September 28, 2010
Book review: The Grand Design (Part 2 of 4: The basic ideas)
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.
It is like the way we create accurate but flat maps of the Earth's surface. Because the Earth's surface is curved, no single flat map can ever do the entire job for us. Instead we are forced to take small portions of the globe and map each region separately. As long as the boundaries match up correctly, we effectively have a global flat map, although such a collection is not as elegant as having a single flat map. The versions of M-theory in each domain are referred to as 'effective' theories and are supposedly as real as those theories can get.
One big problem with dealing with the origins of the universe is how to deal with the so-called 'singularity' problem, in which the gravitational fields are so large due to the compression of the universe into a tiny space that space becomes so warped that the laws of physics we have (which were designed for flat spaces) break down. Hawking suggests that there is a way to overcome this hurdle, which he calls the 'no boundary' condition. He says that, "once we add the effects of quantum theory to the theory or relativity, in extreme cases warpage can occur to such a great extent that time behaves like another dimension of space." (p. 134) This is because of a technical maneuver in which time is treated as an imaginary quantity. ('Imaginary' in the scientific sense has a very precise mathematical meaning and does not have the everyday meaning of existing only in one's head.) "The realization that time behaves like space… removes the age-old objection to the universe having a beginning, but also means that that the beginning of the universe was governed by the laws of science and doesn't need to be set in motion by some god." (p. 135) (In chapter 8 of his earlier book A Brief History of Time Hawking describes the no boundary proposal in more detail and says that its predictions have been borne out.)
The amalgamation of M-theory with the no boundary condition is the central feature of Hawking's argument.
M-theory itself is a combination of string theory (in which elementary particles are assumed to be not point-like but like bits of vibrating string, either open or closed in loops) and supergravity (which itself is a combination of the theory of gravity and a theory of particle physics known as supersymmetry, one feature of which is that every particle we are familiar with has to have a partner particle with specific properties.)
M-theory requires eleven space-time dimensions. We cannot directly determine (at least as yet) the form of the laws of science in the eleven-dimensional space. Since we appear to exist in four space-time dimensions (three space and one time), the absence of those other dimensions need to be explained. The unobservable seven dimensions are assumed to be curled up to be so tiny that we cannot detect them at the present time with our present technology, giving us the illusion that we live in just four dimensions. The way the seven extra dimensions curl up is not uniquely determined and how they do so determines the nature of the laws we perceive in our reduced four-dimensional space. The number of ways in which they can be curled up, and hence the resulting number of potential universes each with its own laws and matter and parameters, can be as high as 10500! This is a staggeringly high number that is hard to even wrap our minds around but, as I will discuss in the next part of this review, it plays an important role in answering the questions raised in the book.