Ultimate Explanations of the Universe (10 page)

Hartle and Hawking’s paper caused a lot of excitement. By using the mathematical formalism composed of a combination of relativistic and quantum methods, a model had been constructed for the creation of the universe out of nothing. Putting it more precisely, according to this model one could calculate the probability of the universe in a certain state arising from a state that was non-existent. However, we have to distinguish the psychological effect evoked by the comments on the Hartle-Hawking model (including its authors’ comments) from the rigorous analysis of the model.

Above all we have to realise that the Hartle-Hawking model is not the cosmological application of a well-established theory of quantum gravitation, as we would like it to be, but an extremely hypothetical attempt to make a provisional model stand in for such a theory. It is a hybrid model, one that is not derived from any general laws or principles, only the result of constraining two different methods (integration over paths and the geometry of space-time) to collaborate with each other. Furthermore, the model is based on three fairly arbitrarily chosen assumptions. The assumptions are as follows:

First, the replacement of the time coordinate
t
by the imaginary time coordinate
it
. This operation allows the integration over paths to be accomplished,
⁹
but it is based on entirely technical grounds. Hartle and Hawking bolster this operation with the claim that thanks to it they have obtained a universe “with no boundaries”, which in turn is to make the world “self-explanatory.” But we must remember that in the model they propose the universe is represented not by space-time, which may or may not have a boundary, but by a wave function, and we do not really know how to interpret the presence or absence of boundaries for a wave function.
¹⁰

Secondly, the identification of the wave function of the universe with the propagator. Admittedly, this is an ingenious step, and of key significance for the whole model. Thanks to it the model works. But at the same time we should realise that this operation is an arbitrary investment, the only justification of which would be the model’s theoretical success.

Thirdly, the interpretation of the wave function Ψ
₀
=
K
(Ø;
S
₂
, γ
₂
, φ
₂
) as a description of “the emergence of the universe out of nothing.” While the first two assumptions were in the model’s “internal mechanisms,” this assumption is purely interpretative in character. What’s more, it is a highly doubtful interpretation. As Gordon McCabe has remarked,
¹¹
the symbol Ø for the empty set in the expression
K
(Ø;
S
₂
, γ
₂
, φ
₂
) does not denote a nothingness, out of which the state of the universe (
S
₂
, γ
₂
, φ
₂
) is said to have evolved, but rather no constraints on the “initial state” of the transition to the state (
S
₂
, γ
₂
, φ
₂
). In other words the expression
K
(Ø;
S
₂
, γ
₂
, φ
₂
) describes the probability of a transition to the state (
S
₂
, γ
₂
, φ
₂
) from “anything whatsoever” rather than from nothingness.

A further reservation may be added, this time a philosophical one. Even if we agree with Hartle and Hawking that their model describes the “quantum creation” of the universe, it is not a creation “out of nothingness” in the philosophical sense of the term. The Hartle-Hawking model assumes the existence of the laws of physics, and in particular the coordinated operation of the laws of quantum physics and relativistic physics, which is very far from the concept of nothingness, in other words from the concept of the absence of anything at all.

Nonetheless the Hartle-Hawking model played an important part in the philosophical reflections on cosmology. Notwithstanding its controversial nature, it showed how far the methods of contemporary theoretical physics may go. They are capable of approaching the great metaphysical questions associated with “the beginning of existence” – seemingly to within just one small step away. Admittedly, on closer scrutiny it turns out to be just a step away from the abyss of methods and conceptual distinctions separating physics from metaphysics, but the close approach itself to questions of this kind shows their inevitability. We are speaking not only of the traditional metaphysical questions; there are also new questions, characteristic of scientific cognition, and carrying a considerable philosophical charge. These questions pertain to the boundaries of the scientific method and to the explanation of the premises at the basis of this method. Physics operates on the basis of the laws of nature. But what is the nature of these laws, and where do they come from?

For a long time Man has been assigning a special place in reality to himself. Already in ancient times Protagoras said that Man was the measure of all things, and later that maxim was understood in many ways, but never in a derogatory way with respect to mankind. Frequently Bishop Berkeley is accused of being of the opinion that the world existed because we perceived it: the table exists when I am looking at it; if I close my eyes the table will cease to exist. Kant claimed that how we perceived the world was more a consequence of our perception of the world than what it was really like. And the Positivists were even less modest: they said that whatever transcended our faculties of perception, which are based on experience and precise articulation, was completely meaningless.

But alongside such tendencies there was also another process going on in scholarship – the ousting of Man from his hitherto privileged place in the universe. It all started with the Copernican Revolution. Admittedly, its main ideological consequence, the degradation of the Earth to the role of an average planet in orbit around an average star – came much later, but the process launched by Copernicus certainly left its imprint on our culture’s spiritual profile. The well-known historian of art, Alexandre Koyré, claimed that the cultural shock effected by the “cosmic degradation of Man” was one of the chief factors shaping the style of thinking of the fifteenth-century German mystics. On the one hand they were profoundly moved by Man’s insignificance in the face of Infinity; on the other, they tried to compensate for Man’s marginalisation in the universe by drawing attention to his relations with God. Koyré held that nineteenth-century German Idealist philosophy (Fichte, Schelling, and Schopenhauer) was a direct continuation of this tradition, while Hegel merely reiterated and developed in a secularised manner some of the theses put forward by the mystic Jakob Boehme. We may regard Positivism as a reaction to this sort of philosophy, but essentially it was a still more secularised version of the same tendency – the focusing of attention on human perception and the recognition of the boundaries of that perception as the bounds of all meaning whatsoever.

By the early twentieth century philosophers of science had reconciled themselves with the statement that “objective knowledge” was knowledge cleansed of “the human element,” and that in the empirical and natural sciences there was no room for subjective factors. Nonetheless the “complex of the margin” still lingered in their cultural sub-conscious. No wonder then that when calls for a “revaluation of Man” appeared in twentieth-century scholarship, they immediately gained popularity both with the natural scientists who dabbled in philosophy as well as with the general public. The first signal of this came in the first half of the century, in as avant-garde a field as quantum mechanics in its youthful stage. The point in question was the measurement issue, a key problem for science. Prior to the taking of a measurement all that may be assigned a quantum system (e.g. an electron) is a probability that it has a certain property (e.g. a given position). The property is given an actual value only once the measurement has been done. So much the mathematical formalism of quantum mechanics; however, from this point it’s only one step to the claim that it is the observer who creates the physical reality at the moment of measurement. Soon a whole spectrum of such interpretations had emerged. Not much insight is required to notice that at least some of them would espouse the character of an “ultimate explanation”: if there were no human observer there would be no physical reality. Man was being promoted to the rank of the ultimate instance of explanation.

A second signal of this type appeared in the latter half of the twentieth century in cosmology, when progress made in this science had entered on a fast course, chiefly thanks to the advances in techniques of observation. It turned out that the existence of life – and all the more so of a rational observer – on at least one planet in the universe imposed some very rigorous constraints on admissible cosmological models. From here it was just one step to the statement that the universe was as it is because we were here. The diverse versions of this ideology are known as the “anthropic principles.” Some of them also stake a claim to being ultimate explanations. In this chapter we shall take a closer look at this.

It all began still in the early twentieth century. Already Eddington observed some interesting numerical relationships between the magnitudes characteristic of the world in its cosmic scale and those characteristic of its microscopic scale. A comparison of the magnitudes characteristic for the two scales reveals that the dimensionless ratios between them are numbers of the order of 10
⁴⁰
.
¹
Let’s take a look at this from another angle.

Let
G
be the gravitational constant, ρ
₀
the mean density of matter in the universe, and
T
the age of the universe.
²
It turns out that if we take the square of
T
and multiply all the other parameters by each other, we obtain a result of the order of unity,
³
viz.:

What an amazing result! The age of the universe is growing all the time, and the universe is expanding, so its mean density is decreasing, but the product of these two magnitudes and the gravitational constant remains constant! Why are we alive precisely at an instant in time when such a relationship holds? A coincidence? Physicists don’t like such coincidences. There must be some deeper reason behind it. Dirac suggested what seemed to be the obvious explanation: presumably the gravitational constant was not constant, but was slowly changing such that
held for all eras.
⁴
It turned out, however, that the rate of change in the gravitational constant required by Dirac was high enough to be observable not only in the movement of the planets, but also in the movement of the earth’s crust. But we do not observe any phenomena of this kind. The mysterious equation
was still calling for an explanation.

Sometimes solutions can be surprisingly simple. In 1961 a brief note by R.H. Dicke was published in
Nature
, marking a breakthrough in the approach to this issue.
⁵
Dicke observed that the problem was not in the gravitational constant
G
, but rather in the age of the universe
T
. He pointed out that in an evolutionary universe life could not appear in any arbitrary era, but only within a certain limited interval of the universe’s age. This limitation was an outcome of the physical conditions necessary for life to appear. The first of these conditions was that the universe, and therefore also the galaxy, should be old enough for chemical elements other than hydrogen to have been created in it. “It is well known that carbon is required to make a physicist,” he wrote. This last sentence turned well-nigh proverbial. Indeed, carbon was a key issue. In the young universe there was only hydrogen. “The Era of Man” could have not ensued until the series of nuclear reactions within the interiors of stars had produced carbon; but neither can it come any later, when there are no more stars hot enough to provide a sufficient amount of energy to the surface of a planet endowed with life. Once Dicke had formulated these constraints in the language of the data drawn from the theory of stellar evolution it turned out that in “the Era of Man” the age of the universe had to be related to the gravitational constant and the mean density of matter, in terms of order of magnitude, by the formula
Gρ
₀
T
 
²
˜ 1. The relationship is by no means a coincidence; we simply could not exist in any other era, for either there would be no carbon, the building material of organic chemistry, or the universe would be too cold to support life.

1973 marked the fifth centenary of the birth of Copernicus. To celebrate the occasion the Cosmological Section of the International Astronomical Union held a symposium in Kraków. The subject was a comparison of the cosmological models with observational data. One of the sessions was presided over by John Archibald Wheeler. During the discussion he invited Brandon Carter to present his ideas on “Man’s place in the universe.” Carter asked for time to prepare, and on one of the following days delivered a fairly long lecture. Later its extended version entitled “Large Number Coincidences and the Anthropic Principle in Cosmology” was published in the proceedings of the symposium.
⁶
It was in Carter’s lecture that the expression “the anthropic principle” appeared for the first time. Later its author was to say that if he had known that his ideas would cause such confusion he would never have made them public. We shall try to present them with the special amount of attention that they require.

Carter followed and developed the line of thinking Dicke had initiated. Summarising his ideas, we may say that he used the expression “the anthropic principle” in the sense of the mode of reasoning applied to investigate and show the relationships between certain parameters characteristic for the universe and the possibility of life emerging in it. On account of the nature of these relationships he made a distinction between the weak anthropic principle and the strong anthropic principle.

The weak anthropic principle boils down to the following statement: We are observing the universe from this particular position, in this particular era, and we see it in this particular way, since we would not be capable of life in any other place or time. In this sense, and only in this sense, may we say that our existence is the explanation of the particular properties of the universe that we observe. However, this is not a causal sense: it does not mean that our existence is the cause of these properties of the universe. On the contrary: we are the factor which is a consequence of cosmic evolution; but for mankind to be able to come into existence, cosmic evolution had to bring the universe into a particular state. No wonder, then, since we are here, that we observe the universe precisely in this state.

Formulated in this way, the weak anthropic principle is a typical selection principle. We are observing a universe with certain particular properties. Out of all the possible models of the universe we must select only those which allow for the existence of these properties (above all it is a question of the selection of time and place). We reject all the other models as incompatible with observation.
⁷
If there is anything amazing about the anthropic principle understood in this way it is only that it eliminates so many of the cosmological models. The existence of life, at least on one planet in the universe, turns out to be a highly restrictive condition for models of the universe.

Carter formulated the strong anthropic principle in the following way: “the universe must be such as to admit the creation of observers within it at some stage.” We have to concede that such a formulation is a bit confusing, and it did indeed confuse many authors, who read it as containing a postulate of causality, or even a covert assumption of the existence of an intelligent Creator.
⁸
However, if we carefully read Carter’s argumentation right through to the end, we get a precise exposition of his intended meaning. He draws attention to the already well-established fact that a slight perturbation in the universe’s initial conditions would have led to a universe in which biological evolution could not have come about, and life would have been impossible. However, it cannot be denied that we do exist; therefore the initial conditions were such as to make this possible. Such initial conditions need not have been intentionally determined, although such an eventuality is not to be ruled out a priori. The initial conditions might have resulted from the interaction of physical laws we do not know of today, e.g. deriving from the fundamental theory we are still looking for; while the potential for biological evolution could have been only a side effect. The strong anthropic principle applies not only to the initial conditions, but also to the values of the fundamental physical constants and the other parameters characteristic of the universe (if their values had been slightly different, life would have been impossible). The time factor does not come into this line of reasoning, as in the case of initial conditions: the initial conditions were determined at a certain time, but life did not appear until much later. It was the time factor which could have led some authors astray, making them see the strong anthropic principle as entailing the attributes of causality.

The strong anthropic principle is a typical example of “reasoning back”: from the consequence (we exist) to the necessary condition (the right initial conditions, the right values of the constants and other parameters). Carter did not intend the strong anthropic principle to savour of finality, which does not mean that it is not worth while considering its teleological versions as well. We shall do so below.

Carter underpinned the line of reasoning which led him to the formulation of the strong anthropic principle with the following heuristic picture. Let’s imagine an ensemble of universes (in Carter’s terminology) which may be described “by all conceivable combinations of initial conditions and fundamental constants.” He did not ascribe a real existence to this ensemble of universes, but considered it purely as a mental construct to dramatise his line of reasoning. He wrote: “The existence of any organism describable as an observer will only be possible for certain restricted combinations of parameters, which distinguish within the world-ensemble an exceptional cognisable subset.” Of course he meant “cognisable” in the sense that only a universe belonging to this subset may be cognised by an observer living in it. The drama of the situation rests in the fact that the “cognisable” subset is dramatically small. In view of this it is hard to resist the impression that our existence is something that has been “fine-tuned” – fitted very precisely into the entire structure. No wonder that the anthropic principles evoked such a tempestuous wave of discussion, in which the participants did not refrain from excursions into metaphysics. It was in this context that speculations arose on the existence of “all possible” universes not just as an attitudinal metaphor, but as a physical reality.