Stephen Hawking: The universe arises from scientific processes, not God + documentary "Master of the Universe"

Hold the front page: the big bang was an inevitable consequence of the laws of physics. Or indeed, as the front page of the London Times put it: "Hawking: God did not create universe". Media furore over Stephen Hawking's new book, The Grand Design, has made it the biggest science news story of the day. But it's not like Hawking has suddenly given up a religious belief – let alone proved that God doesn't exist.

Hawking's position on religion has remained unchanged since he wrote his bestseller, A Brief History of Time. At the end of that book he famously used God as a metaphor for the laws of nature: "If we discover a complete theory, it would be the ultimate triumph of reason – for then we should know the mind of God." This quotation is billed in The Times today as his "previous view" on religion. It was certainly influential – the book sold 6 million copies – but Hawking has always looked at God metaphorically, in much the same way, incidentally, as Einstein. "I cannot believe that God plays dice with the cosmos" was Einstein's famous quip about his discomfort with quantum mechanics. He also declared, "I want to know how God created the world."

But Einstein was not really religious. He remarked that "the idea of a personal God is an anthropological concept which I cannot take seriously". When asked if he believed in God, Einstein explained: "I believe in Spinoza's God who reveals himself in the orderly harmony of what exists, not in a God who concerns himself with fates and actions of human beings."

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Dodging the inquisition

Likewise, in 2001 I interviewed Hawking and he made a telling remark underlining how he was not religious. He told me: "If you believe in science, like I do, you believe that there are certain laws that are always obeyed. If you like, you can say the laws are the work of God, but that is more a definition of God than a proof of his existence."

And in a piece by him that I edited in 2008, he described how he attended a conference on cosmology at the Vatican, where the pope told the delegates they should not inquire into the beginning of the universe itself, because that was the moment of creation and the work of God.

Hawking joked, "I was glad he didn't realise I had already presented a paper at the conference investigating precisely that issue: I didn't fancy the thought of being handed over to the inquisition like Galileo."

Silly season

As Hawking's long-suffering assistant dealt with a deluge of enquiries from journalists from around the world, she told me how the furore says more about the silly season than any change of mind. It also says much about how God is used to sell science to the public. The Higgs boson, labelled the "God particle" – a moniker that Peter Higgs himself finds embarrassing – springs to mind. And after all, The Times is serialising Hawking's book, which he wrote with Leonard Mlodinow.

In it, Hawking describes how M-theory, a candidate ultimate theory of everything, may offer answers to the question of creation. "According to M-theory, ours is not the only universe," Hawking writes. "Instead M-theory predicts that a great many universes were created out of nothing. Their creation does not require the intervention of some supernatural being or god."

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Why Steven Hawking's Cosmology Precludes a Creator

by Quentin Smith......... Atheists have tacitly conceded the field to theists in the area of philosophical cosmology, specifically, in the enterprise of explaining why the universe exists. The theistic hypothesis is that the reason the universe exists lies in God's creative choice, but atheists have not proposed any reason why the universe exists. I argue that quantum cosmology proposes such an atheistic reason, namely, that the universe exists because it has an unconditional probability of existing based on a functional law of nature. This law of nature ("the wave function of the universe") is inconsistent with theism and implies that God does not exist. I criticize the claims of Alston, Craig, Deltete and Guy, Oppy and Plantinga that theism is consistent with quantum cosmology.
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Explaining the Universe

Atheists have traditionally conceded in advance the theoretical arena in cosmology to the theists. Atheists have offered no explanation of why the universe exists, and theists have offered an explanation. It can be argued that since theism has greater explanatory power, it is preferable according to this theoretical criterion. Atheists have traditionally taken a merely negative route, arguing that the theistic explanation is false, disconfirmed, or meaningless. But this seems to be a tacit admission that theism is prima facie theoretically superior to atheism, since theism at least purports to explain something that atheism does not even attempt to explain.

But I think this prima facie superiority of theism to atheism can be countered by showing that atheism offers an explanation of the universe, and a better explanation, than theism. I believe that contemporary physical cosmology can explain (in principle and in simplified models) the universe's existence. Quantum gravity cosmology, I believe, does show how the universe can be explained in atheistic terms.

In Fang and Wu's introduction to the book Quantum Cosmology, which collects the major technical papers by Stephen Hawking, James Hartle, John Wheeler, and others, they say quantum cosmology implies that "in principle, one can predict everything in the universe solely from physical laws. Thus, the long-standing 'first cause' problem intrinsic in cosmology has been finally dispelled."[1] This cosmology has eliminated the need to postulate (or even the possibility of postulating) a first cause (originating cause) of the universe's beginning. Stephen Hawking has famously said "there is no place for a Creator." However, there is little or no actual arguments to be found either in their technical or popular writings to support such "atheistic" claims. Apparently they want to leave to philosophers the task of figuring out how their mathematical equations both imply that there is no First Cause and that there is an atheistic explanation of the universe's existence. Some attempts to carry out this task in partial form will be made in this paper. I will also show that the very explanation of the universe offered by quantum cosmology implies that quantum cosmology is logically incompatible with theism, that is, implies that God does not exist.......................... read all
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Stephen Hawking and the Mind of God (1996)

by Antony Flew......................... Many of the greatest scientists of earlier centuries -- Michael Faraday, for instance -- believed that all natural laws, and not only the yet to be discovered most fundamental, provide insights into the mind of God. For these natural laws were and are, in their view, the principles upon which God designs and controls His universe.
For them, and presumably for most of Hawking's readers, the word 'God' refers to an hypothesized omnipotent, omniscient, incorporeal yet personal Creator; the traditional Mosaic God of Judaism, Christianity and Islam. This conception of God needs to be, but here is not, sharply distinguished from that of Einstein; which, I suspect, is for at least part of the time that of Hawking. Einstein was once asked -- to settle an argument -- whether he believed in God. He replied that he believed in Spinoza's God.[5] Since for Spinoza the words 'God' and 'Nature' were synonymous Einstein was, in the eyes of Judaism, Christianity and Islam, unequivocally an atheist.[6] It was in this Spinozistic understanding of the word 'God' that Einstein protested against quantum theory "The Lord God does not play dice." And it is in a similar way that we have to interpret his statement, now inscribed over a fireplace in Fine Hall in Princeton University: "God who creates and is nature is very difficult to understand, but he is not arbitrary or malicious."

However, if we discover a complete theory, it should in time be understandable by everyone, not just by a few scientists. Then we shall all, philosophers, scientists and just ordinary people, be able to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason -- for then we should know the mind of God. (p.193)

WAS THERE A BIG BANG BEGINNING?

Suppose now that having made this distinction we proceed to ask what if any evidencing reason Hawking has provided for believing that the universe was and/or is caused to exist and to have the characteristics which it is observed to have by a God in the first and more traditional and popular of the two understandings distinguished. Despite that concluding sentence in his first book the answer in that book appears to be "None at all." It was in 1981 that he first entertained "the possibility that space-time was finite but had no boundary, which means that it had no beginning, no moment of Creation" (p.128). This possibility he has now come to believe is the actuality; an actuality which "has profound implications for the role of God in the affairs of the universe"(p. 158):

So long as the universe had a beginning, we could suppose it had a creator. But if the universe is really self-contained, having no boundary or edge, it would have neither beginning nor end, it would simply be. What place, then, for a creator? (pp. 156 - 157)

Hubble's observations suggested that there was a time, called the big bang, when the universe was infinitesimally small and infinitely dense. Under such conditions all the laws of science, and therefore all the ability to predict the future, would break down. If there were events earlier than this time, then they could not affect what happens at the present time. Their existence can be ignored because it would have no observational consequences. One may say that time had a beginning at the big bang, in the sense that earlier times simply would not be defined. (p. 10)

The consequence, therefore, seems to be that, even if it were to be allowed that the universe as we know it began with the Big Bang, still physics must always remain radically agnostic: it is physically impossible to discover what if anything caused that Big Bang.

In writing that "an expanding universe does not preclude a creator, but it does place limits on when he might have carried out his job" (p. 10), and elsewhere also, Hawking writes as if for him, or perhaps it is only for his readers, the problem is: not to discover whether there is sufficient or even any evidencing (as opposed to motivating) reason for believing in the existence and activities of a Creator; but instead to find some suitable cosmological employment for a God already known or believed to exist and to be active. So once Hawking is persuaded that, since the universe had no beginning, there is no room for God to serve as a First Cause "in the beginning," he starts to look elsewhere for suitable Divine employment.

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This distinction between two conceptions of the problem is of crucial importance. For it is only in so far as you believe that you have sufficient evidencing reasons rationally to justify your believing in the existence and activities of God that it becomes reasonable for you to hypothesize that your God caused the universe to exist and the Big Bang to occur. Absent such a prior belief, physicists choosing to speculate about the nature of the possible but physically unknowable cause of the Big Bang would be bound to seek for a cause of the kind which they and their colleagues have discovered to be operating within the knowable Universe. Just about the last idea which would ever enter such unprejudiced heads is that of creation by an omnipotent, omniscient, incorporeal, personal Being. And, even if they did entertain such an idea, they would surely hesitate to add to it the idea that the Creator acts as a partisan within the creation, favouring some kinds of conduct and penalizing others.

Although of the greatest importance, this last point is almost always overlooked. The reason, surely, is that almost all those who have ever essayed to seek evidencing (as opposed to motivating) reasons for believing in the Mosaic God of Judaism, Christianity and Islam have themselves been raised among what Islam knows as "peoples of the Book"? Men and women raised in such environments have been, and most of us still are, prejudiced by the prophetic teachings of generations of parents and pedagogues, of priests and rabbis, of Imams and Ayatollahs, into accepting without question or surprise a conception of the hypothesized initiating and sustaining cause of the Universe as an omnipotent, omniscient, incorporeal yet personal Being who is at the same time a partisan approving and rewarding some sorts of human behaviour while disapproving and punishing others. But, to anyone who was for the first time and open-mindedly entertaining the idea of an omniscient and omnipotent Creator, it would surely appear obvious that everything that occurs or does not occur within a created universe must be expected to be precisely and only what its Creator wants to occur or not to occur. Certainly we are all members of a kind of creature who can, and cannot but, make choices between possible alternative courses of action. But an hypothesized omnipotent and omniscient Creator must be presumed -- absent any supernatural revelation to the contrary -- to ensure that we all are such individuals as will freely choose to make all the choices which we do freely choose to make in whatever senses that Creator wants those choices to be freely made.

In this perspective we may see the achievement traditionally attributed to Moses as possessing a truly world-historical significance. For it was he who is supposed to have produced the God of Mosaic theism by an extraordinary marriage of a limited, finite, tribal god with an omniscient, omnipotent Creator. Although hugely fertile that was nevertheless a case of theological miscegenation. Tribal gods are naturally devoted to the values and the best interests of the tribe. That, after all, is what they evolved to become. But it is equally natural to characterize a or the Creator -- as it is said that some Indian thinkers unprejudiced by any Mosaic commitments do characterize a or the Creator -- as being, essentially and in the nature of the case, "beyond good and evil."

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SO WHY DOES THE UNIVERSE EXIST?

At the very end of A Brief History of Time, as we have seen, Hawking does momentarily transcend the austere agnosticism which would seem to be the appropriate stance for physicists who do not assume that they have been vouchsafed some supernatural revelation. For he there entertains the possibility that one day everyone may be able to play an informed part in "the discussion of the question why it is that we and the universe exist" (p. 193). This possibility will, he believes, be realized "if we do discover a complete theory. For such a theory should in time be understandable in broad principle by everyone" (p. 193). But, as he has said before:

Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe?... Why does the universe go to all the bother of existing? Is the unified theory so compelling that it brings about its own existence? Or does it need a creator, and, if so does he have any other effect on the universe? And who created him? (p. 192)

Indeed you can. But it is important to appreciate how little has been achieved by this verbal manoeuvre. You have simply stipulated that the word 'God' is to be equivalent to the expression 'the cause of the existence of the Universe'. And this verbal manoeuvre does nothing to establish even that there actually is or was a cause of the existence of the universe, much less that that cause was and is the Mosaic God of Judaism, Christianity and Islam.

It can be illuminating here to refer to Hume's Dialogues Concerning Natural Religion.[9] For in Part I of those Dialogues Philo, who is usually taken to have been for the most part the mouthpiece of Hume himself, suggests that:

where reasonable men treat these subjects the question can never be concerning the being, but only the nature of the Deity. The former ... is unquestionable and self-evident. Nothing exists without a cause; and the original cause of this universe (whatever it be) we call God. (emphasis original)

In a lecture given in 1987, and printed as Chapter 9 of Black Holes and Baby Universes, Hawking said that "science...cannot answer the question why does the universe bother to exist," and confessed "I don't know the answer to that" (p. 90). But, if the universe had no beginning, why should we assume that there must be or have been a cause of its existence, even if neither Hawking nor anyone else knows what it was? Hawking himself, as we have seen, went on to argue in A Brief History of Time that if, as he now believes, "the universe is really self-contained, having no boundary or edge, it would have no beginning nor end, would simply be. What place then for a creator?" (p. 157). But what place then for any other kind of cause? Why should we not simply accept the existence of the universe, as theists simply accept the existence of their God, as being itself the ultimately unexplained and inexplicable brute fact?

It is important here to recognize that any explanatory system has ultimately to end in something which is not, or some things which are not, themselves explained. This is a consequence which follows from the essential nature of explanations why something, which is in fact the case, is in fact the case. Suppose, for instance, that we notice and are puzzled by the fact that the new white paint above our gas cooker so quickly turns a dirty brown. The first stage is to discover that this is what always happens, with that sort of stove, and that kind of paint. Pressing our questioning to a second stage we learn that this phenomenon is to be explained by certain wider and deeper regularities of chemical combination: the sulphur in the gas fumes forms a compound with something in the paint, and that is what changes its colour. Driving on still further we are led to see the squalor in our kitchen as one of the innumerable consequences of the truth of an all-embracing atomic-molecular theory of the structure of matter. And so on. At every stage explanation is and has to be in terms of something or some things which, at least at that stage, has or have to be accepted as unexplained brute facts that is just how things are.
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The conclusion, therefore, is that until and unless he can find sufficient evidencing reason rationally to justify him in believing that the universe is created and maintained by a personal Being having a purpose in so doing, Hawking ought to adopt the position which Hume in deference to Pierre Bayle called not Stratonian but Stratonician atheism. This position is named for Strato of Lampsacus, who was next but one after Aristotle as Director of the Lyceum. Strato's contention was that the existence of the universe and the subsistence of whatever may be discovered to be its most fundamental laws ought simply to be accepted as the explanatory ultimates for which no further explanation is either necessary or possible.

Stephen Hawking - "Gödel and the end of physics"

In this talk, I want to ask how far can we go, in our search for understanding and knowledge.wIll we ever find a complete form of the laws of nature. bY a complete form, I mean a set of rules, that in principle at least, enable us to predict the future to an arbitrary accuracy, knowing the state of the universe at one time. A qualitative understanding of the laws, has been the aim of philosophers and scientists, from Ahristottal onwards. But it was Newton's Principia Mathematica in 1687, containing his theory of universal gravitation, that made the laws quantitative and precise. This led to the idea of scientific determinism, which seems first to have been expressed by Le-plass. iF at one time, one knew the positions and velocities of all the particles in the universe, the laws of science should enable us to calculate their positions and velocities, at any other time, past or future. The laws may or may not have been ordained by God, but scientific determinism asserts that he does not intervene, to break them.
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At first, it seemed that these hopes for a complete determinism would be dashed, by the discovery early in the 20th century, that events like the decay of radio active atoms, seemed to take place at random. It was as if God was playing dice, in Einstein's phrase. But science snatched victory from the jaws of defeat, by moving the goal posts, and redefining what is meant by a complete knowledge of the universe. It was a stroke of brilliance, whose philosophical implications have still not been fully appreciated.mUch of the credit belongs to Paul Dirac, my pree-decessor but one in the Lucasian chair, though it wasn't motorized in his time. Dirac showed how the work of Erwin Schroedinger and Werner Heisenberg, could be combined in new picture of reality, called quantum theory. In quantum theory, a particle is not characterized by two quantities, its position and its velocity, as in classical Newtonian theory.iNstead it is described by a single quantity, the wave function. tHe size of the wave function at a point, gives the probability that the particle will be found at that point, and the rate at which the wave function changes from point to point, gives the probability of different velocities. One can have a wave function that is sharply peaked at a point.tHis corresponds to a state in which there is little uncertainty in the position of the particle.hOwever, the wave function varies rapidly, so there is a lot of uncertainty in the velocity. Similarly, a long chain of waves has a large uncertainty in position, but a small uncertainty in velocity.oNe can have a well defined position, or a well defined velocity, but not both.

This would seem to make complete determinism impossible.iF one can't accurately define both the positions, and the velocities, of particles at one time, how can one predict what they will be in the future. It is like weather forecasting.tHe forecasters don't have an accurate knowledge of the atmosphere at one time.jUst a few measurements at ground level, and what can be learnt from satellite photographs.tHats why weather forecasts are so unreliable. However, in quantum theory, it turns out one doesn't need to know both the positions, and the velocities. If one knew the laws of physics, and the wave function at one time, then something called the Schroedinger equation, would tell one how fast the wave function was changing with time. This would allow one to calculate the wave function at any other time. One can therefore claim that there is still determinism, but it is a determinism on a reduced level.iNstead of being able accurately to predict two quantities, position and velocity, one can predict only a single quantity, the wave function. We have re-defined determinism, to be just half of what Le-plass thought it was. sOme people have tried to connect the unpredictability of the other half, with con'shusness, or the intervention of supernatural beings.bUt it is difficult to make either case, for something that is completely random.
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In order to calculate how the wave function develops in time, one needs the quantum laws that govern the universe.sO how well do we know these laws. As Dirac remarked, Maxwell's equations of light, and the relativistic wave equation, which he was too modest to call the Dirac equation, govern most of physics, and all of chemistry and biology. So in principle, we ought to be able to predict human behavior, though I can't say I have had much success myself. The trouble is that the human brain contains far too many particles, for us to be able to solve the equations.bUt it is comforting to think we might be able to predict the nematode worm, even if we can't quite figure out humans. Quantum theory, and the Maxwell and Dirac equations, indeed govern much of our life, but there are two important areas beyond their scope.oNe is the nuclear forces.tHe other is gravity. The nuclear forces are responsible for the Sun shining, and the formation of the elements, including the carbon and oxygen of which we are made. And gravity caused the formation of stars and planets, and indeed, of the universe itself.sO it is important to bring them into the scheme.

The so called weak nuclear forces, have been unified with the Maxwell equations, by Abdus Salahm and Stephen Weinberg, in what is known as, the Electro weak theory. The predictions of this theory have been confirmed by experiment, and the authors rewarded with Nobel prizes. The remaining nuclear forces, the so called strong forces, have not yet been successfully unified with the electro weak forces, in an observationally tested scheme. Instead, they seem to be described by a similar but separate theory, called QCD. It is not clear who, if anyone, should get a Nobel prize for QCD, but David Gross and Gerard teh Hooft, share credit for showing the theory gets simpler at high energies. I had quite a job to get my speech synthesizer to pronounce Gerrard's surname.iT wasn't familiar with ap-osstrophee t. The electro weak theory, and QCD, together constitute the so called Standard Model of particle physics, which aims to describe everything except gravity.
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The standard model seems to be adequate for all practical purposes, at least for the next hundred years.bUt practical or economic reasons, have never been the driving force in our search for a complete theory of the universe. No one working on the basic theory, from Galeelaeo onward, has carried out their research to make money, though Dirac would have made a fortune if he had patented the Dirac equation. He would have had a royalty on every television, walkman, video game and computer.

The real reason we are seeking a complete theory, is that we want to understand the universe, and feel we are not just the victims of dark and mysterious forces.iF we understand the universe, then we control it, in a sense. The standard model is clearly unsatisfactory in this respect. fIrst of all, it is ugly and ad hoc.tHe particles are grouped in an apparently arbitrary way, and the standard model depends on 24 numbers, whose values can not be deduced from first principles, but which have to be chosen to fit the observations. What understanding is there in that?cAn it be Nature's last word. The second failing of the standard model, is that it does not include gravity.iNstead, gravity has to be described by Einstein's General Theory of Relativity. General relativity, is not a quantum theory, unlike the laws that govern everything else in the universe. aLthough it is not consistent to use the non quantum general relativity, with the quantum standard model, this has no practical significance at the present stage of the universe, because gravitational fields are so weak. However, in the very early universe, gravitational fields would have been much stronger, and quantum gravity would have been significant. Indeed, we have evidence that quantum uncertainty in the early universe, made some regions slightly more or less dense, than the otherwise uniform background. We can see this in small differences in the background of microwave radiation from different directions. The hotter, denser regions will condense out of the expansion as galaxies, stars and planets. All the structures in the universe, including ourselves, can be traced back to quantum effects in the very early stages.iT is therefore essential to have a fully consistent quantum theory of gravity, if we are to understand the universe.

Constructing a quantum theory of gravity, has been the outstanding problem in theoretical physics, for the last 30 years. It is much, much more difficult than the quantum theories of the strong and electro weak forces.tHese propagate in a fixed background of space and time.oNe can define the wave function, and use the Schroedinger equation to evolve it in time. But according to general relativity, gravity is space and time.sO how can the wave function for gravity, evolve in time.aNd anyway, what does one mean by the wave function for gravity. It turns out that, in a formal sense, one can define a wave function, and a Schroedinger like equation for gravity, but that they are of little use in actual calculations.
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Instead, the usual approach is to regard the quantum spacetime, as a small perturbation of some background spacetime, generally flat space. The perturbations can then be treated as quantum fields, like the electro weak and QCD fields, propagating through the background spacetime. In calculations of perturbations, there is generally some quantity, called the effective coupling, which measures how much of an extra perturbation, a given perturbation generates. If the coupling is small, a small perturbation, creates a smaller correction, which gives an even smaller second correction, and so on.pErturbation theory works, and can be used to calculate to any degree of accuracy. An example is your bank account.tHe interest on the account, is a small perturbation.a very small perturbation if you are with one of the big banks). The interest is compound.tHat is, there is interest on the interest, and interest on the interest on the interest.hOwever, the amounts are tiny.tO a good approximation, the money in your account, is what you put there. On the other hand, if the coupling is high, a perturbation generates a larger perturbation, which then generates an even larger perturbation. An example would be borrowing money from loan sharks.tHe interest can be more than you borrowed, and then you pay interest on that.iT is disastrous.

With gravity, the effective coupling is the energy or mass of the perturbation, because this determines how much it warps spacetime, and so creates a further perturbation. However, in quantum theory, quantities like the electric field, or the geometry of spacetime, don't have definite values, but have what are called, quantum fluctuations. These fluctuations have energy.iN fact, they have an infinite amount of energy, because there are fluctuations on all length scales, no matter how small. Thus treating quantum gravity as a perturbation of flat space, doesn't work well, because the perturbations are strongly coupled.

Supergravity was invented in 1976 to solve, or at least improve, the energy problem.It is a combination of general relativity with other fields, such that that each species of particle, has a super partner species. tHe energy of the quantum fluctuations of one partner is positive, and the other negative, so they tend to cancel.It was hoped the infinite positive and negative energies would cancel completely, leaving only a finite remainder. In this case, a perturbation treatment would work, because the effective coupling would be weak. However in 1985, people suddenly lost confidence that the infinities would cancel. tHis was not because anyone had shown that they definitely didn't cancel.iT was reckonned it would take a good graduate student, 300 years to do the calculation, and how would one know they hadn't made a mistake on page two. Rather it was because Ed Witten declared that string theory, was the true quantum theory of gravity, and supergravity was just an approximation, valid when particle energies are low, which in practice, they always are. In string theory, gravity is not thought of as the warping of spacetime.iNstead, it is given by string diagrams, networks of pipes that represent little loops of string, propagating through flat spacetime. The effective coupling, that gives the strength of the junctions where three pipes meet, is not the energy, as it is in supergravity. Instead it is given by what is called, the dilaton, a field that has ~not been observed.if the dilaton had a low value, the effective coupling would be weak, and string theory, would be a good quantum theory.bUt it is no earthly use for practical purposes.

In the years since 1985, we have realized that both supergravity and string theory, belong to a larger structure, known as M theory.why it should be called M Theory, is completely obscure. M theory, is not a theory in the usual sense.Rather it is a collection of theories, that look very different, but which describe the same physical situation. These theories are related by mappings, or correspondences, called dualities, which imply that they are all reflections of the same underlying theory. Each theory in the collection, works well in the limit, like low energy, or low dilaton, in which its effective coupling is small, but breaks down when the coupling is large. This means that none of the theories, can predict the future of the universe, to arbitrary accuracy.for that, one would need a single formulation of M-theory, that would work in all situations.

Up to now, most people have implicitly assumed that there is an ultimate theory, that we will eventually discover.Indeed, I myself have suggested we might find it quite soon. However, M-theory has made me wonder if this is true.Maybe it is not possible to formulate the theory of the universe in a finite number of statements. This is very reminiscent of Goedel's theorem.This says that any finite system of axyoms, is not sufficient to prove every result in mathematics.

Goedel's theorem is proved using statements that refer to themselves.sUch statements can lead to paradoxes.aN example is, this statement is false. If the statement is true, it is false.and if the statement is false, it is true. Another example is, the barber of Corfoo shaves every man who does not shave himself. Who shaves the barber?if he shaves himself, then he doesn't, and if he doesn't, then he does. Goedel went to great lengths to avoid such paradoxes, by carefully distinguishing between mathematics, like 2+2 =4,and meta mathematics, or statements about mathematics, such as mathematics is cool, or mathematics is consistent. that is why his paper is so difficult to read.but the idea is quite simple. First Goedel showed that each mathematical formula, like 2+2=4, can be given a unique number, the Goedel number.the Goedel number of 2+2=4, is *. Second, the meta mathematical statement, the sequence of formulas A, is a proof of the formula B, can be expressed as an arithmetical relation between the Goedel numbers for A- and B. Thus meta mathematics can be mapped into arithmetic, though I'm not sure how you translate the meta mathematical statement, 'mathematics is cool'. Third and last, consider the self referring Goedel statement, G.tHis is, the statement G can not be demonstrated from the axyoms of mathematics. Suppose that G could be demonstrated.tHen the axyoms must be inconsistent, because one could both demonstrate G, and show that it can not be demonstrated. On the other hand, if G can't be demonstrated, then G is true.bY the mapping into numbers, it corresponds to a true relation between numbers, but one which can not be deduced from the axyoms. Thus mathematics is either inconsistent, or imcomplete.tHe smart money, is on imcomplete.
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What is the relation between Goedels theorem, and whether we can formulate the theory of the universe, in terms of a finite number of principles. One connection is obvious.aCcording to the positivist philosophy of science, a physical theory, is a mathematical model.sO if there are mathematical results that can not be proved, there are physical problems that can not be predicted. One example might be the Golbach conjecture.gIven an even number of wood blocks, can you always divide them into two piles, each of which can not be arranged in a rectangle.tHat is, it contains a prime number of blocks.

Although this is incompleteness of sort, it is not the kind of unpredictability I mean.gIven a specific number of blocks, one can determine with a finite number of trials, whether they can be divided into two primes. But I think that quantum theory and gravity together, introduces a new element into the discussion, that wasn't present with classical Newtonian theory. In the standard positivist approach to the philosophy of science, physical theories live rent free in a Platonic heaven of ideal mathematical models. That is, a model can be arbitrarily detailed, and can contain an arbitrary amount of information, without affecting the universes they describe. But we are not angels, who view the universe from the outside.iNstead, we and our models, are both part of the universe we are describing. Thus a physical theory, is self referencing, like in Goedels theorem.oNe might therefore expect it to be either inconsistent, or imcomplete.tHe theories we have so far, are ~both inconsistent, and imcomplete.

Quantum gravity is essential to the argument..THe information in the model, can be represented by an arrangement of particles.aCcording to quantum theory, a particle in a region of a given size, has a certain minimum amount of energy. Thus, as I said earlier, models don't live rent free.tHey cost energy.By Einsteins famous equation, E = mc squared, energy is equivalent to mass.aNd mass causes systems to collapse under gravity. It is like getting too many books together in a library.tHe floor would give way, and create a black hole that would swallow the information. Remarkably enough, Jacob Bekenstein and I, found that the amount of information in a black hole, is proportional to the area of the boundary of the hole, rather than the volume of the hole, as one might have expected. The black hole limit on the concentration of information, is fundamental, but it has not been properly incorporated into any of the formulations of M theory that we have so far. They all assume that one can define the wave function at each point of space.bUt that would be an infinite density of information, which is not allowed. On the other hand, if one can't define the wave function point wise, one can't predict the future to arbitrary accuracy, even in the reduced determinism of quantum theory. What we need, is a formulation of M theory, that takes account of the black hole information limit.bUt then our experience with supergravity and string theory, and the analogy of Goedels theorem, suggest that even this formulation, will be imcomplete.

Some people will be very disappointed if there is not an ultimate theory, that can be formulated as a finite number of principles.I used to belong to that camp, but I have changed my mind. I'm now glad that our search for understanding will never come to an end, and that we will always have the challenge of new discovery.wIthout it, we would stagnate. Goedels theorem ensured there would always be a job for mathematicians.I think M theory will do the same for physicists. I'm sure Dirac would have approved.

Thank you for listening.

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