In Modern Physics and Ancient Faith, I discussed some of the speculative scenarios in which time has no beginning and the Big Bang is merely the beginning of one part of the universe or one epoch in its history. Another line of physics speculation accepts the idea that time has a beginning, either the Big Bang that occurred some 15 billion years ago, or some earlier perhaps even bigger Bang, but seeks to give that beginning a scientific explanation. Many scientists are under the impression that such an explanation would render a divine creator superfluous. As I will explain later, this notion is based on a misunderstanding of the idea of Creation. However, let us put that issue aside for now and focus on the scientific ideas.
The Reasons to Look for a Theory of the Beginning
Theories of the beginning of the universe generally are formulated within the field called “quantum cosmology.” There are several motivations for this work. At the most basic level, scientists seek to understand phenomena, and the Big Bang is a phenomenon. (I will refer to the beginning of time as “the Big Bang,” whether it is the Big Bang that happened about 15 billion years ago or some earlier event.) Scientists want to understand it in the sense of finding an adequate mathematical description of it in terms of the laws of physics. There is no reason why the Big Bang should not have such a description, and if such a description is possible it is an important goal of science to find it. A second reason to study the Big Bang is that a correct scientific understanding of it is likely to give us a better understanding of what happened after the Big Bang. For example, an important unsolved problem in physics is to explain the so-called “arrow of time.” Why is there such a profound asymmetry between past and future? The “microscopic” laws of physics that we so far know are (for the most part) “time symmetric” and do not explain time’s arrow. The arrow of time is connected with the Second Law of Thermodynamics, which says that entropy increases as one goes from past to future. Many physicists think that the arrow of time is due to the fact that the universe had extremely low entropy at the time of the Big Bang, but why the initial entropy should have been so low remains somewhat mysterious. It is to be hoped that when the Big Bang is better understood we will have answers to such questions.
The Initial Singularity
Another motivation for research on the Big Bang is the desire to avoid what is called the “initial singularity.” The word singularity has several meanings in mathematics, but it generally refers to a special point where something breaks down, often because some quantity becomes infinite. For example, in the equation near t = 0.) The point t = 0 is the so-called “initial singularity” of the universe.
Physicists do not like infinities in the solutions to their equations, or rather they tend not to believe them. The reason for this is that when infinities do show up in solving the equations that describe a physical system, it is almost always due to the fact that the system in question has been “idealized” in some way. For example, an ideal mathematical cone has infinite curvature at its tip, but the actual conical objects that are found in the real world are not perfect cones and do not have infinitely sharp points.
In physics one must often make what are called “simplifying assumptions.” It is necessary to do so, because real physical systems are far too complex to study exactly. For example, if one wants to understand the motion of a billiard ball, it makes sense for many purposes to treat the ball as if it were a perfect sphere of infinite rigidity. To treat it exactly would mean worrying about every microscopic scratch on its surface, its chemical composition, and all sorts of other details. Indeed, it would ultimately mean keeping track of every one of its atoms, which would be impossible in practice.
So, scientists have to make approximations. Sometimes they go too far, like the physicist in the old joke scientists like to tell about the “spherical cow approximation.” But a vital part of scientific training is learning how to make sensible and useful approximations. It frequently happens, because of some approximation or idealization of a system that has been made, that the calculation of a physical quantity gives an infinite result.
Suppose, for example, that one were to calculate the force experienced by two billiard balls when they collide, using the approximation that they are absolutely rigid spheres. One would find that the force, at the “instant” of collision, is infinite. Of course, that is not realistic. What happens when real billiard balls collide is that they get slightly deformed, stay in contact for some small but finite interval of time, and then spring apart. During that interval of contact the force is large but not infinite. The more rigid the balls are, the less they get deformed, the less time they remain in contact, and the greater the force they exert on each other while they are in contact. Real billiard balls, however, are not infinitely rigid, and the forces they undergo are never infinite.
Long experience has taught physicists that when they find infinities in their answers it is generally due to some invalid approximation, rather than some infinity in the real world. Therefore, it is quite natural for physicists to have the same suspicion about the “initial singularity” of the universe, and to try to find a more exact description of the Big Bang that gives finite answers.
Moreover, physicists already are aware of one improper idealization that they are making when they describe the Big Bang using Einstein’s equations: they are leaving quantum theory out of account. Normally, this is justified when dealing with gravitation, because “quantum gravity” effects are ordinarily extremely small. In fact, no quantum gravity effect has ever been observed. However, theoretical arguments imply that when the density of matter and the curvature of space-time get large enough quantum gravity effects can no longer be neglected. Such conditions were certainly realized in the Big Bang. Most physicists who think about these issues expect that in the proper quantum theoretical description of the Big Bang the initial singularity will turn out to be “softened” or washed out. Whether this happens and how it happens are obviously important questions for study. Unfortunately, at the moment, no exact quantum version of Einstein’s theory of gravity exists. Nevertheless, enough is understood about quantum theory and gravity to make some interesting speculations, and this is what quantum cosmologists do.
There are other considerations that motivate work in quantum cosmology. Some of them have to do with what are called “initial conditions.” If one wants to calculate the behavior of a physical system, it is not enough to know what the laws of physics are. One also has to have sufficient information about what that system was doing at some particular time. For example, to calculate how a baseball is going to move after it leaves the bat, one has to know exactly where it was when it left the bat, how fast it was moving, and in what direction it was moving. That means knowing six numbers: three for where the ball is in three-dimensional space, one for its speed, and two for its direction. If one specifies the condition of a system at the beginning of a process, that is called specifying the initial conditions.
One can also specify the conditions at the end of a process, so-called “final conditions.” For example, if one knows exactly how a home-run ball is moving as it goes over the fence, one can calculate how it was moving before it got there. Actually, there are many kinds of “boundary conditions” used in physics besides initial and final conditions. However, initial conditions are probably the most commonly used, because we know the past and do not know the future.
The same considerations apply to that enormous physical system we call the universe. To describe the universe completely, some appropriate boundary conditions must be specified. There is a problem, however, in specifying initial conditions for the universe: many physical quantities are infinite at t = 0, the initial singularity, and therefore cannot be specified at that point. One could always use other kinds of boundary conditions for the universe instead. One could, for example, specify the condition of the universe at some time after the beginning. But somehow that does not seem like the natural thing to do. One would like to be able to say how things started off and work forward from there. This is an additional reason why many physicists would like to get rid of the initial singularity.
However, some physicists would not be happy just finding a non-singular beginning for the universe where its initial conditions could be specified. They would prefer to avoid the necessity of specifying initial conditions for the universe altogether. The reasons for this are both aesthetic and philosophical. We have every reason to believe that the fundamental laws of physics are extremely beautiful mathematically, and in some sense even simple.(This was discussed in chapter 12 of Modern Physics and Ancient Faith.) However, as a rule, initial conditions are neither simple nor beautiful. They are just some set of numbers that do not have to have any rhyme or reason to them. In the baseball example that I used earlier, only six numbers were required to specify the initial conditions. But to specify initial conditions for the entire physical universe would presumably require a vast set of numbers—perhaps an infinite number of numbers!
This is the aesthetic motivation for trying to avoid initial conditions. The philosophical motivation is what might be called “theophobia.” One can think of the initial conditions of the universe as the cause, in some sense, of all the later developments that take place. But who set those initial conditions? One obvious candidate is God, and indeed this is precisely the role that is assigned to God by “deists”: he “wound up the universe like a watch” and let it go. Atheists would like the cosmic “watch” to be the self-winding kind.
Quantum Creation of the Universe from “Nothing”
A very interesting idea that has come out of quantum cosmology is that the creation of the universe from nothing can be explained as a “quantum fluctuation.” This is thought by some people (both atheists and theists) to be a scientific alternative to the idea of a creator. As we will explain later, it is not. But to appreciate the real significance of these ideas one must understand something of the physics involved. A full explanation would require the reader to take a course in quantum theory. Fortunately, this will not be necessary. A rough summary will suffice for our purposes.
What Quantum “Creation” Means
I will begin by describing the phenomenon of quantum creation in a more modest setting: the quantum creation of subatomic particles rather than the quantum creation of an entire “universe.” In particular, I will describe the process called the “pair creation” of particles.
Every type of particle has an opposite type called its “anti-particle.” By “opposite” I mean that certain properties of the anti-particle, such as its electric charge, are opposite to those of the particle. For example, an electron has an electric charge of -1, while its anti-particle, the “positron,” has an electric charge of +1. On the other hand, in certain respects, a particle and its anti-particle are exactly the same, rather than opposite. For example, they have exactly the same mass. Some particles are their own anti-particles, like “photons”—particles of light.
If a particle and an anti-particle—say an electron and a positron—collide, they can “annihilate.” The word annihilate literally means to reduce to “nothing” (in Latin, nihil), but that is not what actually happens when particles annihilate. Each particle has energy. Even an electron which is not moving has, as Einstein discovered, a “rest energy” equal to is the mass of the electron. The same is true of a positron, which has the same mass as an electron, as we have already mentioned. Together, then, an electron and a positron have a total rest energy of . They will have more energy than that if they are moving, for then in addition to their rest energy they will have energy of motion or “kinetic energy.” All this energy has to go somewhere when the electron and positron “annihilate,” because, as we know, energy is “conserved.” What happens (most of the time) is that gamma rays are emitted—very energetic photons—so the electron and positron “annihilate” into a burst of light.
The same process can happen in reverse. Under suitable conditions, light energy can materialize, so to speak, into an electron and a positron. This process is called pair creation.
Pair creation can also be caused by other things, for example an electric field. Imagine a volume of space permeated by an electric field, but otherwise completely empty. In that situation there
is a certain probability that suddenly an electron-positron pair will pop out of empty space. The pair creation of particles by an electric field is an inherently quantum phenomenon. Such a thing cannot happen in classical (i.e., pre-quantum) physics. Let us see why.
One might imagine the pair creation happening in the following steps. (1) There is just empty space filled with an electric field, but no particles. (2) At some instant of time, the electron and positron suddenly appear at the same point of space. (3) The electron and positron move away from each other, pulled apart by the electric field (since they have opposite charges the electric field pulls them in opposite directions). As the electric field pulls them apart, they move faster and faster, becoming more and more energetic. The kinetic energy they thus obtain comes from the electric field.
The trouble with this scenario lies in step 2. The pair of particles suddenly appearing out of empty space would mean that the amount of energy jumps by , as Einstein tells us. But the amount of energy cannot change, since energy is conserved. That is why, classically, an electric field cannot cause pair creation. So how does it happen in quantum theory? It happens by a process called quantum tunneling.
Quantum tunneling can be thought about in many ways. One way is the following. When the pair of particles suddenly appears at zero distance from each other they have rest energy equal to . Let us suppose that to compensate this they have kinetic energy, i.e., energy of motion, that is minus , a negative amount! Then their total energy would be zero, and it would cost no energy to produce them. Therefore, the principle that energy must always be conserved
would not prevent them from being produced.
But how can the particles have negative kinetic energy? Classically, they cannot. Classically, the smallest amount of kinetic energy that something can have is zero—when it is not moving. When it is moving, it has positive kinetic energy. In fact, Newton tells us that the kinetic energy of a body is proportional to the square of its velocity; and the square of a number is never negative. Quantum theory, however, allows particles to have negative kinetic energy, even though only temporarily.
What happens in the pair creation of an electron and positron by an electric field can be thought of in the following way. The pair of particles is created with total energy zero: positive rest energy and negative kinetic energy negative . The pair of particles is pulled apart by the electric field, gaining in the process more and more kinetic energy, while the energy in the electric field is correspondingly reduced. At a certain point the kinetic energy of the particles has increased to the point that it becomes positive, as classical physics says it should be. Thereafter, the behavior of the particles can be described fairly well using classical physics.
One sees, then, that the actual process of “creating” the particles and the first stage of their existence (where they have negative kinetic energy) must be described using the strange rules of quantum theory. Classical concepts become inadequate. One might say that the conception and embryonic stage of the particles’ life is only describable quantum-theoretically, whereas the post-partum period is describable fairly well classically. One of the classical concepts that breaks down during the embryonic phase of the particles’ existence is time.
We saw that during their embryonic phase the particles can be thought of as having negative kinetic energy, even though, according to Newton, kinetic energy is proportional to the square of velocity. But if the square of the velocity is negative, then the velocity itself must be an “imaginary number.” (See: chapter 12 of Modern Physics and Ancient Faith which explains why the imaginary number i is defined to be the square root of -1.) Since velocity is distance divided by time, an imaginary velocity means that the time interval is also an imaginary quantity. Thus, during the process of quantum creation of particles by “tunneling,” time itself must be thought of using radically different concepts. This will be a very important point when we come to discuss the idea of quantum creation of the universe.
One thing that should be emphasized is that one cannot predict where and when such a pair creation event will happen. Because it is a quantum process it can only be predicted probabilistically. Quantum theory tells us that fields and particles are always undergoing so-called “quantum fluctuations.” When these fluctuations get large enough, they can produce, say, a pair of particles. Another thing that should be emphasized is that this phenomenon of pair creation of particles by electric fields is not a matter of mere hypothesis or speculation. It has been observed in the laboratory, and physicists know how to calculate the proba- bility of its happening, because they have an extremely well-tested theory that describes the behavior of electrons, positrons, and electric fields called quantum electrodynamics.
Quantum Creation of Universes
The idea of quantum creation of universes has been proposed in analogy to the quantum creation of particles. To grasp this idea, we first must understand what is meant by a “universe” here. A universe is a self-contained space having some non-zero volume and possibly filled with matter of some sort. I say “a” universe, because one can imagine a plurality of such universes, having different volumes, and shapes, and matter content. In chapter 7 of Modern Physics and Ancient Faith we used the analogy of the surface of a balloon for our universe. We said that if the universe is expanding, it is like the surface of the balloon expanding, as it does when the balloon is inflated. Well, there is no reason one cannot imagine several different balloons, each balloon representing a different universe.
Just as we saw that a pair of particles can suddenly appear out of nothing (or rather out of an electric field) by a “quantum fluctuation,” so one can imagine a tiny “balloon” suddenly popping into existence out of thin air by a quantum fluctuation. Of course, we do not mean “out of thin air” literally. The little universe actually would pop into existence out of . . . out of what? Out of nothing, really. Not even out of empty space.
Remember, space is something that is part of a universe. It is the surface of the balloon that represents space. Chapter 7 of my Modern Physics and Ancient Faith tells us that we are not to imagine any inside or outside of the balloon. The only space that there is is the rubber sheet of the balloon. We are to wipe away from our imaginations any thought of an inside or outside filled with air or anything else.
So we can imagine a situation where there are seven universes, and an eighth universe suddenly pops into existence by a “quantum fluctuation.” One way that this can happen is that a small region of one of the universes (or balloons) gets “pinched off” to form a distinct universe. (The surfaces of the balloons quantum fluctuate, and one of these quantum fluctuations might happen to be large enough to pinch off.) Or it can just pop into existence apart from any of the already existing universes. One can also imagine a situation where there are no universes, and one universe suddenly pops into existence by a quantum fluctuation.
If this is the way things happened, then (as was the case with the pair creation of particles) the conception and embryonic stage of the universe we live in would have to be described using quantum concepts. This means that one could no longer take seriously the “initial singularity” that was a feature of the classical description of the Big Bang. In fact, our very ideas about the nature of time are likely to break down when applied to the beginning of the universe, for reasons already explained, so that even to talk about “an initial time” t = 0 is probably meaningless. But what concepts will be needed to speak correctly about what happened at the time of the Big Bang, no one yet knows.
The idea that our universe began as a quantum fluctuation is a very beautiful and interesting one, and quite possibly correct. However, unlike the quantum creation of particles, the quantum creation of universes remains at present just a speculative idea. We do have a theory—Einstein’s theory of gravity (the General Theory of Relativity)—that describes the way spaces or universes behave, and it is very well tested. But people do not understand sufficiently how to calculate quantum effects in that theory. Therefore, no one really knows how to give an adequate mathematical description of such a process as the quantum creation of a universe. It is hoped that someday, superstring theory will tell us how to do this. Until that day comes, we cannot say whether the idea that our universe began by a quantum fluctuation really makes sense, let alone is correct.
When Is “Nothing” Really Something?
In quantum theory—as in the classical physics that came before—one is always interested in the behavior of some “system.” The system can be as simple as a pendulum, or as complex as the whole universe. The system for a “condensed matter physicist” might be a piece of solid matter or a volume of liquid. For a nuclear physicist it might be the nucleus of an atom, or several nuclei interacting with each other. For an astrophysicist it might be a star.
In quantum theory every system no matter what it might be has a set of possible “states.” The laws of physics, in their quantum-theoretical form, tell one how to calculate the probability that a system, which initially was in one state, will later be in some other state. Thus every state has definite characteristics and is related to the other possible states of the system by definite laws.
For example, in the case of the pair creation of an electron and a positron, one starts with “the system” in a state that has an electric field but no particles, and ends up with the system in a
state that has an electron, a positron, and a somewhat different electric field. Note: the characteristics of the state have changed, but they are states of the same system.
How does one compute the likelihood that there will be a transition within a certain period of time from the former state to the latter? To perform such a calculation, one has to have a theory that describes in a precise mathematical way the interaction of electrons and positrons with electric fields. There exists such a theory, as was noted earlier, and it is called quantum electrodynamics, or QED for short. Within the framework of that theory, electrons, positrons, and electric fields act in certain prescribed ways. They do not act in an arbitrary manner. For example, in QED it is not allowed for a state with no particles to make a transition to a state with only electrons, or only positrons; the electrons and positrons must be paired. Moreover, there is greater probability for the state with no particles to make a transition to a state with one electron-positron pair than to make a transition to a state with two such pairs; and the relative probabilities can be precisely computed.
That is, the states of a system have very definite properties and relationships with other states of the same system, and these properties and relationships are governed by definite mathematical rules. It is important not to confuse a state of the system with the system itself. The system does not consist of, say, an electric field with an electron-positron pair; that is just one state of the system. The system itself is something more encompassing.
Now let us turn to “quantum creation of the universe from nothing.” What one would be calculating there, in essence, is some sort of probability that a transition would occur from a “state” with “no universe” to a “state” with “one universe.” (Or one might calculate the transition probability from a state with seven universes to one with nine universes.) No one really knows how to do such calculations yet, but let us not worry about that. Let us suppose that someday they will, and that the whole scenario will turn out to be correct. The key question for us is in what sense such a scenario can claim to explain the creation of the universe from “nothing.”
In a sense it is correct to say, in the quantum creation of the universe scenario, that there was “nothing” before the universe appeared. There were no particles, and not even any space for particles to be in. Indeed, there was not even any time, so that using words like was and were and before is an abuse of language. Of course, all this was equally true in the classical (i.e., non-quantum) description of the Big Bang, with its initial singularity, that we are trying to go beyond. In both the classical and the quantum picture, there is a universe of finite age, before the beginning of which there was nothing, not even a “before.” The more correct quantum description of the Big Bang really does not change anything fundamental in this regard.
Nevertheless, the idea of the universe appearing by means of a quantum fluctuation appears somehow to give a scientific explanation of how “nothing” can turn into something in a natural way. But does it really?
Let us look at the “no-universe state” that precedes (if we may use that word) the appearance of the universe. In a rather obvious sense the no-universe state is not really “nothing.” It is a state! It is a specific “state” of a specific, complicated quantum “system.” One can talk about a “no-universe state” only within the framework of a definite quantum system governed by definite laws. Within that framework, the no-universe state is one state among many, and has certain definite relationships to the other states. All those states are states of one system, and the equations used to calculate the transitions among those states follow from the laws governing that system, and in effect define the characteristics of that system.
One could imagine a different quantum system where the “universes” in question had not three but, say, seven dimensions, and had not the familiar kinds of matter, like electrons, but different kinds. Such a system would have different possible states. One of those states might be a state with “one universe,” but a “universe” in this case would mean something quite different from what it meant before: it would mean something seven-dimensional filled with strange stuff. There would also be a “no-universe state” of this system. But this would be something quite different from the no-universe state of the system we contemplated before. It would be part of a completely different mathematical structure. For example, this no-universe state could make transitions to states with one or more seven-dimensional universes, but not to states with three-dimensional universes. The no-universe state we were discussing previously could only make transitions to states containing one or more three-dimensional universes. Now, clearly, if one can talk about different kinds of no-universe states—as I have just shown is possible—one is clearly not talking about “nothing.”
In other words, there is a subtle equivocation going on about the word nothing. An analogy might help here. There is a difference between my having a bank account with no money in it, and having no bank account at all. The difference is not a spendable one. I may be broke in either case. But there is a difference nonetheless. For me to have a bank account—even one which has a zero or negative balance—presupposes several things: the existence of a bank, a system of money, an agreement between the bank and me that governs how money may be deposited or withdrawn (i.e., rules governing transitions between one state of my bank account and another), and so on. A complex system is in place. That system has many states. One state corresponds to there being one hundred dollars in my account, while another corresponds to there being no money in my account. That “no-money state,” in certain practical terms, but not all, may be a lot like a situation where I have no bank account at that bank, or where there is no bank or banking system at all. But it is not the same situation.
What “Creation from Nothing” Really Means
The idea that quantum theories of the Big Bang are competing against God as Creator is based on some crude misunderstandings. The real question that monotheism is attempting to deal with is a much more basic question than whether the Big Bang can be described by a mathematically consistent set of laws. It is rather why anything exists at all. Why are there any physical systems, any “states,” any laws, any anything?
Just having a mathematical framework which describes a universe with a beginning, whether the
framework is classical or quantum, or whether the beginning is smooth or mathematically singular, does not explain why that mathematical framework describes anything real. I can tell a story which gives a perfectly consistent and intelligible account of my becoming rich and explaining how I did it, but that does not imply that the story describes any real state of affairs. Such a story told about Bill Gates describes a reality; told about me it is a fantasy. One may contemplate some set of mathematical equations that purports to describe the beginnings of a universe. But is that a description of real events or of merely hypothetical events?
Physics will someday, one hopes, describe what happened at the Big Bang, but it will not tell us why it really happened rather than being just some mathematically self-consistent but never realized scenario.
The crucial question was lucidly posed by Stephen Hawking, who pointed out that a theory of physics is “just a set of rules and equations,” and then went on to ask, "What is it that breathes fire into the equations and makes a universe for them to describe?" The usual approach of science of constructing a mathematical model cannot answer the question of why there should be a universe for the model to describe.
Editorial Note: This essay is adapted from Stephen M. Barr's Modern Physics and Ancient Faith (Notre Dame, Indiana: University of Notre Dame Press, 2003), 268-278. Reprinted by permission of the University of Notre Dame Press.