In part 1 of this review I discussed the main issues raised by the book and in part 2 I said that the book by Hawking and Mlodinow argued that M-theory and the no boundary condition can provide answers to the three big questions: Why is there something rather than nothing? Why do we exist? Why this particular set of laws and not some other?

To understand what lies at the basis of M-theory, we need to appreciate a key difference between classical physics (which describes the large-scale structure of the everyday world we live in and from which we draw our intuitions about how the world works) and quantum mechanics (which describes the microscopic atomic and subatomic world).

What classical physics says is that if we release an object at some point A, it will subsequently wander off on some trajectory (or path) that depends on its initial state of motion and the forces that act on it. This is what enables good football quarterbacks to throw passes to receivers with such accuracy. If the ball is poorly thrown on a windy day and/or we stop observing the ball, we may not know or be able to predict which path the ball will take or where it will land but our classical intuition tells us that it will go along some specific path that is determined by the initial throw and the wind conditions.

But quantum mechanics has this counter-intuitive idea that once we stop observing the object, the object takes every conceivable path simultaneously. This means that there is no unique location for the object at any given time, that it is everywhere at the same time and could eventually end up anywhere at all. Another way to say it is that an object has many different histories. This is what boggles most people’s (including scientists’) minds about quantum theory but we have to learn to live and work with it (i.e., develop ‘quantum intuition’, so to speak) because this theory is phenomenally successful and there seems to be no getting around it at this time. Some people are working on developing alternative theories that do not have its strange features but have not had much success so far.

Now if we detect the object at some later time to be at some point B, this eliminates some of the potential paths we started with because they would not have resulted in the object ending up where we detected it. So the act of detection picks out a subset of the initial set of possible histories, limiting the ones of interest to those that began at point A at the specified time and ended at B at the later time, which still includes an infinite number of paths or histories. An elaborate mathematical machinery (called the ‘sum over histories’ or more technically ‘path integrals’) has been created to add up all the possible paths the particle could have taken in going from A to B. The calculated results correctly predict the empirical observations, which is why scientists have confidence in quantum theory despite its counter-intuitive features.

What M-theory does is take this key idea of quantum mechanics and apply the ‘sum over histories’ approach to the universe as a whole. Building on the idea of the inflationary universe (see part 9 and part 13 of my series Big Bang for Beginners for more details), since the net energy of the universe is zero, there is no restriction on the number of new universes that can ‘pinch’ off from previously existing universes. Since the Heisenberg uncertainty principle states that you can never have truly empty and inert space (p. 113) but that space constantly has particles coming into existence and disappearing again, any one of those fluctuations in space could form the seed of a quantum fluctuation that triggers the birth of a new universe.

So universes are being created all the time and there are a vast number of possible histories of the universe, of the order of 10⁵⁰⁰. They each have their own forms of matter and their own laws. According to the ‘sum over histories’ in quantum mechanics, all these universes exist simultaneously, giving rise to the name ‘multiverse theory’. When we observe our universe, we are picking out just those histories that could produce the present state we see. As Hawking and Mlodinow state:

Quantum physics tells us that no matter how thorough our observation of the present, the (unobserved) past, like the future, is indefinite and exists only as a spectrum of possibilities. The universe, according to quantum physics, has no single past, or history. (p. 82)
…
We seem to be at a critical point in the history of science, in which we must alter our conception of goals and of what makes a physical theory acceptable. It appears that the fundamental numbers, and even the form, of the apparent laws of nature are not determined by logic or physical principle. The parameters are free to take on many values and the laws to take on any form that leads to a self-consistent mathematical theory, and they do take on different values and forms in different universes. (p. 143)

Given the staggeringly large number of possible histories, it was almost inevitable that one of those universes would have the properties that ours has. It is like rain. If you pick a point on the ground, the probability of it being hit by a raindrop is infinitesimally small. But in a rainstorm, there is such a huge number of drops that it is inevitable that at least one will hit the ground there.

Hawking and Mlodinow’s book does not shy away from making strong claims, such as that the theory they describe has to be the right one. “M-theory is the only candidate for a complete theory of the universe… M-theory is the unified theory Einstein was hoping to find.” (p. 181, emphasis in original.)

That seems hubristic to me. If the history of science teaches us anything it is that theories, however successful at any given time, tend to be later replaced by other theories as the questions that need to be addressed change. However obviously important they may seem, is usually a mistake to think that the questions that concern us now will be the same questions that future generations care about. Also the theory of supersymmetry, which is central to M-theory though not necessarily to the idea of multiverses, has been around since 1970 or so, with none of the exotic partner particles it predicts having been detected as yet. The theory’s supporters are pinning their hopes on the Large Hadron Collider that has just started operations, hoping that its energies will be sufficient to produce these particles.

In the last part of this review, I will look at the implications of M-theory for religion and give some of my reactions to other features of the book.

In part 1 of this review, I argued that the lack of a unified theory of gravity and quantum mechanics is what has stymied scientists in their attempt to understand the origins of our universe and even what came ‘before’, assuming that the question even makes sense. M-theory and the no boundary condition is what Hawking proposes as the candidate for a unified theory that can address the physics of the early universe.

M-theory is not an elegant theory expressed in a single equation (like Newton’s law of gravity) or even a few equations (like Maxwell’s equations of electromagnetism) but instead consists of a patchwork of theories, each with its domain of application, and overlapping with other theories so that the whole space of nature is covered. Hawking argues that this patchwork feature may not be due to our lack of imagination or inventiveness but intrinsic to the nature of the laws of science.
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This new book by Stephen Hawking and Leonard Mlodinow has generated some publicity and so I thought I’d check it out. The first part of my review will explain the basic questions that are being addressed by the book, the second will describe the physics behind the solutions that the authors propose, the third part will provide some of the more basic physics background that lies behind those ideas, and the last part will discuss the religious implications of the book, which have received the most attention, and some of my own reactions.

I should warn readers that cosmology and general relativity are not my fields of study, although I am a theoretical physicist and thus familiar with the basic theories of modern physics. So my knowledge of the book’s subject matter is likely to be not that much greater than that of an informed layperson. If you want a really authoritative reaction, you will need to ask your friendly neighborhood cosmologist or read reviews by them such as the one by Sean Carroll in the Wall Street Journal.

The book seeks to address three questions: Why is there something rather than nothing? Why do we exist? Why this particular set of laws and not some other? These are, of course, big questions that have long been the province of philosophers and theologians. But modern science has wrestled such questions away from them and made them into empirical questions to be addressed the same way that science addresses any questions about the physical world, making purely philosophical and theological speculations about them superfluous. Needless to say, philosophers and theologians are not happy about this development and are trying to assert that they still have a contribution to make and it is this that largely constitutes the modern science-religion debate.

To begin, we live in a universe that has three space dimensions and one time dimension, which we think of as distinct from the space dimensions. We are comfortable with the idea that there is no ‘beginning’ to space but with the conventional big bang theory there is the sense that there is a beginning to time, which naturally raises the question of what existed before that time or what triggered the start of the universe.

One answer could well be that the universe began as a quantum fluctuation and that there was no such thing as time before the universe began. The laws of science came into being with the universe and there is no mystery of why they happened to be such as to produce life like ours because if they hadn’t been, we would not be here to ponder such questions. The laws had to take some form and the very fact of our existence means that that laws happened to be such as to produce us. Such as answer is sufficient for many people.

But the authors seek answers that go beyond that, hence the book.

At present, our understanding of the physical world is spanned by theories of gravity, quantum mechanics, electromagnetism, and the weak and strong nuclear forces, each successfully working in a specific domain of application. There has been some success in straddling the boundaries of the domains, especially those areas in which quantum mechanics, electromagnetism and the strong and weak nuclear forces overlap.

Gravity has been the tough nut, the outlier, resisting strongly all attempts at combining it with other theories, and its unification with quantum mechanics has been the major challenge. Gravity is important in dealing with massive objects like planets, stars, and galaxies, while quantum mechanics deals with the very small. We use the theories of gravity to explain the large-scale structure of the universe and quantum mechanics to explain the sub-atomic world. For most things, the two domains do not overlap. But the unification of gravity and quantum mechanics becomes important in dealing with cosmological questions because when we speak of the beginning of the universe, we are talking about the entire universe being compressed into a tiny region of space and so we need a theory that combines the two domains if we are to make sense of that early state.

The main difficulty that has stumped scientists for so long is that space and time are not distinct but are intertwined due to the warping of space by gravity. At low speeds and in the presence of weak gravitational fields, the mixing is so slight as to be not noticeable which is why we perceive them as independent. The highly successful theory of quantum mechanics was developed for use in space that is ‘flat’, i.e., not warped by gravitational effects. But when we are dealing with the origins of the universe at very early times, the density of matter is extremely high. Consequently the gravitational fields are so large and the warping of space so great that the laws of physics, which were developed for use in flat spaces, appear to break down, depriving us of the only tools we have to study the world. As a result, we could not say what happened at times very close to zero or before. This has been a big barrier to progress.

The search for a quantum theory of gravity was the search for a theory that would work even under conditions of the extreme curvature of space that constituted the beginning of our universe. The original hope of Einstein and his successors in the search for such a unified theory was that it would be simple and elegant. But many have failed in this search and that goal has proved to be frustratingly elusive.

This book outlines a solution to this problem that is currently in vogue among cosmologists. It is based on what is known as M-theory and the ‘no boundary’ condition. The book lays this out in chapter 5, which is the heart of the book. (No one seems to know who coined the name M-theory or even what M stands for. I suspect that it was tossed out casually at a physics conference and became adopted by word of mouth.)

Next: M-theory and the no boundary condition.