In this book, a philosopher and a theoretical physicist discuss natural philosophy based on three ideas:
- the singularity of the universe (there is only one universe that contains everything, although not everything in it is observable)
- the reality of time (everything has a history and hence can vary in time and hence has a causal relation with its past although this causality does not obey timeless laws)
- the selective realism of mathematics (as opposed to Platonism, mathematics wants to formulate the laws of nature and thus it has to play a reasonable, yet limited role in physics).
The first two thirds of the book are written by the philosopher Unger, the rest by the physicist Smolin, followed by a short discussion on topics they do not fully agree. On the fundamentals of the three previous axioms, they however generally agree. Both of them have a reputation of being iconoclasts in a their respective scientific communities. Hence this book, as are their previous publications, is provocative and will be the subject of much debate. With their arguments they want to criticize and redirect science. They conclude that the present, generally accepted views on cosmology are wrong and should be redirected using instruments already at hand.
Why is our universe as it is? Why precisely these physical constants? Why are we here? All questions current cosmology will not be able to answer. Even though cosmology currently knows its greatest successes, it is in crisis. The standard model of physics is only valid in a middle range of the scale. It fails at a subatomic and at a cosmological scale. The authors suggest a different, historical approach to cosmology following from their three postulates. The role of mathematics is over-emphasized. It cannot be an abstract timeless mirror of the physical reality.
Unger formulates fallacies of current cosmology: laws and observations applying to a subset of the universe cannot be applied to the whole universe. This subset refers to a limited scale as well as to a limited time window. The standard model is not applicable at a subatomic scale and not at the scale of the universe and we do not have access to the moment of the big bang nor do we know the future of the universe. The one universe may however go through different stages. There may be cyclic phases, or drastic changes with transitions at moments such as the big bang, or it may just evolve in a linearly changing phase. Each of these phases may have different physical laws or these may change during the evolution. This poses the problem of a meta-law. Which laws govern these transitions? Smolin gives several singularity theorems that speculate about the very beginning or the ultimate evolution of the universe, but we have no evidence for any of them. He also presents a theory of his own that the meta-law results from some nonlinear meta-dynamical system with many, yet a finite number of degrees of freedom which will define the physical laws of our universe. But whatever the answer is, these meta-laws are not fixed either and are varying as well. Change changes, which is intrinsic to the reality of time. Such vision is accepted in evolution theory, but it never got accepted in physics.
Unger continues by placing his arguments against recent developments in physics, cosmology and science in general. He then elaborates extensively on the three main topics and gives arguments why they should be accepted followed by recommendations for the further development of cosmology. Unger does not believe in several universes or stages of one universe, cyclic or not. This reduces the problem of answering the cosmological questions to deciding on the initial conditions. Smolin is more relaxed on the evolution of the universe, and does not want to speculate about what is beyond our horizon of observation in the cosmological past as well as in the future. Unger does not believe in infinity either. Smolin argues that this would also exclude continuity, and accepts it as a useful tool in mathematics.
Concerning time, Unger rejects a preferred cosmic time. Since this would contradict general relativity, confirmed by experiments, general relativity should be reformulated independent of the Riemannian spacetime concept which has been enforced on physics by mathematics. The only reality is now. The past is not real, but it has been real, so that we can acquire information about it through its consequences in the present time. The future is not real though. Although Smolin argues that we can make predictions of the future, these are always approximate and we can never be sure what the future will really bring.
While Unger's discussion of the reality of time and the mutability of physical laws is rather extensive, his discussion of the role of mathematics is shorter. The question whether mathematics is invented or discovered is a false one. It is not discovered because that would mean that it exists independent of time. This is impossible because in a causal universe, everything is the consequence of its history. If it is invented, it only follows its own rules and the choice of the inventor without being bound or corrected by the physical reality, and hence would be useless for physics. Smolin says it is 'evoked', meaning that it did not exist before, but it is bound by specific properties. A clear distinction must be made between a mathematical concept and the corresponding non-mathematical reality. Mathematics should never dictate physics, it can only be partially of service to physics. While Smolin accepts the possibility that mathematics evokes structures that are helpful in physics. It is impossible though that mathematics acts as an oracle for the future. Even mathematics itself is subject to evolution and its own future is unpredictable. Unger is less permissive and reproaches mathematics that it is completely timeless, hence violating the reality of time and that it is evolving on its own away from reality.
In his essay, Smolin goes, with some variations, more or less through the same arguments as Unger but he is at some points a bit more technical. I mentioned some of the differences already. His agenda for science that is the consequence of his views is as follows. The evolution of science should mainly influence cosmology, quantum gravity and the foundations of quantum theory. Multiverses are excluded since they can never be observed and hence are not real, but the universe passing through successive stages needs to be investigated. Passing from one stage to another in the cosmic evolution of the universe will also influence the way the laws of physics will evolve, but the main problem is that we do not know whether such changes can ever be observed. A decisive interpretation of quantum mechanics needs to be developed. As pressing is the investigation of the existence of global time and of the arrow of time. Other open problems are the nature of quantum gravity, and clearly the solution of the meta-laws and the cosmological dilemmas. He gives guidelines and constraints within which all this research should be performed.
This is not an easy read. It is not a pure philosophical book, and neither is it a book about physics or cosmology. Neither is it a confrontation of the philosopher versus the theoretical physicist. Both do a bit of each, and I can imagine that they will get opponents from all directions, be it philosophy of science, or the mainstream cosmologists or theoretical physicists. In my view mathematics plays an essential role here, but it is somewhat pushed into a corner leaving it not much room to move, being a humble, though 'reasonably effective' servant to physics. Anyway, if you are concerned with your reason of existence as a mathematician or of mathematics in general, this book is something that will give you material to ponder. You may need a bit of a background on philosophy and on cosmology and theoretical physics, but the book is not over-technical in either direction. It may need checking some of the terms or references though. Speaking of references, the numbers in the text of Smolin (Unger gives no references) do not correspond to the numbers in the bibliography at the end of the book, which is very annoying.