous cat can exist simultaneously in two possible states: dead and alive. So
by going back in time and altering the past, we merely create a parallel
universe. So we are changing someone ELSE's past by saving, say, Abraham Lincoln
from being assassinated at the Ford Theater, but our Lincoln is still dead. In
this way, the river of time forks into two separate rivers.
But does this mean that we will be able to jump into H.G. Wells' machine, spin a
dial, and soar several hundred thousand years into England's future?
No. There are a number of difficult hurdles to overcome.
First, the main problem is one of energy. In the same way that a car needs
gasoline, a time machine needs to have fabulous amounts of energy. One either
has to harness the power of a star, or to find something called
"exotic" matter (whtime machine needs to have fabulous amounts of
energy. One either has to harness the power of a star, or to find something
called "exotic" matter (which falls up, rather than down) or find a
source of negative energy. (Physicists once thought that negative energy was
impossible. But tiny amounts of negative energy have been experimentally
verified for something called the Casimir effect.
Then there is the problem of stability. The Kerr black hole, for example, may be
unstable if one falls through it. Similarly, quantum effects may build up and
destroy the wormhole before you enter it. Unfortunately, our mathematics is not
powerful enough to answer the question of stability because you need a
"theory of everything" which combines both quantum forces and gravity.
At present, superstring theory is the leading candidate for such a theory (in
fact, it is the ONLY candidate; it really has no rivals at all). But superstring
theory, which happens to be my specialty, is still to difficult to solve
completely. The theory is well-defined, but no one on earth is smart enough to
solve it.
Interestingly enough, Stephen Hawking once opposed the idea of time travel. He
even claimed he had "empirical" evidence against it. If time travel
existed, he said, then we would have been visited by tourists from the future.
Since we see no tour- ists from the future, ergo: time travel is not possible.
Because of the enormous amount of work done by theoretical physicists within the
last 5 years or so, Hawking has since changed his mind, and now believes that
time travel is possible (although not necessarily practical). (Furthermore,
perhaps we are simply not very interesting to these tourists from the future.
Anyone who can harness the power of a star would consider us to be very
primitive. Imagine your friends coming across an ant hill. Would they bend down
to the ants and give them trinkets, books, medicine, and power? Or would some of
your friends have the strange urge to step on a few of them?)
In conclusion, don't turn someone away who knocks at your door one day and
claims to be your future great-great-great grandchild. They may be right.
HYPERSPACE AND A THEORY OF EVERYTHING
When I was a child, I used to visit the Japanese Tea Garden in San Francisco.
I would spend hours fascinated by the carp, who lived in a very shallow pond
just inches beneath the lily pads, just beneath my fingers, totally oblivious to
the universe above them. I would ask myself a question only a child could ask:
what would it be like to be a carp?
What a strange world it would be! I imagined that the pond would be an entire
universe, one that is two-dimensional in space. The carp would only be able to
swim forwards and backwards, and left and right. But I imagined that the concept
of "up", beyond the lily pads, would be totally alien to them. Any any
carp scientist daring to talk about "hyperspace", i.e. the third
dimension "above" the pond, would immediately be labelled a crank.
I wondered what would happen if I could reach down and grab a carp scientist and
lift it up into hyperspace. I thought what a wondrous story the scientist would
tell the others!
The carp would babble on about unbelievable new laws of physics: beings who
could move without fins. Beings who could breathe without gills. Beings who
could emit sounds without bub- bles.
I then wondered: how would a carp scientist know about our existence? One day it
rained, and I saw the rain drops forming gentle ripples on the surface of the
pond.
Then I understood.
The carp could see rippling shadows on the surface of the pond. The third
dimension would be invisible to them, but vibra- tions in the third dimensions
would be clearly visible. These ripples might even be felt by the carp, who
would invent a silly concept to describe this, called "force." They
might even give these "forces" cute names, such as light and gravity.
We would laugh at them, because, of course, we know there is no
"force" at all, just the rippling of the water.
Today, many physicists believe that we are the carp swimming in our tiny pond,
blissfully unaware of invisible, unseen uni- verses hovering just above us in
hyperspace. We spend out life in three spatial dimensions, confident that what
we can see with our tele- scopes is all there is, ignorant of the possibility of
10 dimen- sional hyperspace. Although these higher dimensions are invisi- ble,
their "ripples" can clearly be seen and felt. We call these ripples
gravity and light.
The theory of hyperspace, however, languished for many decades for lack of any
physical proof or application. But the thoery, once considered the province of
eccentrics and mystics, is being revived for a simple reason: it may hold the
key to the greatest theory of all time, the "theory of everything."
Einstein spent the last 30 years of his life futilely chas- ing after this
theory, the Holy Grail of physics. He wanted a theory that could explain the
four fundamental forces that govern the universe: gravity, electromagnetism, and
the two nuclear forces (weak and strong). It was supposed to be the crowning
achievement of the last 2,000 years of science, ever since the Greeks asked what
the world was made of. He was searching for an equation, perhaps no more than
one-inch long, that could be placed on a T-shirt, but was so powerful it could
explain every- thing from the Big Bang, exploding stars, to atoms and molecules,
to the lilies of the field.
He wanted to read the mind of God.
Ultimately, Einstein failed in his mission. In fact, he was shunned by many of
his younger compatriots, who would taunt him with the ditty, "What God has
torn asunder, no man can put to- gether."
But perhaps Einstein is now having his revenge. For the past decade, there has
been furious research on merging the four fundamental forces into a single
theory, especially one that can meld general relativity (which explains gravity)
with the quantum theory (which can explain the two nuclear forces and electro-
magnetism).
The problem is that relativity and the quantum theory are precise opposites.
General relativity is a theory of the very large: galaxies, quasars, black
holes, and even the Big Bang. It is based on bending the beautiful four
dimensional fabric of space and time. The quantum theory, by contrast, is a
theory of the very small, i.e. the world of sub-atomic particles. It is based on
discrete, tiny packets of energy called quanta.
Over the past 50 years, many attempts have been tried to unite these polar
opposites, and have failed. The road to the Unified Field Theory, the Theory of
Everything, is littered with the corpses of failed attempts.
The key to the puzzle may be hyperspace. In 1915, when Einstein said space-time
was four dimensional and was warped and rippled, he showed that this bending
produced a "force" called gravity. In 1921, Theodr Kaluza wrote that
ripples of the fifth dimension could be viewed as light. Like the fish seeing
the ripples in hyperspace moving in their world, many physicists believe that
light is created by ripples in five-dimensional space-time.
But what about dimensions higher than 5??
In principle, if we add more and more dimensions, we can ripple and bend them in
different ways, thereby creating more forces. In 10 dimensions, in fact, we can
accomodate all four fundamental forces!
Actually, it's not that simple. By naively going to 10 dimensions, we also
introduce a host of esoteric mathematical inconsistencies (e.g. infinities and
anomalies) that have killed all previous theories. The only theory which has
survived every challenge posed to it is called superstring theory, in which this
10 dimensional universe is inhabited by tiny strings.
In fact, in one swoop, this 10 dimensional string theory gives us a simple,
compelling unification of all forces. Like a violin string, these tiny strings
can vibrate and create resonances or "notes". That explains why there
are so many sub- atomic particles: they are just notes on a superstring.
(This seems so simple, but in the 1950s, physicists were drowning in an
avalanche of sub-atomic particles. J.R. Oppenheim- er, who helped build the
atomic bomb, even said, out of sheer frustration, that the Nobel Prize should go
to the physicist who does NOT discover a new particle that year!)
Similarly, when the string moves in space and time, it warps the space around it
just as Einstein predicted. Thus, in a re- markably simple picture, we can unify
gravity (as the bending of space caused by moving strings) with the other
quantum forces (now viewed as vibrations of the string).
Of course, any theory with this power and majesty has a problem. This theory,
because it is a theory of everything, is really a theory of Creation. Thus, to
fully test the theory requires re-creating Creation!
At first, this might seem hopelessly impossible. We can barely leave the earth's
puny gravity, let alone create universes in the laboratory. But there is a way
out to this seemingly intractable problem.
A theory of everything is also a theory of the everyday. Thus, this theory, when
fully completed, will be able to explain the existence of protons, atoms,
molecules, even DNA. Thus, the key is to fully solve the theory and test the
theory against the known properties of the universe.
At present, no one on earth is smart enough to complete the theory. The theory
is perfectly well-defined, but you see, superstring theory is 21st Century
physics that fell accidentally into the 20th century. It was discovered purely
by accident, when two young physicists were thumbing through a mathematics book.
The theory is so elegant and powerful, we were never "destined" to see
it in the 20th century. The problem is that 21st century mathematics has not yet
been invented yet.
But since physicists are genetically predisposed to be opti- mists, I am
confident that we will solve the theory someday soon. Perhaps a young person
reading this article will be so inspired by this story that he or she will
finish the theory. I can't wait!
M-THEORY: MOTHER OF ALLSUPERSTRING?
Every decade or so, a stunning breakthrough in string theory sends shock
waves racing through the theoretical physics communi- ty, generating a feverish
outpouring of papers and activity. This time, the Internet lines are burning up
as papers keep pouring into the Los Alamos National Laboratory's computer
bulletin board, the official clearing house for superstring papers.
John Schwarz of Caltech, for example, has been speaking to conferences around
the world proclaiming the "second superstring revolution."
Edward Witten of the Institute for Advanced Study in Prince- ton gave a
spell-binding 3 hour lecture describing it. The after- shocks of the
breakthrough are even shaking other disciplines, like mathematics. The director
of the Institute, mathematician Phillip Griffiths, says, "The excitement I
sense in the people in the field and the spinoffs into my own field of
mathematics ... have really been quite extraordinary. I feel I've been very
privileged to witness this first hand."
And Cumrun Vafa at Harvard has said, "I may be biased on this one, but I
think it is perhaps the most important develop- ment not only in string theory,
but also in theoretical physics at least in the past two decades."
What is triggering all this excitement is the discovery of something called
"M-theory," a theory which may explain the origin of strings. In one
dazzling stroke, this new M-theory has solved a series of long-standing puzzling
mysteries about string theory which have dogged it from the beginning, leaving
many theoretical physicists (myself included!) gasping for breath.
M-theory, moreover, may even force string theory to change its name. Although
many features of M-theory are still unknown, it does not seem to be a theory
purely of strings. Michael Duff of Texas A & M is already giving speeches
with the title "The theory formerly known as strings!"
String theorists are careful to point out that this does not prove the final
correctness of the theory. Not by any means. That may make years or decades
more. But it marks a most significant breakthrough that is already reshaping the
entire field.
PARABLE OF THE LION
Einstein once said, "Nature shows us only the tail of the lion. But I do
not doubt that the lion belongs to it even though he cannot at once reveal
himself because of his enormous size." Einstein spent the last 30 years of
his life searching for the "tail" that would lead him to the
"lion," the fabled unified field theory or the "theory of
everything," which would unite all the forces of the universe into a single
equation. The four forces (gravity, electromagnetism, and the strong and weak
nucle- ar forces) would be unified by an equation perhaps one inch long.
Capturing the "lion" would be the greatest scientific achievement in
all of physics, the crowning achievement of 2,000 years of scientific
investigation, ever since the Greeks first asked themselves what the world was
made of.
But although Einstein was the first one to set off on this noble hunt and track
the footprints left by the lion, he ulti- mately lost the trail and wandered off
into the wilderness.
Other giants of 20th century physics, like Werner Heisenberg and Wolfgang Pauli,
also joined in the hunt. But all the easy ideas were tried and shown to be
wrong. When Niels Bohr once heard a lecture by Pauli explaining his version of
the unified field theory, Bohr stood up and said, "We in the back are all
agreed that your theory is crazy. But what divides us is whether your theory is
crazy enough!"
The trail leading to the unified field theory, in fact, is littered with the
wreckage of failed expeditions and dreams. Today, however, physicists are
following a different trail which might be "crazy enough" to lead to
the lion. This new trail leads to superstring theory, which is the best (and in
fact only) candidate for a theory of everything. Unlike its rivals, it has
survived every blistering mathematical challenge ever hurled at it. Not
surprisingly, the theory is a radical, "crazy" departure from the
past, being based on tiny strings vibrating in 10 dimen- sional space-time.
Moreover, the theory easily swallows up Ein- stein's theory of gravity. Witten
has said, "Unlike conventional quantum field theory, string theory requires
gravity. I regard this fact as one of the greatest in- sights in science ever
made."
But until recently, there has been a glaring weak spot: string theorists have
been unable to probe all solutions of the model, failing miserably to examine
what is called the "non- perturbative region," which I will describe
shortly. This is vitally important, since ultimately our universe (with its won-
derfully diverse collection of galaxies, stars, planets, sub- atomic particles,
and even people) may lie in this "non-perturba- tive region." Until
this region can be probed, we don't know if string theory is a theory of
everything -- or a theory of noth- ing!
That's what today's excitement is all about. For the first time, using a
powerful tool called "duality," physicists are now probing beyond just
the tail, and finally seeing the outlines of a huge, unexpectedly beautiful lion
at the other end. Not knowing what to call it, Witten has dubbed it
"M-theory." In one stroke, M-theory has solved many of the
embarrassing features of the theory, such as why we have 5 superstring theories.
Ultimately, it may solve the nagging question of where strings come from.
PEA BRAINS AND THE MOTHER OF ALL STRINGS
Einstein once asked himself if God had any choice in making the universe.
Perhaps not, so it was embarrassing for string theorists to have five different
self-consistent strings, all of which can unite the two fundamental theories in
physics, the theory of gravity and the quantum theory.
Each of these string theories looks completely different from the others. They
are based on different symmetries, with exotic names like E(8)xE(8) and O(32).
Not only this, but superstrings are in some sense not unique: there are other
non-string theories which contain "super- symmetry," the key
mathematical symmetry underlying superstrings. (Changing light into electrons
and then into gravity is one of the rather astonishing tricks performed by
supersymmetry, which is the symmetry which can exchange particles with
half-integral spin, like electrons and quarks, with particles of integral spin,
like photons, gravitons, and W-particles).
In 11 dimensions, in fact, there are alternate super theo- ries based on
membranes as well as point particles (called super- gravity). In lower
dimensions, there is moreover a whole zoo of super theories based on membranes
in different dimensions. (For example, point particles are 0-branes, strings are
1-branes, mem- branes are 2-branes, and so on.) For the p-dimensional case, some
wag dubbed them p-branes (pronounced "pea brains").
But because p-branes are horribly difficult to work with, they were long
considered just a historical curiosity, a trail that led to a dead-end. (Michael
Duff, in fact, has collected a whole list of unflattering comments made by
referees to his National Science Foundation grant concerning his work on p-
branes. One of the more charitable comments from a referee was: "He has a
skewed view of the relative importance of various concepts in modern theoretical
physics.")
So that was the mystery. Why should supersymmetry allow for 5 superstrings and
this peculiar, motley collection of p-branes? Now we realize that strings,
supergravity, and p-branes are just different aspects of the same theory.
M-theory (M for "membrane" or the "mother of all strings,"
take your pick) unites the 5 superstrings into one theory and includes the p-branes
as well.
To see how this all fits together, let us update the famous parable of the blind
wise men and the elephant. Think of the blind men on the trail of the lion.
Hearing it race by, they chase after it and desperately grab onto its tail (a
one-brane). Hanging onto the tail for dear life, they feel its one- dimensional
form and loudly proclaim "It's a string! It's a string!"
But then one blind man goes beyond the tail and grabs onto the ear of the lion.
Feeling a two-dimensional surface (a mem- brane), the blind man proclaims,
"No, it's really a two-brane!"
Then another blind man is able to grab onto the leg of the lion. Sensing a
three-dimensional solid, he shouts, "No, you're both wrong. It's really a
three-brane!"
Actually, they are all right. Just as the tail, ear, and leg are different parts
of the same lion, the string and various p- branes appear to be different limits
of the same theory: M- theory. Paul Townsend of Cambridge University, one of the
archi- tects of thilion, the string and various p- branes appear to be different
limits of the same theory.
Schwarz puts a slightly different spin on this. He says, "we are in an
Orwellian situation: all p-branes are equal, but some (namely strings) are more
equal than others. The point is that they are the only ones on which we can base
a perturbation theo- ry."
To understand unfamiliar concepts such as duality, perturba- tion theory, non-perturbative
solutions, it is instructive to see where these concepts first entered into
physics.
DUALITY
The key tool to understanding this breakthrough is something
"duality." Loosely speaking, two theories are "dual" to each
other if they can be shown to be equivalent under a certain interchange. The
simplest example of duality is reversing the role of electricity and magnetism
in the equations discovered by James Clerk Maxwell of Cambridge University 130
years ago. These are the equations which govern light, TV, X-rays, radar,
dynamos, motors, transformers, even the Internet and computers. The re- markable
feature about these equations is that they remain the same if we interchange the
magnetic B and electric fields E and also switch the electric charge e with the
magnetic charge g of a magnetic "monopole": E <--> B and e
<--> g
(In fact, the product eg is a constant.) This has important implications. Often,
when a theory cannot be solved exactly, we use an approximation scheme. In first
year calculus, for example, we recall that we can approximate certain functions
by Taylor's expansion. Similarly, since e^2 = 1/137 in certain units and is
hence a small number, we can always approximate the theory by power expanding in
e^2. So we add contributions of order e^2 + e^4 + e^6 etc. in solving for, say,
the collision of two parti- cles. Notice that each contribution is getting
smaller and small- er, so we can in principle add them all up. This
generalization of Taylor's expansion is called "perturbation theory,"
where we perturb the system with terms containing e^2.
(For example, in archery, perturbation theory is how we aim our arrows. With
every motion of our arms, our bow gets closer and closer to aligning with the
bull's eye.)
But now try expanding in g^2. This is much tougher; in fact, if we expand in
g^2, which is large, then the sum g^2 + g^4 + g^6 etc. blows up and becomes
meaningless. This is the reason why the "non-perturbative" region is
so difficult to probe, since the theory simply blows up if we try to naively use
perturbation theory for large coupling constant g. So at first it appears
hopeless that we could ever penetrate into the non-perturbative region.
(For example, if every motion of our arms got bigger and bigger, we would never
be able to zero in and hit the target with the arrow.)
But notice that because of duality, a theory of small e (which is easily solved)
is identical to a theory of large g (which is difficult to solve). But since
they are the same theo- ry, we can use duality to solve for the non-perturbative
region.
S,T, AND U DUALITY
The first inkling that duality might apply in string theory was discovered by
K. Kikkawa and M. Yamasaki of Osaka Univ. in 1984. They showed that if you
"curled up" one of the extra dimen- sions into a circle with radius R,
the theory was the same if we curled up this dimension with radius 1/R. This is
now called T- duality: R <--> 1/R When applied to various superstrings,
one could reduce 5 of the string theories down to 3 (see figure). In 9
dimensions (with one dimension curled up) the Type IIa and IIb strings were iden-
tical, as were the E(8)xE(8) and O(32) strings.
Unfortunately, T duality was still a perturbative duality. The next breakthrough
came when it was shown that there was a second class of dualities, called S
duality, which provided a duality between the perturbative and non-perturbative
regions of string theory. Another duality, called U duality, was even more
powerful.
Then Nathan Seiberg and Witten brilliantly showed how anoth- er form of duality
could solve for the non-perturbative region in four dimensional supersymmetric
theories.
However, what finally convinced many physicists of the power of this technique
was the work of Paul Townsend and Edward Wit- ten. They caught everyone by
surprise by showing that there was a duality between 10 dimensional Type IIa
strings and 11 dimension- al supergravity! The non-perturbative region of Type
IIa strings, which was previously a forbidden region, was revealed to be
governed by 11 dimensional supergravity theory, with one dimen- sion curled up.
At this point, I remember that many physicists (myself included) were rubbing
our eyes, not believing what we were seeing. I remember saying to myself, "But's
that's impossible!"
All of a sudden, we realized that perhaps the real "home" of string
theory was not 10 dimensions, but possibly 11, and that the theory wasn't
fundamentally a string theory at all! This revived tremendous interest in 11
dimensional theories and p- branes. Lurking in the 11th dimension was an
entirely new theory which could reduce down to 11 dimensional supergravity as
well as 10 dimensional string theory and p-brane theory.
DETRACTORS OF STRING THEORIES
To the critics, however, these mathematical developments still don't answer
the nagging question: how do you test it? Since string theory is really a theory
of Creation, when all its beautiful symmetries were in their full glory, the
only way to test it, the critics wail, is to re-create the Big Bang itself,
which is impossible. Nobel Laureate Sheldon Glashow likes to ridicule
superstring theory by comparing it with former Pres. Reagan's Stnagging
question: how do you test it? Since string theory is really a theory of
Creation, when all its beautiful Actually, most string theorists think these
criticisms are silly. They believe that the critics have missed the point.
The key point is this: if the theory can be solved non- perturbatively using
pure mathematics, then it should reduce down at low energies to a theory of
ordinary protons, electrons, atoms, and molecules, for which there is ample
experimental data. If we could completely solve the theory, we should be able to
extract its low energy spectrum, which should match the familiar particles we
see today in the Standard Model. Thus, the problem is not building atom smashers
l,000 light years in diameter; the real problem is raw brain power: of only we
were clever enough, we could write down M-theory, solve it, and settle
everything.
EVOLVING BACKWARDS
So what would it take to actually solve the theory once and for all and end
all the speculation and back-biting? There are several approaches. The first is
the most direct: try to derive the Standard Model of particle interactions, with
its bizarre collection of quarks, gluons, electrons, neutrinos, Higgs bosons,
etc. etc. etc. (I must admit that although the Standard Model is the most
successful physical theory ever proposed, it is also one of the ugliest.) This
might be done by curling up 6 of the 10 dimensions, leaving us with a 4
dimensional theory that might resemble the Standard Model a bit. Then try to use
duality and M- theory to probe its non-perturbative region, seeing if the symme-
tries break in the correct fashion, giving us the correct masses of the quarks
and other particles in the Standard Model.
Witten's philosophy, however, is a bit different. He feels that the key to
solving string theory is to understand the under- lying principle behind the
theory.
Let me explain. Einstein's theory of general relativity, for example, started
from first principles. Einstein had the "happi- est thought in his
life" when he leaned back in his chair at the Bern patent office and
realized that a person in a falling eleva- tor would feel no gravity. Although
physicists since Galileo knew this, Einstein was able to extract from this the
Equivalence Principle. This deceptively simple statement (that the laws of
physics are indistinguishable locally in an accelerating or a gravitating frame)
led Einstein to introduce a new symmetry to physics, general co-ordinate
transformations. This in turn gave birth to the action principle behind general
relativity, the most beautiful and compelling theory of gravity. Only now are we
trying to quantize the theory to make it compatible with the other forces. So
the evolution of this theory can be summarized as: Principle -> Symmetry
-> Action -> Quantum Theory
According to Witten, we need to discover the analog of the Equivalence Principle
for string theory. The fundamental problem has been that string theory has been
evolving "backwards." As Witten says, "string theory is 21st
century physics which fell into the 20th century by accident." We were
never "meant" to see this theory until the next century.
IS THE END IN SIGHT?
Vafa recently added a strange twist to this when he intro- duced yet another
mega-theory, this time a 12 dimensional theory called F-theory (F for
"father") which explains the self-duality of the IIb string.
(Unfortunately, this 12 dimensional theory is rather strange: it has two time
co-ordinates, not one, and actu- ally violates 12 dimensional relativity.
Imagine trying to live in a world with two times! It would put an episode of
Twilight Zone to shame.) So is the final theory 10, 11, or 12 dimensional?
Schwarz, for one, feels that the final version of M-theory may not even have any
fixed dimension. He feels that the true theory may be independent of any
dimensionality of space-time, and that 11 dimensions only emerges once one tries
to solve it. Townsend seems to agree, saying "the whole notion of
dimensional- ity is an approximate one that only emerges in some semi-classi-
cal context."
So does this means that the end is in sight, that we will someday soon derive
the Standard Model from first principles?
I asked some of the leaders in this field to respond to this question. Although
they are all enthusiastic supporters of this revolution, they are still cautious
about predicting the future.
Townsend believes that we are in a stage similar to the old quantum era of the
Bohr atom, just before the full elucidation of quantum mechanics. He says,
"We have some fruitful pictures and some rules analogous to the Bohr-Sommerfeld
quantization rules, but it's also clear that we don't have a complete
theory."
Duff says, "Is M-theory merely a theory of supermembranes and super
5-branes requiring some (as yet unknown) non- perturbative quantization, or (as
Witten believes) are the under- lying degrees of freedom of M-theory yet to be
discovered? I am personally agnostic on this point."
Witten certainly believes we are on the right track, but we need a few more
"revolutions" like this to fi"revolutions" like this to
finally solve the theory. "I think there are still a couple more
superstring revo- lutions in our future, at least.
Vafa says, "I hope this is the 'light at the end of the tunnel' but who
knows how long the tunnel is!"
Schwarz, moreover, has written about M-theory: "Whether it is based on
something geometrical (like supermembranes) or some- thing completely different
is still not known. In any case, finding it would be a landmark in human
intellectual history."
Personally, I am optimistic. For the first time, we can see the outline of the
lion, and it is magnificent. One day, we will hear it roar.
BEFORE THE BIG BANG
What's the farthest object in the universe? I am sometimes asked that age-old
question to kick off discussion during a grueling 15-city tour lecturing about
my book, Hyperspace.
I point out that with the naked eye, one can easily see out to several hundred
light years, the distance to the flickering stars making up the dazzling
firmament on a clear night. In fact, the seemingly "infinite" heavenly
display we see makes up only the tiniest wrinkle in the Orion arm of the Milky
Way galaxy.
With a pair of binoculars turned on the Milky Way itself, a dim, white haze
becomes a brilliant sheet of stars which are tens of thousands of light years
away.
With the world's most powerful telescopes, you can detect the quasars. Because
of their enormous redshift, we estimate that they lie billions of light years
away, close to the very edge of the visible universe.
At even farther distances, we are peering into Creation itself. In 1992 the COBE
satellite allowed astronomers to carry out detailed measurements on the
"echo of Creation," the 3 degree microwave radiation that uniformly
fills up the universe. This ancient, relic radiation, older than the stars
themselves, dates back to just 300,000 years after the Big Bang, which took
place perhaps 15 to 20 billion years ago.
But without fail, someone in the audience then asks the innocent-sounding
question, "But professor, what happened before the Big Bang?"
At this point, I usually detect a faint, satisfied smirk developing on the faces
of a few people in the audience, as if they have finally stumped the lecturer. I
know that they expect me to throw up my hands, gaze glassy-eyed into the
heavens, and sigh philosophically, "We scientists just don't know. We don't
even have a clue. It's one of the great unanswered mysteries of nature. Perhaps
we'll never know."
Actually, I see a lot of startled faces when I reply, "I'm glad you asked,
because that is the subject of today's lecture. Today, we will discuss what
probably happened before Creation. Analyzing this question is what I do for a
living."
QUANTUM COSMOLOGY: A NEW SCIENCE IS BORN
What catches them off guard is that in the leading physics laboratories
around the world, the universe before the Big Bang has become one of the hottest
areas of research. There is a tangible air of excitement and anticipation as we
witness the birth of a new science called "quantum cosmology."
Although there is no experimental proof for quantum cosmology, the theory is so
compelling and beautiful that it has become the center of intense research.
Already, the theory has forced us, almost against our will, to confront the
bizarre possibility of parallel universes, wormholes, and the 10th dimension.
Many physicists are leaping into this game, following the lead of such pioneers
as Stephen Hawking and Nobel laureate Murray Gell-Mann.
At first, "quantum cosmology" appears to be an oxymoron, a
contradiction in terms. After all, cosmology is based on Einstein's general
theory of relativity, a theory of gravity which compares the expanding universe
to a smooth balloon being inflated by a child, with trillions of tiny galaxies
sprinkled on the surface like star dust. By contrast, the quantum theory refers
to the sub-atomic world, populated by thousands of strange denizens such as
electrons, protons, quarks, and possibly superstrings.
Like oil and water, general relativity and the quantum theory don't mix. For
example, they take precisely opposite strategies in describing gravity. General
relativity views gravity emerging from the warping of the continuous, smooth
fabric of space-time, while the quantum theory, by contrast, sees gravity
emerging by the exchange of tiny packets of energy, called
"gravitons."
For the past 50 years, there has been a "cold war" between general
relativity and the quantum theory; each theory has developed independently of
the other, and has had unparalleled success as long as they stayed within their
own domain. However, the two theories must necessarily collide at the instant of
the Big Bang, when gravitational forces and temperatures were so fierce that
even particles would have been ripped apart. At these energies, Einstein's
theory becomes useless and the quantum theory takes over. One can calculate the
energy at which quantum effects overwhelm general relativity, and it is 10^19
billion electron volts - a quadrillion times greater than the energy of the
canceled supercollider, or SSC. (By comparison, this temperature is a trillion
trillion times greater than that found at the center of a hydrogen bomb).
In other words, the secret of the origin of the Big Bang lies with merging the
two theories into a higher one, a "theory of everything" which can
explain both theories. What is needed is a quantum theory of gravity which can
simultaneously describe both the sub-atomic quantum world and the structure of
the universe. And this shotgun marriage of general relativity and the quantum
theory is producing even more bizarre progeny, such as parallel universes and
hyperspace.
PARALLEL UNIVERSES
One of the principles of quantum cosmology is that we must treat the entire
universe just like we treat a quantum particle, and the simplest particle is the
electron. As students learn in chemistry class, we never know for certain which
energy level an electron is in; quantum fluctuations are always bouncing an
electron into various energy levels simultaneously.
Similarly, once we treat the universe like an electron, then we are forced to
conclude that the universe can exist in several different states simultaneously,
i.e. parallel universes.
The simplest analogy is that of boiling of water, which is a quantum mechanical
effect. Tiny bubbles constantly form in the water, which then expand very
rapidly. If we treat the universe like a bubble, then we see that our universe
co-exists with an infinite sea of other bubbles. Our universe, then, may be
nothing but a quantum bubble, a quantum fluctuation in an infinite ocean
frothing with universes, which is constantly generating new universes, called
the "multiverse." In this picture, Big Bangs are constantly taking
place, each representing a quantum fluctuation in the vacuum. (Treating the
universe as a quantum fluctuation was first proposed by Prof. Edward Tryon of
Hunter College).
Creating universes out of Nothing may seem to violate cherished conservation
principles, until we realize that it takes no energy to create a universe. If
the universe is closed like a bubble, then the energy content of its matter is
positive, while the energy of its gravity is negative: the sum is exactly zero.
Thus, it takes no net energy to create new bubbles, which are constantly being
created in the sea of Nothing.
[To visualize negative energy, think of the earth in the solar system, or a dog
stuck in a hole. In each case, we have to add (italicize "add") energy
to pull the earth out of the solar system into deep space, or the dog out of the
hole. Since we define deep space and the ground outside the hole to have zero
energy, both the earth and the dog originally have negative gravitational
energy).
Universes are for free. There is a free lunch, after all, and it is called a
universe. (This doesn't help if you are trying to create a universe in the
laboratory. As Alan Guth, originator of the "inflationary universe,"
has pointed out, one would have to heat up matter to l,000 trillion trillion
degrees to create a "baby universe" in your basement! The net energy
of this system, however, might still be zero, since the gravitational energy is
negative and cancels the positive energy of the system).
Andre Linde of Stanford University, one of the pioneers of the inflationary
universe, believes that these bubbles are constantly churning and peeling off
other bubbles. Writing in the cover article in the Nov. issue of Scientific
American, he said, "If my colleagues and I are right, we may soon be saying
good-bye to the idea that our universe was a single fireball created in the Big
Bang."
GENESIS OR NIRVANA?
This new picture of cosmology creates a new twist on religious mythology. In
theology, most myths concerning the origin of the universe fall into one of two
categories: the Judeo-Christian myth of Genesis (or the Cosmic Egg), which
describes a definite instant called Creation, or the Hindu-Buddhist myth of
Nirvana, which states that the universe is endless, with no beginning in time or
space. In this new picture, we are combining these two mythologies into one
coherent picture: We have a constant genesis, or boiling of universes, being
born in an ocean of cosmic Nothing or Nirvana.
I was once interviewed on Australian Broadcasting Co. along with Nobel laureate
Steve Weinberg and cosmologist Paul Davies. When I mentioned this picture of
millions of Big Bangs constantly emerging from Nothing, Weinberg said, "I
find this an attractive picture and [it's] certainly worth thinking about very
seriously. An important implication is that there wasn't a beginning; that there
were increasingly large Big Bangs, so that the [multiverse] goes on forever -
one doesn't have to grapple with the question of it before the Bang. The [multiverse]
has just been here all along. I find that a very satisfying picture."
Weinberg cautioned, however, that there may not be life in these other
universes. Most of them, in fact, are probably dead universes, where the proton
lifetime is less than, say, 10 billion years, the minimum time necessary to
create stable organic chemicals, DNA, and life itself. These other universes may
be lifeless, consisting of a sea of neutrinos, photons, and electrons, incapable
of combining to form life. Our universe, in fact, may be one of the few
universes that are compatible with life.
ANTHROPIC PRINCIPLE REVISITED
This compelling picture of Creation emerging from quantum cosmology may also
solve the curious puzzle of the "anthropic principle." Cosmologists
have long noticed a remarkable observation, that the fundamental constants of
the universe fall within an exceedingly narrow band which is compatible with
life. Is life, therefore, a special property of the universe? As Freeman Dyson
of the Institute for Advanced Study has said, "It's as if the universe were
expecting us." For example, if the electric charge or the gravitational
constant were changed slightly, then stable DNA molecules would not be possible.
The "strong anthropic principle," in fact, concludes that this proves
the existence of a divine entity or God.
Some physicists have objected to the anthropic principle, stating that it can
never be tested, i.e. it cannot be falsified, and therefore is not a scientific
principle. Perhaps. But this does not explain the origin of this remarkable
"coincidence."
In quantum cosmology, however, we have a simple explanation; perhaps there are
an infinite number of possible universes, with different physical constants. We
just happen to live in the one that is compatible with life. That is why we are
here to discuss the question in the first place. So it is not an accident at all
that the physical constants are compatible with life; we co-exist with plenty of
dead universes where the physical constants are not compatible with stable
DNA-type molecules.
LIFE IN A PARALLEL UNIVERSE
But if most of the universes are dead universes, this raises the ticklish
question of whether some of the universes might look just like ours. Some of
them, in fact, may be carbon copies of our own universe, except with a tiny
quantum twist. There is the story of a Russian physicist visiting the United
States for the first time, asking to be taken to Las Vegas. Considering him to
be a seasoned gambler, his American hosts were curious to learn what his
gambling strategy might be. The Russian said that he would put all his money,
every penny, on the first bet. But, his hosts protested, "That's a
ridiculous strategy." "Yes," he replied, "but in one
parallel universe, I shall be rich beyond my wildest imagination!"
Strange, but perhaps true. In millions of other universes, however, he will be
broke!
This raises another delicate question: can we visit these parallel universes?
Can we walk down Main Street one day, only to find a hole in space emerging in
front of us, leading us to another dimension or universe, like some episode of
the Twilight Zone? Or can we wake up one morning finding ourselves in a world
where our loved ones never heard o walk down Main Street one day, only to find a
hole in space emerging in front of us, leading us to another dimension or
universe, like some episode of the Twilight Zone? Or can we wake up one morning
finding ourselves in a world where our loved ones never heard of us?
So in principle, the answer is yes, wormholes connect our universe with others.
But don't worry about falling into one. After performing a rough
back-of-the-envelope estimate of the probability of such an event, I find that
it won't happen within the lifetime of the known universe!
THE 10TH DIMENSION
There is still, however, an important defect in this picture, which is still
largely qualitative. Once we try to mathematically calculate these quantum
fluctuations that give rise to new universes, the answer blows up, i.e. the
theory becomes meaningless. Simply splicing Einstein's general theory of
relativity with the quantum theory is too crude. The problem of constructing a
true, rigorous quantum theory of gravity - i.e. a unification of quantum theory
with general relativity - has, in fact, frustrated the finest minds of the 20th
century, including Einstein.
Once, Nobel laureate Wolfgang Pauli presented his proposal for a theory of
everything while Niels Bohr was in the audience. Bohr was not impressed. He
raised his hand and said, "We in the audience are all agreed that your
theory is crazy. But what divides us is whether your theory is crazy
enough."
All the "sane" proposals for a theory of everything have been shown to
be mathematically inconsistent. We are forced, in fact, to go to a higher
theory, which unifies both general relativity and the quantum theory into a
coherent whole. At present, the only (I repeat: only) candidate for a theory of
everything is the superstring theory.
Superstring theory is certainly crazy enough. It postulates that the particles
we see in the universe, including the atoms in our bodies, are composed of tiny,
vibrating strings. The resonances or "notes" of the strings determine
the particle "zoo" (electrons, quarks, photons, etc.). The universe is
a symphony of vibrating strings, and the laws of harmony are the known laws of
physics.
Einstein once asked the question, "Did God have any choice in making the
universe?" Apparently not. The principles of general relativity and the
quantum theory are so alien to each other that any theory which melds them into
a coherent whole must not only have enormous power, it must also be highly
constrained.
A theory of everything must satisfy two important criteria
a) at large distances, it must reproduce Einstein's theory of gravity, but at
small distances, it must reproduce the quantum theory of particles.
b) it must be simple conceptually
These conditions are so stringent that there may be only one solution to them.
What is surprising, however, is that superstring theory is so constrained that
it fixes the dimension of space and time to be 10! The unique feature of
superstring theory is that these tiny strings (about 100 billion billion times
smaller than a proton) can only vibrate in 10 dimensional space-time.
Mystics, charlatans, philosophers, and science fiction writers have always been
fascinated by higher dimensions. But we now have a mathematical reason for
believing in 10 dimensional space-time: only in that dimension do we have
"enough room" to accommodate both the quantum theory and Einstein's
theory! (If we write down superstring theories in, say, 11 or 12 dimensions, the
theory becomes mathematically inconsistent. A universe starting out in these
dimensions is apparently not stable and will decay down to 10 dimensions.)
This gives us a startling new picture of quantum cosmology. These bubbles are
actually 10 dimensional bubbles, but they are unstable. Our bubble, soon after
itactually 10 dimensional bubbles, but they are unstable. Our bubble, soon after
its creation, "fissioned" in half, into four and six dimensional
universes. The six dimensional universe collapsed, these dimensions are so
"curled up" (they are 10 trillion trillion times smaller than an atom)
we can't see them. But the collapse of the six dimensional universe allowed our
four dimensional universe to expand, giving us the expanding universe that we
see today.
This also means that there may be bubbles which fission into 5, 6, 7, etc.
dimensions. However, once again one can show that these bubbles are probably not
compatible with life. Physics tells us that stable solar systems, atoms, and
protons can probably only exist in our four dimensional universe. Our universe
is four dimensional because if it weren't, we probably wouldn't be here to
debate the question in the first place.
TESTING THE UNTESTABLE
There is a fundamental difference, however, between religious mythology and
quantum cosmology. Mythology makes no pretense of being scientific; it fails the
test of being "falsifiable," i.e. there is no experiment which can
rigorously exclude the possibility of miracles, angels, etc. which are not (by
definition) reproducible. Quantum cosmology, however, may eventually be verified
or falsified. But we do not have to wait until we fall into a parallel universe
to test these ideas. For example, the COBE satellite detected tiny ripples in
the otherwise uniform microwave background radiation. This is significant,
because these ripples most likely correspond to quantum fluctuations that
existed at the instant of the Big Bang. We are, in fact, "children" of
these ripples. The quantum fluctuations at the beginning of time gradually grew
in size over billions of years, becoming the galaxies, stars, and planets that
we see today.
Other "tests" of this scenario may come from dark matter. Numerous
observations have conclusively verified the existence of a mysterious, new form
of matter which makes up perhaps 90% of the mass of the universe. For example,
our own Milky Way Galaxy is so lightweight that it would have disintegrated
billions of years ago if it weren't held together by a large hollow sphere that
extends several hundred thousand light years beyond the edge of our galactic
disk, weighing 10 times as much as the stars in our galaxy. One of the leading
candidates for dark matter is a new form of matter called "sparticles"
(short for super particles), which are some of the lowest frequency vibrations
of the superstring. Early in the next century, we should be able to identify the
precise nature of dark matter, which in turn should verify or rule out many of
the conjectures in superstring theory and quantum cosmology.
Looking further ahead, we may one day even detect a new form of
"relic" radiation left over from the Big Bang, the neutrino background
(see "Curtains at the Edge of the Universe," November 1995). If this
notoriously elusive radiation can be detected, then we will have a snap shot of
the universe when it was only 3 seconds old! Then "ripples" on the
neutrino background will give us a breathtaking look into the cosmic fireball
itself.
So what's the farthest object in the multiverse? Probably something floating in
a bubble-universe and dimension far, far away. As the British philosopher J.B.S.
Haldane once said, "Our universe is not only queerer than we suppose, it is
queerer than we can suppose."
***
Credits:
- A Theory of Everything? Published in Mysteries of Life and the
Universe, edited by William Shore, Harcourt Brace Jovanovich, 1992.
-
Black Hole, Wormholes, and the 10th Dimension. Published in the
Sunday London Times, Literary Supplement 1994.
-
What Happened Before the Big Bang? Published in the London Daily
Telegraph. 1995.
-
Hyperspace: A Scientific Odyssey Through the 10th Dimension. Published
in Thesis Magazine. The Physics of Time Travel Reprinted from the PBS-TV Web
Page.
-
Hyperspace and the Theory of Everything Reprinted from the PBS-TV
Web Page.
-
M-theory: Mother of All Superstrings? Reprinted from Jan. 1997
issue of New Scientist magazine.
-
Before the Big Bang Reprinted from April 1996 issue of Astronomy
Magazine.
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