1.2 Anthropic Definitions

From: The Cosmological Anthropic Principle
John Barrow and Frank Tipler,
Oxford University Press 1988
ISBN 0-19-282147-4

"Definitions are like belts. The shorter they are, the more elastic they need to be." S. Toulmin

Although the Anthropic Principle is widely cited and has often been discussed in the astronomical literature, (as can be seen from the bibliography to this chapter alone), there exist few attempts to frame a precise statement of the Principle; rather, astronomers seem to like to leave a little flexibility in its formulation perhaps in the hope that its significance may thereby more readily emerge in the future. The first published discussion by Carter saw the introduction of a distinction between what he termed 'Weak' and 'Strong' Anthropic statements. Here, we would like to define precise versions of these two Anthropic Principles and then introduce Wheeler's Participatory Anthropic Principle' together with a new Final Anthropic Principle which we shall investigate in Chapter 10.

The Weak Anthropic Principle (WAP) tries to tie a precise statement to the notion that any cosmological observations made by astronomers are biased by an all-embracing selection effect: our own existence. Features of the Universe which appear to us astonishingly improbable, a priori, can only be judged in their correct perspective when due allowance has been made for the fact that certain properties of the Universe are necessary if it is to contain carbonaceous astronomers like ourselves. This approach to evaluating unusual features of our Universe first re-emerges in modern times in a paper of Whitrow" who, in 1955, sought an answer to the question 'why does space have three dimensions?'. Although unable to explain why space actually has, (or perhaps even why it must have), three dimensions, Whitrow argued that this feature of the World is not unrelated to our own existence as observers of it. When formulated in three dimensions, mathematical physics possesses many unique properties that are necessary prerequisites for the existence of rational information-processing and 'observers' similar to ourselves. Whitrow concluded that only in three-dimensional spaces can the dimensionality of space be questioned. At about the same time Whitrow also pointed out that the expansion of the Universe forges an unbreakable link between its overall size and age and the ambient density of material within it.16 This connection reveals that only a very 'large' universe is a possible habitat for life. More detailed ideas of this sort had also been published in Russian by the Soviet astronomer Idlis." He argued that a variety of special astronomical conditions must be met if a universe is to be habitable. He also entertained the possibility that we were observers merely of a tiny fraction of a diverse and infinite universe whose unobserved regions may not meet the minimum requirements for observers that there exist hospitable temperatures and stable sources of stellar energy.

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Our definition of the WAP is motivated in part by these insights together with later, rather similar ideas of Dicke" who, in 1957, pointed out that the number of particles in the observable extent of the Universe, and the existence of Dirac's famous Large Number Coincidences 'were not random but conditioned by biological factors'. This motivates the following definition:

Weak Anthropic Principle (WAP): The observed values of all physical and cosmological quantities are not equally probable but they take on values restricted by the requirement that there exist sites where carbon-based life can evolve and by the requirement that the Universe be old enough for it to have already done so.

Again we should stress that this statement is in no way either speculative or controversial. It expresses only the fact that those properties of the Universe we are able to discern are self-selected by the fact that they must be consistent with our own evolution and present existence. WAP would not necessarily restrict the observations of non-carbon-based life but our observations are restricted by our very special nature. As a corollary, the WAP also challenges us to isolate that subset of the Universe's properties which are necessary for the evolution and continued existence of our form of life. The entire collection of the Universe's laws and properties that we now observe need be neither necessary nor sufficient for the existence of life. Some properties, for instance the large size and great age of the Universe, do appear to be necessary conditions; others, like the precise variation in the distribution of matter in the Universe from place to place, may not be necessary for the development of observers at some site. The non-teleological character of evolution by natural selection ensures that none of the observed properties of the Universe are sufficient conditions for the evolution and existence of life.

Carter, and others, have pointed out that as a self-selection principle the WAP is a statement of Bayes' theorem. The Bayesian approach" to inference attributes a priori and a posteriori probabilities to any hypothesis before and after some piece of relevant evidence, E, is taken into account. In such a situation we call the before and after probabilities p, and PA, respectively. The fact that for any particular outcome 0, the probability of observing 0 before the evidence E is known equals the probability of observing 0 given the evidence E, after E was accounted for, is expressed by the equation,

(1. 1)

where/ denotes a conditional probability. Bayes' formula" then gives the relative plausibililty of any two theories a and 0 in the face of a piece of evidence E as

(1.2)

 

Thus the relative probabilities of the truth of or are modified by the conditional probabilities and which account for any bias of the experiment (or experimenter) towards gathering evidence that favours a rather than 0 (or vice versa). The WAP as we have stated it is just an application of Bayes' theorem. The WAP is certainly not a powerless tautalogical statement because cosmological models have been defended in which the gross structure of the Universe is predicted to be the same on the average whenever it is observed. The, now defunct, continuous creation theory proposed by Bondi, Gold and Hoyle is a good example. The WAP could have been used to make this steady-state cosmology appear extremely improbable even before it came into irredeemable conflict with direct observations. As Rees points out:

the fact that there is an epoch when [the Hubble time, tH which is essentially equal to the age of the Universe] is of order the age of a typical star..... is not surprising in any 'big bang' cosmology. Nor is it surprising that we should ourselves be observing the universe at this particular epoch. In a steady-state cosmology, however, there would seem no a priori reason why the timescale for stellar evolution should not be either [much less than] tH (in which case nearly all the matter would be in dead stars or 'burnt-out' galaxies) or [much greater than] t, (in which case only a very exceptionally old galaxy would look like our own). Such considerations could have provided suggestive arguments in favour of 'big bang' cosmologies ...

We can also give some examples of how the WAP leads to synthesizing insights that deepen our appreciation of the unity of Nature. Observed facts, often suspected at first sight to be unrelated, can be connected by examining their relation to the conditions necessary for our own existence and their explicit dependence on the constants of physics. Let us reconsider, from the Bayesian point of view, the classic example mentioned in section 1.1, relating the size of the Universe to the period of time necessary to generate observers. The requirement that enough time pass for cosmic expansion to cool off sufficiently after the Big Bang to allow the existence of carbon ensures that the observable Universe must be relatively old and so, because the boundary of the observable Universe expands at the speed of light, very large. The nuclei of carbon, nitrogen, oxygen and phosphorus of which we are made, are cooked from the light primordial nuclei of hydrogen and helium by nuclear reactions in stellar interiors. When a star nears the end of its life, it disperses these biological precursors throughout space. The time required for stars to produce carbon and other bioactive elements in this way is roughly the lifetime of a star on the 'main-sequence' of its evolution, given by (1.3)

where G is Newton's gravitation constant, c is the velocity of light, h is Planck's constant and mN is the proton mass. Thus, in order that the Universe contain the building-blocks of life, it must be at least as old as t* and hence, by virtue of its expansion, at least ct* (roughly ten billion light years) in extent. No one should be surprised to find the Universe to be as large as it is. We could not exist in one that was significantly smaller. Moreover, the argument that the Universe should be teeming with civilizations on account of its vastness loses much of its persuasiveness: the Universe has to be as big as it is in order to support just one lonely outpost of life. Here, we can see the deployment of (1.2) explicitly if we let the hypothesis that the large size of the Universe is superfluous for life on planet Earth be a and let hypothesis 0 be that life on Earth is connected with the size of the Universe. If the evidence E is that the Universe is observed to be greater than ten billion light years in extent then, although << 1, the hypothesis is not necessarily then improbable because we have argued that ~ 1. We also observe the expansion of the Universe to be occurring at a rate which is irresolvably close to the special value which allows it the smallest deceleration compatible with indefinite future expansion. This feature of the Universe is also dependent on the epoch of observation. And again, if galaxies and clusters of galaxies grow in extent by mergers and hierarchical clustering,' then the characteristic scale of galaxy clustering that we infer will be determined by the cosmic epoch at which it is observed.

Ellis has stressed the existence of a spatial restriction which further circumscribes the range of observed astronomical phenomena. What amounts to a universal application of the principle of natural selection would tell us that observers may only exist in particular regions of a spatially inhomogeneous universe. Since realistic mathematical models of inhomogeneous universes are extremely difficult to construct, various unverifiable cosmological 'Principles' are often used by theoretical cosmologists to allow simple cosmological models to be extracted from Einstein's general theory of relativity. These Principles invariably make statements about regions of the Universe which are unobservable not only in practice but also in principle (because of the finite speed of light). Principles of this sort need to be used with care. For example, Principles of Mediocrity like the Copernican Principle or the Principle of Plenitude (see Chapter 3) would imply that if the Universe did possess a preferred place, or centre, then we should not expect to find ourselves positioned there. However, general relativity allows possible cosmological models to be constructed which not only possess a centre, but which also have conditions conducive to the existence of observers only near that centre. The WAP would offer a good explanation for our central position in such circumstances, whilst the Principles of Mediocrity would force us to conclude that we do not exist at all! According to WAP, it is possible to contemplate the existence of many possible universes, each possessing different defining parameters and properties. Observers like ourselves obviously can exist only in that subset containing universes consistent with the evolution of carbon-based life.

This approach introduces necessarily the idea of an ensemble of possible universes and was suggested independently by the Cambridge biologist Charles Pantin in 1965. Pantin had recognized that a vague principle of amazement at the fortuitous properties of natural substances like carbon or water could not yield any testable predictions about the World, but the amazement might disappear if4ll

we could know that our Universe was only one of an indefinite number with varying properties, [so] we could perhaps invoke a solution analogous to the principle of Natural Selection; that only in certain universes which happen to include otirs, are the conditions suitable for the existence of life, and unless that condition is fulfilled there will be no observers to note the fact

However, as Pantin also realized, it still remains an open question as to why any permutation of the fundamental constants of Nature allows the existence of life, albeit a question we would not be worrying about were such a fortuitous permutation not to exist. If one subscribes to this 'ensemble interpretation' of the WAP one must decide how large an ensemble of alternative worlds is to be admitted. Many ensembles can be imagined according to our willingness to speculate-different sets of cosmological initial data, different numerical values of fundamental constants, different space-time dimensions, different laws of physics-some of these possibilities we shall discuss in later chapters.

The theoretical investigations initiated by Carter' reveal that in some sense the subset of the ensemble containing worlds able to evolve observers is very 'small'. Most perturbations of the fundamental constants of Nature away from their actual numerical values lead to model worlds that are still-born, unable to generate observers and become cognizable. Usually, they allow neither nuclei, atoms nor stars to exist. Whatever the size and variety of permutations allowed within a hypothetical ensemble of 'many worlds', one might introduce here an analogue of the Drake equation" often employed to guess the number of extraterrestrial civilizations in our Galaxy. Instead of expressing the probability of life existing elsewhere as a product of independent probabilities for the occurrence of processes like planetary formation, protocellular evolution and so forth, one could express the probability of life existing anywhere as a product of probabilities that encode the fact that life is only possible if parameters like the fine structure constant or the strong coupling constant lie in a particular numerical range."" The existence of the fundamental cosmic timescale like (1.3), fixed only by invariant constants of Nature, c, h, G, and m,, was exploited by Dicke to produce a powerful WAP argument against Dirac's conclusion that the Newtonian gravitation constant, G, is decreasing with time. Dirac had noticed that the dimensionless measure of the strength of gravity

(1.4)

is roughly of order the inverse square root of the number of nucleons in the observable Universe, N(t), at the present time t,) 1 O'o yrs. At any time, t, the quantity N(t) is simply

(1.5)

if we use the cosmological relation that the density of the Universe, p,, is related to its age by pu (Gt2)-i. (The present age of roughly 10")yrs is displayed in the last step.) Dirac argued that it is very unlikely that these two quantities should possess simply related dimensionless magnitudes which are both so vastly different from unity and yet be independent. Rather, there must exist an approximate equality between them of the form

(1.6)

However, whereas ac, is a time-independent combination of constants, N(t) increases linearly with the time of observation, t, which for us is the present age of the Universe. The relation (1.6) can only hold for all times if one component of a, is time-varying and so Dirac suggested that we must have . The quantities N(t) and are now observed to be of the same magnitude because (as a result of some unfound law of Nature) they are actually equal, and furthermore, they are of such an enormous magnitude because they both increase linearly in time and the Universe is very old-although this 'oldness' can presumably only be explained by the WAP even in this scheme of 'varying' constants for the reasons discussed above in connection with the size of the Universe.

However, the WAP shows Dirac's radical conclusion of a time-varying Newtonian gravitation constant to be quite unnecessary. The coincidence that today we observe N-a-, 2 is necessary for our existence. Since we would not expect to observe the Universe either before stars form or after they have burnt out, human astronomers will most probably observe the Universe close to the epoch t* given by (1.3). Hence, we will observe the time-dependent quantity N(t) to take on a value of order N(t*) and, by (1.3) and (1.4), this value is necessarily just

(1.7)

where the second relation is a consequence of the value of t, in (1.3). If we let delta be Dirac's hypothesis of time-varying G, while beta is the hypothesis that G is constant while the 'evidence', E, is the coincidence (1.6); then, although the a priori probability that we live at the time when the numbers N(t) and are equal is very low, << 1), this does not render hypothesis beta (the constancy of G) implausible because there is an anthropic selection effect which ensures ~ 1. This selection effect is the one pointed out by Dicke. We should notice that this argument alone explains why we must observe N(t) and to be of equal magnitude, but not why that magnitude has the extraordinarily large value _ 1 079. (We shall have a lot more to say about this problem in Chapters 4, 5 and 6). As mentioned in section 1.1, Carter' introduced the more speculative Strong Anthropic Principle (SAP) to provide a 'reason' for our observation of large dimensionless ratios like 1071; We state his SAP as follows:

Strong Anthropic Principle (SAP): The Universe must have those properties which allow life to develop within it at some stage in its history.

An implication of the SAP is that the constants and laws of Nature must be such that life can exist. This speculative statement leads to a number of quite distinct interpretations of a radical nature: firstly, the most obvious is to continue in the tradition of the classical Design Arguments and claim that:

(A) There exists one possible Universe 'designed' with the goal of generating and sustaining 'observers'.

This view would have been supported by the natural theologians of past centuries, whose views we shall examine in Chapter 2. More recently it has been taken seriously by scientists who include the Harvard chemist Lawrence Henderson' and the British astrophysicist Fred Hoyle, so impressed were they by the string of 'coincidences' that exist between particular numerical values of dimensionless constants of Nature without which life of any sort would be excluded. Hoyle points out how natural it might be to draw a teleological conclusion from the fortuitous positioning of nuclear resonance levels in carbon and oxygen:

I do not believe that any scientist who examined the evidence would fail to draw the inference that the laws of nuclear physics have been deliberately designed with regard to the consequences they produce inside the stars. If this is so, then my apparently random quirks have become part of a deep-laid scheme. If not then we are back again at a monstrous sequence of accidents.

The interpretation (A) above does not appear to be open either to proof or to disproof and is religious in nature. Indeed it is a view either implicit or explicit in most theologies. This is all we need say about the 'teleological' version of the SAP at this stage. However, the inclusion of quantum physics into the SAP produces quite different interpretations. Wheeler' has coined the title 'Participatory Anthropic Principle' (PAP) for a second possible interpretation of the SAP:

(B) Observers are necessary to bring the Universe into being.

This statement is somewhat reminiscent of the outlook of Bishop Berkeley and we shall see that it has physical content when considered in the light of attempts to arrive at a satisfactory interpretation of quantum mechanics." It is closely related to another possibility:

(C) An ensemble of other different universes is necessary for the existence of our Universe.

This statement receives support from the 'Many-Worlds' interpretation of quantum mechanics and a sum-over-histories approach to quantum gravitation because they must unavoidably recognize the existence of a whole class of real 'other worlds' from which ours is selected by an optimizing principle." We shall express this version of the SAP mathematically in Chapter 7, and we shall see that this version of the SAP has consequences which are potentially testable. Suppose that for some unknown reason the SAP is true and that intelligent life must come into existence at some stage in the Universe's history. But if it dies out at our stage of development, long before it has had any measurable non-quantum influence on the Universe in the large, it is hard to see why it must have come into existence in the first place. This motivates the following generalization of the SAP:

Final Anthropic Principle (FAP): Intelligent information-processing must coine into existence in the Universe, and, once it comes into existence, it will never die out.

We shall examine the consequences of the FAP in our final chapter by using the ideas of intormation theory and computer science. The FAP will be inade precise in this chapter. As we shall see, FAP will turn out to require the Universe and elementary particle states to possess a number of definite properties. These properties provide observational tests for this statement of the FAP. Although the FAP is a statement of physics and hence ipso facto" has no ethical or moral content, it nevertheless is closely connected with moral values, for the validity of the FAP is the physical precondition for moral values to arise and to continue to exist in the Universe: no moral values of any sort can exist in a lifeless cosmology. Furthermore, the FAP seems to imply a melioristic cosmos. We should warn the reader once again that both the FAP and the SAP are quite speculative; unquestionably, neither should be regarded as well-established principles of physics. In contrast, the WAP is just a restatement, albeit a subtle restatement, of one of the most important and well-established principles of science: that it is essential to take into account the limitations of one's measuring apparatus when interpreting one's observations.

Roger Penrose on the Anthropic Principle (from The Emperor's New MInd)

How important is consciousness for the universe as a whole? Could a universe exist without any conscious inhabitants whatever'? Are the laws of physics specially designed in order to allow the existence of conscious life? Is there something special about our particular location in the universe, either in space or in time? These are the kinds of question that are addressed by what has become known as the anthropic principle. This principle has many forms. (See Barrow and Tipler 1986.) The most clearly acceptable of these addresses merely the spatiotemporal location of conscious (or 'intelligent') life in the universe. This is the weak anthropic principle. The argument can be used to explain why the conditions happen to be just right for the existence of (intelligent) life on the earth at the present time. For if they were not just right, then we should not have found ourselves to be here now, but somewhere else, at some other appropriate time. This principle was used very effectively by Brandon Carter and Robert Dicke to resolve an issue that had puzzled physicists for a good many years. The issue concerned various striking numerical relations that are observed to hold between the physical constants (the gravitational constant, the mass of the proton, the age of the universe, etc.). A puzzling aspect of this was that some of the relations hold only at the present epoch in the earth's history, so we appear, coincidentally, to be living at a very special (line (give or take a few million years!). This was later explained, by Carter and Dicke, by the fact that this epoch coincided with the lifetime of what are called main-sequence stars, such as the sun. At any other epoch, so the argument ran, there would be no intelligent life around in order to measure the physical constants in question-so the coincidence had to hold, simply because there would be intelligent life around only at the particular time that the coincidence did hold! The strong anthropic principle goes further. In this case, we are concerned not just with our spatio-temporal location within the universe, but within the infinitude of possible universes. Now we can suggest answers to questions as to why the physical constants, or the laws of physics generally, are specially designed in order that intelligent life can exist at all. The argument would be that if the constants or the laws were any different, then we should not be in this particular universe, but we should be in some other one! In my opinion, the strong anthropic principle has a somewhat dubious character, and it tends to be invoked by theorists whenever they do not have a good enough theory to explain the observed facts (i.e. in theories of particle physics, where the masses of particles are unexplained and it is argued that if they had different values from the ones observed, then life would presumably be impossible, etc.). The weak anthropic principle, on the other hand, seems to me to be unexceptionable, provided that one is very careful about how it is used.

By the use of the anthropic principle either in the strong or weak form-one might try to show that consciousness was inevitable by virtue of the fact that sentient beings, that is 'we', have to be around in order to observe the world, so one need not assume, as I have done, that sentience has any selective advantage! In my opinion, this argument is technically correct, and the weak anthropic argument (at least) could provide a reason that consciousness is here without it having to be favoured by natural selection. On the other hand, I cannot believe that the anthropic argument is the real reason (or the only reason) for the evolution of consciousness. There is enough evidence froni other directions to convince me that consciousness is of powerful selective advintage, and I do not think that the anthropic argument is needed.