Introduction

When discussing the concept of multiple universes, it is a major challenge to keep the discourse within the bounds of science. There is an acute need to define what is being talked about. The issues include the following questions. How does one in general define a universe? Should one entertain different laws of physics in different universes? What are the most important parameters and/or features that characterize a universe? Once a parametrization has been attained, what is the differential probability of finding a universe with specified parameters? Is the integral of this distribution function finite or infinite?

A useful and familiar analogy is to consider planet Earth as a universe. It is, after all, not so long ago that this was mankind's paradigm. Then one may take the ensemble of universes, or multiverse, to be the set of all compact massive objects within the solar system which orbit the Sun and/or each other. Alternatively, one may take as a toy multiverse the set of all planets in the Galaxy or our universe. In either case, it is clear that the characterization of individual members of the ensemble is a very difficult task and requires a sophisticated understanding of much of planetary science, especially the experimental side of the subject.

One simplification of the general problem of classification is to restrict the consideration to that subset of universes (or — in the analogy — planets) which are nearly the same as our own. And this restriction can be naturally expressed in anthropic terms, by asking that the subset in question be that which admits in principle the existence of life as we know it. Even so, in the case of planets, this restricted problem is still very difficult. It is not clear whether our universe contains a large set of such planets, or whether the set only consists of our own planet. The problem is nicely described in the book Rare Earth by Brownlee and Ward [1].

Introduction

If the Universe is a quantum mechanical system, then it has a quantum state. This state provides the initial condition for cosmology. A theory of this state is an essential part of any final theory summarizing the regularities exhibited universally by all physical systems and is the objective of the subject of quantum cosmology. This chapter is concerned with the role that the state of the Universe plays in anthropic reasoning — the process of explaining features of the Universe from our existence in it [1]. The thesis will be that anthropic reasoning in a quantum mechanical context depends crucially on assumptions about the Universe's quantum state.

A model quantum universe

Every prediction in a quantum mechanical universe depends on its state, if only very weakly. Quantum mechanics predicts probabilities for alternative possibilities, most generally the probabilities for alternative histories of the Universe. The computation of these probabilities requires both a theory of the quantum state as well as the theory of the dynamics specifying its evolution.

To make this idea concrete while keeping the discussion manageable, we consider a model quantum universe. The details of this model are not essential to the subsequent discussion of anthropic reasoning but help to fix the notation for probabilities and provide a specific example of what they mean. Particles and fields move in a large — perhaps expanding — box, say, presently 20 000 Mpc on a side.

Introduction

Although the mathematical structure of quantum mechanics was understood within a few years after it was invented, numerous quantum paradoxes still disturb ‘simple-minded’ physicists. Most of them, as ‘naïve realists’, would probably never take Bohr's own over-philosophical and over-complicated treatment of these paradoxes seriously if they realized the philosophical consequences of the Copenhagen interpretation. To make my meaning clearer, let me quote Bohr's answer to Professor Hoffding's question regarding the double-slit experiment [1]. Bohr was asked: ‘What can the electron be said to be in its travel from the point of entry to the point of detection?’ And he replied: ‘To be? To be? What does it mean to be?’ However, if one questions the existence of microscopic constituents of macroscopic bodies, then the next logical step would be to question the existence of the macroscopic bodies and even ourselves.

Needless to say, very few (if any) of us, when making experiments or analyzing their results, address the question of what it means ‘to be’ every time. Even in the context of elementary particles, probably nobody doubts that the particles exist and somehow travel from the point of entry to the point of detection. Moreover, within the accuracy allowed by the uncertainty relation, these particles can be localized and described just as well as macroscopic ‘classical’ objects.

This book grew out of a conference entitled ‘Universe or Multiverse?’ which was held at Stanford University in March 2003 and initiated by Charles Harper of the John Templeton Foundation, which sponsored the event. Paul Davies and Andrei Linde were in charge of the scientific programme, while Mary Ann Meyers of the Templeton Foundation played the major administrative role. The meeting came at a critical point in the development of the subject and included contributions from some of the key players in the field, so I was very pleased to be invited to edit the resulting proceedings. All of the talks given at the Stanford meeting are represented in this volume and they comprise about half of the contents. These are the chapters by James Bjorken, Nick Bostrom, Robin Collins, Paul Davies, Savas Dimopoulos and Scott Thomas, Renata Kallosh, Andrei Linde, Viatschelav Mukhanov, Martin Rees, Leonard Susskind, Max Tegmark, Alex Vilenkin, and my own second contribution.

Several years earlier, in August 2001, a meeting on a related theme — entitled ‘Anthropic Arguments in Fundamental Physics and Cosmology’ — had been held in Cambridge (UK) at the home of Martin Rees. This was also associated with the Templeton Foundation, since it was partly funded out of a grant awarded to myself, Robert Crittenden, Martin Rees and Neil Turok for a project entitled ‘Fundamental Physics and the Problem of Our Existence’.

Multiverse explanations for fine-tuning

Many of the physical parameters of the observed part of the Universe, whether constants of nature or cosmological boundary conditions, seem fine-tuned for life and us [1—4]. There are three common explanations for this. One is that there is a ‘Fine-Tuner’ who providentially selected the physical parameters so that we can be here. Another is that it is just a coincidence that the parameters turned out to have the right values for us to be here. A third is that the observed Universe is only a small part of a much vaster Universe or multiverse or megaverse or holocosm (my own neologism for the whole), and that the physical parameters are not the same everywhere but take values permitting us in our part.

These three explanations are not necessarily mutually exclusive. For example, combining a Fine-Tuner with coincidence but without a multiverse, perhaps the Universe was providentially created by a God who had a preference for a particularly elegant single universe which only coincidentally gave values for the physical parameters that allowed us to exist. Or, for a Fine-Tuner with a multiverse but without coincidences, perhaps God providentially created a multiverse for the purpose of definitely creating us somewhere within it. Or, for coincidence and a multiverse without a Fine-Tuner, if the Universe were not providentially created, it might be a multiverse that has some parts suitable for us just coincidentally.

Introduction

We know that nature is governed by mathematics and symmetries. Not very long ago, it was an article of faith among most physicists that everything about physics would eventually be explained in terms of fundamental symmetries — that nothing in the make-up of physical laws is accidental, that nature ultimately has no choices, and that all the properties of particles and fields are fixed purely by mathematics.

In the thirty years since modern anthropic reasoning was introduced into cosmology [1, 2], the competing idea that anthropic selection might have an indispensable role in fundamental physical theory has gradually become, if not universally accepted, at least mainstream. There are now concrete physical models for realizing anthropic selection in nature. Cosmology has provided not only a concrete mechanism (inflation) for manufacturing multiple universes, but also a new phenomenon (dark energy) whose value is most often explained by invoking anthropic explanations. String theory has uncovered a framework by which many different symmetries and parameters for fields can be realized in the low-energy, 4-dimensional universe; this depends on the topology and size of the manifold of the other seven (truly fundamental) dimensions and on the configurations of p-branes within it, especially the local environment of the 3-brane on which our own Standard Model fields live.

Introduction

At the beginning of the 1980s, when the inflationary theory was first proposed, one of our main goals was to explain the amazing uniformity of the Universe. We were trying to find out why the Universe looks approximately the same in all directions. Of course, locally the Universe does not look uniform — there are such large deviations from uniformity as planets, stars and galaxies. But if one considers the density of matter on scales comparable to the size of the observable Universe, lobs ~ 1028 cm, one finds that this is uniform to an accuracy better than one part in 10 000. The most surprising thing about this is that, according to the standard big bang theory, the distant parts of the Universe which we can see with a powerful telescope were not in causal contact at the time of the big bang and could not have been in such contact until very late stages of cosmic evolution. So one could only wonder what made these distant parts of the Universe so similar to each other.

In the absence of any reasonable explanation, cosmologists invented the so-called ‘cosmological principle’, which claims that the Universe must be uniform. But the Universe is not perfectly uniform, since it contains inho-mogeneities — such as stars and galaxies — which are crucial for life. Because of these small but important violations, the cosmological principle cannot be a true principle of nature, just like a person who takes only small bribes cannot be called a man of principle.

Introduction

Parallel universes are now all the rage, cropping up in books, movies and even jokes: ‘You passed your exam in many parallel universes — but not this one.’ However, they are as controversial as they are popular, so it is important to ask whether they are within the purview of science or merely silly speculation. They are also a source of confusion, since many people fail to distinguish between the different types of parallel universes proposed.

In the big bang model, the farthest one can observe is the distance that light has travelled during the 14 billion years since the expansion began. The most distant visible objects are now about 4 χ 1026 m away. A sphere of this radius defines our observable universe or our horizon volume. We will sometimes loosely refer to this as ‘our universe’, although this may be part of a region which extends much further. In this article, I will survey theories of physics involving what are termed ‘parallel universes’ or ‘multiverses’. These form a four-level hierarchy, allowing progressively greater diversity.

1. • Level I A generic prediction of cosmological inflation is an infinite ‘ergodic’ space, which contains Hubble volumes realizing all initial conditions — including one with an identical copy of you about 101029 m away.

2. • Level II Given the fundamental laws of physics that physicists one day hope to capture with equations on a T-shirt, different regions of space can exhibit different effective laws of physics (physical constants, dimensionality, particle content, etc.), corresponding to different local minima in a landscape of possibilities.

3. • Level III In unitary quantum mechanics, other branches of the wave-function add nothing qualitatively new, which is ironic given that this level has historically been the most controversial.

4. • Level IV Other mathematical structures give different fundamental equations of physics for that T-shirt.

The landscape

The world-view shared by most physicists is that the laws of nature are uniquely described by some special action principle that completely determines the vacuum, the spectrum of elementary particles, the forces and the symmetries. Experience with quantum electrodynamics and quantum chromodynamics suggests a world with a small number of parameters and a unique ground state. For the most part, string theorists bought into this paradigm. At first, it was hoped that string theory would be unique and explain the various parameters that quantum field theory left unexplained. When this turned out to be false, the belief developed that there were exactly five string theories with names like ‘type 2a’ and ‘heterotic’. This also turned out to be wrong. Instead, a continuum of theories were discovered that smoothly interpolated between the five and also included a theory called ‘M-theory’. The language changed a little. One no longer spoke of different theories, but rather of different solutions of some master theory.

The space of these solutions is called the ‘moduli space of supersymmetric vacua’. I will call it the ‘supermoduli-space’. Moving around on this supermoduli-space is accomplished by varying certain dynamical ‘moduli’. Examples of moduli are the size and shape parameters of the compact internal space that 4-dimensional string theory always needs. These moduli are not parameters in the theory, but are more like fields. As you move around in ordinary space, the moduli can vary and have their own equations of motion.

Introduction

Though there has been much discussion of the Anthropic Principle (AP) over the last 35 years or so, it is still a very tantalizing and controversial subject, on the boundary between scientific cosmology and philosophy. As new scenarios and theories emerge for describing and explaining the origin of our observable universe, AP considerations inevitably surface. So, a critical review of the meaning and status of the AP — as well as of the directions anthropic arguments are now taking, their legitimacy and the fundamental philosophical issues involved — is perhaps warranted.

The anthropic idea was first introduced in 1961 by Robert Dicke, who noted the comparability of several very large numbers when fundamental physical constants are combined, and suggested that this might be connected with the conditions necessary for the presence of observers [1]. A decade later, Barry Collins and Stephen Hawking, realizing that the initial conditions for our universe seemed to be very special, suggested the following: ‘The fact that we have observed the universe to be isotropic is therefore only a consequence of our own existence’ [2]. One way of explaining this, they speculated, would be to have an ‘infinite set of universes with all possible initial conditions’ — thus anticipating the way many cosmologists now interpret the AP.

Introduction

In articles published in physics journals, the multiverse hypothesis is strictly regarded from a non-theistic perspective, as a possible explanatory hypothesis for the life-permitting values of the constants of physics. Further, there have been several attempts to make specific predictions with regard to the values of these constants from a multiverse hypothesis, such as the value of the cosmological constant [1—3]. Such approaches reflect the legitimate methodological naturalism of physics. However, in wider-ranging philosophical discussions of the multiverse hypothesis — as found in various books on the topic — the issue arises as to what is the relation between the multiverse hypothesis and much larger philosophical issues, particularly whether reality is ultimately impersonal or personal in nature. In such contexts, the multiverse hypothesis is often presented as the atheistic alternative to a theistic explanation — such as that offered by John Polkinghorne [4] — of the purported fine-tuning of the cosmos for intelligent life. In this contribution, I will attempt to explain why, contrary to the impression one often gets, contemporary physics and cosmology are not only compatible with theism, but could arguably be thought to suggest a theistic explanation of the Universe or multiverse. I do not expect necessarily to convince anyone of the theistic point of view, realizing that many factors — both theoretical and personal — underlie our views of the ultimate nature of reality.

Introduction

The idea of a multiverse – an ensemble of universes or expanding domains like the one we see around us – has recently received increasing attention in cosmology. It has been conceived of as occurring either in separate places or times in the same overall encompassing universe (as in chaotic inflation) or through splitting of the quantum wave-function (as in the Everett interpretation of quantum mechanics) or as a set of totally disjoint universes, with no causal connection whatsoever. Physical properties may be different in the different universes or in different expanding domains within a single universe.

In this context, definitions are important. Some workers refer to the separate expanding regions in chaotic inflation as ‘universes’, even though they have a common causal origin and are all part of the same single spacetime. In keeping with long established use, I prefer to use the word ‘universe’ to refer to the single unique connected spacetime of which our observed region (centred on our galaxy and bounded by our visual horizon in the past) is a part. I will describe situations such as chaotic inflation — with many expanding domains — as a ‘multi-domain universe’. Then we can reserve the term ‘multiverse’ for a collection of genuinely disconnected spacetimes, which are not causally related. When the discussion pertains to both disjoint collections of universes and different domains of a multi-domain universe, I will refer to an ‘ensemble of universe domains’ or ‘ensemble’ for short.

Do the ‘special’ values of the constants of physics and cosmology need an explanation?

In his book Galaxies, Nuclei and Quasars [1], Fred Hoyle wrote that ‘one must at least have a modicum of curiosity about the strange dimensionless numbers that appear in physics’. Hoyle was among the first to conjecture that the so-called ‘constants of nature’ might not be truly universal. He outlined two possible attitudes to them. One is that ‘the dimensionless numbers are all entirely necessary to the logical consistency of physics’; the second possibility is that the numbers are not in the broadest sense universal, but that ‘in other places their values would be different’. Hoyle favoured this latter option because then

Whatever one thinks of its motivation, Hoyle's conjecture is now even more attractive. The ‘portions of the universe’ between which the variation occurs must now, we realise, be interpreted as themselves vastly larger than the spacetime domain our telescopes can actually observe — perhaps even entire ‘universes’ within a multiverse.

If we ever established contact with intelligent aliens, how could we bridge the ‘culture gap’? One common culture (in addition to mathematics) would be physics and astronomy. We and the aliens would all be made of atoms, and we would all trace our origins back to the big bang 13.7 billion years ago. We would all share the potentialities of a (perhaps infinite) future. But our existence (and that of the aliens, if there are any) depends on our universe being rather special.

Naturalness versus the anthropic principle

The cosmological constant problem (CCP) is one of the most pressing problems in physics. It has eluded traditional approaches based on symmetries or dynamics. In contrast, the anthropic principle has scored a significant success in accounting for both the smallness of the cosmological constant (CC) and the proximity of the vacuum and matter energies in our universe [1]. Once we accept the anthropic principle as a legitimate approach for solving the CCP, it is natural to ask whether it might be applicable to other problems that can also be addressed with traditional methods. In this case, nature would have the interesting dilemma of choosing between an anthropic and a normal solution. An example is the gauge hierarchy problem (GHP). Like the CCP, it is a naturalness problem characterized by a small dimensionless number. Unlike the CCP, it can be solved with traditional symmetries, such as low-energy supersymmetry. As we will argue later, the GHP can also be addressed via anthropic arguments. So does nature choose the supersymmetric or the anthropic solution to the GHP? This question is far from academic, since the answer will be revealed experimentally by 2007 at the Large Hadron Collider (LHC).

The rise of naturalness as a principle for physics in the late 1970s led to the apparent need for a natural solution to the GHP and has convinced the majority of particle physicists that the LHC will discover either supersymmetry or another ‘natural’ theory that solves GHP. So if the LHC discovers nothing beyond the Standard Model, it will be a surprise. In our opinion, such a (non-)discovery would significantly strengthen the case for the anthropic principle and would cause a shift away from the usual naturalness-driven paradigm of attempting to understand the parameters of the Standard Model via symmetries or string theory. Instead, the nature of the dynamics that leads to the multiverse, and consequently provides a home for the anthropic principle, will become a primary question of physics. We now turn to this question.