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Authors: Michael Heller

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1.4  
Anthropic Principles and Other Universes

The goal of unity is firmly encoded in scientific method. Modern science started when giants like Copernicus, Galileo, Kepler and Newton managed to unite “earthly physics” and “celestial physics,” in other words to show that the same laws of physics hold on Earth and in astronomy. For some time thereafter it seemed that the laws of mechanics discovered by Newton were the ultimate, “unified” theory governing everything. The discovery of electricity and magnetism finally swept this illusion away, but soon Maxwell showed that these two classes of phenomena could be put together in a single, mathematically very elegant theory of electromagnetism. Einstein was the first to come up with the idea that Maxwell’s theory should be combined with the theory of gravitation, and devoted the rest of his life to the implementation of this idea. Today we know that Einstein’s concept had no chance of success, since apart from electromagnetism and gravitation there are two other fundamental physical forces: the weak nuclear force (the lepton interaction), and the strong nuclear force (the hadron interaction). We now have an experimentally confirmed theory (the Weinberg-Salam theory) uniting the electromagnetic force with the weak nuclear force in a single interaction, known as the electroweak interaction. In principle we also know how to combine the strong nuclear force with this interaction. We have several scenarios for the unification and are only waiting for the experimental data which will select the right scenario. Only gravitation, by virtue of its different character, is defying the successful application of the unifying schema with respect to itself. No wonder that more and more tension is building up in the search for a quantum theory of gravitation – for it is almost certain that gravitation will have to be quantised before it can be unified with the other interactions. Virtually every new mathematical model, as a rule more sophisticated than its predecessors, at first generates enthusiasm and new hopes, but is soon relegated to the gallery of interesting but abortive constructions.

The multiplicity of unifying models put forward hitherto is splitting up physics into separate schools and trends rather than uniting it. This process of fragmentation has reached an apogee in the theory which probably the largest group of physicists regard as the most promising today – the M-theory, a development and generalisation of the superstring theory, which has become well-known outside physics. According to the good old quantum theory there should be one minimum energy state, that is the fundamental state. In M-theory there is “practically an infinite number” of fundamental states (estimated at even as many as 10
500
). The problem is that it is the fundamental state that to a large extent determines the physics of the universe. What are we to do with such a vast number of fundamental states? Unless we reject all of the theory leading up to them, the only solution is to accept that there is a very large number of different universes – as many as there are possible fundamental states – each with its own, different physics. M-theory people speak of the “string landscape” of the various universes, and conduct research on it.

It was easier to accept such a situation psychologically, as the idea of many universes had been circulating for some time in discussions on certain issues in cosmology. It first appeared in connection with the anthropic principles, which in various ways formulated the observation that the existence of living organisms on at least one planet in the universe depended in a very sensitive manner on the universe’s initial conditions and its other characteristic parameters. A slight change in any of these conditions or parameters in general gives rise to drastic changes in the universe’s evolution, rendering the emergence of biological evolution impossible. For instance, a very small change in the universe’s initial rate of expansion (either its slight acceleration or retardation) would preclude the emergence of carbon, the very cornerstone of organic chemistry. There are many such “coincidences.”

What has made the universe “friendly to life”? This brings to mind the notion of a purposeful design of the universe. But such an idea is alien to the rule of “explaining the universe by means of the universe itself.” To neutralise it, the following argument was employed: suppose there exists an infinite number of universes representing all the possible combinations of initial conditions and other parameters characteristic of the given universe. Only a very few of those universes are life-friendly, and we live in one of them, since we could not have come into existence in any other. Some of those taking part in the discussion immediately acknowledged the hypothesis of many universes as more rational than the hypothesis of the existence of God, while others said that there was no need to “proliferate existences” if a single God was enough.

Regardless of these theological disputes, the idea of a multiverse (as it soon came to be called) launched into a life of its own. Soon fairly concrete cosmological models, e.g. inflationary models or certain unifying scenarios, started to identify mechanisms which could have produced either different universes, completely separated from ours, or regions in our own universe to which we shall never have perceptive access. At any rate, the multiverse trend became a reality. But was it still science? Can something which we will never be able to access by observation, even in principle, still be a subject for scientific study? Or maybe the scientific method was being transformed before our very eyes, and something that was not science before was now turning into science? Nonetheless, I think we should not be too hasty in undermining scientific method – that’s right: in rashly undermining the scientific method, which is rightly regarded as the greatest achievement of science, and on which all the other achievements of science depend. Instead we should once more recall that the boundaries of rationality do not coincide with the bounds of scientific method, and therefore it is sometimes worthwhile to transcend those boundaries in order to be able to carry on a rational discourse “once on the other side.” Although we should not expect any empirical solutions in that area, critical argumentation and rational appraisal will still be relevant there.

1.5  
Creation of the Universe

The discussions on the anthropic principles and the multiverse are as it were on an extension of scientific research. On the whole it is quite difficult to identify the point at which we cross the boundary between what may still be called a cosmological model, and what definitely belongs to speculation beyond that boundary. But we could be even more daring and locate our observation point well beyond the boundary of scientific method (yet still within the area of rationality), and once we are on the other side take a look how the mathematical and experimental method works within the area proper to it, and what happens to its explanations as it approaches the limits of its possibilities. The area “beyond” is very well-known in the history of human thought: it is the region inhabited by philosophical and theological concepts. It is vast and highly “speculative.” To prevent us from losing our way on its tortuous paths, I shall limit the area by applying two restrictions: First, in practice I shall not go beyond the concept of creation as rooted in Judaeo-Christian thought. The concept of creation undoubtedly entails the ambition to explain, though in a theological sense. It is a theological concept, but has acquired numerous philosophical accounts (in the light of diverse philosophical systems), and it is chiefly the philosophical aspect of the idea which will be our subject of study. I shall touch on other philosophical concepts of ultimate explanations (or attempts to undermine them) only incidentally, more for the sake of a fuller picture of the philosophical ideas involved than of their analysis in depth. Secondly, out of all the versions and interpretations of the creation concept I shall only select ones which may be referred in one way or another to contemporary science, or those which, albeit historically distant from the present times, are still indispensable for the right understanding of such reference. This criterion is not so restrictive, as the history of ideas, in science as well as in philosophy, shows that ever since Christian Antiquity right through to the modern period, the mainstream thought on creation has been strictly linked genetically with the evolution of the ideas which led up to the development of the modern sciences. However, it is not my intention to compile a history of those genetic links, but to try to look at ultimate explanations from a different perspective than the one usually taken up on the grounds of physics and cosmology.

Is the philosophical and theological speculation located on a long extension of the investigations based on scientific theories and models? Perhaps the two are somehow mutually complementary to each other? Or perhaps – as some people claim – although apparently concerned with much the same thing, scientific inquiry and theological and philosophical deliberation are mutually untranslatable? Regardless of which of these possibilities (or maybe yet another one) is true, all of them are an expression of the same instinct ingrained in human rationality: to leave no stone unturned in seeking for an answer to every valid question.

Michael Heller,
Ultimate Explanations of the Universe
, DOI: 10.1007/978-3-642-02103-9_2, © Springer-Verlag Berlin Heidelberg 2009
2. Problems with the Eternity of the Universe

Michael Heller

(1) 
ul. Powstańców Warszawy 13/94, 33-110 Tarnów, Poland
Michael 
Heller
Email:
[email protected]
Abstract
One of the simplest ways to explain the world is the attempt to convince oneself that there is nothing to explain. If the universe has always existed, then there is nothing to explain. Reality is simply “given us” and the problem is removed. No wonder that the doctrine of the “eternity of matter” has always constituted one of the pivotal claims of all manner of materialisms
2.1  
The Eternity and Infinity of the Universe

One of the simplest ways to explain the world is the attempt to convince oneself that there is nothing to explain. If the universe has always existed, then there is nothing to explain. Reality is simply “given us” and the problem is removed. No wonder that the doctrine of the “eternity of matter” has always constituted one of the pivotal claims of all manner of materialisms.

But such an explanation is only apparent. Already St. Augustine observed that if someone were to stand barefoot on the beach for all eternity, then his footmark on the sand would be eternal too, but nonetheless it would still have its cause – the foot making it. If we wanted to neutralise this argument as well, we could query the sense of asking about any kind of cause. This device was employed in the diverse forms of Positivism: it was claimed that experience can inform us only of the sequence in which phenomena occur, but not of their inner causal relations. This type of therapeutic manoeuvre has survived only within some of the more exotic trends in philosophy. Various sciences relating to the world are still searching for causal chains within those aspects of the world subject to their fields of study.

It is a historical fact that for a long time, more or less from the French Enlightenment onwards, the belief in the “world’s eternity” has generally been regarded as something in the way of an ultimate explanation with no further questions asked relating to other “deeper causes of existence.” Admittedly, the image of an eternal world has been consolidated by the progress made in classical physics. Newton himself was deeply convinced that his mechanics, when applied to the system of the universe, called for a Grand Architect to fix the initial conditions for the laws of mechanics, but his concept of absolute space and absolute time set the stage on which processes could take place without being influenced by space and time. True enough, the differential equations describing the laws of nature require initial conditions, but these may be selected for any arbitrary moment in time. Thus the word “initial” turns out to be established purely by consensus, and the initial (or boundary) conditions themselves serve only to enable us to select the right solution out of the entire class of possible solutions, therefore they do not appear to give rise to any serious problems from the philosophical point of view.

In the eighteenth and nineteenth centuries the image of an eternal universe extending out to infinity in a Euclidian space was one of those beliefs which are so obvious that they are not even discussed. This did not mean, however, that there were no problems pertaining to this image – generally accepted beliefs need not be unquestionable. Newton himself observed that his law of gravitation applied to an infinite universe containing an approximately homogeneous distribution of stars generated serious problems. How could the stability of such a system be ensured? An arbitrarily small disturbance in the density of the distribution of the stars would cause the collapse of the entire system into one gigantic body.
1
In 1895 the German astronomer Hugo von Seeliger said that this problem was so fundamental (and today it is called Seeliger’s paradox) that he put forward an alternative. We should either query the infinity of the universe, or amend Newton’s law of gravitation. And he decided on the latter option. A year later and absolutely independently, Carl Neumann, a mathematician, did the same. Both Seeliger and Neumann proposed that an additional constant be introduced to Newton’s laws to stabilise the system of the universe.

2.2  
The Thermal Death Hypothesis

The belief in an eternal universe was well-nigh a dogma of the mechanistic worldview. The emergence of thermodynamics in the nineteenth century was hailed as yet another success for this philosophy. The theory of heat based on the concept of phlogiston, a “thermal fluid” flowing from warmer bodies to colder ones, was successfully replaced by statistical mechanics, in other words simply the Newtonian mechanics, in which the mean values of various magnitudes referred to large numbers of material molecules. However, this success cast a shadow over the doctrine of the eternal universe.

The first law of thermodynamics is the law of the conservation of energy applied to heat changes. So far there are no problems looming ahead. If we consider the universe as a single large thermodynamic system, the first law of thermodynamics may be regarded as an argument in favour of an eternal universe. If the energy of such a system is conserved, then it must have always been so, since energy can neither be lost not created.

The second law of thermodynamics was formulated in 1850 by Rudolf Clausius, who expressed it in the form of a theorem that no machine can be constructed which can transfer heat from a body at a lower temperature to a body at a higher temperature. Four years later he gave this principle a more mathematical form, introducing a function which he later named entropy. The principle expresses the tendency prevailing in an isolated thermodynamic system to equalise temperature, and it takes the form of a theorem which says that in such systems entropy increases (or remains constant in systems with reversible processes). Clausius himself did not refrain from drawing cosmological conclusions, observing that the entropy in the world was tending to a maximum, that is to the establishment of a uniform temperature throughout. Later Hermann Helmholtz called this state the heat death of the universe.

William Thomson drew further conclusions from the second law of thermodynamics. If heat death has not occurred yet, then the cooling down of the universe (viz. the equalising of temperatures to a uniform value throughout) must have started a finite time ago, in other words the process must have had a beginning. Thomson wrote of “some finite epoch [with] a state of matter derivable from no antecedent by natural laws.”
2
This was too reminiscent of the notion of a beginning of the world not to evoke controversy and heated debate. They still recur even today in diverse publications.

Nonetheless most scientists did not treat all these cosmological discussions and speculations very seriously. The well-known Irish astronomer Agnes Mary Clerke expressed the prevailing opinion when she wrote in 1890 that whatever lay beyond the boundaries of the Milky Way was not the subject of scientific study, since “with the infinite possibilities beyond, science has no concern.”
3
Cosmology would not become a respectable science until Albert Einstein and his general theory of relativity. The consolidation of the relativistic cosmology was a process which went on for several decades in the twentieth century, starting in 1917 with Einstein’s first paper on cosmology.

2.3  
Einstein’s First Model

Already at first glance Einstein’s article is extremely pioneering, though otherwise it looks just like a standard scientific paper.
4
When he wrote it Einstein had the field equations available for the general theory of relativity, which show the gravitational field as a deformation of space-time caused by the distribution of all the sources of the field. In such a situation the cosmological question appears quite naturally. We simply have to answer the question in what way the mean distribution of the sources of the gravitational field deforms the space-time geometry. Of course in answering that question we have to resolve a whole series of conceptual and technical issues. The way in which Einstein accomplished this made his paper a breakthrough.

Above all, since Einstein’s field equations are a set of differential equations there is the problem of boundary conditions, which is in turn connected with the distribution of the sources of the gravitational field (Einstein simply spoke of stars). The natural solution often applied in astronomical enquiries is to assume that we are dealing with an isolated system of bodies, on which the gravitational influence of other bodies is negligible enough to be ignored (the gravitational field disappears at the “boundary of the problem”). In cosmology this would correspond to one “island of stars” (e.g. the Milky Way) in the empty space surrounding it. Astronomers had been debating for quite a long time over “the island distribution of matter”: some held that the spiral nebulae visible with a telescope were clouds of dust and gas in our own galaxy (the Milky Way), while others said that they were different galaxies, separate “island universes”. The dispute continued, but for the time being neither side could put forward a clinching argument. Einstein probably did not know of the controversy, but in a sense he resolved it with one sweep of the pen. Considering the issue of boundary conditions, he observed that the assumption that the gravitational field disappeared at infinity could not hold in cosmology. A simple statistical approach convinced him that if we assumed just one “island of stars” in an otherwise empty space, then sooner or later the stars, agitated by random motion, would have to evaporate from the island. A solitary galaxy would be an unstable structure. Therefore we have to assume a statistically uniform distribution of stars (galaxies or clusters of galaxies, in the terminology used today) in space.

But then what boundary conditions should be applied? Somewhat earlier the Dutch astronomer Wilhelm de Sitter had hinted at a solution. In Einstein’s theory we do not have to insist on a flat space: we know that gravitation distorts its geometry. So we may do away completely with the “boundary,” and hence with the need to adopt any kind of boundary conditions. Such a situation would hold if space were spherical in shape, analogous to the surface of a sphere (if we move along it, nowhere do we encounter an edge). Einstein calculated that there was a solution to the field equations which had these properties.

There was just one remaining problem, the one that had troubled Newton – the question of gravitational instability: why would the stars in a spherical universe not collapse into a single point? To obviate the difficulty, Einstein did what von Seeliger and Neumann had proposed earlier with respect to Newton’s theory of gravitation: he augmented his equations with a component entailing a constant the purpose of which was to stabilise the model. This constant – Einstein named it the cosmological constant – is an exact counterbalance of the attracting gravitational force. That is how the first cosmological model based on the theory of relativity was constructed. Today we call it Einstein’s static model.

2.4  
The Universe and Philosophy

Let’s not be led astray by appearances, however. True enough, Einstein’s paper is an example of a fine piece of research opening up new horizons while at the same time addressing the old problems. But his aim went much further: it was precisely to reach the ultimate explanation. Naturally, such intentions are not to be disclosed in a research paper submitted for publication in a scientific journal, although they may often inspire many an author. On the other hand we have to admit that Einstein cared far less about conventions than many of his colleagues. The attentive reader will quite readily identify a certain philosophical motif in his 1917 paper: “In a consistent theory of relativity,” he wrote, “there can be no inertia relatively to ‘space,’ but only an inertia of masses relatively to one another.”
5
Again this sounds technical, but it’s fairly easy to decipher what Einstein was thinking of. The inertia of a particular body with respect to space, which would have to be something like Newton’s absolute space, would mean that the body’s mass, which is a measure of its inertia, would be its absolute property, something with which the body was endowed a priori. But the world should be a “closed system,” all of its justifications should remain within it, not assumed a priori. The only sensible solution to this situation was to assume that the mass of a particular body was as it were induced in it by all the other bodies in the universe. Hence there would be no inertia with respect to space, only with respect to other masses. Einstein took this idea from the writings of the physicist and philosopher Ernst Mach, and in his honour called it Mach’s principle. The intention to create a theory of physics incorporating Mach’s principle was one of the main motives behind Einstein’s efforts which eventually led to the emergence of the general theory of relativity. No wonder that this motive is clearly visible in his first paper on cosmology.

But Einstein’s philosophical inspirations went even further. Ever since his young days he was interested in the life and work of Baruch Spinoza, a seventeenth-century philosopher. Spinoza was so fascinated with instances of rationality in the world that he identified the world with God. “By God,” he wrote, “I understand a being absolutely infinite, that is, a substance consisting of an infinity of attributes, of which each one expresses an eternal and infinite essence.”
6
Understood in this way, God is identical with the universe; hence God is the “substance” which exists “of itself” and is “self-explanatory.” Einstein was quite open about his sympathy with pantheistic views of this kind. He, too, was fascinated by the “rationality of the universe” and often spoke of his “cosmic religion” in connection with this. No wonder, then, that the universe was “to explain itself”; the right cosmological theory should be the ultimate theory.
7

Einstein immediately took up de Sitter’s suggestion that troublesome boundary conditions could be evaded by assuming that the universe was spatially closed. The logical enclosure of the universe, that is the idea that all of its explanations should be enclosed within the universe, found its expression in the geometrical enclosure of the universe. On finishing his paper Einstein had every reason to feel pleased with himself. There was only one solution to the gravitational field equations which met all of his philosophical criteria. That solution presented an eternal universe, spatially closed and obeying Mach’s principle.

Einstein thought that the “cosmological problem” had been solved. I wonder what research problems he was pondering about after that?

2.5  
An Expanding Vacuum

The “universe’s rationality” is indeed one of its fascinating features. It certainly needn’t have been so that our minds would be capable of fathoming the mysteries of its structure. For we have managed to fathom so much. Einstein’s first paper on cosmology was undoubtedly a milestone on the road to understanding cosmic structure. As we think about this a disconcerting question comes to mind: are our brains advanced enough to allow us to completely solve the mystery of the universe? Or to put it in another way; does the structure of the universe have to correspond to our brain structure to such an extent as to allow us full access to discovering the way it works? On finishing his paper Einstein did not realise how far he still was from ultimate solutions. But he was soon to find out.

Still in 1917 de Sitter published a paper presenting a new cosmological solution to Einstein’s equations (with the cosmological constant).
8
In this paper de Sitter embarked on a dispute with Einstein’s understanding of Mach’s principle and put forward his own interpretation. But this was not what proved fatal to the views of Einstein. The very existence of de Sitter’s solution put them to a difficult test. In de Sitter’s solution the density of matter is equal to zero. In other words de Sitter’s model is empty, and in spite of this the structure of space-time is still well-defined. Therefore it is not defined by means of a distribution of “material sources” and Mach’s principle (as Einstein understood it) is not obeyed in the general theory of relativity. Soon it turned out, thanks to the work of Georges Lemaître,
9
that although de Sitter’s world was empty, his space was expanding: if we were to put into this world two particles the masses of which could be ignored as negligible, so as to still be able to consider the model as empty, then those masses would begin to move away from each other.

Meanwhile ever since 1912 Vesto Slipher had been measuring shifts in the spectra of galactic nebulae. In 1918, on the basis of his own and Slipher’s observations, Carl Wirtz expressed an opinion that the prevalence of red shifts in the spectra of nebulae could mean that these nebulae were moving away from each other. In the same year Eddington wrote in a letter to Shapley that the spreading out of the nebulae had been predicted in de Sitter’s model.
10
The recession of the nebulae came to be known as the de Sitter effect.

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