Where are fundamental physics and cosmology going? It is of course, impossible to know for sure: This is science, where the ultimate worth of one’s ideas is that they lead to a genuine understanding of nature. To be part of science, an idea or theory must make predictions that survive comparison with observation and experiment. Having said this, I can offer one scientist’s view on the major themes in our search for the fundamental principles and laws that underlie the universe.
The most important principle of 20th-century physics is that all observable properties of things are about relationships. Even space and time must be spoken about in terms of relationships. There is no such thing as space independent of that which exists in it and no such thing as time apart from change. This is an old idea that philosophers such as Leibniz have argued for centuries, but general relativity is the first physical theory to be based on it. Many of the important problems facing theoretical physics have to do with the change from an absolute view of properties to this relational view. For example, I think it is highly likely that this is the key to further progress in string theory.
A very important part of turning cosmology into a science is to understand all the implications of a seemingly trivial statement:
There is nothing outside the universe. One aspect of this is that there can be no observer outside the universe. We must understand the universe in a way in which the scientific description of it is a description made and used by observers who are part of the system itself. This seems to go against the idea that the scientific view of nature is objective, and an objective description is always based on observations of a system from outside. If cosmology is to be a science, we must invent a new notion of objectivity that allows the observers of the system also to be part of it.
Another aspect of this is that a scientific cosmology can contain no residue of the idea that the world was constructed by some being who is not a part of it. As the creatures who makes things, it is our most natural impulse to ask: When we come upon something beautifully or intricately structured, who made it? We must learn to give up this impulse if we are to do scientific cosmology. As there can, by definition, be nothing outside the universe, a scientific cosmology must be based on a conception that the universe made itself.
This is possible because, since Darwin, we know that structure and complexity can be self-organized. We understand that there are natural processes, easily comprehensible, by which organization can arise naturally and spontaneously, without any need for a maker outside of the system. This requires, however, that we take a more historical view of fundamental physics and cosmology. We must be open to the possibility that the answers to many of the questions we have about why the elementary particles or the fundamental forces are as they are—and not otherwise—may have answers that are, at least in part, historical.
This goes against the expectation that the more fundamental an explanation, the less historical it is. It also goes against the expectation that the ultimate answers to all questions about the elementary particles will be found with the discovery of a final, unified theory. This theory is presumed to be based on some mathematical principles that are both powerful and beautiful, in a way that will single it out for consideration as the unique possible fundamental theory.
Which fundamental theory holds true in our universe?
It hasn’t turned out this way. The best candidate we have for a fundamental theory, string theory, comes in a great many versions, which each describe different possible universes with different elementary particles governed by different laws. As far as we know, all are equally consistent unified theories. So it seems like we do have to ask why one theory rather than another describes our universe.
It is possible that all these theories are aspects of a single theory. Recent work tends to suggest that they all describe something like different phases: Just as water molecules may be organized into a liquid, solid or gas, the fundamental “stuff” seems to come in a large number of different phases, which look to observers on large scales like different fundamental theories.
We are recently making some progress towards this unified string theory.
Although its shape is not yet completely clear to us, it already has a name: “M” theory. Indeed, part of the search for this theory involves reformulating string theory in a way that is more relational, and less based on notions that space and time are absolute and independent of what exists. But it looks more and more like this theory will not allow the world to exist in a great many phases, and it will even be possible for the world to make a transition from one phase to another. Just as ice can be melted, it seems likely that in sufficiently energetic and violent events, the world may change from one phase to another, resulting in a change in the apparent laws of nature. Such violent events certainly include the approach to black hole singularities and the Big Bang of our universe.
Is There a Theory of Everything?
Thus, rather than leading to the discovery of a single fundamental theory, string theory seems itself to point to the need to include an historical aspect in fundamental physics. If we want to know all the answers to our questions about electrons and protons, we are going to have to understand why the universe we see around us emerged from the Big Bang with one set of laws rather than another.
“We in the audience are all agreed that your theory is crazy. But what divides us is whether it is crazy enough.”
—NIELS BOHR, after listening to Wolfgang Pauli present a theory of everything.
One possible answer: something like natural selection acts on the choice of the laws of physics. The basic idea is that black holes give rise to new regions of space and time, and that at these events, which resemble our Big Bang, the laws of physics can change. When worked out in detail, this idea leads to a scientific theory which makes predictions which are testable. The basic prediction is that no small change in the masses of the elementary particles or the strengths of the forces would lead to a world with more black holes than ours.
So far, although a number of astronomers have tried to find counterexamples, this prediction has held up. A neutron star with a mass at least three times that of our sun is incompatible with the theory. If one is seen, the theory is disproved!
It is also possible to imagine other ways in which historical elements could come into the laws of nature. Indeed, we are discovering that there it may be that space is itself the result of spontaneous processes of self-organization. Processes of self-organization other than natural selection have been studied by people like Per Bak and Stuart Kauffman for some time, and they are known to occur in a variety of situations. It may very well be that mechanisms like self-organized criticality, which Bak and Kauffman describe, may play a role in the emergence of space itself, from a complex primordial network of interactions.
This idea is being studied now by a number of people.
The geometry of space must be discrete. Just like matter is made of atoms, space itself must be made of discrete bits.
This conclusion has arisen from several points of view. First of all, it seems to be required by the thermodynamics of black holes, as Jacob Bekenstein has been pointing out for years. It also seems to be implied by string theory, as Lenny Susskind and Gerard ’tHooft, among others, have been arguing.
In the last few years we have also understood that the ultimate discreteness of space is loosely a consequence of combining the basic principles of quantum mechanics and general relativity. Quantum gravity predicts that the volumes of regions in space and the areas of surfaces must come in discrete units, like the energy levels of atoms. We are even able to make precise predictions about the discrete units of area and volume.
This discovery was a great pleasure because we rediscovered a beautiful set of structures, called spin networks, that our theory tells us are descriptions of the discrete forms of space.
These structures were originally invented by Roger Penrose more than thirty years ago, as a first guess of what a discrete geometry of space would look like. It has been very gratifying to be able to confirm that Penrose's intuition was essentially correct.
Once this is understood, we are faced with a new question: How do these discrete bits of space assemble themselves into a smooth structure that looks like the space we see around us? This turns out to be very much like asking why atoms often assemble themselves into solids, like plastics or metals, that look smooth when examined at scales larger than the atoms. It seems to be the case that without some special organization, the discrete bits of space—the networks—do not assemble themselves into big smooth structures that could describe the featureless space we observe. Instead, they typically form chaotic structures that do not resemble any previous notion of space.
Thus, we are faced with the very real possibility that the fact that the world has any spatial extension at all is a contingent historical fact, that also requires explanation by some principle of self-organization. We are working on this now, and there seems to be good progress. The outcome of this work will be a unification of the different approaches that have led to an expectation that space is discrete, including string theory and black hole thermodynamics.
Most provocative is the possibility that, for this to work, we will have to extend the Darwinian idea that the structure of a system must be formed from within by natural processes of self-organization—to the properties of space and time themselves.
In fact, there are other reasons to expect that space and time should be self-organized. Systems which are self-organized turn out to be complex systems. What is a complex system? What is complexity? One approach to this question, is to define the complexity of a system in terms of the variety of the interactions of the parts of the system. Roughly speaking, the more variety a system has, the easier it is to distinguish the parts of the system from each other by describing each of their neighborhoods. In these terms, a complex universe is one in which the view from every place is different from the view from any other place. But, space itself is defined only by the relationships among things.
This means that the more complex a universe is, the easier it is to define space in terms of relationships.
This means that there is a deep and fundamental connection between the idea that space and time are to be defined solely in terms of relationships and the idea that the world is a complex system whose structure is to be explained, in part, by its having undergone processes of self-organization.
The first is the key idea behind general relativity, the second the idea behind modern biology. What joins them is that in the end both sets of ideas make sense as descriptions of systems, like the universe or life on earth, that must structure themselves from the inside, without being made or observed from the outside.
But these themes are not only essential for understanding what is happening in cosmology and fundamental physics. First, in science, one sees the same constellation of themes reflected in the work of people such as Per Bak and Stuart Kauffman, who are attempting to understand the principles of self-organization at work in biology and other complex systems, such as the economy. One even sees these themes in the work of pure mathematicians, such as Louis Crane, John Baez and others, who are exploring the use of category theory as the basis of understanding topology, algebra and logic. Beyond science, if one reads political thinkers such as Drucilla Cornell or Roberto Unger; explores the architectural adventures of Frank Geary and Charles Jenks; or looks at the sculpture and painting of artists like Saint Clair Cemin or Donna Moylan, one sees they also are captivated by the idea that the world is constructed from evolving relationships rather than eternal and static absolutes.
Of course, this does not mean that these ideas are right; only observation and experiment can, in the end, tell us that. But it does mean that the late twentieth century pessimists, the postmodernists and social constructivists, and the end-of-this-and-that-ists have it completely wrong. We enter the 21st century with new ideas and wide horizons, with much to do and everything to talk about.