Introduction

Theory testing in the physical sciences has been revolutionized in recent decades by Bayesian approaches to probability theory. Here, I will consider Bayesian approaches to theory extensions, that is, theories like inflation which aim to provide a deeper explanation for some aspect of our models (in this case, the standard model of cosmology) that seem unnatural or fine tuned. In particular, I will consider how cosmologists can test the multiverse using observations of this universe.

Cosmologists will only ever get one horizon-full of data. Our telescopes will see so far, and no further. At any particular time, particle accelerators reach to a finite energy scale and no higher. And yet, it would be an unnatural constraint on our theories for them to fall silent beyond the edge of the observable universe and above a certain energy. Natural, simple theories need not confine themselves to the observable. How do we speculate beyond current data?

In particular, how do we evaluate (what I will call) theory extensions? That is, physical

theories whose main attraction is that they provide a deeper, more natural understanding of some effective theory. For example, the appeal of cosmic inflation is its natural explanation of some of the “initial conditions” of the standard model of cosmology. The postulates of the standard model – a homogeneous and isotropic Robertson–Walker (RW) spacetime, a set of energy components and their densities (matter, radiation and a cosmological constant), and an initial set of adiabatic, Gaussian density and tensor perturbations – can explain all (or almost all) the cosmological data at our disposal: the expansion of the universe, big bang nucleosynthesis, the angular power spectrum of the cosmic microwave background (CMB), the galaxy and Lyman alpha forest power spectra, the baryon acoustic oscillation (BAO) scale, the luminosity distance-redshift relation of type Ia supernovae, and more.

So, why not simply declare cosmology to be finished? We have a model that explains all the data. Consider the following kind of reason for extending our cosmological theory. In the standard model of cosmology, photons in the CMB that are separated in the sky by more than∼1 degree were scattered by patches of gas that have never been in causal contact with each other. And yet the entire CMB is at the same temperature, to one part in 100,000.

Introduction

In cosmology, we would like to explain our observations and predict future observations from theories of the entire universe. Such cosmological theories make ontological assumptions of what entities exist and what their properties and relationships are. One must also make epistemological assumptions or metatheories of how one can test cosmological theories. Here I shall propose a Bayesian analysis in which the likelihood of a complete theory is given by the normalized measure it assigns to the observation used to test the theory. In this context, a discussion is given of the trade-off between prior probabilities and likelihoods of the measure problem of cosmology, of the death of Born's rule, of the Boltzmann brain problem, of whether there is a better principle for prior probabilities than mathematical simplicity, and of an Optimal Argument for the Existence of God.

Cosmology is the study of the entire universe. Ideally in science, one would like the simplest possible theory from which one could logically deduce a complete description of the universe. Such theories must make implicit assumptions about the ontology of the universe, what are its existing entities and their nature. They may also make implicit assumptions about the ontology of the entire world (all that exists), particularly if other entities beyond the universe have relationships with the universe.

For example, I am a Christian who believes that the universe was created by an omnipotent, omniscient, omnibenevolent, personal God who exists outside it but who relates to it as His creation. Therefore, the ontology I assume for the world includes not only our universe but also God and other entities He may have created (such as new heavens and new earth for us after death). However, my assumption that God has created our universe as an entity essentially separate from Himself means that one can also look for a theory of the universe itself, without including its relationship to God, although there may be some aspects of such a theory that can only be explained by the assumption that the universe was created by God. (For example, even though a complete theory of our universe would necessarily imply the facts that there is life and consciousness within it, since such entities do exist within our universe, there may not be a good explanation of these aspects of the theory apart from the concept of creation by a personal God.)

Introduction

It has recently been discovered that Einstein once attempted – and subsequently abandoned – a ‘steady-state’ model of the expanding universe (Nussbaumer, 2014a; O'Raifeartaigh, 2014; O'Raifeartaigh et al., 2014). An unpublished manuscript on the Albert Einstein Online Archive (Einstein, 1931a) demonstrates that Einstein explored the possibility of a universe that expands but remains essentially unchanged due to a continuous formation of matter from empty space (Figure 23.1). Several aspects of the manuscript indicate that it was written in the early months of 1931, during Einstein's first trip to California, and the work therefore probably represents Einstein's first attempt at a theoretical model of the cosmos in the wake of emerging evidence for an expanding universe (Nussbaumer, 2014a; O'Raifeartaigh et al., 2014). It appears that Einstein abandoned the idea when he discovered that his steady-state model led to a null solution, as described below.

Many years later, steady-state models of the expanding cosmos were independently proposed by Fred Hoyle, Hermann Bondi and Thomas Gold (Bondi and Gold, 1948; Hoyle, 1948). The hypothesis formed a well-known alternative to ‘big bang’ cosmology for many years (Kragh, 1996, pp. 186–218; North, 1965, pp. 208–22; Nussbaumer and Bieri, 2009, pp. 161–3), although it was eventually ruled out by observations such as the distribution of the galaxies at different epochs and the cosmic microwave background (Kragh, 1996, pp. 318–80, 2007, pp. 201–6; Narlikar, 1988, p. 219).While it could be argued that steady-state cosmologies are of little practical interest now, we find it most interesting that Einstein conducted an internal debate between steady-state and evolving models of the cosmos decades before a similar debate engulfed the cosmological community. In particular, the episode offers several new insights into Einstein's cosmology, from his view of the role of the cosmological constant to his attitude to the question of cosmic origins. More generally, Einstein's exploration of steady-state cosmology casts new light on his philosophical journey from a static, bounded cosmology to the dynamic, evolving universe, and is indicative of a pragmatic, empiricist approach to cosmology.

Historical Context

Following the successful formulation of his general theory of relativity (Einstein, 1915, 1916), Einstein lost little time in applying his new theory of gravity, space and time to the universe as a whole.

Our everyday macroscopic experience of being in the world is saturated with asymmetries – thermodynamic asymmetries, and radiative asymmetries, and epistemic asymmetries, and phenomenological asymmetries, and asymmetries of over-determination, and asymmetries of influence, and what have you – between the past and the future.

And there is a long-cherished hope – something that has its origins in the work of Boltzmann, and which has been pursued, by any number of other investigators, through any number of fits and starts and revelations and wrong turns, ever since – that all of those asymmetries can ultimately be traced back to some relatively simple characteristic of the initial macrocondition of the universe. The thought (as people put it now) is that all we need to do, in order to account for these asymmetries, is to add to the fundamental time-reversalsymmetric dynamical laws, and to the standard statistical-mechanical probability-measure over the space of possible fundamental physical states, a simple postulate – a so-called past-hypothesis – to the effect that the world first came into being in whatever particular low-entropy macrocondition it is that the normal inferential procedures of cosmology are eventually going to present to us.

The business of working this thought out in detail is a large undertaking, which is still very much in its infancy, and which is still very much under debate – and I do not want to attempt anything along the lines of an overview of that project here. All I want to talk about in this chapter is a widespread and fundamental and perennial sort of puzzlement about how such a project could even seriously be entertained – a puzzlement (that is) about how it is that the macrocondition of the universe 14 billion years ago – all by itself – could even imaginably be up to the job of explaining so much about the feel, now and on earth, of the passing of time.

This puzzlement takes a number of different forms, and arises in a number of different contexts.

On the most trivial level, there is a question of how the lowness of the entropy of the world 14 billion years ago can impose any genuinely profound and vivid constraints whatever on what the world is doing now.

Introduction

In my opinion, nothing useful has ever been written on the question in the title, and small is the contribution that I have to offer. I outline an explanation for why there is something rather than nothing, an explanation which, however, I believe is incorrect because it makes a certain empirical prediction (absence of qualia) that is incorrect. Nevertheless, it may be interesting to discuss this reasoning. It allows, in principle though not in practice, to derive the laws of nature and all physical facts about the universe. Then I elucidate which objections to this explanation are, in my opinion, valid and which are not.

Explanation in physics usually works this way: observable phenomena get explained by physical theories. A physical theory is the hypothesis that the physical world consists of certain kinds of physical objects governed by certain laws. From this hypothesis we derive, or we make it plausible that it can be derived, that the phenomenon in question (typically) occurs; then we say that the theory explains the phenomenon. The physical theory does not explain why these kinds of physical objects exist, why others do not, and why these laws hold; instead of explaining them, the theory merely posits them. At best, some theories are simpler and more elegant than others (e.g. Einstein's general relativity more than Newton's theory of gravity). But no physical theory comes close to explaining why these laws hold, or why there exist any physical objects at all. Thus, no physical theory contributes to the question in the title.

Specifically, some physical theories allow for the possibility of a vacuum state, i.e. that at a certain time there is no matter in space, and for the possibility of a transition from a vacuum state to a non-vacuum state, i.e. that at some other time there is some matter in space. While such a theory has some explanatory value, it does not touch upon the question in the title, as it does not explain the physical laws, nor why space-time exists,1 nor why certain kinds of matter (described by certain kinds of mathematical variables) exist and others do not. For related discussion, see Holt's overview [4] and Albert's critique [1] of Krauss's book [5].