Mysteries of the Universe

There are few scientists of whom it can be said that their mistakes are more interesting
than their colleagues' successes, but Albert Einstein was one. Few "blunders" have had a
longer and more eventful life than the cosmological constant, sometimes described as the
most famous fudge factor in the history of science, that Einstein added to his theory of
general relativity in 1917. Its role was to provide a repulsive force in order to keep the
universe from theoretically collapsing under its own weight. Einstein abandoned the
cosmological constant when the universe turned out to be expanding, but in succeeding
years, the cosmological constant, like Rasputin, has stubbornly refused to die, dragging
itself to the fore, whispering of deep enigmas and mysterious new forces in nature,
whenever cosmologists have run into trouble reconciling their observations of the
universe with their theories.
This year the cosmological constant has been propelled back into the news as an
explanation for the widely reported discovery, based on observations of distant exploding
stars, that some kind of "funny energy" is apparently accelerating the expansion of the
universe. "If the cosmological constant was good enough for Einstein," the cosmologist
Michael Turner of the University of Chicago remarked at a meeting in April, "it should
be good enough for us."
Einstein has been dead for 43 years. How did he and his 80-year-old fudge factor come to
be at the center of a revolution in modern cosmology?
The story begins in Vienna with a mystical concept that Einstein called Mach's principle.
Vienna was the intellectual redoubt of Ernst Mach (1838-1916), a physicist and
philosopher who bestrode European science like a Colossus. The scale by which
supersonic speeds are measured is named for him. His biggest legacy was philosophical;
he maintained that all knowledge came from the senses, and campaigned relentlessly
against the introduction of what he considered metaphysical concepts in science, atoms
for example.
Mysteries of the Universe

Another was the notion of absolute space, which formed the framework of Newton's
universe. Mach argued that we do not see "space," only the players in it. All our
knowledge of motion, he pointed out, was only relative to the "fixed stars." In his books
and papers, he wondered if inertia, the tendency of an object to remain at rest or in
motion until acted upon by an outside force, was similarly relative and derived somehow
from an interaction with everything else in the universe.
"What would become of the law of inertia if the whole of the heavens began to move and
stars swarmed in confusion?" he wrote in 1911. "Only in the case of a shattering of the
universe do we learn that all bodies, each with its share, are of importance in the law of
inertia.".....

Mach never ventured a guess as to how this mysterious interaction would work, but
Einstein, who admired Mach's incorrigible skepticism, was enamored of what he
sometimes called Mach's principle and sometimes called the relativity of inertia. He
hoped to incorporate the concept in his new theory of general relativity, which he
completed in 1915. That theory describes how matter and energy distort or "curve" the
geometry of space and time, producing the phenomenon called gravity.
In the language of general relativity, Mach's principle required that the space-time
curvature should be determined solely by other matter or energy in the universe, and not
any initial conditions or outside influences -- what physicists call boundary conditions.
Among other things, Einstein took this to mean that it should be impossible to solve his
equations for the case of a solitary object -- an atom or a star alone in the universe --
since there would be nothing to compare it to or interact with.
So Einstein was surprised a few months after announcing his new theory, when Karl
Schwarzschild, a German astrophysicist serving at the front in World War I, sent him just
such a solution, which described the gravitational field around a solitary star. "I would
not have believed that the strict treatment of the point mass problem was so simple,"
Einstein said.
Perhaps spurred in part by Schwarzschild's results, Einstein turned his energies in the fall
of 1916 to inventing a universe with boundaries that would prevent a star from escaping
its neighbors and drifting away into infinite un-Machian loneliness. He worked out his
ideas in a correspondence with a Dutch astronomer, Willem de Sitter, which are to be
published this summer by the Princeton University Press in Volume 8 of "The Collected
Papers of Albert Einstein." Like most of his colleagues at the time, Einstein considered

the universe to consist of a cloud of stars, namely the Milky Way, surrounded by vast
space. One of his ideas envisioned "distant masses" ringing the outskirts of the Milky
Way like a fence. These masses would somehow curl up space and close it off.
His sparring partner de Sitter scoffed at that, arguing these "supernatural" masses would
not be part of the visible universe. As such, they were no more palatable than Newton's
old idea of absolute space, which was equally invisible and arbitrary.
In desperation and laid up with gall bladder trouble in February of 1917, Einstein hit on
the idea of a universe without boundaries, in which space had been bent around to meet
itself, like the surface of a sphere, by the matter within. "I have committed another
suggestion with respect to gravitation which exposes me to the danger of being confined
to the nut house," he confided to a friend.
This got rid of the need for boundaries -- the surface of a sphere has no boundary. Such a
bubble universe would be defined solely by its matter and energy content, as Machian
principles dictated. But there was a new problem; this universe was unstable, the bubble
had to be either expanding or contracting. The Milky Way appeared to be neither
expanding nor contracting; its stars did not seem to be going anywhere in particular.
Here was where the cosmological constant came in. Einstein made a little mathematical
fix to his equations, adding "a cosmological term" that stabilized them and the universe.
Physically, this new term, denoted by the Greek letter lambda, represented some kind of
long range repulsive force, presumably that kept the cosmos from collapsing under its
own weight.
Admittedly, Einstein acknowledged in his paper, the cosmological constant was "not
justified by our actual knowledge of gravitation," but it did not contradict relativity,
either. The happy result was a static universe of the type nearly everybody believed they
lived in and in which geometry was strictly determined by matter. "This is the core of the
requirement of the relativity of inertia," Einstein explained to de Sitter. "To me, as long
as this requirement had not been fulfilled, the goal of general relativity was not yet
completely achieved. This only came about with the lambda term."
The joke, of course, is that Einstein did not need a static universe to have a Machian one.
Michel Janssen, a Boston University physicist and Einstein scholar, pointed out,
"Einstein needed the constant not because of his philosophical predilections but because
of his prejudice that the universe is static."

Moreover, in seeking to save the universe for Mach, Einstein had destroyed Mach's
principle. "The cosmological term is radically anti-Machian, in the sense that it ascribes
intrinsic properties (energy and pressure-density) to pure space, in the absence of matter,"
said Frank Wilczek, a theorist at the Institute for Advanced Study in Princeton.
In any event, Einstein's new universe soon fell apart. In another 10 years the astronomer
Edwin Hubble in California was showing that mysterious spiral nebulae were galaxies far
far away and getting farther -- in short that the universe might be expanding.
De Sitter further confounded Einstein by coming up with his own solution to Einstein's
equations that described a universe that had no matter in it at all.
"It would be unsatisfactory, in my opinion," Einstein grumbled, "if a world without
matter were possible."
De Sitter's empty universe was also supposed to be static, but that too proved to be an
illusion. Calculations showed that when test particles were inserted into it, they flew
away from each other. That was the last straw for Einstein. "If there is no quasi-static
world," he said in 1922, "then away with the cosmological term."
In 1931, after a trip to the Mount Wilson observatory in Pasadena, Calif., to meet Hubble,
Einstein turned his back on the cosmological constant for good, calling it "theoretically
unsatisfactory anyway."
He never mentioned it again.
In the meantime, the equations for an expanding universe had been independently
discovered by Aleksandr Friedmann, a young Russian theorist, and by the Abbe Georges
Lemaitre, a Belgian cleric and physicist. A year after his visit with Hubble, Einstein
threw his weight, along with de Sitter, behind an expanding universe without a
cosmological constant.
But the cosmological constant lived on in the imagination of Lemaitre, who found that by
judicious application of lambda he could construct universes that started out expanding
slowly and then sped up, universes that started out fast and then slowed down, or one that
even began expanding, paused, and then resumed again.
This last model beckoned briefly to some astronomers in the early 1950's, when
measurements of the cosmic expansion embarrassingly suggested that the universe was

only two billion years old -- younger Earth. A group of astronomers visited Einstein in
Princeton and suggested that resuscitating the cosmological constant could resolve the
age discrepancy. Einstein turned them down, saying that the introduction of the
cosmological constant had been the biggest blunder of his life. George Gamow, one of
the astronomers, reported the remark in his autobiography, "My World Line," and it
became part of the Einstein legend.
Einstein died three years later. In the years after his death, quantum mechanics, the
strange set of rules that describe nature on the subatomic level (and Einstein's bete noire)
transformed the cosmological constant and showed just how prescient Einstein had been
in inventing it. The famous (and mystical in its own right) uncertainty principle decreed
that there is no such thing as nothing, and even empty space can be thought of as foaming
with energy.
The effects of this vacuum energy on atoms had been detected in the laboratory, as early
as 1948, but no one thought to investigate its influence on the universe as a whole until
1967, when a new crisis, an apparent proliferation of too-many quasars when the universe
was about one-third its present size, led to renewed muttering about the cosmological
constant. Jakob Zeldovich, a legendary Russian theorist who was a genius at marrying
microphysics to the universe, realized that this quantum vacuum energy would enter into
Einstein's equations exactly the same as the old cosmological constant.
The problem was that a naive straightforward calculation of these quantum fluctuations
suggested that the vacuum energy in the universe should be about 118 orders of
magnitude (10 followed by 117 zeros) denser than the matter. In which case the
cosmological constant would either have crumpled the universe into a black hole in the
first instant of its existence or immediately blown the cosmos so far apart that not even
atoms would ever have formed. The fact that the universe had been sedately and happily
expanding for 10 billion years or so, however, meant that any cosmological constant, if it
existed at all, was modest.
Even making the most optimistic assumptions, Dr. Zeldovich still could not make the
predicted cosmological constant to come out to be less than a billion times the observed
limit.
Ever since then, many particle theorists have simply assumed that for some as-yetunknown
reason the cosmological constant is zero. In the era of superstrings and
ambitious theories of everything tracing history back to the first micro-micro second of
unrecorded time, the cosmological constant has been a trapdoor in the basement of

physics, suggesting that at some fundamental level something is being missed about the
world. In an article in Reviews of Modern Physics in 1989, Steven Weinberg of the
University of Texas referred to the cosmological constant as "a veritable crisis," whose
solution would have a wide impact on physics and astronomy.
Things got even more interesting in the 1970's with the advent of the current crop of
particle physics theories, which feature a shadowy entity known as the Higgs field, which
permeates space and gives elementary particles their properties. Physicists presume that
the energy density of the Higgs field today is zero, but in the past, when the universe was
hotter, the Higgs energy could have been enormous and dominated the dynamics of the
universe. In fact, speculation that such an episode occurred a fraction of a second after
the Big Bang, inflating the wrinkles out of the primeval chaos -- what Dr. Turner calls
vacuum energy put to a good use -- has dominated cosmology in the last 15 years.
"We want to explain why the effective cosmological constant is small now, not why it
was always small," Dr. Weinberg wrote in his review. In their efforts to provide an
explanation, theorists have been driven recently to talk about multiple universes
connected by space-time tunnels called wormholes, among other things.
The flavor of the crisis was best expressed, some years ago at an astrophysics conference
by Dr. Wilczek. Summing up the discussions at the end of the meeting, he came at last to
the cosmological constant. "Whereof one cannot speak, thereof one must be silent," he
said, quoting from Ludwig Wittgenstein's "Tractatus Logico-Philosophicus."
Now it seems that the astronomers have broken that silence.