The crisis of contemporary physics and cosmology begins with the triumphs of the standard model of particle physics and its counterpart in cosmology. The crisis arises out of our failure to go beyond the successes of these models to a deeper understanding of nature. As I will argue in detail, these failures have a common cause, which is the breakdown of the Newtonian paradigm when faced with cosmological questions. The questions left unanswered by these models then serve as the primary challenges to the science framed by the new, cosmological principles we have just outlined.

The message of the data from particle physics

What we know about the elementary particles and forces is neatly summarized in the standard model of particle physics, which has been tested by numerous experiments since first proposed in 1973. As of this date, experiments at Fermilab and CERN have so far failed to discover any phenomena not accounted for by the standard model.

The problem presented: how much of nature exists in time?

Time is real, and everything that exists, or has ever existed, or will ever exist, takes place in time. From this thesis there results the idea that the laws of nature must in principle be susceptible to change. Like everything else in this one real universe, they have a history.

The inclusive reality of time is not a tautology or a truism. It is a revolutionary proposition. Rightly and therefore radically understood, it is incompatible with a major element in the dominant tradition of modern science, the tradition that goes from Galileo and Newton to the particle physics of today. In particular, it contradicts the “block-universe” picture of the universe as well as the application of the Newtonian paradigm – the explanatory practice that explores law-governed phenomena within a configuration space bounded by initial conditions – to the universe as a whole. It puts pressure on our conventional notions of causality. It compels us to reconsider our beliefs about the possible and the new in nature. It suggests that the laws of nature are mutable and that the relation between laws of nature and states of affairs varies. It gives us reason fundamentally to invert the relation between historical and structural explanation in natural science, so that we may come to see the former as more fundamental than the latter rather than as derivative from it.

The crisis introduced

For those who want to know the answers to the big questions about the natural world, the fundamental sciences whose role is to discover the answers to those questions are in a most puzzling state. There is certainly reason to celebrate the greatest triumphs in the history of the physical sciences. Powerful theories based on great principles have given us an unprecedented understanding of nature on a vast array of scales of space, time, and energy. The great theories invented through the twentieth century – general relativity, quantum mechanics, quantum field theory, and the standard model of particle physics – have yet to fail experimental test. These theories have given us detailed and precise predictions for phenomena as diverse as gravitational waves emitted by orbiting neutron stars, the scattering of elementary particles, the configurations of large molecules, and the patterns of radiation produced in the big bang – and in all these phenomena, which were not even dreamed of a century ago, those predictions have proven correct.

But just as the physical sciences celebrate their greatest triumphs, they face their greatest crisis. This crisis lies in our failure, despite what has been now many decades of effort by increasing numbers of scientists, to complete the scientific revolution that was initiated by Einstein’s discovery of the quantum nature of radiation and matter and his simultaneous invention of relativity theory. These two revolutions are each successful in its own domain, but remain unjoined.

The singular existence of the universe

This book develops three connected ideas about the nature of the universe and of our relation to it. The first idea is that there is only one universe at a time. The second idea is that time is real and inclusive. Nothing, including the laws of nature, stands outside time. The third idea is that mathematics has this one real, time-drenched world as its subject matter, from a vantage point abstracting from both time and phenomenal particularity.

On the view defined by these three ideas, the universe is all that exists. That there is only one universe at a time justifies using the terms universe and world interchangeably. If there were a plurality of universes, the world would be that plurality. The singular universe must, however, be distinguished from the observable universe, for our universe may be much larger than the part of it that we can observe. In this book, we use the words cosmology and cosmological to designate what pertains to the universe as a whole, not just to its observable portion. Observational astronomy has continued, in recent decades, to make remarkable discoveries about the observable universe. Cosmology, however, risks losing its way. The arguments of this work are cosmological: they concern the whole of the universe and the way to think about it.

If the view proposed in previous chapters is to have a chance of succeeding it must resolve several puzzles connected with the nature of mathematics and its role in physics. The problem is that our two principles – that there is one real world and that time is real and goes all the way down – make trouble for our received accounts of mathematics and of its role in the scientific study of nature. According to the view most commonly held among physicists and mathematicians, mathematics is the study of a timeless but real realm of mathematical objects. This contradicts our principles twice over, both because there is no real realm other than our one universe and because there is nothing real or true that is timeless.

A new conception: mathematics as evoked reality

The choice between whether mathematics is discovered or invented is a false choice. Discovered implies something already exists and it also implies we have no choice about what we find. Invented means that it did not exist before AND we have choice about what we invent.

The idea that an acceptable cosmological theory needs to be formulated in a framework different from that of the so far successful theories of physics is not new. There is a tradition of critique of Newtonian physics, which leads to what is often called the relational position on the nature of space and time. Relationalism is associated with Leibniz [15], Mach [16],and Einstein [17] and, in the present period, Barbour [18], Rovelli [19], and others. Much of the critique concerns issues that only arise if you aspire to a theory of the whole universe rather than a part of it. General relativity is partly – but only partly, as I will explain – a response to that critique.

The roots of relationalism

We can draw criteria for a truly cosmological theory from that tradition of critique. The starting point is Leibniz’s great principle:

My view is that we should take the PSR as an aspiration and a goal, perhaps never to be completely reached but, nonetheless, a beacon illuminating the direction in which we are to search for the answer to cosmological questions. We can state this as follows:

In this form the PDSR is best used as a means to evaluate progress (has sufficient reason increased?) or to judge the likelihood of success of competing research programs. It is especially useful in judging the promise of novel research programs.

It was less than four hundred years ago that Harvey taught us that the heart was a pump. The great Aristotle had conjectured that the heart was the seat of intellect, reserving for the brain the function of a cooling system, which (in addition to some other functions of more than minor interest) it is. In dealing with questions about our own nature we have to survive ideology – endless discussions about organic versus inorganic, vital versus non-vital, living versus non-living. These hotly disputed questions quietly fade away when the cool light of patient investigation and hard thought finally provide illumination. Today we are engaged in the quest of understanding our brain. When we have finally worked out the details, this remarkable organ, for all of its lofty pretensions – seat of intellect, home of the soul – will very likely join other remarkable pieces of biological machinery. Remarkable, certainly, but not mysterious or possessed of any supernatural qualities.

How then do we go about trying to understand a system as complex as the brain? Obviously we cannot just make observations.

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Not so long ago the eye was thought to be a somewhat miraculous organ functioning in a more prosaic body. We smile indulgently at the naïveté of our intellectual grandparents. Today, though we regard our eyes with great respect, few attribute magical properties to them. The same might be said for kidneys, the heart, and other organs. We appreciate their importance, we may understand how they work, we may not be able to build them as efficiently as nature does, yet we hardly regard them as mysterious.

The same calm does not seem to prevail when we consider the brain. Although the brain could be regarded in the same way we regard the heart, the eye, or a muscle, the functions associated with the physical entity “brain” such as thought, consciousness, and awareness of self – those most precious human characteristics – are not as easily attributed to the earthy material in which they may or may not originate, as the function of pumping might be attributed to the heart.

Recently, Hans Moravec discussed a transition from humans to what he calls a “Universal Robot.” The prospect that such a transition might be carried out inspires fear and raises many doubts. In this lecture, we analyze some of the problems that lie in the path of constructing robots or machines that think. In particular, we discuss the relation of Turing's famous test to a theory of mind and, drawing on the wisdom of Lessing and Goethe, explore possible implications for the meaning and worth of human experience.

In the program for the 1993 conference, “Neural Networks and the Mind,” in Dusseldorf, Germany we read:

Preparing for a talk on the fiftieth anniversary of the Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity I was struck by a footnote on the first page of our 1957 paper: “This work was supported in part by the Office of Ordnance Research, U.S. Army” – a program officer whose mission might have included improving artillery shells found it appropriate to fund a project in fundamental science. This spurred me into reflection on funding for scientific research, then and now.

Money is required to do science and, as systems become more complex, more people, equipment, and therefore more money is required for each new result. Naturally, people hark back with sentimentality to the good old days when results could be obtained on a tabletop. In fact, some results are still obtained on tabletops, but the tables are getting larger and the tops more expensive.

On this hundredth anniversary of Kamerlingh Onnes' discovery of superconductivity, we may well reflect on the technological and theoretical marvels that are the descendants of his discovery. We may also reflect on the benefits science has showered on us (antibiotics and modern electronics to mention just two). Young people who want to participate in this adventure on a professional level must become technically proficient, so of course they must study science.

But why study science if you don't intend to become a scientist? Why should a lawyer, businessman, or artist study science? We might just as well ask: Why should they read Kemal, Kaya, or even Shakespeare? Why should they watch TV or drink beer?

I would like to present the antique and possibly quixotic view that we should study science because it can give us pleasure. Now the notion of pleasure associated with the physics or chemistry we remember from high school is a hard sell.

It is gratifying to hear the courageous and thoughtful discourse of His Holiness for the inauguration of this symposium organized on the occasion of the 350th anniversary of the publication of the book by Galileo Galilei entitled Dialogo sopra i due massimi sistemi del mondo.

To address ourselves to those issues producing unnecessary confrontation between science and faith in the spirit so movingly expressed by John Paul, to follow the wish of Saint Robert Bellarmine “that useless tensions and harmful rigidities between faith and science be avoided,” we must turn our attention to current propositions that produce controversy. Today these are often biological: such questions as the origin of intellect, the nature of consciousness, the meaning of soul, the construction from ordinary materials of the special entity that is ourselves and the definition of life itself.

It is more than fifty years since Paul Dirac gave us one of the most beautiful inventions of the twentieth century:

H = ca · p + βmc2

I once asked Professor Dirac how he came upon his masterpiece. If my memory serves (I hope he will correct me if it does not), he said that in the late 1920s most physicists, trying to calculate with relativistic quantum mechanics, were content to use the Klein–Gordon equation modified with ad-hoc corrections. In his attempt, Dirac did not try to put in the electron spin but rather to treat in a consistent manner the simplest possible problem: that of a spinless, relativistic electron. The critical moment came when he realized that 4 × 4 matrices were required. “How long did it take you from that point?” “About two weeks”. I couldn't refrain: “why so long?” He was a bit taken aback; then, his attention focused perhaps on those two glorious past weeks, he nodded as though to agree in silence why so long?

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In a world full of noise about the evils of science and technology, a world overflowing with PCBs, nuclear wastes, carcinogenic agents of every description, a world threatened with ozone depletion, recombinant DNA, to mention a few, I am asked to write on the role of values in what Theodore Roszak, a not too friendly critic, labeled “this strange intellectual passion we call science.” Presumably what is expected is something in the vein of the 1808 Elements of Natural Philosophy, where we are informed that: “The great object of science is to ameliorate the condition of man, by adding to the advantages which he naturally possesses.”

Call it wide-eyed innocence, but I believe most people are not taken in by much of the nonsense they are subjected to and, though confused and troubled, are too sensible to be swept along with seasonal intellectual fashion.