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Black holes...quarks...dark
matter. It seems like the cosmos gets a little stranger every
year. Until recently, the astronomical universe known to humans
was populated by planets, stars, galaxies, and scattered nebulae
of dust and gas. Now, theoretists tell us it may also be inhabited
by objects such as superstrings, dark matter and massive neutrinos
-- objects that have yet to be discovered if they exist at
all!
As bizarre as these new constituents may sound, you don't
have to be a rocket scientist to appreciate the most mysterious
ingredient of them all. It is the inky blackness of space
itself that commands our attention as we look at the night
sky; not the sparse points of light that signal the presence
of widely scattered matter.
During the last
few decades, physicists and astronomers have begun to recognize
that the notion of empty space presents greater subtleties
than had ever before been considered. Space is not merely
a passive vessel to be filled by matter and radiation, but
is a dynamic, physical entity in its own right.
One chapter
in the story of our new conception of space begins with a
famous theoretical mistake made nearly 75 years ago that now
seems to have taken on a life of its own.
In 1917, Albert
Einstein tried to use his newly developed theory of general
relativity to describe the shape and evolution of the universe.
The prevailing idea at the time was that the universe was
static and unchanging. Einstein had fully expected general
relativity to support this view, but, surprisingly, it did
not. The inexorable force of gravity pulling on every speck
of matter demanded that the universe collapse under its own
weight.
His remedy for
this dilemma was to add a new 'antigravity' term to his original
equations. It enabled his mathematical universe to appear
as permanent and invariable as the real one. This term, usually
written as an uppercase Greek lambda, is called the 'cosmological
constant'. It has exactly the same value everywhere in the
universe, delicately chosen to offset the tendency toward
gravitational collapse at every point in space.
A simple thought
experiment may help illustrate the nature of Lambda. Take
a cubic meter of space and remove all matter and radiation
from it. Most of us would agree that this is a perfect vacuum.
But, like a ghost in the night, the cosmological constant
would still be there. So, empty space is not really empty
at all -- Lambda gives it a peculiar 'latent energy'. In other
words, even Nothing is Something!
Einstein's fudged
solution remained unchallenged until 1922 when the Russian
mathematician Alexander Friedmann began producing compelling
cosmological models based on Einstein's equations but without
the extra quantity. Soon thereafter, theorists closely examining
Einstein's model discovered that, like a pencil balanced on
its point, it was unstable to collapse or expansion. Later
the same decade, Mount Wilson astronomer Edwin P. Hubble found
direct observational evidence that the universe is not static,
but expanding.
All this ment
that the motivation for introducing the cosmological constant
seemed contrived. Admitting his blunder, Einstein retracted
Lambda in 1932. At first this seemed to end the debate about
its existence. Yet decades later, despite the great physicist's
disavowal, Lambda keeps turning up in cosmologists' discussions
about the origin, evolution, and fate of the universe.
THEORY MEETS OBSERVATION
Friedmann's standard 'Big Bang' model without a cosmological
constant predicts that the age of the universe, t0, and its
expansion rate (represented by the Hubble parameter, H0) are
related by the equation t0 = 2/3H0. Some astronomers favor
a value of H0 near 50 kilometers per second per megaparsec
(one megaparsec equals 3.26 million light years). But the
weight of the observational evidence seems to be tipping the
balance towards a value near 100. In the Friedmann model,
this implies that the cosmos can be no more than 7 billion
years old. Yet some of our galaxy's globular clusters have
ages estimated by independent methods of between 12 and 18
billion years!
In what's called
the Einstein-DeSitter cosmology, the Lambda term helps to
resolve this discrepancy. Now a large value for the Hubble
parameter can be attributed in part to "cosmic repulsion".
This changes the relationship between t0 and H0, so that for
a given size, the universe is older than predicted by the
Friedmann model.
In one formulation
of Einstein's equation, Lambda is expressed in units of matter
density. This means we can ask how the cosmological constant,
if it exists at all, compares with the density of the universe
in the forms of stars and galaxies.
So far, a careful
look at the available astronomical data has produced only
upper limits to the magnitude of Lambda. These vary over a
considerable range - from about 10 percent of ordinary matter
density to several times that density.
The cosmological
constant can also leave its mark on the properties of gravitational
lenses and faint galaxies. One of the remarkable features
of Einstein's theory of general relativity is its prediction
that space and time become deformed or 'warped' in the vicinity
of a massive body such as a planet, star or even a galaxy.
Light rays passing through such regions of warped "space-time"
have their paths altered. In the cosmological arena, nearby
galaxies can deflect and distort the images of more distant
galaxies behind them. Sometimes, the images of these distant
galaxies can appear as multiple images surrounding the nearby
'lensing' galaxy.
At Kyoto University
M. Fukugita and his coworkers predicted that more faint galaxies
and gravitational lenses will be detected than in a Friedmann
universe if Lambda is more than a few times the matter density.
Edwin Turner, an astrophysicist at Princeton University also
reviewed the existing, scant, data on gravitational lenses
and found that they were as numerous as expected for Lambda
less that a few times the matter density. By the best astronomical
reconning, Lambda is probably not larger than the observed
average matter density of the universe. For that matter, no
convincing evidence is available to suggest that Lambda is
not exactly equal to zero. So why not just dismiss it as an
unnecessary complication? Because the cosmological constant
is no longer, strictly, a construct of theoretical cosmology.
NOTHING AND EVERYTHING
To understand how our universe came into existence, and how
its various ingredients have evolved, we must delve deeply
into the fundamental constituents of matter and the forces
that dictate how it will interact. This means that the questions
we will have to ask will have more to do with physics than
astronomy. Soon after the big bang, the universe was at such
a high temperature and density that only the details of matter's
composition (quarks, electrons etc) and how they interact
via the four fundamental forces of nature were important.
They represented the most complex collections of matter in
existence, long before atoms, planets, stars and galaxies
had arrived on the scene.
For two decades
now, physicists have been attempting to unify the forces and
particles that make up our world - to find a common mathematical
description that encompasses them all. Some think that such
a Theory of Everything is just within reach. It would account
not only for the known forms of matter, but also for the fundamental
interactions among them: gravity, electromagnetism, and the
strong and weak nuclear forces.
These unification
theories are known by a variety of names: grand unification
theory, supersymmetry theory and superstring theory. Their
basic claim is that Nature operates according to a small set
of simple rules called symmetries.
The concept
of symmetry is at least as old as the civilization of ancient
Greece, whos art and archetecture are masterworks of simplicity
and balance. Geometers have known for a long time that a simple
cube can be rotated 90 degrees without changing its outward
appearance. In two dimensions, equalateral triangles look
the same when they are rotated by 120 degrees. These are examples
of the geometric concept of Rotation Symmetry.
There are parallels
to geometric symmetry in the way that various physical phenomena
and qualities of matter express themselves as well. For example,
the well-known principle of the Conservation of Energy is
a consequence of the fact that when some collections of matter
and energy are examined at different times, they each have
precisely the same total energy, just as a cube looks the
same when it is rotated in space by a prescribed amount. Symmetry
under a 'shift in time' is as closely related to the Conservation
of Energy as is the symmetry of a cube when rotated by 90
degrees.
Among other
things, symmetries of Nature dictate the strengths and ranges
of the natural forces and the properties of the particles
they act upon. Although Nature's symmetries are hidden in
today's cold world, they reveal themselves at very high temperatures
and can be studied in modern particle accelerators.
The real goal
in unification theory is actually two-fold: not only to uncover
and describe the underlying symmetries of the world, but to
find physical mechanisms for 'breaking' them at low energy.
After all, we live in a complex world filled with a diversity
of particles and forces, not a bland world with one kind of
force and one kind of particle!
Theoreticians
working on this problem are often forced to add terms to their
equations that represent entirely new fields in Nature. The
concept of a field was invented by mathematicians to express
how a particular quantity may vary from point to point in
space. Physicists since the 18th century have adopted this
idea to describe quantitatively how forces such as gravity
and magnetism change at different distances from a body.
The interactions
of these fields with quarks, electrons and other particles
cause symmetries to break down. These fields are usually very
different than those we already know about. The much sought
after Higgs boson field, for example, was introduced by Sheldon
Glashow, Abdus Salam and Steven Weinberg in their unified
theory of the electromagnetic and weak nuclear forces.
Prior to their
work, the weak force causing certain particles to decay, and
the electromagnetic force responsible for the attraction between
charged particles and the motion of compass needles, were
both considered to be distinct forces in nature. By combining
their mathematical descriptions into a common language, they
showed that this distinction was not fundamental to the forces
at all! A new field in nature called the Higgs field makes
these two forces act differently at low temperature. But at
temperatures above 1000 trillion degrees, the weak and electromagnetic
forces become virtually identical in the way that they affect
matter. The corresponding particles called the Higgs Boson
not only cause the symmetry between the electromagnetic and
weak forces to be broken at low temperature, but they are
also responsible for confiring the property of mass on particles
such as the electrons and the quarks!
There is, however
a price that must be paid for introducing new fields into
the mathematical machinery. Not only do they break symmetries,
but they can also give the vacuum state an enormous latent
energy that, curiously, behaves just like Lambda in cosmological
models.
The embarrassment
of having to resurrect the obsolete quantity Lambda is compounded
when unification theories are used to predict its value. Instead
of being at best a vanishingly minor ingredient to the universe,
the predicted values are in some instances 10 to the power
of 120 times greater than even the most generous astronomical
upper limits!
It is an unpleasant
fact of life for physicists that the best candidates for the
Theory of Everything always have to be fine-tuned to get rid
of their undesirable cosmological consequences. Without proper
adjustment, these candidates may give correct predictions
in the microscopic world of particle physics, but predict
a universe which on its largest scales looks very different
from the one we inhabit.
Like a messenger
from the depths of time, the smallness - or absence - of the
cosmological constant today is telling us something important
about how to craft a correct Theory of Everything. It is a
signpost of the way Nature's symmetries are broken at low
energy, and a nagging reminder that our understanding of the
physical world is still incomplete in some fundamental way.
A LIKELY STORY
Most physicists expect the Theory of Everything will describe
gravity the same way we now describe matter and the strong,
weak and electromagnetic forces - in the language of quantum
mechanics. Gravity is, after all, just another force in Nature.
So far this has proven elusive, due in part to the sheer complexity
of the equations of general relativity. Scientists since Einstein
have described gravity ( as well as space and time) in purely
geometric terms. Thus we speak of gravity as the "curvature
of space-time".
To acheive complete
unification, the dialects of quantum matter and geometric
space have to be combined into a single language. Matter appears
to be rather precisely described in terms of the language
of quantum mechanics. Quarks and electrons exchange force-carrying
particles such as photons and gluons and thereby feel the
electromagnetic and strong nuclear forces. But, gravity is
described by Einstein's theory of general relativity as a
purely geometric phenomenon. These geometric ideas of curvature
and the dimensionality of space have nothing to do with quantum
mechanics.
To unify these
two great foundations of physics, a common language must be
found. This new language will take some getting used to. In
it, the distinction between matter and space dissolves away
and is lost completely; matter becomes a geometric phenomenon,
and at the same time, space becomes an exotic form of matter.
Beginning with
work on a quantum theory of gravity by John Wheeler and Bryce
DeWitt in the 1960's, and continuing with the so-called superstring
theory of John Schwartz and Michael Green in the 1980's, a
primitive version of such a 'quantum-geometric' language is
emerging. Not surprisingly, it borrows many ideas from ordinary
quantum mechanics.
A basic concept
in quantum mechanics is that every system of elementary particles
is defined by a mathematical quantity called a wave function.
This function can be used, for example, to predict the probability
of finding an electron at a particular place and time within
an atom. Rather than a single quantity, the wave function
is actually a sum over an infinite number of factors or 'states',
each representing a possible measurement outcome. Only one
of these states can be observed at a time.
By direct analogy,
in quantum gravitation, the geometry of space-time, whether
flat or curved, is only one of an infinite variety of geometric
shapes for space-time, and therefore the universe. All of
these possibilities are described as separate states in the
wave function for the universe.
But what determines
the probability that the universe will have the particular
geometry we now observe out of the infinitude of others? In
quantum mechanics, the likelihood that an electron is located
somewhere within an atom is determined by the external electric
field acting on it. That field is usually provided by the
protons in the atomic nucleus. Could there be some mysterious
field 'outside' our universe that determines its probability?
According to
Cambridge University theorist Stephen Hawking, this is the
wrong way to look at the problem. Unlike the electron acted
upon by protons, our universe is completely self-contained.
It requires no outside conditions or fields to help define
its probability. The likelihood that our universe looks the
way it does depends only on the strengths of the fields within
it.
Among these
internal fields, there may even be ones that we haven't yet
discovered. Could the cosmological constant be the fingerprint
in our universe of a new 'hidden' field in Nature? This new
field could affect the likelihood of our universe just as
a kettle of soup may contain unknown ingredients although
we can still precisely determine the kettle's mass.
A series of
mathematical considerations led Hawking to deduce that the
weaker the hidden field becomes, the smaller will be the value
we observe for the cosmological constant, and surprisingly,
the more likely will be the current geometry of the universe.
This, in turn,
implies that if Lambda were big enough to measure by astronomers
in the first place, our universe would be an improbable one.
Philosophically, this may not trouble those who see our cosmos
as absolutely unique, but in a world seemingly ruled by probability,
a counter view is also possible. There may, in fact, exist
an infinite number of universes, but only a minority of them
have the correct blend of physical laws and physical conditions
resembling our life-nurturing one.
Hawking continued
his line of speculation by suggesting that, if at the so-called
Planck scale of 10 to the power of -33 centimeters the cosmos
could be thought of as an effervescent landscape, or "space-time
foam", then perhaps a natural mechanism could exist for
eliminating the cosmological constant for good.
One of the curiosities
of combining the speed of light and Newton's constant of gravitation
from general relativity, with Planck's constant from quantum
mechanics, is that they can be made to define unique values
for length, time and energy. Physicists believe that at these
Planck scales represented by 10 to the power of -33 centimeters
and 10 to the power of -43 seconds, general relativity and
quantum mechanics blend together to become a single, comprehensive
theory of the physical world: The Theory Of Everything. The
energy associated with this unification, 10 to the power of
19 billion electron volts, is almost unimaginably big by the
standards of modern technology.
The universe
itself, soon after the Big Bang, must also have passed through
such scales of space, time and energy during its first instants
of existence. Cosmologists refer to this period as the Planck
Era. It marks the earliest times that physicists are able
to explore the universe's physical state without having a
complete Theory of Everything to guide them.
WORMHOLES
Harvard University physicist Sidney Coleman has recently pursued
this thought to a possible conclusion. Instead of some mysterious
new field in Nature, maybe the Lambda term appears in our
theories because we are using the wrong starting model for
the geometry of space at the Planck scale.
Previous thinking
on the structure of space-time had assumed that it behaved
in some sense like a smooth rubber sheet. Under the action
of matter and energy, space-time could be deformed into a
variety of shapes, each a possible geometric state for the
universe. Nearly all candidates for the Theory of Everything's
embed their fields and symmetries in such a smooth geometrical
arena.
But what if
space-time were far more complicated? One possibility is that
'wormholes' exist, filling space-time with a network of tunnels.
The fabric of space-time may have more in common with a piece
of Swiss cheese than with a smooth rubber sheet.
According to
Coleman, the addition of wormholes to space-time means that,
like the ripples from many stones tossed into a pond, one
geometric state for the universe could interfere with another.
The most likely states ( or the biggest ripples) would win
out. The mathematics suggest that quantum wormhole interference
at the Planck scale makes universes with cosmological constants
other than zero exceedingly unlikely.
How big would
wormholes have to be to have such dramatic repurcussions?
Surprisingly, the calculations suggest that small is beautiful.
Wormholes the size of dogs and planets would be very rare.
Universes containing even a few of them would exist with a
vanishingly low probability. But wormholes smaller than 10
to the power of -33 centimeters could be everywhere. A volume
the size of a sugar cube might be teeming with uncounted trillions
of them flashing in and out of existence!
Coleman proposes
that the action of these previously ignored mini- wormholes
upon the geometric fabric of the universe that forces Lambda
to be almost exactly zero. Like quantum 'Pac Men', they gobble
up all the latent energy of space-time that would otherwise
have appeared to us in the form of a measureable cosmological
constant!
The addition
of wormholes to the description of space-time admits the possibility
that our universe did not spring into being aloof and independent,
but was influenced by how other space-times had already evolved
- ghostly mathematical universes with which we can never communicate
directly.
The most likely
of these universes had Lambda near zero, and it is these states
that beat out all other contenders. In a bizarre form of quantum
democracy, our universe may have been forced to follow the
majority, evolving into the high probability state we now
observe, without a detectable cosmological constant.
EPILOG
Wormholes? Wave functions? Hidden fields? The answer to the
cosmological constant's smallness, or absence, seems to recede
into the farthest reaches of abstract thinking, faster than
most of us can catch up.
As ingenious
as these new ideas may seem, the final pages in this unusual
story have probably not been written, especially since we
can't put any of these ideas to a direct test. It is a tribute
to Einstein's genius that even his 'biggest blunder' made
near the beginning of this century still plagues physicists
and astronomers as we prepare to enter the 21st century. Who
would ever have thought that something that may not even exist
would lead to such enormous problems!
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