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Theologians have often welcomed any evidence for the beginning of the universe, regarding it as evidence for the existence of God. In the 1950s the accumulating evidence for the big bang inspired enthusiasm in theological circles and among some religiously inclined scientists. “As to the first cause
of the universe,” wrote the British physicist Edward Milne, “in the context of expansion, this is left for the reader to insert, but our picture is incomplete without Him.”
10
The big bang theory even received an official endorsement from the Roman Catholic Church. In his 1951 address to the Pontifical Academy of Sciences, Pope Pius XII said that it “has confirmed … the well-founded deduction as to the epoch when the cosmos came forth from the hands of the Creator. Hence, Creation took place. Therefore there is a Creator. Therefore God exists!”
11
of the universe,” wrote the British physicist Edward Milne, “in the context of expansion, this is left for the reader to insert, but our picture is incomplete without Him.”
10
The big bang theory even received an official endorsement from the Roman Catholic Church. In his 1951 address to the Pontifical Academy of Sciences, Pope Pius XII said that it “has confirmed … the well-founded deduction as to the epoch when the cosmos came forth from the hands of the Creator. Hence, Creation took place. Therefore there is a Creator. Therefore God exists!”
11
For the same reasons that made the pope so exuberant, the natural instinct of most scientists has been to reject the idea of a cosmic beginning. “To deny the infinite duration of time,” asserted the Nobel Prize-winning German chemist Walter Nernst, “would be to betray the very foundations of science.”
12
The beginning of the universe looked too much like a divine intervention; there seemed to be no possibility to describe it scientifically. This was one thing scientists and theologians seemed to agree upon.
12
The beginning of the universe looked too much like a divine intervention; there seemed to be no possibility to describe it scientifically. This was one thing scientists and theologians seemed to agree upon.
So, what do we make of a proof that the beginning is unavoidable? Is it a proof of the existence of God? This view would be far too simplistic. Anyone who attempts to understand the origin of the universe should be prepared to address its logical paradoxes. In this regard, the theorem that I proved with my colleagues does not give much of an advantage to the theologian over the scientist. As evidenced by Jinasena’s remarks earlier in this chapter, religion is not immune to the paradoxes of Creation.
Also, the scientists might have been too rash to admit that the cosmic beginning cannot be described in purely scientific terms. True, it is hard to see how this can be done. But things that seem to be impossible often reflect only the limitations of our imagination.
Creation of Universes from Nothing
Nothing can be created from nothing.
—LUCRETIUS
B
ack in 1982, inflation was still a very new field, full of unexplored ideas and challenging problems—a gold mine for an aspiring young cosmologist. The most intriguing of these problems, and perhaps the least relevant for the present state of the universe, was the question of how inflation could have started. An inflating universe quickly “forgets” its initial conditions, so the state at the onset of inflation has little effect on what happens afterward. Thus, if you want to find ways of testing inflation observationally, you should not waste your time worrying about how it began. But the puzzle of the beginning was still there and could not be avoided. It drew me like a magnet.
ack in 1982, inflation was still a very new field, full of unexplored ideas and challenging problems—a gold mine for an aspiring young cosmologist. The most intriguing of these problems, and perhaps the least relevant for the present state of the universe, was the question of how inflation could have started. An inflating universe quickly “forgets” its initial conditions, so the state at the onset of inflation has little effect on what happens afterward. Thus, if you want to find ways of testing inflation observationally, you should not waste your time worrying about how it began. But the puzzle of the beginning was still there and could not be avoided. It drew me like a magnet.
At first sight, the problem looked relatively simple. We know that a small region of space filled with false vacuum is enough to drive inflation. So, all I had to figure out was how such a region could have arisen from some earlier state of the universe.
The prevailing view at the time was based on the Friedmann model, where the universe expanded from a singular state of infinite curvature and
infinite matter density. Assuming that the universe is filled with a high-energy false vacuum, any matter that was initially present is diluted, and the vacuum energy eventually dominates. At that point, the repulsive gravity of the vacuum takes over, and inflation begins.
infinite matter density. Assuming that the universe is filled with a high-energy false vacuum, any matter that was initially present is diluted, and the vacuum energy eventually dominates. At that point, the repulsive gravity of the vacuum takes over, and inflation begins.
This would be fine, except, Why was the universe expanding to begin with? One of the achievements of inflation was to explain the expansion of the universe. Yet, it looked as if we needed to have expansion before inflation even started. The attractive gravity of matter is initially much stronger than the gravitational repulsion of the vacuum, so if we don’t postulate a strong initial blast of expansion, the universe would simply collapse and inflation would never begin.
I pondered this argument for a while, but the logic was very simple and there seemed to be no escape. Then, suddenly, I realized that instead of collapsing, the universe could do something much more interesting and dramatic …
Suppose we have a closed spherical universe, filled with a false vacuum and containing a certain amount of ordinary matter. Suppose also that this universe is momentarily at rest, neither expanding nor contracting. Its future will depend on its radius. If the radius is small, the matter is compressed to a high density and the universe will collapse to a point. If the radius is large, the vacuum energy dominates and the universe will inflate. Small and large radii are separated by an energy barrier, which cannot be crossed unless the universe is given a large expansion velocity.
What I suddenly realized was that the collapse of a small universe was inevitable only in classical physics. In quantum theory, the universe could
tunnel
through the energy barrier and emerge on the other side—like a nuclear particle in Gamow’s theory of radioactive decay.
tunnel
through the energy barrier and emerge on the other side—like a nuclear particle in Gamow’s theory of radioactive decay.
This looked like a neat solution to the problem. The universe starts out extremely small and is most likely to collapse to a singularity. But there is a small chance that instead of collapsing, it will tunnel through the barrier to a bigger radius and start inflating (see
Figure 17.1
). So, in the grander scheme of things, there will be loads of failed universes that will exist only for a fleeting moment, but there will also be some that will make it big.
Figure 17.1
). So, in the grander scheme of things, there will be loads of failed universes that will exist only for a fleeting moment, but there will also be some that will make it big.
I felt that I was making progress, so I pressed on. Is there any bound to how small the initial universe could be? What happens if we allow it to get smaller and smaller? To my surprise, I found that the tunneling probability
did not vanish as the initial size approached zero. I also noticed that my calculations were greatly simplified when I allowed the initial radius of the universe to vanish. This was really crazy: what I had was a mathematical description of a universe tunneling from a zero size—from nothing!—to a finite radius and beginning to inflate. It looked as though there was no need for the initial universe!
did not vanish as the initial size approached zero. I also noticed that my calculations were greatly simplified when I allowed the initial radius of the universe to vanish. This was really crazy: what I had was a mathematical description of a universe tunneling from a zero size—from nothing!—to a finite radius and beginning to inflate. It looked as though there was no need for the initial universe!
Figure 17.1
.
On the left, a spacetime diagram of a closed Friedmann universe expanding from a singularity, reaching a maximum radius and recollapsing. Time grows in the vertical direction, and horizontal circles give snapshots of the universe at different moments of time. On the right, a universe dominated by vacuum energy, which contracts and re-expands (de Sitter spacetime). Instead of recollapsing, the universe on the left can tunnel through the energy barrier to a larger radius and start expanding. The spacetime history of the universe will then include only the shaded parts of the two spacetimes.
.
On the left, a spacetime diagram of a closed Friedmann universe expanding from a singularity, reaching a maximum radius and recollapsing. Time grows in the vertical direction, and horizontal circles give snapshots of the universe at different moments of time. On the right, a universe dominated by vacuum energy, which contracts and re-expands (de Sitter spacetime). Instead of recollapsing, the universe on the left can tunnel through the energy barrier to a larger radius and start expanding. The spacetime history of the universe will then include only the shaded parts of the two spacetimes.
The concept of a universe materializing out of nothing boggles the mind. What exactly is meant by “nothing”? If this “nothing” could tunnel into something, what could have caused the primary tunneling event? And what about energy conservation? But as I kept thinking about it, the idea appeared to make more and more sense.
The initial state prior to the tunneling is a universe of vanishing radius, that is, no universe at all. There is no matter and no space in this very peculiar state. Also, there is no time. Time has meaning only if something is happening
in the universe. We measure time using periodic processes, like the rotation of the Earth about its axis, or its motion around the Sun. In the absence of space and matter, time is impossible to define.
in the universe. We measure time using periodic processes, like the rotation of the Earth about its axis, or its motion around the Sun. In the absence of space and matter, time is impossible to define.
And yet, the state of “nothing” cannot be identified with
absolute
nothingness. The tunneling is described by the laws of quantum mechanics, and thus “nothing” should be subjected to these laws. The laws of physics must have existed, even though there was no universe. I will have more to say about this in Chapter 19.
absolute
nothingness. The tunneling is described by the laws of quantum mechanics, and thus “nothing” should be subjected to these laws. The laws of physics must have existed, even though there was no universe. I will have more to say about this in Chapter 19.
As a result of the tunneling event, a finite-sized universe, filled with a false vacuum, pops out of nowhere (“nucleates”) and immediately starts to inflate. The radius of the newborn universe is determined by the vacuum energy density: the higher the density, the smaller the radius. For a grand-unified vacuum, it is one hundred-trillionth of a centimeter. Because of inflation, this tiny universe grows at a staggering rate, and in a small fraction of a second it becomes much greater than the size of our observable region.
If there was nothing before the universe popped out, then what could have caused the tunneling? Remarkably, the answer is that no cause is required. In classical physics, causality dictates what happens from one moment to the next, but in quantum mechanics the behavior of physical objects is inherently unpredictable and some quantum processes have no cause at all. Take, for example, a radioactive atom. It has some probability of decaying, which is the same from this minute to the next. Eventually, it will decay, but there will be nothing that causes it to decay at that particular moment. Nucleation of the universe is also a quantum process and does not require a cause.
Most of our concepts are rooted in space and time, and it is not easy to create a mental picture of a universe popping out of nothing. You cannot imagine that you are sitting in “nothing” and waiting for a universe to materialize—because there is no space to sit in and there is no time.
In some recently proposed models based on string theory, our space is a three-dimensional membrane (brane) floating in a higher-dimensional space. In such models, we can imagine a higher-dimensional observer watching small bubble universes—braneworlds—pop out here and there, like bubbles of vapor in a boiling pot of water. We live on one of the bubbles, which is an expanding three-dimensional spherical brane. For us, this brane is the only space there is. We cannot get out of it and are unaware of the extra dimensions. As we follow the history of our bubble universe back in
time, we come to the moment of nucleation. Beyond that, our space and time disappear.
time, we come to the moment of nucleation. Beyond that, our space and time disappear.
From this picture, there is only a small step to the one that I originally proposed. Simply remove the higher-dimensional space. From our internal point of view, nothing will change. We live in a closed, three-dimensional space, but this space is not floating anywhere. As we go back in time, we discover that our universe had a beginning. There is no spacetime beyond that.
An elegant mathematical description of quantum tunneling can be obtained using the so-called
Euclidean time
. This is not the kind of time you measure with your watch. It is expressed using imaginary numbers, like the square root of -1, and is introduced only for computational convenience. Making the time Euclidean has a peculiar effect on the character of spacetime : the distinction between time and the three spatial dimensions completely disappears, so instead of spacetime we have a four-dimensional space. If we could live in Euclidean time, we would measure it with a ruler, just as we measure length. Although it may appear rather odd, the Euclidean-time description is very useful: it provides a convenient way to determine the tunneling probability and the initial state of the universe as it emerges into existence.
Euclidean time
. This is not the kind of time you measure with your watch. It is expressed using imaginary numbers, like the square root of -1, and is introduced only for computational convenience. Making the time Euclidean has a peculiar effect on the character of spacetime : the distinction between time and the three spatial dimensions completely disappears, so instead of spacetime we have a four-dimensional space. If we could live in Euclidean time, we would measure it with a ruler, just as we measure length. Although it may appear rather odd, the Euclidean-time description is very useful: it provides a convenient way to determine the tunneling probability and the initial state of the universe as it emerges into existence.
The birth of the universe can be graphically represented by the spacetime diagram in
Figure 17.2
. The dark hemisphere at the bottom corresponds to quantum tunneling (time is Euclidean in this part of the spacetime). The light surface above it is the spacetime of the inflating universe. The boundary between the two spacetime regions is the universe at the moment of nucleation.
Figure 17.2
. The dark hemisphere at the bottom corresponds to quantum tunneling (time is Euclidean in this part of the spacetime). The light surface above it is the spacetime of the inflating universe. The boundary between the two spacetime regions is the universe at the moment of nucleation.
A remarkable feature of this spacetime is that it has no singularities. A Friedmann spacetime has a singular point of infinite curvature at the beginning, where the mathematics of Einstein’s equations breaks down. It is represented by the sharp point (labeled “singularity”) at the bottom on the left-hand side of
Figure 17.1
. In contrast, the Euclidean spherical region has no such points; it has the same finite curvature everywhere. This was the first mathematically consistent description of how the universe could be born. The spacetime diagram of
Figure 17.2
, which looks a bit like a badminton shuttlecock is now on the logo of the Tufts Institute of Cosmology.
Figure 17.1
. In contrast, the Euclidean spherical region has no such points; it has the same finite curvature everywhere. This was the first mathematically consistent description of how the universe could be born. The spacetime diagram of
Figure 17.2
, which looks a bit like a badminton shuttlecock is now on the logo of the Tufts Institute of Cosmology.
I wrote all this up in a short paper entitled “Creation of Universes from
Nothing.”
1
Before submitting it to a journal, I made a day trip to Princeton University, to discuss these ideas with Malcolm Perry, a well-known expert on the quantum theory of gravitation. After an hour at the blackboard, Malcolm said, “Well, maybe this is not so crazy … How come I have not thought of it myself ?” What better compliment can you get from a fellow physicist!
Nothing.”
1
Before submitting it to a journal, I made a day trip to Princeton University, to discuss these ideas with Malcolm Perry, a well-known expert on the quantum theory of gravitation. After an hour at the blackboard, Malcolm said, “Well, maybe this is not so crazy … How come I have not thought of it myself ?” What better compliment can you get from a fellow physicist!
Figure 17.2
.
A spacetime diagram of the universe tunneling from nothing.
.
A spacetime diagram of the universe tunneling from nothing.
My model of the universe tunneling out of nothing did not appear from nothing—I had some predecessors. The first suggestion of this sort came from Edward Tryon of Hunter College, City University of New York. He proposed the idea that the universe was created out of vacuum as a result of a quantum fluctuation.
The thought first occurred to him in 1970, during a physics seminar. Tryon says that it struck him like a flash of light, as if some profound truth had suddenly been revealed to him. When the speaker paused to collect his thoughts, Tryon blurted out, “Maybe the universe is a vacuum fluctuation!” The room roared with laughter.
2
2
As we discussed earlier, the vacuum is anything but dull or static; it is a site of frantic activity. Electric, magnetic, and other fields are constantly fluctuating on subatomic scales because of unpredictable quantum jerks. The spacetime geometry is also fluctuating, resulting in a frenzy of spacetime foam at the Planck distance scale. In addition, the space is full of
virtual
particles, which spontaneously pop out here and there and instantly disappear. The virtual particles are very short-lived, because they live on borrowed energy. The energy loan needs to be paid off, and according to Heisenberg’s uncertainty principle, the larger the energy borrowed from the vacuum, the faster it has to be repaid. Virtual electrons and positrons typically disappear in about one-trillionth of a nanosecond. Heavier particles last even less than that, as they require more energy to materialize. Now, what Tryon was suggesting was that our entire universe, with its vast amount of matter, was a huge quantum fluctuation, which somehow failed to disappear for more than 10 billion years. Everybody thought that was a very funny joke.
virtual
particles, which spontaneously pop out here and there and instantly disappear. The virtual particles are very short-lived, because they live on borrowed energy. The energy loan needs to be paid off, and according to Heisenberg’s uncertainty principle, the larger the energy borrowed from the vacuum, the faster it has to be repaid. Virtual electrons and positrons typically disappear in about one-trillionth of a nanosecond. Heavier particles last even less than that, as they require more energy to materialize. Now, what Tryon was suggesting was that our entire universe, with its vast amount of matter, was a huge quantum fluctuation, which somehow failed to disappear for more than 10 billion years. Everybody thought that was a very funny joke.
But Tryon was not joking. He was devastated by the reaction of his colleagues, to the extent that he forgot his idea and suppressed the memory of the whole incident. But the idea continued brewing at the back of his mind and resurfaced three years later. At that time, Tryon decided to publish it. His paper appeared in 1973 in the British science journal
Nature
, under the title “Is the Universe a Vacuum Fluctuation?”
Nature
, under the title “Is the Universe a Vacuum Fluctuation?”
Tryon’s proposal relied upon a well-known mathematical fact—that the energy of a closed universe is always equal to zero. The energy of matter is positive, the gravitational energy is negative, and it turns out that in a closed universe the two contributions exactly cancel each other. Thus, if a closed universe were to arise as a quantum fluctuation, there would be no need to borrow energy from the vacuum and the lifetime of the fluctuation could be arbitrarily long.
The creation of a closed universe out of the vacuum is illustrated in
Figure 17.3
. A region of flat space begins to swell, taking the shape of a balloon. At the same time, a colossal number of particles are spontaneously created in that region. The balloon eventually pinches off, and—voilà—we have a closed universe, filled with matter, that is completely disconnected from the original space.
3
Tryon suggested that our universe could have originated in this way and emphasized that such a creation event would not require
a cause. “In answer to the question of why it happened,” he wrote, “I offer the modest proposal that our universe is simply one of those things which happen from time to time.”
4
Figure 17.3
. A region of flat space begins to swell, taking the shape of a balloon. At the same time, a colossal number of particles are spontaneously created in that region. The balloon eventually pinches off, and—voilà—we have a closed universe, filled with matter, that is completely disconnected from the original space.
3
Tryon suggested that our universe could have originated in this way and emphasized that such a creation event would not require
a cause. “In answer to the question of why it happened,” he wrote, “I offer the modest proposal that our universe is simply one of those things which happen from time to time.”
4
Figure 17.3
.
A closed universe pinches off a large region of space.
.
A closed universe pinches off a large region of space.
The main problem with Tryon’s idea is that it does not explain why the universe is so large. Closed baby universes are constantly pinched off any large region of space, but all this activity occurs at the Planck distance scale, as in the spacetime foam picture shown in
Figure 12.1
. Formation of a large closed universe is possible in principle, but the probability for this to happen is much smaller than that for a monkey to randomly type the full text of Shakespeare’s
Hamlet
.
Figure 12.1
. Formation of a large closed universe is possible in principle, but the probability for this to happen is much smaller than that for a monkey to randomly type the full text of Shakespeare’s
Hamlet
.
In his paper Tryon argued that even if most of the universes are tiny, observers can only evolve in a large universe and therefore we should not be surprised that we live in one. But this falls short of resolving the difficulty, because our universe is much larger than necessary for the evolution of life.
A more fundamental problem is that Tryon’s scenario does not really explain the origin of the universe. A quantum fluctuation of the vacuum assumes that there was a vacuum of some pre-existing space. And we now know that “vacuum” is very different from “nothing.” Vacuum, or empty space, has energy and tension, it can bend and warp, so it is unquestionably
something
.
5
As Alan Guth wrote, “In this context, a proposal that the universe was created from empty space is no more fundamental than a proposal that the universe was spawned by a piece of rubber. It might be true, but one would still want to ask where the piece of rubber came from.”
6
something
.
5
As Alan Guth wrote, “In this context, a proposal that the universe was created from empty space is no more fundamental than a proposal that the universe was spawned by a piece of rubber. It might be true, but one would still want to ask where the piece of rubber came from.”
6
The picture of quantum tunneling from nothing has none of these problems. The universe is tiny right after tunneling, but it is filled with a false vacuum and immediately starts to inflate. In a fraction of a second, it blows up to a gigantic size.
Prior to the tunneling, no space or time exists, so the question of what happened
before
is meaningless.
Nothing
—a state with no matter, no space, and no time—appears to be the only satisfactory starting point for the creation.
before
is meaningless.
Nothing
—a state with no matter, no space, and no time—appears to be the only satisfactory starting point for the creation.
A few years after publishing my tunneling-from-nothing paper, I realized that I had missed an important reference. Normally, one finds out about such things much sooner, by way of pesky e-mails from the omitted authors. But this author did not write to me, and for a good reason: he did his work more than 1,500 years ago. He was Saint Augustine, the bishop of Hippo, one of the major cities in northern Africa.
Augustine grappled with the question of what God was doing before the creation—a quest he eloquently described in his
Confessions
. “For if he was idle … and doing nothing, then why did he not continue in that state forever—doing nothing, as he has always done?” Augustine thought that in order to answer his question, he first had to figure out what time is: “What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know.” A lucid analysis led him to the realization that time could be defined only through motion and could not, therefore, exist before the universe. Augustine’s final conclusion was that “[t]he world was made not in time, but simultaneously with time. There was no time before the world.” And thus it is meaningless to ask what God was doing then. “If there was no time, there was no ‘then.’”
7
This is very close to what I argued in my tunneling-from-nothing scenario.
Confessions
. “For if he was idle … and doing nothing, then why did he not continue in that state forever—doing nothing, as he has always done?” Augustine thought that in order to answer his question, he first had to figure out what time is: “What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know.” A lucid analysis led him to the realization that time could be defined only through motion and could not, therefore, exist before the universe. Augustine’s final conclusion was that “[t]he world was made not in time, but simultaneously with time. There was no time before the world.” And thus it is meaningless to ask what God was doing then. “If there was no time, there was no ‘then.’”
7
This is very close to what I argued in my tunneling-from-nothing scenario.
I learned about Augustine’s ideas accidentally, in a conversation with my Tufts colleague Kathryn McCarthy. I read the
Confessions
and quoted Saint Augustine in my next paper.
8
Confessions
and quoted Saint Augustine in my next paper.
8
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