Ultimate Explanations of the Universe (21 page)

Somewhat earlier there is an analogous passage on space.

Relations arranging events in an order of successions one after another constitute time; while relations arranging events such that they are “coexistent” constitute space.
²²

If time and space are the relations between events, then they cannot exist if there are no events. Therefore God did not create the universe
in
time and space, but
with
time and space. In this sense Leibniz returned to St. Augustine’s concept, but with a new, fuller validation. The world is not so much a collection of objects, but rather – to use the language of today – a structure, in other words the set of relations from which objects derive their essentiality.

If the universe is the result of divine calculation, then it is the work of the Mathematician and is mathematical itself. Today the mathematical nature of the world is understood to mean the assertion that there is an astonishing correspondence between the structure of the world and certain mathematical structures: a correspondence so astonishing that more information on the world may be obtained more efficiently by the study of a given mathematical structure than by the laborious collection of experimental data. In any case, in advanced theories of physics it is impossible to design any experiment without resorting to a highly developed mathematical apparatus. Of course experimentation is a salient part of a research strategy, if only to obtain confirmation that we have selected the right mathematical structure for the examination of the given part of the world.
²³
Although in Leibniz’s days mathematical (theoretical) physics was only at the beginning of its spectacular career, his genius showed an amazing grasp of this extraordinary method. Let us, for instance, scrutinise the following sentence: “the Region of the Eternal Verities must be substituted for matter when we are concerned with seeking out the source of things.”
²⁴
“Eternal Verities” is a term used by St. Augustine, and for Leibniz it means “mathematical beings” (or in a more modern expression “mathematical structures”). According to the notions prevalent at the time, physics was to study the material world, but here was Leibniz saying that anyone who wanted to study the world at its source should “substitute” mathematical structures for matter.

The modern version of the concept of the world as a mathematical structure is usually associated with mathematical Platonism (though there is no inevitable link between these two doctrines), in other words with the belief that mathematical structures (or mathematical objects) exist objectively, independently of the human mind and aprioristically with respect to the physical world. In this sense Leibniz was undoubtedly a Platonist, but a special type of Platonist, who held that mathematical beings exist in God and draw their power from Him. We could say that he was a Platonist of the Augustinian type.

Mathematical Platonism is a doctrine which is fairly widespread today among mathematicians and physicists engaged in philosophy, but not so popular with philosophers of physics. An objection which the latter group often raise against mathematical Platonism is that mathematical beings cannot exert a causal impact on the world, since they are beyond the world. For example, Michael Dummett writes that abstract objects, which is what mathematical beings are, do not have “causal power” and therefore “cannot explain anything, and … the world would appear just the same to us if they did not exist.”
²⁵

Leibniz not only anticipated this criticism, but also reversed it: the world (“matter”) does not explain anything of itself; to find the “source of things” we must turn to mathematical structures. Matter has no “causal power;” all causality comes from mathematics, to which matter is “subordinated.” To refer to a modern example, when a particle of cosmic rays collides with atoms in the upper atmosphere and produces a cascade of other particles, the reason why this happens is not because a mathematical structure gives an approximately accurate description of this process, but because the particles are the implementation of a given mathematical structure and do exactly what is encoded in that structure. Leibniz would have said that if there were no mathematical structures there would be nothing.

In the previous chapters we carried out an overview – albeit briefly – of various ideas of creation. We saw that it is a wide-ranging concept, and comes into play in many different opinions and controversies in philosophy, theology, and even the natural sciences. It is certainly not a static concept and has been making an active contribution to the development of doctrines and visions of the world. The question arises what the contemporary advances in science and the critical review of those advances have added to the career of the concept of creation. Only now are we putting the question directly, but both the question itself as well as an attempt to answer it have been present in this book well-nigh from its first page. The doctrine of the creation of the world seems to call for confrontation with at least two features of the world image as delineated by contemporary science. These two features are the evolutionary nature of the picture of the world, and the problem of the origin of cosmic evolution, better known as the question of the initial singularity. Let’s start with some general remarks on evolution, then (in this chapter) ask about its origin, and later (in the next chapter) return to a consideration of the relation between evolution and creation.

The system subject to evolution is a system which changes with time. The conceptual problems start already at this point. As we recall, the arena of what happens in the universe is not time and space taken separately, but the conjunction of time and space in one structure called space-time, which, as we known, is static, viz. all of it exists all at once. Of course we may impose conditions on space-time to make it resolved into a single time and distinct spaces, one for every moment in time, but the possibility of such a resolution is a very special exception, not the rule. Moreover, for the abstract space-time to become the space-time of a specific universe it must be a solution of Einstein’s equations and satisfy strictly defined conditions (see in Chap. 4 Sects. 4 and 5). The overwhelming majority of solutions do not permit a resolution of space-time into a single time and momentary spaces, and those that do constitute a “zero measure” subset in the set of all possible solutions. A perusal of the textbooks on the theory of relativity gives the false impression that quite the contrary is true. This impression is due to the fact that on the whole physicists are not interested in solutions which do not have a single time and do not study them. This is because the universe in which we live, or at least that part of it which we can survey by observation has a single universal time. One of the great successes of the standard cosmological model is that it has managed to reconstruct the history of the universe from the first moments of the Big Bang up to the present day. That history is measured out by a single, universal time. Again it turns out that we are living in a very exceptional universe. The adherents of the anthropic principle gain yet another argument. In a universe without a single time it would be hard to imagine an evolution long enough to have led – from the primordial quark soup through the nucleosynthesis of the chemical elements and the chemistry of carbon, the development of galaxies, stars, and planets – to the emergence of biological evolution and the origin of life.

The geometry of the standard cosmological model predicts the existence not only of a universal time, but also of its beginning. Time emerges in the form of the initial singularity, which we came across on many occasions in the previous chapters. For instance, in Chap. 3 we saw how the existence of the initial singularity cast doubt on the viability of a cyclical cosmological model, and in Chap. 7 we had the opportunity to see what kind of “quantum tricks” Hartle and Hawking had to resort to in order to get rid of the initial singularity. We know from our deliberations so far on the various concepts of creation that the creation of the world does not necessarily mean the same as its temporal beginning, but since many authors have simply ignored this principle, it might be worthwhile to look at the initial singularity in relation to the idea of the world being created by God.

The initial singularity may be regarded as the mathematical equivalent of the Big Bang. When the first relativistic models of the universe were constructed in the 1920s and were compared with observations soon afterwards, it turned out that the universe was expanding and the galaxies moving away from each other at continually accelerating velocities. It became obvious intuitively that the universe’s phase of expansion must have started from something like a gigantic explosion. Originally this was called “the initial fireball;” only later was the “Big Bang” adopted as its name. In the first cosmological models this super-dense beginning was described by means of a theoretical expression: “the volume of the universe tends to zero and its density tends to infinity as time tends to ‘
t
=0’.” Later the term “initial singularity” was established for this “limiting process.” It became natural to identify the physical intuitions about the Big Bang with the mathematical intuitions associated with the initial singularity, and it all linked up in a suggestive picture of a beginning of the world.

Intuitions and suggestive pictures were enough to set off the debates on world view which soon erupted. Some wanted to see the initial singularity as the moment when the world was created, while others tried to disavow such a conclusion by constructing a variety of rival models, such as the cyclical universe (Chap. 3), closed-history universes (Chap. 4), or the steady-state cosmology (Chap. 5). But intuitions and suggestive images are not enough for rigorous research. As soon as the question was put how to remove the initial singularity from the cosmological model it turned out that first a proper definition had to be given for the singularity. An expression like “as time tends to ‘
t
=0’” is not a good definition, as in most cosmological models there is no universal time. The problem turned out to be quite formidable, and it was not until the early 1960s that not so much a definition of the singularity was put forward, but rather a criterion whereby it was possible to establish whether there existed a singularity for the given space-time.
¹
In the theory of relativity the histories of particles and photons are represented by curves in space-time – the histories of particles by time-like curves, and the histories of photons by zero curves (we met time-like curves in Chap. 4, in the discussion of Gödel’s cosmological model). If the histories of all the particles and photons, in other words all the time-like and zero curves, in a particular space-time may be extended indefinitely in both directions,
²
then in that space-time there is no singularity.
³
If it is impossible to extend the history of at least one particle or observer indefinitely, then there is a singularity in that space-time; its history “breaks down” at the singularity. Note that it is not a question only of the initial singularity; the history may break down at the final singularity into which the entire closed universe collapses, or at a singularity in the centre of a black hole.

The formulation of this criterion soon led to the proof of some important theorems concerning the existence of singularities. The proof was arrived at by Penrose and Hawking (as well as others), as we mentioned in Chap. 3 Sect.6. There is a whole collection of these theorems and they all have a similar structure: if certain conditions are met in a given space-time, then in that space-time there exists a singularity (viz. at least one time-like or zero curve breaks down in it). The various theorems in the collection formulate a variety of conditions which must be satisfied for a singularity to occur, but in general these conditions are “natural,” that is they are fulfilled in space-times that are “physically realistic.”
⁴
The general conclusion from these theorems is that the occurrence of singularities in cosmological models is the rule rather than an exception, and that they cannot be eliminated by simple means from those models in which they do occur.

The last sentence is not just a reservation made by physicists who do not want to stray into areas which are beyond their bound. It has its grounds in the formalism of the theory. If the criterion for the occurrence of a singularity is the breaking down of the history of particles or observers, then we know nothing about the nature of the singularity other than that it is a borderline at which our knowledge comes to an end.

However, soon after the publication of Hawking and Ellis’s monograph relativists started to become more and more interested in the quantisation of gravitation and the consequences of this operation for cosmology, in other words in quantum cosmology. Hawking himself addressed the problem (one of the outcomes was the quantum model of the creation of the universe he and Hartle constructed: see Chap. 7). From the outset it was known that the singularity theorems were applicable only to “classical singularities,” viz. when the quantum effects of gravitation were not taken into account. As soon as interest was aroused in the search for a quantum theory of gravitation, the philosophical significance of the singularity theorems ceased to be so obvious. The quantum effects of gravitation may break one of the conditions in the singularity theorems, hence there might be no need for the occurrence of a singularity in the history of the universe.

Whether that will be so or not will depend on the future theory of quantum gravity. As yet we have not developed such a generally accepted theory. The various theories and models which have been proposed offer different answers to the question. Though most of these models do away with the singularities. But this might be a “selection effect,” since in general physicists tend to look for models with no singularities. However, it cannot be ruled out that the future theory of quantum gravitation will bring a tremendous surprise, with conclusions nobody is expecting today. A thorough grasp of the history of science teaches us to be prepared for such surprises.
⁶

From what we have said so far it is clear that the question of the initial singularity is neutral with respect to the creation problem, for scientific, methodological, as well as theological reasons. Let’s review the scientific reasons first.

If we disregard the quantum nature of gravitation,
⁷
we still do not know anything about the physical nature of the singularity, as we recall. All we know is that at the singularity there is a breakdown in all the information that we may obtain on the universe on the grounds of the non-quantum laws of physics. Metaphorically speaking, even if there was something “before” the singularity, the world is oblivious to it (I have put “before” into inverted commas because at the singularity time breaks down and the concept of “before the singularity” has no sense). Perhaps the future quantum theory of gravitation will change the situation. Moreover, we have reasons to expect it to do so, but until it does we cannot really draw any definitive conclusions.

The methodological grounds are even more cogent than the scientific ones. The fundamental rule in the methodology of science is never to stop in our research efforts, never to call it a day and say we can go no further. In Chap. 1 we called this attitude the totalitarianism of scientific method. The task of science is to “explain the universe by means of the universe itself,” and not to invoke causes which lie beyond the universe. But we must bear in mind that this is a
methodological
principle, that is it should be treated as an assumption concerning the method of research, not as an ontological certainty. After all, God might as well have created the world out of nothing last night, along with all the tree-lines and fossils ready-made and testifying to their antiquity. He might have encoded in our minds a memory of events that never happened. But science may not take such “miracles” into account. Even if the future theory of quantum gravitation confirms the existence of a “strong singularity” at the beginning of the present phase of the universe’s evolution, it will not pass on such a conclusion to the theologians for further processing, but will face a new scientific challenge.

Finally there are the theological reasons. The question of the initial singularity is certainly a gap in our present scientific knowledge. But filling up this gap with God would be a return to the strategy used in the age of physico-theology (see in Chap. 17 Sect. 3), subsequently labelled rather ironically the God-of-the-gaps method. Contemporary theology should not stray back into that historic error.

All the more so as there are even deeper theological reasons. The overview of a selection (not all) of the philosophical and theological concepts of creation we carried out in Chaps. 13–18 showed that the creation idea does not fully overlap with the concept of the beginning of the universe. The creation concept may entail the idea of a beginning (although it need not from the philosophical point of view), but it is far ampler. Moreover, in the course of history the human view of the universe and its creation has evolved. The extension of our cosmological horizon and progress in science have played a significant role in this process. In times past God was Lord of the World, that is the Earth, while the stars were not much more than a trimming; nowadays we imagine God in terms commensurable at least with the Cosmos as we understand it today, and when we think of creation we sub-consciously assume this means the creation of all that contemporary cosmology is about. Meanwhile one of the principal theological truths is that God is a transcendental being, that is He transcends all that we are capable of imagining. Thus we should bear in mind that His act of creation entailed much more than what is accessible to our contemporary scrutiny. In Chaps. 8–12 we discussed the concept of many universes, perhaps an infinite number of them. A scientist may have serious misgivings as to whether this is a scientific concept or not, but a theologian should definitely take it into consideration. If God is infinite, then – as someone appositely observed – He may not be interested in anything that is less than infinity. Furthermore, a good theologian has grounds to think that the created reality is far richer than what we are able to ask about in our inquiries.