Many Worlds in One: The Search for Other Universes (3 page)
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Authors: Alex Vilenkin
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Creation and Its Discontents
As a scientist I simply do not believe that the universe began with a bang.
—SIR ARTHUR EDDINGTON
T
he cold and hungry Petrograd of the early 1920s was not on anyone’s list of places where the next breakthrough in cosmology was likely to occur. Classes at Petrograd University had just resumed, after six years of war and Russian revolution. A young, bespectacled professor was lecturing in a freezing classroom to an audience of students in overcoats and fur hats. His name was Alexander Friedmann. The lectures were meticulously prepared and emphasized mathematical rigor. The courses he taught ranged from mathematics and meteorology, his main areas of expertise, to his most recent passion, the general theory of relativity.
he cold and hungry Petrograd of the early 1920s was not on anyone’s list of places where the next breakthrough in cosmology was likely to occur. Classes at Petrograd University had just resumed, after six years of war and Russian revolution. A young, bespectacled professor was lecturing in a freezing classroom to an audience of students in overcoats and fur hats. His name was Alexander Friedmann. The lectures were meticulously prepared and emphasized mathematical rigor. The courses he taught ranged from mathematics and meteorology, his main areas of expertise, to his most recent passion, the general theory of relativity.
Friedmann was fascinated by Einstein’s theory and threw himself into studying it with his usual intensity. “I am an ignoramus,” he used to say. “I don’t know anything. I have to sleep even less and not allow myself any distractions, because all this so-called ‘life’ is a complete waste of time.”
1
It was as if he knew that he had only a few years left to live—and so much to accomplish.
1
It was as if he knew that he had only a few years left to live—and so much to accomplish.
Having mastered the mathematics of general relativity, Friedmann focused on what he thought was its central problem: the structure of the entire
universe. He learned from Einstein’s paper that without a cosmological constant, the theory had no static solutions. He wanted to know, however, what kind of solutions it did have. Here, Friedmann made a radical step that would immortalize his name. Following Einstein, he assumed that the universe was homogeneous, isotropic, and closed, having the geometry of a three-dimensional sphere. But he broke away from the static paradigm and allowed the universe to move. The radius of the sphere and the density of matter could now change with time. With the requirement of a static universe lifted, Friedmann found that Einstein’s equations do have a solution. It describes a spherical universe that starts from a point, expands to some maximum size, and then recollapses back to a point. At the initial moment, which we now call the big bang, all matter in the universe is packed into a single point, so the density of matter is infinite. The density decreases as the universe expands and then grows as it recontracts, to become infinite again at the moment of the “big crunch,” when the universe shrinks back to a point.
universe. He learned from Einstein’s paper that without a cosmological constant, the theory had no static solutions. He wanted to know, however, what kind of solutions it did have. Here, Friedmann made a radical step that would immortalize his name. Following Einstein, he assumed that the universe was homogeneous, isotropic, and closed, having the geometry of a three-dimensional sphere. But he broke away from the static paradigm and allowed the universe to move. The radius of the sphere and the density of matter could now change with time. With the requirement of a static universe lifted, Friedmann found that Einstein’s equations do have a solution. It describes a spherical universe that starts from a point, expands to some maximum size, and then recollapses back to a point. At the initial moment, which we now call the big bang, all matter in the universe is packed into a single point, so the density of matter is infinite. The density decreases as the universe expands and then grows as it recontracts, to become infinite again at the moment of the “big crunch,” when the universe shrinks back to a point.
The big bang and the big crunch mark the beginning and the end of the universe. Because of the vanishing size and the infinite density of matter, the mathematical quantities appearing in Einstein’s equations become ill-defined, and spacetime cannot be extended beyond these points. Such points are called
spacetime singularities
.
spacetime singularities
.
A two-dimensional spherical universe can be pictured as an expanding and recontracting balloon (see
Figure 3.1
). The squiggles on the surface of the balloon represent galaxies, and as the balloon expands, the distances between the galaxies grow. Hence, an observer in each galaxy sees other galaxies rush away. The expansion is gradually slowed down by gravity; it will eventually come to a halt and be followed by the contraction. In the contracting phase, the distances between the galaxies will decrease and all observers will see galaxies moving toward them.
Figure 3.1
). The squiggles on the surface of the balloon represent galaxies, and as the balloon expands, the distances between the galaxies grow. Hence, an observer in each galaxy sees other galaxies rush away. The expansion is gradually slowed down by gravity; it will eventually come to a halt and be followed by the contraction. In the contracting phase, the distances between the galaxies will decrease and all observers will see galaxies moving toward them.
It does not make much sense to ask what the universe is expanding into. We picture the balloon universe as expanding into the surrounding space, but this does not make any difference for its inhabitants. They are confined to the surface of the balloon and are not aware of the third, radial dimension. Similarly, for observers in a closed universe, the three-dimensional spherical space is all the space there is, with nothing else outside it.
Shortly after publishing these results, Friedmann discovered another class of solutions with a different geometry. Instead of curving back on itself, the space in these solutions curves, in a certain sense, away from itself, resulting in an infinite (open) universe. A two-dimensional analogue of this type of space is the surface of a saddle (
Figure 3.2
).
Figure 3.2
).
Figure 3.1
. An expanding and recontracting spherical universe.
. An expanding and recontracting spherical universe.
Once again, Friedmann found that the distance separating any pair of galaxies in an open universe grows, starting from zero at the initial singularity. The expansion slows down initially, but in this case the force of gravity is not strong enough to turn it around, so at late times galaxies move apart at nearly constant speeds.
Figure 3.2
.
A two-dimensional analogue of an open universe.
.
A two-dimensional analogue of an open universe.
On the borderline between the open and closed models is the universe
with a flat, Euclidean geometry.
2
It expands without limit, but barely so, with the expansion rate becoming smaller and smaller with time.
with a flat, Euclidean geometry.
2
It expands without limit, but barely so, with the expansion rate becoming smaller and smaller with time.
A remarkable feature of Friedmann’s solutions is that they establish a connection between the geometry of the universe and its ultimate fate. If the universe is closed, it must recollapse, and if it is open or flat, it will expand forever.
c
In his papers Friedmann gave no preference to either model.
c
In his papers Friedmann gave no preference to either model.
Unfortunately, Friedmann did not live to see his work become the foundation of modern cosmology. He died of typhoid fever in 1925, at the age of thirty-seven. Although Friedmann’s papers were published in a leading German physics journal, they went almost unnoticed.
3
His papers were unearthed in the 1930s, in the wake of Hubble’s discovery of the expansion of the universe.
d
3
His papers were unearthed in the 1930s, in the wake of Hubble’s discovery of the expansion of the universe.
d
Whatever Friedmann’s solutions have to say about the future of the universe, their most unexpected and intriguing aspect is the presence of the initial singularity—the big bang, where the mathematics of general relativity breaks down. At the singularity, matter is compressed to infinite density, and the solutions cannot be extended to earlier times. Thus, taken literally, the big bang should be interpreted as the beginning of the universe. Was that the creation of the world? Could it be that the whole universe began in a singular event a finite time ago?
For most physicists this was too much to take. A singular jump-starting of the universe looked like a divine intervention, for which they thought there should be no place in physical theory. But although the “beginning of the world” was—and to a large degree remains—a source of discomfort for most scientists, it also had some benefits to offer. It helped to resolve some perplexing paradoxes that haunted the picture of a static, eternally unchanging universe.
To begin with, an eternal universe appears to be in conflict with one of
the most universal laws of nature: the second law of thermodynamics. This law says that physical systems evolve from ordered to more disordered states. If you neatly organize papers into piles on your desk and the wind suddenly blows into the window, the papers are scattered randomly all over the floor. However, you never see the wind picking up papers from the floor and assembling them into neat piles on your desk. Such a spontaneous reduction of disorder is not impossible in principle, but it is so unlikely that it is never seen to occur.
the most universal laws of nature: the second law of thermodynamics. This law says that physical systems evolve from ordered to more disordered states. If you neatly organize papers into piles on your desk and the wind suddenly blows into the window, the papers are scattered randomly all over the floor. However, you never see the wind picking up papers from the floor and assembling them into neat piles on your desk. Such a spontaneous reduction of disorder is not impossible in principle, but it is so unlikely that it is never seen to occur.
Mathematically, the amount of disorder is characterized by the quantity called
entropy
, and the second law says that the entropy of an isolated system can only increase. This relentless increase of disorder leads eventually to the state of maximum possible entropy,
thermal equilibrium
. In this state all the energy of ordered motion has been turned into heat and a uniform temperature has been established throughout the system.
entropy
, and the second law says that the entropy of an isolated system can only increase. This relentless increase of disorder leads eventually to the state of maximum possible entropy,
thermal equilibrium
. In this state all the energy of ordered motion has been turned into heat and a uniform temperature has been established throughout the system.
The cosmic implications of the second law were first pointed out in the mid-1800s by the German physicist Hermann von Helmholtz. He argued that the whole universe can be regarded as an isolated system (since there is nothing external to the universe). If so, then the second law is applicable to the universe as a whole, and thus the universe should be headed toward an inevitable “heat death” in the state of thermal equilibrium. In that state the stars will all be dead and have the same temperature as their surroundings, and all motion will come to a halt, other than the disordered thermal jostling of the molecules.
Another consequence of the second law is that if the universe existed forever, it should have already reached thermal equilibrium. And since we do not find ourselves in the state of maximum entropy, it follows that the universe could not have existed forever.
4
4
Helmholtz did not emphasize this second conclusion and was more concerned about the “death” part (which by the way inspired much apocalyptic prose in the late nineteenth and early twentieth centuries). But other physicists, including giants like Ludwig Boltzmann,
e
were well aware of the problem. Boltzmann saw the way out in the statistical nature of the second law. Even if the universe
is
in the maximally disordered state, spontaneous reductions
of disorder will occasionally happen by chance. Such events, called
thermal fluctuations
, are common on the microscopic scale of a few hundred molecules, but become increasingly unlikely as you move toward larger scales. Boltzmann suggested that what we are observing around us is a huge thermal fluctuation in an otherwise disordered universe. The probability for such a fluctuation to happen is unbelievably small. However, improbable things do eventually happen if you wait long enough, and they will definitely happen if you have infinite time at your disposal. Life and observers can exist only in the ordered parts of the universe, and this explains why
we
are observing this incredibly rare event.
5
e
were well aware of the problem. Boltzmann saw the way out in the statistical nature of the second law. Even if the universe
is
in the maximally disordered state, spontaneous reductions
of disorder will occasionally happen by chance. Such events, called
thermal fluctuations
, are common on the microscopic scale of a few hundred molecules, but become increasingly unlikely as you move toward larger scales. Boltzmann suggested that what we are observing around us is a huge thermal fluctuation in an otherwise disordered universe. The probability for such a fluctuation to happen is unbelievably small. However, improbable things do eventually happen if you wait long enough, and they will definitely happen if you have infinite time at your disposal. Life and observers can exist only in the ordered parts of the universe, and this explains why
we
are observing this incredibly rare event.
5
The problem with Boltzmann’s solution is that the ordered part of the universe appears to be excessively large. For observers to exist, it would be enough to turn chaos into order on the scale of the solar system. This would have a much higher probability than a fluctuation on the scale of billions of light-years that would be needed to account for the observed universe.
Another problem, having an even longer pedigree, arises if one assumes that the universe is infinite and that stars (or galaxies) are distributed more or less uniformly throughout the infinite space. If this were the case, then no matter where you looked in the sky, your line of sight would eventually hit upon a star. The sky would then constantly glare with a nearly uniform brilliance—which leaves us with a simple question: Why is it dark at night? The problem was first recognized in 1610 by Johannes Kepler, whose conclusion was that the universe could not be infinite.
Both the entropy problem and the night sky paradox are naturally resolved if the age of the universe is finite. If the universe came into being only a finite time ago and was initially in a highly ordered (low entropy) state, then we are now observing the descent from that state into chaos and should not be surprised that the state of maximum disorder has not yet been reached. The night sky paradox is resolved because, in a universe of a finite age, light from very distant stars has not had enough time to reach us. We can only observe the stars within the
horizon
radius, equal to the distance traveled by light during the lifetime of the universe. The number of stars within that radius is clearly finite, even if the entire universe is infinite.
horizon
radius, equal to the distance traveled by light during the lifetime of the universe. The number of stars within that radius is clearly finite, even if the entire universe is infinite.
Given these arguments, how could anyone ever believe that the universe as we know it has existed forever? The reason is, of course, that the idea of a cosmic beginning that occurred a finite time ago creates perplexing problems
of its own. If the universe began a finite time ago, then what determined the initial conditions at the big bang? Why did the universe start in a homogeneous and isotropic state? It could in principle start in any state at all. Should we attribute the choice of the initial state to the Creator? Not surprisingly, physicists were slow to embrace the big bang cosmology and made numerous attempts to avoid dealing with the problem of “the beginning.”
of its own. If the universe began a finite time ago, then what determined the initial conditions at the big bang? Why did the universe start in a homogeneous and isotropic state? It could in principle start in any state at all. Should we attribute the choice of the initial state to the Creator? Not surprisingly, physicists were slow to embrace the big bang cosmology and made numerous attempts to avoid dealing with the problem of “the beginning.”
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