Chapter 6: Emerging questions and uncertainties

Section 6.1: Observational limits and horizons

Section 6.2: Testing the nature of fundamental forces

Section 6.5: The Uniqueness of the Universe

Section 6.6: Uncertainty at the Foundations

We have seen in the preceding chapter that as we touch the larger issues of cosmology, we begin to reach the limits of certainty that can be achieved by the scientific method. In this chapter we consider some of these problems and emergent questions. This helps to put in perspective the achievements and limits of science in understanding the material Universe. We consider in turn, uncertainty due to observational limits and horizons; problems in testing the nature of fundamental forces; uncertainty about physical origins of the universe; puzzles concerning deep connections (Olber's paradox, Mach's principle, the arrow of time). Then we turn to the fundamental underlying issues, problems arising from the uniqueness of the Universe; and uncertainty at the foundations.

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Section 6.1: Observational limits and horizons

Our ability to directly determine the geometry and distribution of matter in the Universe is restricted by many observational difficulties [98], including the faintness of the images we are trying to understand. However there are much more fundamental restrictions on what we can observe.

We can only detect distant matter by means of particles or radiation it emits that travel to us, receiving most of our information from light (It is understood that "light" is a generic term for any form of electromagnetic radiation by which we can see distant objects: radio waves, infra-red radiation, ultraviolet radiation, and X-rays as well as ordinary light [28]). There are therefore fundamental limitations on the region of the Universe we can see, because the radiation conveying information travels towards us at the speed of light (and any material particles travel slower than this speed (see the discussion of Relativity in Chapter 3). As we look out to further and further distances, we are necessarily looking further and further back in time (for example the Andromeda galaxy is 1 million light years away; this means we see it as it was 1 million years ago). We are therefore seeing the sources at earlier stages in their evolution. This makes it very difficult to disentangle the effects of physical evolution of the sources observed, from geometrical evolution of the Universe. This is the main reason we are unable to tell directly from observations of the rate of change of redshift with distance if the Universe will recollapse or not.

6.1.1 The Particle Horizon

Furthermore, because the Universe has a finite age, light can only have travelled a finite distance since the origin of the Universe. This feature implies that we can only see out to those particles whose present-day distance corresponds to the age of the Universe; the particles beyond cannot be seen by us no matter what detectors we may use (light has not had time to travel to us from them since the creation of the Universe). The effect is the same as the horizon we see when we look at distant objects on the Earth: there are many further objects we cannot see because they lie beyond the horizon. In the case of the expanding Universe, we call the horizon separating those particles (Which later will become galaxies) that we can have seen (or indeed have had any causal contact with) from those we cannot, the particle horizon [31,79,98]. Actually we cannot even see as far as the particle horizon, because the Universe is opaque at early times (before decoupling), as explained in the previous chapter.

In reality we can see only as far as the visual horizon, where the universe becomes transparent; this lies inside the particle horizon, and corresponds to looking back as far as matter that emitted the blackbody background radiation (at the time of decoupling) [31]. The region beyond (up to the particle horizon) is accessible only by neutrino or gravitational wave telescopes. These do not yet have the sensitivity or directional capability to tell us anything useful about this domain, but in the future may provide important evidence.

It is because of these limits that we are able to say very little about the Universe on scales bigger than the Hubble size (the distance we can have seen since the beginning of the Universe, roughly 10 thousand million light years). Thus we cannot observationally distinguish between universe models that are strictly homogeneous in the large (implying conditions are the same at a distance 1 million times the Hubble size away from us, as they are here), and those that are not. If the Universe has finite spatial sections, there are at least as many galaxies outside our view as within it; while if it has infinite spatial sections, we cannot see an infinite number of galaxies, so what we can see is an infinitely small fraction of all there is. Any statements we make about the structure of the Universe on a really large scale (that is, many times the horizon size) are strictly unverifiable.

These limitations make it very difficult to tell if an idea such as the chaotic inflationary Universe idea is a true description of the real Universe, or not. In that case, at the present time huge sections of the Universe that are nearly homogeneous (but with different expansion rates, density parameters, etc.) would be separated from each other by very inhomogeneous transition zones, but these zones would not be visible to us.

It is often stated that the inflationary Universe idea solves the horizon problem. This refers to the issue of microwave background radiation isotropy, which runs into severe causal difficulties in an ordinary (non-inflationary) universe model, for then regions that could not have been in causal contact with each other appear to be in identical physical states, because they emit radiation that we measure to be at the same temperature. These causal problems in the early Universe are solved by inflation, for there the greatly increased early expansion allows these regions causal contact [20,89-91,95].

However there are still visual horizons in these Universes (There are also particle (causal) horizons if the inflationary Universe has infinite spatial sections; but they do not exist if it has closed spatial sections (then the particle horizons are broken at very early times, when light has had time to travel right round the Universe), so the verification problem remains.

6.1.2 Small Universes

There is one exception to this generally pessimistic situation. It is possible (even if the Universe is a low density Universe) that the large-scale connectivity of space could be different from what we expected, so that the Universe is in fact a Small Universe, spatially closed on a scale smaller than the Hubble size. Then if one could go in an arbitrary spatial direction at constant time, one would eventually end up very close to where one began (as in the case of a sphere, torus, or a Mobius strip). If this were the case we would be able to see right round the Universe several times; so we could see each galaxy (including our own) several times through images in different directions in the sky, a relatively small number of galaxies giving a very large number of images [31].

The effect is like being in a room whose walls, floor, and ceiling are all covered with mirrors: you see a huge number of images of yourself fading away into the distance in all directions. Similarly in a Small Universe, despite its small size we would see a large number of images of each galaxy fading away in an apparently infinite universe. In this case (and only in this case) there would be no visual horizon, and we can in principle determine the geometry of the whole Universe by observation, for all the matter that exists is accessible to our observation (in contrast to the usually considered situation, where only a small fraction of that matter can be seen). Furthermore in this case we would be able to study the history of our own Galaxy by optical observations, as we would be able to see it at different times in its history in the different images that would be visible to us.

Such Universes have all the advantages attributed by Einstein and Wheeler to a closed Universe (see previous chapter); thus it is an attractive possibility. Now it is possible we live in such a small Universe, and various observational tests to see if this is so are underway, involving examining statistics of different objects and searching for evidence in the CMB anisotropy pattern. However at presentthere is no solid evidence that this is indeed the case. Thus the working hypothesis is that we do not live in a small Universe, but we should keep an open mind on this matter.

6.1.3 Limits to Observational Verifiability

Overall, what we can say with any degree of certainty is strictly proscribed by observational limits [98]:

· Our ability to observationally determine the geometry of the universe is strongly constrained by the existence of cosmological horizons.

We can in principle observationally determine

(a) a great deal about the region we can observe (which lies inside the visual horizon);

(b) a little about that which lies outside our visual horizon but inside the particle horizon - we can tell nothing about these regions by observations based on electromagnetic waves but we may be able to tell something about them by use of neutrino telescopes, if they ever develop sufficiently, or by gravitational wave telescopes when they come into operation in about 2005;

(d) In a Small Universe there are no visual or particle horizons, horizons, but the real Universe is probably not like that.

The implication is that when our models give predictions of the nature of the Universe on a larger scale than the Hubble radius, these are strictly unverifiable, however appealing they may be.

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Section 6.2: Testing the nature of fundamental forces

In trying to understand the early Universe, we also come up against major limits in terms of our ability to test the predictions of our proposals for physical laws. Even if we could build a super-collider as large as the entire Solar System, we could not reach the kinds of energies that come into play in the very early Universe, so we cannot test the behaviour of matter under the relevant conditions [89]. This puts major limits on our ability to test whether our theories of those times are right or not. Some important events in the past is governed by physics that may or may not be testable by experiments on earth. For example while it is commonly believed that inflation took place in the early Universe, we have been unable so far to detect in experiments on Earth the field responsible for inflation, and so cannot confirm that the proposal for the underlying mechanism is correct. Similarly the proposals as to how synthesis of protons from quarks took place in the early Universe cannot yet be confirmed because we have not seen the relevant particles, and measurements of the decay rate of the proton contradicts that simplest theory that could underlie the proposed mechanism; we do not know which of the more complex possibilities (if any) may be correct.

Indeed the early Universe is the only place where some of the laws of physics come fully into play (apart from what happens to matter in the final state of collapse in a black hole); but that is completely inaccessible to observation. Consequently the situation is reversed from what we might hope, in that instead of being able to take known laws and use them to determine what happened in the very early Universe, we may have to proceed the other way round, regarding the early Universe as the only laboratory where those laws can be tested. This has led to an important discovery; comparison of element abundance observations with studies of nucleosynthesis in the early Universe determined that there are only three neutrino types, rather than four, before this question had been tested experimentally on Earth. Results from the accelerator at CERN later confirmed this conclusion.

However this type of reasoning only works when there are a few clear-cut alternatives that make clear observational predictions, and depends on the assumed cosmological conditions being correct. When we consider the really fundamental questions, whose understanding is the Holy Grail of theoretical physics, even the broad kind of approach to take is not clear. One is concerned here with the unification of our understanding of all the known forces into a single theory that, at a fundamental level, is a "theory of everything", combining together the features of gravity, electromagnetism, the weak force, and the strong force in a way compatible with relativity theory and with quantum theory. Various proposals have been made, see Chapter 3, but we do not know which if any is correct. This kind of physics probably controls the very earliest phases of the expansion of the Universe; we can reject some of the theories on the basis of their cosmological predictions, but cannot in this way select a particular one as being correct, nor can experiments on Earth distinguish between them. We certainly cannot use this broad class of theories to determine a unique history for the very early history of the Universe.

Thus the practical limits of testing of physical laws are major limitations in determining what really happened at very early times (tiny fractions of a second after the Big Bang). In effect,

· Corresponding to the particle horizon, there is a physics horizons limiting our ability to confirm the nature of physics controlling events in the very earliest stages of the expansion of the universe.

· There is an energy limit to what has been tested so far, and an absolute limit to what will ever be testable on earth or even in the solar system by experiments.

The energies attainable in colliders will always be limited by practical considerations. However events in the early universe can attain arbitrarily high energies (unless there was a bounce at very early times; but it is not believed that this is the case, see Chapter 5).

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Section 6.3: Physical origins

This problem occurs a fortiori in considering the origin of the Universe, which set the conditions determining what exists today. The Big Bang theory outlined previously makes it clear that at a very early times there must have been an epoch where the ideas of physics itself simply did not apply. Creation of the universe implies and end to physics. Yet we can only use pour present physical knowledge in speculat8ing about how the universe came into existence.

Various theories have been proposed to explain the origin of the Universe in terms of quantum development from some previous state (a collapsing previous phase, a region of flat space-time, a black hole final state, some kind of `pre-geometry', a region with causal violations) [3,6]. Despite our uncertainty about the nature of quantum gravity, we can claim that major features of quantum mechanics, such as the underlying wave-like nature of matter, must apply here also; on this basis we can make quantum cosmology models with claims to correctly represent the results of the as-yet unknown theory of quantum gravity, when applied to the very origin of the Universe.

Such approaches can provide a whole series of alternative proposals for the origin of the Hot Big Bang which has led to our existence, but of course simply postpones the ultimate issue: for one can then ask, what was the origin of this previous phase? This remains unanswered.

6.3.1 The no-boundary idea

One rather unique and intriguing proposal side-steps this problem neatly. This is the Hartle-Hawking suggestion [3,20] that the initial state of the Universe could be a region where time did not exist: instead of three spatial dimensions and one time dimension, there were four spatial dimensions. This has a great advantage: it is then possible there can be a Universe without a beginning, for (just as there is no boundary to the surface of the Earth at the South Pole) there is no boundary to this initial region of the Universe; it is uniform and smooth at all points. Much is made of this proposal in Hawking's book A brief History of Time [92], for it does indeed describe a Universe without a beginning in the ordinary sense of the word, although time does have a beginning (where there is a transition from this strange `Euclidean' state to a normal space-time structure). While this has originally been developed as a quantum cosmology idea, it is now known there are classical solutions of the Einstein equations with the same property. The implications of this proposal will be considered shortly; but there are concerns about such an approach, related to testability of the underlying propositions of such a theory.

Firstly, such proposals suppose unravelling some of the underlying conundrums of quantum theory that have not yet been solved in a fully satisfactory manner (specifically, the related issues of the role of an observer in quantum theory, and what determines the collapse of the wave function, which is an essential feature of measurement in quantum theory [19,34]). These do not arise as significant problems in the context of laboratory experiments, but become substantial difficulties in the context of applying quantum theory (which is usually applied to sub-microscopic systems) to the Universe as a whole.

Second, we certainly cannot test the Wheeler-de Witt equation underlying quantum cosmology: we have to accept it as a huge extrapolation of existing physics, plausible because of its basis in established physical laws but untestable in its own right. Even some of the underlying concepts(such as "the wave function of the Universe") have a questionable status in this context (for they are associated with a probabilistic interpretation which may not make sense when applied to a unique object, namely the Universe).

6.3.2 The issue of Initial Conditions

Thirdly, and irrespective of our resolution of the previous issues, we are tackling here the problem of initial conditions for the Universe: we are trying to use physical theory to describe something which happened once and only once, and for which no comparable happenings have ever occurred (or at least, none are accessible to our observations). The notion of a law to describe this situation faces considerable difficulties. If a ``law" is only ever applied to one physical object, it is not clear if the usual distinction between a physical law and specific initial conditions makes sense (cf. the following section). That "law" certainly cannot be subject to empirical test in the same way as other physical laws.

Whatever "law" we may set up to describe this situation [20,92], we have one and only one test we can do: we can observe the existent Universe and see if it is congruent with the predictions of that "law". If it passes this test, this supports that law but not uniquely, for there will in general be several laws or underlying approaches that give the same result; these cannot be distinguished from each other on the basis of any experimental tests. We can obtain strong support for one particular view (such as the Hartle-Hawking "no-boundary" proposal) only by utilising the kind of criteria for good theories that were introduced in the Chapter 2.

Whatever explanation we may give for them,

· If the universe had a beginning, as is the most probable situation, a unique initial state occurred at the origin of the Universe and determined both the initial structure of space-time and its matter content. Testable physics cannot tell us how those initial conditions were determined.

· Even if we suppose there was no beginning, the universe exists in a unique state, selected out somehow from all possible states. Testable physics cannot tell us how that state was selected.

The matter we see around us today is the remnants of that initial state, after it has been processed by non-equilibrium processes in the early Universe and then in a first generation of stars, as discussed in the last Chapter. Thus we understand the role of initial conditions; however this analysis does not answer the ultimate issues of origin and existence, in particular why the initial conditions had the form they did. We return to the question of ultimate causation and the issue of existence (Why does anything exist at all?), in the following Chapter.

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Section 6.4: Deep connections

In developing these questions, it is important to understand the interconnectedness of the Universe. As well as determining the initial nature of matter and of the space-time geometry, the choice of initial conditions for the Universe profoundly affects the nature of physics in other ways. We consider here three particular examples, namely Olber's Paradox, Mach's Principle, The Arrow of Time.

6.4.1: Olber's Paradox

The classic illustration of this interconnectedness is known as Olber's paradox, and concerns the question: why is the sky dark at night ? [79,99].

The point is as follows: if we consider a simple static Universe uniformly filled with steadily shining stars, then while the radiation received per star goes down with the inverse square of the distance from the observer, the number of stars goes up with the square of the distance. When we add up the effect of all the stars, the two factors in the square of the distance cancel, and we conclude that the radiation received becomes unboundedly large as we consider the combined effects of more and more distant stars. Thus the night sky should be infinitely bright, according to this simplest model. If we allow for the fact that nearer matter interposes between the observer and more distant sources, we conclude that (because each direction eventually intersects the surface of a star, and the calculation above shows that the surface brightness of a star is independent of its distance from us) the night sky (and for that matter, the day sky) should in every direction be as bright as the surface of the Sun.

Now at first you might think the problem is simply that it would be a bit uncomfortable having a bright sky at night; we'd have to keep the curtains closed to get some sleep. Nothing could be further from the truth. If this were the case, Earth could not radiate its waste energy to the sky, which would everywhere be as hot as the surface of the Sun; consequently the Earth would heat up until it was in equilibrium with that temperature. There would be no possibility of life here (the surface of Earth would be molten rock and any organic molecules would be disintegrated by radiant energy). The dark night sky is essential to life on Earth.

Why then is the real sky dark at night? There are three factors not taken into account in this calculation. Firstly, the expansion of the Universe results in the received light from distant galaxies being redshifted; this causes a diminution in the intensity of light received (proportional to the inverse fourth power of the redshift), greatly reducing the expected radiation from distant stars. Secondly stars cannot shine for an infinite time, because they only have a finite supply of nuclear fuel; so the underlying assumption that stars can shine forever is false. The model ignored conservation of energy.

Thirdly, the Universe itself has a finite age, so if we look back far enough into the past we reach an era when stars had not yet turned on; the matter at that time is dark because it has not yet formed stars, and the pre-existing background radiation is nothing other than the cosmic background radiation, which is only of sufficient density to be seen as 3 K radiation today. All three factors reflect the fact that the Universe is not in a state of equilibrium, as this simple model supposed.

Thus the simple model underlying the paradox did not take into account the real nature of the expanding Universe. This is an interesting and important result in its own right (Updated versions of the calculation determine what background radiation we expect to receive at each wavelength, from vary distant matter in the Universe; this can then be compared with observations), but it also shows us how we cannot ignore the effect of distant matter just because it is so far from us. There is so much of it, that its effects could be very important for daily life.

6.4.2: Mach's principle

Another famous example of this type concerns the origin of inertia, and is known as Mach's Principle. This starts with a simple fact that has puzzled physicists for 300 years: the fixed stars (in modern terminology, very distant galaxies) stay in fixed positions in the sky, when compared with a non-rotating local reference frame, defined by local dynamical experiments. Specifically, while stars appear to move across the sky relative to the (rotating) Earth, they appear fixed relative to the plane defined by a Foucault pendulum (or its modern equivalent, rapidly rotating gyroscopes, as used for the inertial guidance of submarines and aircraft). The question then is, is this rather striking fact just a coincidence, or is there some underlying causal mechanism that can explain it? [100,101]

Now inertia is the property whereby a freely moving body continues in a straight line relative to a non-rotating reference frame, but moves on a curved path relative to a rotating reference frame (due to "inertial forces", such as the centrifugal force that pushes one towards the side of a car as it turns a corner). Indeed it is just the absence of "inertial forces" in a non-rotating reference frame which defines it to be non-rotating; so a causal explanation of the puzzle just posed must relate local inertial properties to distant stars.

This fits in with the ideas of General Relativity, according to which gravity (a long-range force) and inertia are closely related. Thus Mach's Principle posits that local inertial properties are determined by distant matter; just as in the case of Olber's paradox, each single star contributes very little but there are so many of them that the total effect when one sums the contribution from every star, is very large. The identity of the local inertial rest frame and the rest frame of distant stars is then not a coincidence: it arises because local inertia - which underlies all local dynamics - is caused by distant stars.

This is a controversial proposal, and it is difficult even to phrase it in a rigorous way (Einstein developed his static Universe model (1917) in the hope that it would show General Relativity fully incorporates Mach's principle in its structure; however de Sitter's universe model (also found in 1917) showed this is not so). If it were true, we could envisage the following: suppose the entire Universe contained but one galaxy, instead of the hundred billion galaxies we can see; then the inertia of one kilogram of matter would be very much less than we now measure it to be (so for example if a car ran into a brick wall, the damage would be much less than we presently experience on Earth). If we could slowly remove galaxies from the Universe, the inertia of matter would gradually decrease.

Of course we cannot carry out such an experiment, so the issue remains unresolved: there is no way we can test to see if this is correct or not. However a related possibility is that as the Universe expands it is possible that the force of gravity gets weaker; this would result in the gravitational constant decreasing with time. Several theories have been proposed in which this is true, and the effect has been looked for experimentally. The proposal has not been confirmed; if it occurs it is below the detection threshold. However it makes a very important point: it is quite plausible that if the structure of the Universe were totally different, the locally experienced laws of physics might be quite different too.

6.4.3: The Arrow of Time

Perhaps the most celebrated and continuously vexing of these kinds of issues is the origin of the arrow of time [34,102]. It is very easy to get confused about this, for the one-directional nature of time that underlies our daily lives is so deeply ingrained in our experience we find it difficult to query if things could be otherwise.

The problem is that the fundamental laws of physics are time symmetric: they run equally well forwards or backwards in time (there is an exception in the case of some of the weak interactions; this is difficult to detect, and it seems very unlikely it is the fundamental source of the arrow of time). Thus the undeniable existence of an arrow of time (the one-way decay associated with entropy growth, for example) is somewhat mysterious; and the more curious feature is that while one can give arguments as to why such an arrow should exist (for example, by using statistical techniques to predict the behaviour of a gas from the forces between the individual molecules), these arguments seem to work equally well both ways: they may be taken to predict the existence of an arrow of time, but cannot tell which direction of time is the future and which is the past! Thus we know that a broken glass cannot re-assemble itself from its fragments into the whole glass, even though the fundamental laws of physics assert this is a possibility [34].

The problem is compounded in that there are several potentially independent arrows of time (those of quantum mechanics; of thermodynamics; of electrodynamics; of evolutionary biology, for example), and one of the major questions is why they all end up consistent with each other. A vexing problem that relates to this is the question of consciousness and free-will. Assuming we really do have free will, then despite the determinism of classical laws of physics, the future is not predictable from the past (Quite apart from the issue of chaotic dynamics, briefly mentioned in Chapter 4), because human intervention can alter it in a way not predicted by the laws of physics alone. This implies an absolutely fundamental acausality in the workings of the biological world, which are based on the laws of physics. It may well be related to the fact that although the fundamental laws of physics are time symmetric in their classical version, quantum mechanics (in its ordinary interpretation) has a major time asymmetry in terms of collapse of the wave function [34].

There are two suggestions of an answer to this conundrum: on the one hand, the direction of the arrow of time may be related directly to the expansion of the Universe (which would be experienced as a contraction if time ran the other way). If so, the almost inevitable conclusion is that it would be impossible for an observer to ever see a collapsing phase of the Universe; in a Universe which according to the ordinary view, reaches a maximum size and then starts to recollapse, the direction of time would reverse then. The physical situation would actually be experienced as two expansions in the opposite directions of time, coupled by a period of indeterminacy near the maximum as the arrow of time switched direction: a conclusion so strange as to call the idea into question.

On the other hand, the arrow of time may be determined by specific boundary conditions for local physical laws at the beginning and end of the Universe, restricting the physically realised solutions from all possible ones, to those that conform to one consistent time direction [34]. Notice here that we cannot simply say that boundary conditions at the beginning of the universe would suffice to establish this one-way flow, for until that flow is established the beginning and end of the Universe are on an equal footing: there is no intrinsic distinction between them. Thus such conditions have to be set at both the beginning and the end of the Universe.

A key issue here is how initial conditions for some physical field are correlated with each other at the start and end of the Universe. In the past they should be uncorrelated, but in the future they should be correlated. For example [34], after a glass has fallen to the ground and broken, the pieces disperse away from where it has fallen. We cannot simply give the fragments the correct reverse velocities, so as to all come together at the right time and re-assemble the glass; the correlations required are too exact. While this time-reversed motion would certainly also be a solution of the equations, the problem is the incredible degree of coordination required to achieve this.

Similar issues arise, for example, in considering why a radio transmission can only be received after it has been broadcast, and not before (this time-reversed situation being a possible solution of the time-symmetric Maxwell's equations, which determine the behaviour of the electromagnetic field). The point is that in the real world, such a solution would require exact correlations of the incoming field in the past, which are unattainable. However such correlations necessarily occur in the future all the time (the radio signal, after it has been broadcast, arrives in undistorted form in thousand of receivers; the music they all play is therefore highly correlated).

Many see this as the key feature in the arrow of time: there are different correlations in the future and the past. However when one remembers the issue of free-will, one must ask if this is a cause of the arrow of time, or merely a description of its effects. Penrose has suggested that when one takes into account the contribution of gravity to entropy growth, it is smoothness of initial space-time structure that is the key feature distinguishing the beginning of the Universe from irregularity and roughness that characterises its end [34]; but this view is not shared by all. An alternative view, proposed by Prigogine, is that we should aim at a reformulation of the laws of physics that incorporates the arrow of time in its very foundation, contrary to our present understanding of these laws.

Whichever kind of interpretation we may suggest, it is clear that on our present understanding of the nature of physics, the arrow of time is not embedded in the fundamental laws, but is a property of the boundary conditions for physical quantities imposed at the beginning (and probably also at the end) of time. The situation could be quite different in universes with different boundary conditions. Whatever theories we may have about this cannot be tested by any physical experiment; but the conclusion is of the utmost importance for daily life, and indeed for the very existence of life (which could not function without an arrow of time).

6.4.4 The unity of the Universe

Overall these examples point to a deep connections and unity of the physical Universe, not merely in terms of effect of microphysical laws on macroscopic structures, as envisaged in the inflationary Universe picture, but also in terms of the very nature and functioning of those laws [101]. Indeed, the examples just given show there may be no clear-cut distinction between boundary conditions for physical laws at the beginning of the Universe, and the nature of local physical laws; for the boundary conditions for those laws at the beginning of time are given as part of the structure of the Universe, and cannot be changed; but this is the essential feature characterising the physical laws themselves. What from the viewpoint of an ensemble of Universes is just one of a whole set of possible boundary conditions, may critically affect the nature of local physics within a specific Universe in a way that is experienced as absolute and immutable, so that (in that Universe) it is indistinguishable from a immutable physical law. Thus in the cosmological context, the distinction between initial conditions and physical laws can become blurred, or at least these features may be highly interdependent. However it is these interconnections that provide the setting within which life can exist.

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Section 6.5: The Uniqueness of the Universe

What we are running up against time and again is the fundamental feature of the uniqueness of the Universe, and the problems this introduces as we try to unravel its nature [103,104].

Cosmology is the ultimate historical science (Cf. the discussion in Chapter 2), for by definition there is only one Universe. In any other historic science there are other similar objects to compare a particular individual object with (in geology, there are many mountains and a number of continents; in astronomy, there are numerous stars and galaxies, and many planets; in evolutionary theory, there are many different species that have related evolutionary histories).

· The central problem of cosmology is the uniqueness of the universe. Only in the case of cosmology is there nothing whatever that we can compare with the subject of study (the Universe), both in practice and in principle.

This is the ultimate reason why when we penetrate to the heart of the matter - the choice of particular physical laws that govern the Universe, and of the particular initial conditions that occurred in the one unique Universe - our theories simply cannot be subject to confirmation in the normal sense. We should note here that there is a move by some scientists to essentially deny the uniqueness of the universe by proposing the existence of a multiverse, family of many universes as discussed in the next chapter, so our universe is no longer unique - it is but one of many universes. Apart from the fact that this proposal is unverifiable, it just postpones the essential problem, for in this case it is the multiverse that is unique. The problem recurs.

In the case of cosmology, we cannot perform the kinds of experiments that experimental sciences rely on (there is no way we can alter its initial conditions and see the resultant effects), and we cannot even do the kinds of comparisons with similar objects that underlie the other historical sciences. We can only observe what is there, and compare predictions with observations. In this way we can learn a lot about the physical nature of the Universe and the way it functions, as described in Chapter 5, much of this being on a firm observational base; but run into problems when we try to answer issues of the kind considered in this Chapter, particularly those related to initial conditions. In this case we include a theory in a list of possible theories if its conclusions are not in blatant contradiction with the observations (as pointed out previously, small discrepancies can usually be explained in a myriad of ways that maintain the integrity of the main theory: the sources evolved, selection effects occurred, there was an unrecognised interfering factor, and so on). We then choose between the theories on the basis of philosophical (non-verifiable) criteria.

The conclusion is that

· we have to evaluate theories of the Universe knowing that they are testable but intrinsically unverifiable, in the sense just explained. Because of this,

· the choice of competing theories is largely dependent on the philosophical stance adopted (whether this is explicitly acknowledged or not); specifically,

· the crucial feature is the choice of criteria of what is a "good" theory and what is not

(as discussed in Chapter 2). Cosmology is more dependent on such criteria than any other science precisely because of the uniqueness of its object of study. Given a choice of such criteria, the evidence will strongly constrain what is acceptable as a theory and what is not, and may even lead almost uniquely to a specific understanding.

Are such criteria themselves subject to experimental test? To a certain extent, Yes, in that past evidence shows what has worked well in general as criteria in choosing theories in different areas of understanding; and this plays a considerable role in our choice. However cosmology is different from all other areas; in the end there will be an unavoidable choice to be made that is essentially philosophically based, and is not subject to experimental test.

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Section 6.6: Uncertainty at the Foundations

The reader may be beginning to be dismayed by the uncertainties that are apparent at the foundations of fundamental physics and cosmology, despite the hard-won successes of the physical sciences. To complete the picture we must note that, despite what one might think, certainty is not even attainable in the logical sciences.

At a first glance mathematics itself rest on impregnable logical foundations. However determined attempts to prove this to be the case failed, and resulted eventually in the mathematician Kurt Gödel showing that it is impossible to prove the consistency of mathematics [13,34]. Computer science cannot help: indeed Turing and Church have shown there is no general algorithm for deciding mathematical questions [34]. Furthermore the concepts underlying probability theory, which is required in order to test any physical theory on the basis of real (noisy) data, are also on shaky ground, because the concept of a random number is very difficult to pin down [19].

The conclusion of the Chapter is that, within its own domain, there are considerable limitations on what science can determine, relating to verification of laws and confirmation of the nature of reality; these limits prevent directly attaining many of the desired answers and checking the validity of our theories and models. While some of them are related to practicalities and the current state of technology, ultimately some of these limits are absolute; for example (unless the Theory of Relativity is disproved some day) the speed of light is an absolute limit to communication, and consequently the limits on what we can observe in the Universe (in particular, through the existence of the particle and visual horizons) are absolute: no advances in technology will change them. Furthermore the ability of science to answer foundational questions is strictly limited.

What attitude has one to take to all this? I would suggest it confirms the profound conclusion that certainty is unattainable at the foundations of understanding in all areas of life, including fundamental physics and cosmology as well as philosophy; even the apparently impregnable bastion of mathematics is vulnerable to this comment. This is not the same as saying that anything goes (as some in the arts and social sciences appear to believe), but rather that what we can learn with reasonable confidence concerning foundational issues is strictly bounded (As has been emphasized elsewhere in this book, we can attain effective certainty in numerous practical matters, controlled by the regular action and of effectiveness physical laws).

Historically, while people have from time to time shifted the seat of the hoped for certainty (for example from theology to science), they have consistently sought for it. Many who claim to be `rationalist' or `free-thinking' are just as dogmatic as any fundamentalist theologian or reductionist scientist, and the social sciences too are not free from dogmatic stances and closed minds. This does not mean we must give up the hope of attaining a good understanding of the way things work; rather it means that

· A mature attitude must take uncertainty into account, and make it an acknowledged feature of the way we approach understanding the Universe.

This was precisely the aim of the approach advocated in Chapter 2. Furthermore, sometimes the clarity and predictive powers of physical or mathematical models leads us to forget this uncertainty. However the complexities we have run into in terms of interdependencies and even the very notion of physical law, and the limitations of models as representations of the nature of reality, confirm that we need to realise explicitly

· The models and theories on which we base our understandings are partial representations of reality, not to be confused with reality itself.

They can be very useful representations of reality in a limited domain, providing excellent understanding of that domain, but cannot rest on a foundation of absolute certainty. They cannot ever be infallible guides to reality, for they are not the same as reality.

Once we have accepted these limitations, giving up the unattainable hope of certainty, we can attain satisfying and even profound understandings of the Universe and the way it works, at all times regarded as provisional but nevertheless providing a satisfactory world-view and foundation for action.

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References for Chapter 6: Emerging questions and uncertainties

Issues of verifiability in cosmology are discussed in

[98] G F R Ellis Cosmology and Verifiability. In Physical Sciences and the History of Physics. Boston Studies in the Philosophy of Science. Volume 82 Ed. R S Cohen and M W Wartofsky. (Reidel, 1984), 93-114.

A proposal for the nature of quantum cosmology is given in [92] (and see also [20]). Olber's paradox is discussed in

[99] E R Harrison: Darkness at night: a riddle of the universe (Harvard University Press, 1987)

(see also [78]) and Mach's Principle in

[100] D W Sciama: Physical Foundations of General relativity (Heinemann, 1969)

[101] D W Sciama: The Unity of the Universe (Faber, 1959).

The arrow of time is considered in [34] and

[102] P Coveney and R Highfield: The Arrow of time (Flamingo, 1990).

The uniqueness of the universe is commented on in

[103] W H McCrea: Rep Prog Phys 16 32 (1953)

[104] M K Munitz: Brit J Philos Sci 13:104 (1962)

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[Version 2002-07-29].

Chapter 6 of The Universe Around Us by George Ellis

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