Many Worlds in One: The Search for Other Universes (11 page)
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Authors: Alex Vilenkin
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Infinite Islands
I could be bounded in a nutshell, and count myself a king of infinite space …
—SHAKESPEARE,
Hamlet
Hamlet
T
he question that started me thinking about eternal inflation again had more to do with science fiction than with physics. It was about the future of intelligent life in the universe. The long-term prospects for any civilization appear to be rather bleak. Even if a civilization avoids natural catastrophes and self-destruction, it will, in the end, run out of energy. The stars will eventually die, and all other sources of energy will also come to an end. But now eternal inflation appeared to offer some hope.
he question that started me thinking about eternal inflation again had more to do with science fiction than with physics. It was about the future of intelligent life in the universe. The long-term prospects for any civilization appear to be rather bleak. Even if a civilization avoids natural catastrophes and self-destruction, it will, in the end, run out of energy. The stars will eventually die, and all other sources of energy will also come to an end. But now eternal inflation appeared to offer some hope.
Stars will die in our cosmic neighborhood, but an infinite number of new stars will form in the future big bangs of eternal inflation. Our visible region is but a tiny part of one island universe, lost in the inflating sea of false vacuum (see
Figure 8.3
). New island universes constantly emerge in the midst of that sea, bringing in myriads of new stars. In fact, star formation will always continue even within our own island universe.
Figure 8.3
). New island universes constantly emerge in the midst of that sea, bringing in myriads of new stars. In fact, star formation will always continue even within our own island universe.
The frontiers of island universes are constantly advancing into the inflating sea. This relentless advance is caused by the decay of false vacuum in the adjacent inflating regions. These frontiers are thus the regions where
the big bang is happening right now.
x
Newly formed island universes are microscopically small, but they grow without limit as they get older. Central parts of large island universes are very old. They are dark and barren: all stars have long since died there, and life has become extinct. But regions at the periphery of the islands are very new and must be teeming with shining stars.
the big bang is happening right now.
x
Newly formed island universes are microscopically small, but they grow without limit as they get older. Central parts of large island universes are very old. They are dark and barren: all stars have long since died there, and life has become extinct. But regions at the periphery of the islands are very new and must be teeming with shining stars.
Advanced civilizations may wish to send missions to colonize newly formed stellar systems near the boundary of their island. If not, they could at least send messages to new civilizations that will evolve close to the boundary, or in other island universes. Those civilizations could in turn send messages to posterity, and so on. If we follow this path, we could become a branch in an ever-growing “tree” of civilizations and our accumulated wisdom would not be completely lost.
These scenarios were suggested by Andrei Linde in a paper called “Life after Inflation,”
1
and I wanted to know if any of them is actually possible, at least in principle. Linde analyzed various aspects of the problem, but did not commit himself to a definite answer. The fact that stars in some part of the universe are formed later than they are formed here does not necessarily mean that we can get from here to there in the available time. Besides, we know from Einstein that the notions of “earlier” and “later” are not absolute and may be observer-dependent. To make any progress with the problem, I had to understand the spacetime structure of the eternally inflating universe.
1
and I wanted to know if any of them is actually possible, at least in principle. Linde analyzed various aspects of the problem, but did not commit himself to a definite answer. The fact that stars in some part of the universe are formed later than they are formed here does not necessarily mean that we can get from here to there in the available time. Besides, we know from Einstein that the notions of “earlier” and “later” are not absolute and may be observer-dependent. To make any progress with the problem, I had to understand the spacetime structure of the eternally inflating universe.
As we discussed in Chapter 2, space and time in the theory of relativity are united in a four-dimensional entity called spacetime. A point in spacetime is an
event
, which has a certain location and time. Consider, for example, two events that you may wish to attend. One is your class reunion here on Earth and the other is an interstellar superball game, which is scheduled to take place three years later at the star Alpha Centauri, about four light-years away from here. The question is, Can you get to both of these events?
event
, which has a certain location and time. Consider, for example, two events that you may wish to attend. One is your class reunion here on Earth and the other is an interstellar superball game, which is scheduled to take place three years later at the star Alpha Centauri, about four light-years away from here. The question is, Can you get to both of these events?
The answer can be found by calculating the
spacetime interval
between the two events. The interval between events in spacetime plays the role analogous to the distance between points in space. Its mathematical definition is not important for us here; what is important is that the interval can be of
two kinds: it is either
spacelike
or
timelike
. The interval is timelike if a material object can get from one event to the other without violating the basic tenet of relativity—that it should not move faster than the speed of light.
2
In this case all observers will agree on which of the two events is earlier and which is later. Alternatively, if getting from one event to the other is impossible (that is, if it requires faster-than-light motion), the interval is spacelike. None of these events can then be caused by the other. Einstein showed that the time order of such events is observer-dependent and that there always exists an observer who will find that they occurred simultaneously.
spacetime interval
between the two events. The interval between events in spacetime plays the role analogous to the distance between points in space. Its mathematical definition is not important for us here; what is important is that the interval can be of
two kinds: it is either
spacelike
or
timelike
. The interval is timelike if a material object can get from one event to the other without violating the basic tenet of relativity—that it should not move faster than the speed of light.
2
In this case all observers will agree on which of the two events is earlier and which is later. Alternatively, if getting from one event to the other is impossible (that is, if it requires faster-than-light motion), the interval is spacelike. None of these events can then be caused by the other. Einstein showed that the time order of such events is observer-dependent and that there always exists an observer who will find that they occurred simultaneously.
In our example with Alpha Centauri, the interval turns out to be spacelike, so you will have to choose which of the two events you want to attend. In fact, in this example it is easy to figure out the answer without calculating the interval. The distance traveled by light in three years is 3 light-years; so in order to cover the 4-light-year distance to Alpha Centauri, you would have to move faster than light. In the curved spacetime of the eternally inflating universe, the analysis is more complicated, and one does have to calculate the interval.
The spacetime of an island universe is schematically illustrated in
Figure 10.1
. The vertical direction is time, and the horizontal direction is one of the three spatial dimensions; the other two dimensions are not shown. Each horizontal line gives a snapshot of the universe at a moment of time. You can follow the history of the island universe by starting with a horizontal dotted line marked “before” at the bottom of the figure and gradually moving it upward. (The moment of time represented by this line is in the inflating part of spacetime, where the island universe has not yet formed.) The thick solid line labeled “Big Bang” is the boundary between the island universe and the inflationary part of spacetime. The location marked by a black galaxy is the here and now, and white galaxies mark spacetime regions where the conditions are similar to what we have here today. The horizontal dotted line labeled “now” represents the present time. It shows the island universe with a barren central region and some star-forming regions close to the boundaries.
Figure 10.1
. The vertical direction is time, and the horizontal direction is one of the three spatial dimensions; the other two dimensions are not shown. Each horizontal line gives a snapshot of the universe at a moment of time. You can follow the history of the island universe by starting with a horizontal dotted line marked “before” at the bottom of the figure and gradually moving it upward. (The moment of time represented by this line is in the inflating part of spacetime, where the island universe has not yet formed.) The thick solid line labeled “Big Bang” is the boundary between the island universe and the inflationary part of spacetime. The location marked by a black galaxy is the here and now, and white galaxies mark spacetime regions where the conditions are similar to what we have here today. The horizontal dotted line labeled “now” represents the present time. It shows the island universe with a barren central region and some star-forming regions close to the boundaries.
A simple calculation showed that all big bang events, which are located along the solid line in the figure, are separated by spacelike intervals. That was the key observation; it gave me the answer to my question about the future
of civilizations. It also completely changed the way I viewed the island universes.
of civilizations. It also completely changed the way I viewed the island universes.
Figure 10.1
.
Spacetime diagram of an island universe (global view).
.
Spacetime diagram of an island universe (global view).
The spacelike character of the intervals means that you cannot get from any one of the big bang events to any other. In other words, you cannot keep up with the expanding boundaries of the island universe: they are expanding faster than the speed of light. Thus, we will never be able to reach the shores of the inflating sea and bask in the light of the new suns that will be born there. We cannot even send any messages to the future civilizations that will thrive around these suns, since no signal can travel faster than light. Regrettably, eternal inflation does not seem to improve the long-term prospects for humanity.
You may be puzzled by faster-than-light expansion of island universes, as it apparently contradicts Einstein’s ban on superluminal velocities. The ban, however, is very specific: it applies only to the motion of material objects (including radiation, such as light or gravitational waves) relative to one another, while the boundary of an island universe is a geometric entity, which does not have any mass or energy.
The faster-than-light expansion of the boundary means that successive big bangs cannot be causally related. They are not like a row of dominoes,
where the fall of one domino triggers the fall of the next. The progression of false-vacuum decay is predetermined by the pattern of the scalar field that was produced during inflation. The field variation in space is very gradual, and as a result the false-vacuum decay in nearby regions occurs almost simultaneously. That is why the big bangs happen in such a quick succession and the boundary is advancing so fast.
where the fall of one domino triggers the fall of the next. The progression of false-vacuum decay is predetermined by the pattern of the scalar field that was produced during inflation. The field variation in space is very gradual, and as a result the false-vacuum decay in nearby regions occurs almost simultaneously. That is why the big bangs happen in such a quick succession and the boundary is advancing so fast.
I confess to You, Lord, that I still don’t know what time is.
—SAINT AUGUSTINE
What do we actually mean when we say that the big bang at the boundary of an island universe occurred later than it did in the central region? Since all the big bang events are spacelike-separated, different observers will disagree on which of these events occurred earlier and which later. Whom, then, should we listen to? Whose clock should we use to time the big bangs? We shall now stop to reflect upon this issue. The analysis is somewhat intricate, but it’s worth the effort, as it leads to some far-reaching implications.
As a warm-up exercise, let us first consider a homogeneous universe described by one of the Friedmann models. Homogeneity means that matter is uniformly distributed in space at any moment of time. This sounds simple, but we need to define what is meant by a “moment of time.”
When cosmologists talk about a “moment of time,” they picture a large number of observers, equipped with clocks, and scattered throughout the universe. Each observer can see a small region in her immediate vicinity, but the whole assembly of observers is needed to describe the entire universe. We can think of ourselves as one member in this assembly. Our clock now shows the time 14 billion years A.B.
y
“The same time” in another part of the universe is when the clock of the observer located there shows the same reading. We have to decide, though, how observers, who are outside each other’s horizon, are to synchronize their clocks.
y
“The same time” in another part of the universe is when the clock of the observer located there shows the same reading. We have to decide, though, how observers, who are outside each other’s horizon, are to synchronize their clocks.
In the case of Friedmann’s universe, the answer is simple: the big bang is the natural origin of time in that universe, so each observer should count
time starting from the big bang.
z
With this definition of simultaneity, the matter density measured by all observers at the same time will be the same, so the universe is homogeneous.
time starting from the big bang.
z
With this definition of simultaneity, the matter density measured by all observers at the same time will be the same, so the universe is homogeneous.
We could, in principle, imagine an assembly of observers whose clocks are set up differently. For example, we could offset the origin of time by some amount away from the big bang and make this amount vary from one region of space to another. The universe would then look very complex and inhomogeneous. Of course, no one in his right mind would use such a description. It merely complicates matters and conceals the true nature of Friedmann’s universe. But things are not always so straightforward.
Going back to the eternally inflating universe, let us first consider a large region, like the one shown in
Figure 8.3
, which includes both island universes and inflating domains. There is no obvious choice for the origin of time in such a region. The definition of a “moment of time” is therefore largely arbitrary, the only condition being that all events at that “moment” should be separated by spacelike intervals. Once the choice is made for one such moment, the clocks of the observers are set and the notion of time is defined for the whole subsequent history of the region. If we choose the initial moment early enough, when the entire region is in the false-vacuum state, then at later times island universes will appear and expand, as we discussed in the preceding section. But the order of their appearance and the pace and pattern of their expansion can be rather different for different choices of the initial “moment.”
Figure 8.3
, which includes both island universes and inflating domains. There is no obvious choice for the origin of time in such a region. The definition of a “moment of time” is therefore largely arbitrary, the only condition being that all events at that “moment” should be separated by spacelike intervals. Once the choice is made for one such moment, the clocks of the observers are set and the notion of time is defined for the whole subsequent history of the region. If we choose the initial moment early enough, when the entire region is in the false-vacuum state, then at later times island universes will appear and expand, as we discussed in the preceding section. But the order of their appearance and the pace and pattern of their expansion can be rather different for different choices of the initial “moment.”
Suppose now that we are interested in one specific island universe and want to describe it from the point of view of its inhabitants. The situation is then entirely different. As in the case of the Friedmann universe, there is now a natural choice for the origin of time. All observers inhabiting the island universe can count time from the big bang at their respective locations. In other words, the big bang can be chosen as the initial “moment of time.” This choice leads to a new, and drastically different, picture of the island universe. To distinguish between the large-region and single-island descriptions, we shall refer to them as “global” and “local” (or “internal”) views, respectively.
The internal view of the island universe is illustrated in the spacetime diagram of
Figure 10.2
. As in
Figure 10.1
, the moment of the big bang is represented by a solid curve marked “Big Bang.” The density of matter at all the big bang events on this curve is very nearly the same, as it is determined by the density of the decaying false vacuum. Thus, in the local view, the island universe is nearly homogeneous. The present moment in this view is represented by the dotted line marked “now,” which coincides with the line of galaxies in the figure. All points on this line are characterized by the same average density of matter and the same density of stars as observed in our local part of the universe. But most remarkably, from the internal point of view the island universe is infinite!
Figure 10.2
. As in
Figure 10.1
, the moment of the big bang is represented by a solid curve marked “Big Bang.” The density of matter at all the big bang events on this curve is very nearly the same, as it is determined by the density of the decaying false vacuum. Thus, in the local view, the island universe is nearly homogeneous. The present moment in this view is represented by the dotted line marked “now,” which coincides with the line of galaxies in the figure. All points on this line are characterized by the same average density of matter and the same density of stars as observed in our local part of the universe. But most remarkably, from the internal point of view the island universe is infinite!
In the global view, the island universe grows with time, as new big bangs go off at its boundary, and gets arbitrarily large if you wait long enough. But in the local view, the big bangs happen all at once and the island universe is infinitely large from the very beginning. In
Figure 10.2
, this infinity is reflected in the fact that the solid line representing the big bang never comes to an end. Extensions of this curve correspond to later and later big bangs in the global view and to more and more distant regions at the initial moment in the local view. The infinity of time in one view is thus transformed into the infinity of space in the other.
Figure 10.2
, this infinity is reflected in the fact that the solid line representing the big bang never comes to an end. Extensions of this curve correspond to later and later big bangs in the global view and to more and more distant regions at the initial moment in the local view. The infinity of time in one view is thus transformed into the infinity of space in the other.
Figure 10.2
.
Internal view of the island universe spacetime.
.
Internal view of the island universe spacetime.
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