THE ANTHROPIC PRINCIPLE AND MANY-WORLDS COSMOLOGIES

It has seemed to many a remarkable and even astounding coincidence that the world which is actual ‘just happens’ to be suitable for human life. There seem to be many possible worlds which do not permit human life, and only a few that do permit it, and yet---amazingly---the world that is actual is or of the latter. Such reflections, under the guise of the design argument, formerly led metaphysicians to postulate a God that created a world with humans because it is ‘the best of all possible worlds’. But in the past dozen or so years, these reflections have led cosmologists in a different direction --- to the postulate that the numerous other worlds that are unfit for human habitation are themselves actual. An exposition (Part One) and evaluation (Part Two) of these ‘many-worlds cosmologies’ follows.

The theories being examined combine two concepts, the anthropic principle (Section A) and the many-worlds interpretation of quantum mechanic (Section B).

Recent employments of the anthropic principle are usually traced back to R. H. Dicke’s 1961 article on ‘Dirac’s Cosmology and Mach’s Principle’,[1] which in part contains an explanation of the value of the Hubble age (how long the universe has been expanding). Dicke proposes that the present value is not a random choice from a wide range of possible values, but is ‘limited by the biological requirements to be met during the epoch of man’.[2] The first requirement is the existence of elements heavier than hydrogen (for ‘it is well known that carbon is required to make physicists’[3]). This sets the lower limit of the present value of the Hubble age as the age of the shortest lived stars, as elements heavier than hydrogen are formed in the interior of stars. The upper limit is set by the maximum age of nuclear reactive stars, which arc necessary to illuminate planets upon which humans are able to evolve.

This deduction of the present value of the Hubble age, previously regarded by physicists as arbitrary, revealed a certain method of argument. Instead of explaining biological conditions in terms of physical conditions, Dicke explained a physical value by deducing it from biological premises concerning the existence of humans. At the same time this involved the move of explaining the more fundamental by the less fundamental; the age of the entire universe is deduced from the existence of one part of the universe, the human species, Moreover, Dicke’s explanation is retrodictive rather than predictive: a present and subsequent condition, human life, is offered as an explanation of a past and anterior condition, the time elapsed between the beginning of the universe and the present.

This method of argument is not that usually employed in the sciences. Scientific explanations are usually causal, or are derivations of less general laws from more general laws. Dicke’s explanation is neither: the value of the Hubble age is neither an effect of the existence of humans, nor a special case of a law about human nature. Rather the value of the Hubble age is a necessary condition of the existence of humans, and is explained through being deduced from premises about that of which it is a necessary condition. The sense of ‘explanation’ implied here is that some state of affairs S₁ is explained by another state of affairs S₂ if a sentence describing S₁ can be deduced from a set of sentences at least one of which is a description of S₂. The relationship between S₂ and S₁ that serves as the basis of the inference need not be a causal relation; it could be of another sort, such as the relation of the conditioned to one of its necessary conditions. It is a relation of the latter sort that serves as the foundation of Dicke’s explanation. Let us exhibit the structure of such an explanation by a formal statement of Dicke’s argument:

(1) For any x, if x is an intelligent organism, then x is composed of heavy elements formed in the interior of stars, and lives on a planet.

(2) These heavy elements and planets do not both exist earlier than the shortest lived stars or later than the longest lived stars.

(4) Therefore, the lower limit of the present value of the Hubble age is the age of the shortest lived stars, and the upper limit the age of the longest lived stars.

I have given a more detailed account of the logic of such explanations elsewhere, and have demonstrated that although they do not conform to some familiar models of scientific explanation, they do conform to Philip Kitcher’s recently introduced ‘unification model’ of scientific explanation.[4]

The significance of Dicke’s method of argument did not become widely appreciated until after its discussion and development by Brandon Carter in his 1974 essay ‘Large Number Coincidences and the Anthropic Principle’.[5] Carter introduced the phrase ‘the anthropic principle’, and distinguished weak and strong versions of the principle. The weak principle is that ---

our location in the universe is necessarily privileged to the extent of being compatible with our existence as observers.[6]

the Universe (and hence the fundamental parameters on which it depends) must be such as to admit the creation of observers within it at some stage.[7]

The weak principle fully stated is that our particular spatial and temporal location in the universe must have all the characteristics necessary for our existence. In accordance with this principle, we can infer for example that our spatial location must be a planet rather than a hydrogen cloud or the interior of a star, and that our spatial location must be a planet possessing an ozone layer blocking the sun’s deadly ultraviolet rays, rather than a planet without such a layer. Only in such a spatial location could observers like ourselves survive.

Carter makes a plausible case that the weak principle is all that is needed to sanction Dicke’s deduction of the Hubble age. Although the present value of the Hubble age pertains to the entire universe, Dicke deduces it as a necessary characteristic of our temporal location in the universe: we must live at a certain time after the initial singularity, and not earlier or later.

The strong principle, on the other hand, allows inferences to be made about the universe itself, and not merely about certain locations in the universe. Some of the basic parameters of the universe deducible in accordance with the strong principle are mentioned by Carter, but the most exhaustive inventory is given by B. J. Carr and M. J. Rees in their 1979 article on ‘Thc Anthropic Principle and the Structure of the Physical World’.[8] The authors present evidence in support of the hypothesis that the orders of magnitude of most of the fundamental constants of physics are determined by the presence of intelligent life; intelligent life presupposes these orders and no others. The constants include, among others, the gravitational fine structure constant (a_G), the electromagnetic fine structure constant (a), the weak fine structure constant (a_w), the strong force constant (g_s), and such mass ratios as m_e/m_n –1/1837. An illustration of an order of magnitude between them that is deducible in accordance with the strong anthropic principle is a_G~a²⁰; that is, the gravitational fine structure constant is approximately equal to within an order of magnitude to the twentieth power of the electromagnetic fine structure constant. If a_G were slightly larger, no planets would form, and if slightly smaller, supernovae (which make available heavier elements necessary for life) would not occur.

One of the earliest and oft-cited employments of the strong anthropic principle is found in C. B. Collins’ and S. W. Hawking’s explanation of the rate of expansion of the universe at an early stage after the Big Bang.[9] A reduction in the rate of expansion by one part in a million million (10¹²) would have resulted in the universe recollapsing before life could have had a chance to evolve. An increase in the expansion rate would mean that regions of the universe would not form bound systems (galaxies, stars) necessary to life. Why is the expansion rate what it is? ‘Because we are here.’[10]

As we shall see, it is the strong rather than weak anthropic principle that, in conjunction with the many-worlds interpretation of quantum mechanics, provides the theoretical foundation for the many-worlds cosmologies.

A serious difficulty associated with the conventional or Copenhagen interpretation of quantum mechanics is that it cannot be applied to the general relativity space-time geometry of a closed universe. A quantum state of such a universe is describable as a wave function with varying spatial-temporal amplitude; the probability of the state of the universe being found at any given point is the square of the amplitude of the wave function at that point. In order for the universe to make the transition from the superposition of many points of varying probabilities to one of these points---the one in which it actually is---a measuring apparatus must be introduced that collapses the wave function and determines the universe to be at that point. But this is impossible, for there is nothing outside the universe, no external measuring apparatus, that can collapse the wave function.

A possible solution is to develop an interpretation of quantum mechanics that does not rely on the notion of external observation or measurement that is central to the Copenhagen interpretation. A quantum mechanics can be formulated that is internal to a closed system.

It is such an interpretation that Hugh Everett developed in his 1957 paper “‘Relative State’ Formulation of Quantum Mechanics’.[11] Each point in the superposition represented by the wave function is regarded as actually containing one state of the observer (or measuring apparatus) and one state of the system being observed. Thus

With each succeeding observation (or interaction), the observer state ‘branches’ into a number of different states. Each branch represents a different outcome of the measurement and the corresponding eigenstate for the object-system state. All branches exist simultaneously in the superposition after any given sequence of observations.[12]

Each branch is causally independent of each other branch,[13] and consequently no observer will ever be aware of any ‘splitting’ process. The world will seem to each observer as it does in fact seem.

Applied to the universe as a whole, this means that the universe is regularly dividing into numerous different and causally independent branches, consequent upon the measurement-like interactions among its various parts. Each branch can be regarded as a separate world, with each world constantly splitting into further worlds.

By this means a closed universe can be quantised. The difficulty with the Copenhagen interpretation, as we have seen, is that the quantum state transitions of the universe correspond to collapses of wave functions to single points, and these collapses require something impossible---a measuring apparatus external to the universe. According to the many-worlds interpretation, on the other hand, the transitions do not require the wave functions to be collapsed, as each point of the wave functions correspond, to an actual state of the universe. Therefore, no external measuring apparatus is required.

C. The Cosmological Synthesis of the Anthropic Principle and the Many-Worlds Interpretation of Quantum Mechanics

The combination of the strong anthropic principle with the many-worlds interpretation of quantum mechanics was first made by Carter in the essay discussed in Section A. A world ensemble is definable as a set of worlds characterised by all conceivable combinations of initial conditions and fundamental constants. An exceptional cognisable subset within this ensemble is distinguishable in reference to the certain combinations of the parameters that render empirically possible organisms describable as observers.[14] Subject to these premises,

a prediction based on the strong anthropic principle may be regarded as a demonstration that the feature under consideration is common to all members of the cognisable subset. Subject to the further condition that it is possible to define some sort of fundamental a priori measure on the ensemble, it would be possible to make an even more general kind of prediction based on the demonstration that a feature under consideration occurred in ‘most’ members of the cognisable subset.[15]

An example of the first kind of prediction concerns a_G ~ a²⁰. In the members of the cognisable subset of the world ensemble, a_G ~a²⁰, and planets, supernovae and stars of a kind suitable to life form. In members of other subsets, a_G is smaller or larger than a²⁰. In the worlds where a_G is slightly larger, there are no planets and all stars are blue giants that burn out too quickly for life to evolve. In worlds where it is slightly smaller, there are no supernovae and all stars are red dwarfs and radiate too feebly for life to develop on planets. Thus the obtaining of a_G ~a²⁰ in our world can be derived as follows:

Carter does not specify exactly how the Everett doctrine of many worlds is to be applied to Big Bang cosmology, but Bryce S. DeWitt suggests that at a very early stage of the Big Bang the universal wave function possessed an overall coherence not disrupted by condensation into noninterfering branches.[16] Only later do separate worlds evolve, some for example having a_G ~a²⁰ and others having a_G smaller or larger than a²⁰.

At this point it can be stated how the strong anthropic principle in combination with the many-worlds interpretation of quantum mechanics can be used in an attempt to resolve the apparent problem mentioned at the beginning of this essay. The seemingly problematic fact that a world with intelligent life is actual, rather than one of the many lifeless worlds, is found not to be a fact at all. If worlds with life and without life are both actual, then it is not surprising that this world is actual but is something to be expected.

In the remainder of this paper I shall assess the validity of the many-worlds cosmologies by examining their putative grounds in quantum mechanics (Section A) and anthropic considerations (Section B).

Carter finds strong support for his doctrine of a world ensemble in the Everett Interpretation of quantum mechanics, ‘to which one is virtually forced by the internal logic of quantum theory’.[17] It is indeed the case that the Everett Interpretation if true provides grounds for a belief in a many-worlds cosmology, but is one ‘virtually forced’ to this interpretation by quantum theory?

There is no doubt that the Copenhagen interpretation is inapplicable to the space-time geometry of the universe as a whole, and in this respect is disadvantaged relative to the many-worlds interpretation. However, applicability to the universe as a whole is not a necessary condition of the validity of an interpretation of quantum mechanics. Quantum mechanical properties could well be instances of properties that inhere in parts of a whole but not in the whole to which the parts belong. This does not mean that the whole of the universe is subject to classical mechanical laws, or is lawless and chaotic, but that meaningful statements about the whole of the universe cannot be made from within the framework of quantum mechanics. The reason why such statements cannot be made was made plain in Section B of Part One: they presuppose the nonsensical idea of a measuring apparatus external to the universe. If the analogy is not pressed too far, one may think here of Kant’s solution to the antinomies, that statements about a part but not about the whole of the world are meaningful.

It also should be noted that the advantage of greater comprehensiveness that the many-worlds interpretation possesses over the Copenhagen interpretation through providing a quantisation of general relativity is counterbalanced by a loss of parsimony. A theory that postulates one world is more parsimonious than a theory that postulates many, and if both theories lead to the same predictions (and both do) then---all other things being equal---the more parsimonious theory is preferable.

But this is not to say that the Copenhagen interpretation is unquestionably preferable to the Everett doctrine. For it is just not clear what criteria there are, if any, that enable one to decide rationally between considerations of comprehensiveness and those of parsimony. How much comprehensiveness should be sacrificed for the sake of parsimony, and how much parsimony for comprehensiveness? The choice between the Copenhagen and the many-worlds interpretation hinges upon a resolution of this more fundamental problem.

Perhaps an avenue out of this difficulty is provided by the ‘hidden variable’ interpretation of quantum mechanics, which is applicable to the universe as a whole and which postulates only one universe. True, no completely successful version of the ‘hidden variable’ interpretation has yet been developed, even in regard to parts of the universe,[18] but such a version appears possible in principle. The guiding idea of this interpretation is that the behaviour of particles on the quantum mechanical level is determined by causally determined processes on the sub-quantum mechanical level, which are currently ‘hidden’ from experimental observation. The Schrödinger wave equation ψ is not regarded as a mere mathematical symbol, but as a representation of a real field, a field that exerts a force on the quantum mechanical particles in it and inclines them toward the region of the field with the greatest intensity. The particles are also acted upon by sub-quantum mechanical entities, either directly, or indirectly by means of these entities causing random fluctuations in the ψ field which correspondingly affect the particles.[19] The net result of these influences on the quantum mechanical particles is calculable in terms of the observationally confirmed probability distribution p = /ψ/².

One can infer from this that the collapse of the wave function is due to a deterministic sub-quantum mechanical process rather than to the interposition of an external measuring apparatus. Accordingly, the collapses of the universal wave functions and the quantum state transitions of the universe can be thought of as consequences of processes internal to the universe.

H The Putative Grounds of the Many-Worlds Cosmologies in the Anthropic Coincidences

The parameters of the universe that ‘just happen’ to be suitable to intelligent life are the anthropic coincidences. How can the existence of such coincidences be thought to justify a belief in other worlds? John Leslie offers a lucid statement of the line of reasoning at work here:

The chief reason for belief in very many varied universes is that, given sufficiently many of them, random changes could be rung until at long last conditions somewhere became suitable for Life. Which is to say that the ultimate reason for believing in them is that the observed conditions seem not just suitable, but very remarkably suitable.[20]

Leslie’s statement of this reason can be developed if we briefly make a distinction between a posteriori and a priori probability. The former is exemplified by the idea that if two entities or states have been contiguous an all observed cases, then they are likely to be so in all unobserved cases. A posteriori probabilities, in short, are calculated on the basis of observed actualities. A priori probabilities, on the other hand, are determined in reference to possibilities. If there are ten possible states of affairs, only one of which is actual, and nine of these states of affairs are of kind A, and one of kind B, then it is ‘a priori probable’ (all other things being equal) that the actual state of affairs is of kind A.

Now the proponents of the many-worlds cosmologies are arguing that if there is only one actual world, then it is a priori improbable that this world be suitable to intelligent life. In fact, so they say, it is extremely improbable, so improbable as to be unbelievable. Recall Collins’ and Hawking’s observation that if the expansion rate of the universe at a time shortly after the Big Bang had been smaller by one part in a million million then life would not have evolved. A lifeless world would also have resulted if the expansion rate had been greater by one part in a million. Assuming that there is a possible world corresponding to each different possible expansion rate, these numbers render plausible the hypothesis that the number of possible life-supporting worlds is extremely few, whereas the number of life-hostile worlds is countless. Relative to these figures, the a priori probability value of a life-supporting world being the only actual world is almost nil. The values derived from a consideration of the other anthropic coincidences also reveal a staggering a priori improbability that the one actual world is life-supporting. Consider Davies’ calculation based on initial arrangements of matter and energy: the odds against life-supporting stars evolving from the Big Bang rather than an aggregate of black holes is ‘one followed by a thousand billion billion billion zeros, at least’.[21]

Of course, there are noncognisable worlds of several sorts that are also highly improbable, e.g. noncognisable worlds in which light has a velocity of 137,941 m.p.s. rather than some velocity above or below 137,941 m.p.s., but what is thought to distinguish cognisable worlds is that cognisability is a special or distinctive feature (unlike a light velocity of 137,941 m.p.s.). As Paul Davies points out, any hand of cards that is dealt is improbable a priori, but to be dealt a complete suit is not only improbable but remarkable, since a complete suit is a special sort of hand --- one that possesses greater order than the others.[22]

If there be only one world that is actual, it is indeed remarkable that it be our world, for our world is both highly improbable a priori and of a special sort. It is this combination of factors that makes it seem incredible that our world is the only actual world, and that calls for the hypothesis that other worlds are actual as well.

But that is not to say that the assertion that an improbable and special world like our own is actual entails the statement that other worlds are also actual. Rather, so it is argued, it renders probable or reasonable the belief that they are actual. If by postulating the actuality of other worlds the a priori improbability of this world is eliminated, then that provides a reason for the postulation. And such a postulation does eliminate the a priori improbability of this world, for if worlds with all possible initial conditions and fundamental constants are actual, then it is not likely but necessary that a world with these initial conditions and fundamental constants be actual, This world is still very special, but its actuality is no longer remarkable since its a priori probability value is 1.

One could object to this many-worlds hypothesis on the grounds that it is unverifiable in principle. There is no possible observation or experiment that could establish the existence of other worlds. But such an objection is based on a misunderstanding of the theory. The many-worlds hypothesis functions as an explanation of a set of observational data, the anthropic coincidences; the many worlds are the unobservables that are postulated to explain these observed coincidences by showing them to be necessary rather than a priori improbable. Accordingly, to complain that the many worlds are themselves unobservable is to confuse the logical role of the explanans with that of the explanandum; it is he explanandum that needs to be observed, not the explanans.

Another unsuccessful objection to this hypothesis is that it violates the law of parsimony and can be dismissed on this ground alone. This law enjoins one to choose, if all other things are equal, the simplest among competing theories. Now a many-worlds cosmologist would allow that a theory of one world is simpler than a theory of many, but he would deny that ‘all other things are equal’; he would point to the fact that the theory of one world is burdened with an incredible a priori improbability, claiming that is sufficient reason to reject it in favour of the more complex theory.

However, the law of parsimony does warrant a choice of a different many-worlds theory than that selected by such cosmologists as Carter, Collins and Hawking. If the many worlds simultaneously exist, then there is a different set of matter/energy for each world. But if they successively exist, the same .et can belong to each world, differing only in the form it takes in each world. Since the postulation of one set is more parsimonious than the assumption of many, the ‘successive worlds’ theory is on this basis preferable.

This theory of successive worlds is not a physically unfounded speculation, but is worked out in some detail by John Wheeler. The universe according to Wheeler goes through an infinite number of cycles of expansion and contraction, being ‘reprocessed probabilistically’[23] in each collapse. Whereas in the gravitational collapse of a star to a black hole all structures are extinguished except mass, charge and angular momentum, in each gravitational collapse of the universe itself all constants and laws disappear . In the last state of each collapse, a chaotic ‘pregeometry’ prevails out of which geometry and fields and particles are built up in the first stage of the ensuing Big Bang. Since the laws, constants, number of particles, length of cycles, etc. are all transformed probabilistically from one cycle to the next, the universe formed in each cycle represents an actualisation of a different member of the set of possible universes.

It may be wondered how well this theory comports with current observational data. One apparent problem concerns the amount of black-body radiation in the background radiation; the observed amount suggests that no more than approximately 100 cycles could have occurred. The black-body radiation is left over from previous cycles, and gradually accumulates with each new cycle. Joseph Silk concludes:

If we assume that each previous cycle of the expansion results in the generation of as much light as there is in the present universe, we infer that there may have been about 100 previous expansion and collapse cycles of the universe. A much larger number (for example, an infinite sequence), can be excluded on the basis of this argument.[24]

I think this objection can be met by pointing out that Silk assumes that the universe has the same basic parameters each cycle (parameters admitting the formation of stars and galaxies), whereas on Wheeler’s hypothesis previous cycles probably had different parameters. Accordingly, no inferences can be drawn about previous cycles from the recorded amount of black-body radiation. An even stronger response is based on Wheeler’s idea that it is impossible in principle to draw inferences about previous cycles, since all information about a previous cycle is destroyed in each collapse.

A more serious objection to Wheeler’s theory is from recent observational evidence suggesting that the universe is open and will expand forever. This conclusion has been tentatively drawn in J. Richard Gott’s and others’ 1974 article ‘An Unbound Universe?’,[25] as well as in more current summaries of the relevant evidence.[26] This claim may well be disputed,[27] but if true it greatly lessens the credibility of Wheeler’s theory. For it is just not plausible that this expansion ‘just happens’ to be the last of an infinite number of expansions. The chances against this are infinity to one. The extreme a priori improbability that the many-worlds theory was designed to eradicate appears again in a new guise.[28]

It is not impossible, though, that this is the last of an infinite series of expansions, for such a series can have a last member. If all previous expansions are correlated with a member of the negative number of series of order type ω*, then the last expansion can be represented as 0.

If the universe is open, then the conclusion is warranted that the extreme a priori improbability that thereby accrues to Wheeler’s theory annuls the advantage of parsimony it has over the Carter doctrine of coexisting universes. The goal of eliminating the a priori improbability of this universe, whatever form it may take, would then be best achieved by postulating concurrent and independent universes that began to divide from one another at an early stage in the Big Bang.

Dicke and Carter presuppose that life requires planets orbiting main-sequence stars, carbon and other heavy elements. These may well be conditions of life as we know it, but surely other forms of life are possible? Davies defines life as ‘organised electromagnetic energy, probably based on chemical bonding’,[29] but even this seems too restrictive. A view like Carr’s and Rees’ seems more acceptable ---

It is conceivable that some form of intelligence could exist without all of these features [elements heavier than hydrogen and helium, water, galaxies, and special types of stars and planets] ---thermodynamic disequilibrium is perhaps the only prerequisite that one can demand with real conviction.[30]

Cannot we go even further, and state that an intelligent organism can be embodied in any sort of matter or energy or arrangement of matter and energy? There is no contradiction in the idea that a mind is associated with gamma rays or vector bosons, or lives on the surface of neutron stars[31] or near the event horizon of black holes.[32] And is there really a contradiction in the idea that a mind is embodied in a world in a state of thermodynamic equilibrium? There does not even seem to be a contradiction in the idea that there is a changeless world or region of a world embodying a mind which is changelessly thinking one thought. Surely the concepts of intelligent organisms such as these are not like the concepts of round squares or wooden iron?

It might be objected that although such intelligent organisms are logically possible, they are not empirically possible, and consequently are excluded from the worlds envisaged in many-world cosmology. But this objection is untenable, for it is a stipulation of many-world cosmology that the ensemble of worlds is ‘characterised by all conceivable combinations of initial conditions and fundamental constants’,[33] and variations in fundamental constants are variations in laws determining what is empirically possible. If these constants vary from world to world, why cannot other empirical laws vary, like the laws of the association of consciousness with matter and energy? Perhaps in our world consciousness requires neurons, DNA molecules, carbon, planets, etc., but in other words it requires tachyons, virtual particles or radio waves with wavelengths greater than a mile?

To this it might be objected that there is a reason for assuming that the fundamental physical constants vary, but no reason for assuming that the laws of mind-matter correlation do. The assumption about the constants is based in part on the enormous a priori improbability that these values rather than some other values obtain in the one actual world; the postulate that all other values are instantiated in other actual worlds eliminates this a priori improbability. Since there is no reason to postulate other laws of mind-matter correlations, the principle of parsimony dictates that we assume that other worlds instantiate the same law that is observed to be instantiated in our world.

However, I believe there is a reason for assuming that other worlds instantiate other laws, in fact, the very same reason as there is for making this assumption about the constants. Of all the numerous logically possible laws of mind-matter correlation, only one of them is instantiated in our world. Since it is highly a priori improbable that this law be the only instantiated law, it is reasonable to believe that other laws are also instantiated.

But there is this difference, it may be replied: the values of the fundamental physical constants that obtain in our world are not only improbable but also special. Is the law of mind-matter correlation instantiated in this world also special?

The values of the fundamental physical constants that obtain in our world are special because they help to constitute a world that is cognisable by intelligent organisms. But the same is true for the law of mind-matter correlation instantiated in this world; without a law to the effect that consciousness is associated with the electrical activity of neurons in carbon based organisms, the neuronal and carbon-based formations made possible by these values of the fundamental physical constants would not be associated with cognitive states.

These reflections suggest that if there is reason to assume that the values of the fundamental physical constants vary from world to world, then there is also a reason---in fact, the very same reason---to make an analogous assumption in regard to the laws of mind-matter association. And if this is the case, then it can no longer be regarded as highly a priori improbable that if there be one actual world it be cognisable; indeed, it could very well be probable.

If these reflections point towards the conclusion that the hypothesis of many worlds is not sufficiently rationally motivated, they imply no such conclusion about explanations based solely on the anthropic principle. This principle can be used by itself to explain the values of the fundamental physical constants and initial conditions obtaining in our world, by deducing them as necessary conditions for intelligent organisms governed by the law of mind-matter association instantiated in our world. The fact that in other possible worlds different values of the fundamental constants and initial conditions are necessary conditions for intelligent organisms governed by other laws of mind-matter associations does not render invalid our anthropic explanations of the values obtaining in our world.[34]

[1] R.H. Dicke, ‘Dirac’s Cosmology and Mach’s Principle’, Nature 192, 1961, pp. 440-441.

[2] Ibid., p. 440.

[3] Ibid.

[4] Cf. Quentin Smith, ‘The Logic of Anthropic Explanation’, under consideration for publication.

[5] Brandon Carter, ‘Large Number Coincidences and the Anthropic Principle’, in Confrontation of Cosmological Theories with Observational Data, ed. M. S. Longair (Boston: D. Reidel, 1974), pp. 291-298. Carter earlier communicated some of the ideas in this essay in an unpublished 1968 Cambridge University preprint and at the Clifford Memorial Meeting in Princeton in 1970.

[6] Ibid., p. 293.

[7] Ibid., p. 294.

[8] B.J. Carr and M.J. Rees, ‘The Anthropic Principle and the Structure of the Physical World’, Nature 278, 1979, pp. 605-612.

[9] C.B. Collins and S.W. Hawking, ‘Why is the Universe Isotropic?’, The Astrophysical Journal 180, 1973, pp. 317-334. Also see Hawking’s ‘The Anisotropy of the Universe at Large Times’, in Confrontation of Cosmological Theories with Observational Data, op. cit., pp. 283-286.

[10] collins and Hawking, op. cit. , p. 334. The isotropy and expansion rate of the universe have recently been provided with nonanthropic explanations as well. See the discussion of the Inflationary Theory, the New Inflationary Theory, and the as yet undeveloped ‘Newest Inftationary Theory’, in John Barrow and Michael Turner, ‘The Inflationary Universe --- Birth, Death and Transfiguration’, Nature 298, 1982, pp. 801-805.

[11] Hugh Everett, “‘Relative State’ Formulation of Quantum Mechanics”, Reviews of Modern Physics 29, No.3, 1957, pp. 454-462. Reprinted in The Many-Worlds Interpretation of Quantum Mechanics, ed. B. S. DeWitt and N. Graham (Princeton: Princeton University Press, 1973), pp. 141-149.

[12] Everett, op. cit., p. 146.

[13] Although Everett claims that the branches are causally independent (see Ibid., p. 146, note added in proof), others argue that the interpretation in accordance with quantum mechanical formulae is that the branches are almost but not completely causally independent. See for example B. S. De Witt’s ‘The Many-Universes Interpretation of Quantum Mechanics’, in The Many-Worlds Interpretation of Quantum Mechanics, op. cit., p. 190.

[14] John Leslie makes explicit Carter’s tacit supposition that the ‘observers’ made possible by the parameters of the cognisable worlds are not to be understood restrictively as human, but as any intelligent beings. “In ‘our existence as observers’, it is observership and not our being us which is important,” Vide ‘Observership in Cosmology: the Anthropic Principle’, Mind XCII, 1983, p. 573. In this respect the term ‘anthropic’ could be misleading.

[15] Brandon Carter, op. cit., p. 296.

[16] Bryce S. DeWitt, ‘Quantum Mechanics and Reality’ in The Many-Worlds Interpretation of Quantum Mechanics, op. cit., p. 165.

[17] Brandon Carter, op. cit., p. 298.

[18] For example, one of the most successful versions to date, developed by D. Bohm and J. Bub in ‘A Proposed Solution to the Measurement Problem in Quantum Mechanics by a Hidden Variable Theory,’ Reviews of Modern Physics 38, No. 3, 1966, pp. 453-469, is admitted by the authors to be inadequate inasmuch as its equation of motion relies on the empirically unsound idea of instantaneous causal interactions among different parts of space. See p. 467.

A More fundamental objection to all forms of ‘hidden variable’ theory is based on the much-discussed Bell inequalities; for one of the most recent statements of this objection, see Anupam Garg’s and N.D. Mermin’s ‘Bell Inequalities with a Range of Violation that Does Not Diminish as the Spin Becomes Arbitrarily Large’, Physical Review Letters 49, No. 13, Sept. 27, 1982, pp. 901-904. For a discussion of the extent to which ‘hidden variable’ theories can be defended against this objection, see Mermin’s ‘Pair Distributions and Conditional Independence: Some Hints about the Structure of Strange Quantum Correlations’, Philosophy of Science 50, 1983, pp. 359-373.

[19] The possibility of direct action is suggested by David Bohm on page 113 of Causality and Chance in Modern Physics (Princeton: D. Van Nostrand Co., Inc., 1957), and the possibility of indirect action on page 77 of his Wholeness and the Implicate Order (London: Routledge & Kegan Paul, 1980).

[20] John Leslie, op. cit., p.575.

[21] Paul Davies, Other Worlds (New York: Simon and Schuster, 1980), p. 169.

[22] Ibid., p. 142.

[23] Charles W. Misner, Kip S. Thorne. John Archibald Wheeler, Gravitation (San Francisco: W. H. Freemand and Co.. 1973), p. 1214. Wheeler’s theory is presented in Chapter 44. Also see his ‘From Relativity to Mutability’ in The Physicist’s Conception of Nature, ed. Jagdish Mehra (Boston: D. Reidel, 1973), pp. 202-247, esp. pp. 239-244.

[24] Joseph Silk, The Big Bang (San Fransisco: W.H. Freeman and Co., 1980), pp.311-312.

[25] J. Richard Gott III, James E. Gunn, David N. Schramm, and Beatrice M. Tinsley, ‘An Unbound Universe?’ Astrophysical Journal 194, 1974, pp. 543-553.

[26] See for example Silk’s The Big Bang, op. cit., pp. 297-313.

[27] It is argued by some that evidence that neutrinos have a mass, and that there is an ‘unseen mass’ associated with galaxies, increases the plausibility of the hypothesis that the universe is closed.

[28] Theories based on oscillating models can be stated so that the number of expansions is large but finite, but even in this case it is a priori improbable (although less so) that this expansion be the last one.

[29] Paul Davies, Other Worlds, op.cit., p. 150.

[30] Carr and Rees, ‘The Anthropic Principle and the Structure of the Physical World’, op. cit., p. 612.

[31] Cf. G. Feinberg’s and R. Shapiro’s Life Beyond Earth (New York, 1980)

[32] Cf. F.J. Dyson’s ‘Time Without End: Physics and Biology in an Open Universe’, Reviews of Modern Physics 51, No. 3, July,1979, pp. 447-460.

[33] Brandon Carter, op. cit., p. 295.

[34] For a related discussion of the a priori probability value of the existence of what I have called “the world-whole”, see Quentin Smith, The Felt Meanings of the World (West Lafayette, Indiana: Purdue University Press, 1985), Chapter VI, Section 39, ii.

Originally published in: Australasian Journal of Philosophy VoI. 63, No.3; September 1985