The rise of exobiology, the study of the origin of life and of possible life outside the Earth, was intimately related to the birth of the Space Age, and particularly to the birth of the US National Aeronautics and Space Administration (NASA) in 1958. By providing the means to enter space, NASA placed exobiology into the arena where an age-old problem could be empirically tested with in situ observations and experiments. Moreover, in pursuit of exobiology, on the ground NASA funded experiments on the origin of life, revived planetary science, sponsored theoretical and observational studies on planetary systems, and assembled the flagship program in the Search for Extraterrestrial Intelligence (SETI) – all conceptual elements of the budding discipline. Over four decades, at a relatively small but steady level of funding punctuated by the landmark Viking mission to Mars, the American space agency put into place the conceptual, institutional, and community structures necessary for a new discipline, leaving no doubt of NASA's status as the primary patron of exobiology. The interest in the search for life, however, knew no national boundaries. Especially in the post-Viking era, international involvement grew in the field that also became known as “bioastronomy,” and that was transformed at the end of the century into a broadened “astrobiology” effort.

The ability to search for life beyond Earth did not guarantee its adoption as a program within NASA or any other space agency.

Astrobiology: a new discipline?

The controversial assertion in 1996 that the martian meteorite ALH84001 contained evidence for ancient microbial life stoked public, political, and scientific interest in astrobiology. Two years later, the NASA Astrobiology Institute (NAI) was launched, its mission to “study the origin, evolution, distribution, and future of life on Earth and in the Universe.” This mission, though ambitious, is not really new. Indeed, according to this definition, astrobiology has been studied for decades if not centuries (Chapter 1). Astrobiological research would include James Watson and Francis Crick's decipherment half a century ago of the double helix and with it (according to Crick) the “secret of life.” It also would include Stanley Miller and Harold Urey's in vitro synthesis of amino acids by electric discharge, the Viking Mission of 1976 to search for life on Mars, the discovery of hydrothermal vents, and the recognition that a wayward impactor probably drove the dinosaurs extinct. Yet none of this research was carried out under the auspices of astrobiology or required a specific astrobiological framework. Recently, however, during the so-called “Astrobiology Revolution” of the 1990s (Section 2.3; Ward and Brownlee, 2000), increasing attention has been devoted to developing precisely such a framework, as implied by the formation of NAI. Programs oriented to astrobiology research or training have acquired various degrees of formalization throughout the world. Astrobiology journals have been created. You are reading a textbook devoted to astrobiology. These milestones both represent and fuel ambitions to transform astrobiology into a new discipline.

Spin foam models are an attempt at a fully covariant formulation of Loop Quantum Gravity. The subject took off when the Hamiltonian constraint of Chapter 10 was developed and one tried to use it in order to define a path integral formulation of its ‘transition amplitudes’. The field has grown quite a bit since its incarnation and it almost deserves a book of its own. We will devote relatively little space to it because we focus on the most important aspect, namely its relation with the canonical formalism and the interpretation of spin foam models. For an introduction to spin foam models we recommend the really beautiful articles by Baez [671, 672] which contain an almost complete and up-to-date guide to the literature and the historical development of the subject. See also the articles by Barrett [673, 674] for the closely related subject of state sum models and the most updated review article by Perez [675] and the thesis by Oriti [676].

What follows is a structural overview of spin foam models which focuses on mediating the main ideas and the open problems in constructing spin foam models.

Heuristic motivation from the canonical framework

The prototype of spin foam models are state sum models that had been studied extensively [677–681] within the context of topological quantum field theories [682–691] long before spin foam models arose within quantum gravity. The concrete connection of state sum models with canonical quantum gravity was made by Reisenberger and Rovelli in their seminal paper [453], where they used the (Euclidean version of the) Hamiltonian constraint described in Chapter 10 in order to write down a path integral formulation of the theory.

Mars and astrobiology

Mars is at the center of the field of astrobiology in many ways. Today's vigorous program of ongoing exploration is largely motivated by Mars's potential to harbor life at present or at some time in the past. But astrobiology as a discipline is about more than just finding out whether there is or ever was life on Mars or on other planets and satellites. It is about determining the governing principles behind whether life will originate on a given planet or whether it can survive if transplanted there; about what the mechanisms are by which planets and biota can and do interact with each other; and about determining which fundamental factors distinguish a planet that is habitable from one that is not.

We know that the Earth meets the environmental requirements for being habitable. In Mars, we have an example of a planet that evolved under different physical and chemical conditions, allowing us to see what effects these differences can have. Today, Earth has global-scale plate tectonics, and Mars does not. Earth has global oceans at its surface, and Mars does not. Earth has a climate conducive to the coexistence of the solid, liquid, and vapor phases of water, each of which affects the geology and geochemistry of the planet, and Mars does not. In finding out whether Mars has or ever had life, we obtain a second example of whether and how life can occur on a planetary body.

Introduction

Common among the many definitions of life (Chapter 5) is mention of sets of chemical reactions that allow metabolism, replication, and evolution. The specifics of those reactions are generally not part of these definitions, although a century of study of the metabolisms that support life on Earth has given us a rich repertoire of illustrative biochemical examples. Unfortunately, because all known life on Earth is descended from a single common ancestor, our study of terran biochemistry, no matter how extensive, cannot provide a comprehensive view of the full range of possible reactions that might generally support life.

This leaves open an important question. If life exists elsewhere in the Cosmos, will its chemistry be similar to the chemistry of life on Earth? Recent articles addressing this issue are by Irwin and Schulze-Makuch (2001), Crawford (2001), Bains (2004), and Benner et al. (2004), and several popular books are listed under “Further reading” at chapter's end. As in many areas in contemporary astrobiology, no clear methodology exists to address the question of “weird life.” Chemistry, however, including the skills outlined in Chapter 7, provides one set of tools for constructing hypotheses about possible alternative biological chemistries.

The emerging field of synthetic biology (Benner and Sismour, 2005) provides another set of tools. Here, chemists attempt to give substance to concepts about alternative life forms by synthesizing molecules that might support alternative genetic systems or alternative metabolisms.

In this last part of the book we collect some mathematical background material which is heavily used in the physics part of the book. There are several reasons for doing this: First of all, it makes the book almost self-contained. Secondly, some of this material is not covered by the obligatory courses in mathematics for physicists. Thirdly, while the material is covered in some mathematics courses, it is often presented in such a way that a physicist does not recognise it any more or it is not given sufficient attention. Clearly we can mostly give definitions and state theorems, proofs are often omitted for reasons of space. However, we try to motivate the mathematical theory from a physicists’ point of view, explain how the various theorems fit together and indicate their various applications. We thus hope that the ambitious reader feels encouraged to study the mathematical theory in appropriate depth, going through the proofs by himself.

The material is presented in logical order, not in the order as it is applied in the physics part of the book. For instance, topology is needed before one speaks about differential geometry, measure theory and (functional) analysis.

The geological timescale is one of science's great triumphs. It represents “deep time” (McPhee, 1982), millions and billions of years ago, time beyond human comprehension. Geologists use two different ways to discuss geological time: (a) absolute time, and (b) relative time.

Relative time was developed first, and is based on relative age relationships among rock units as determined by geometric relationships, fossils, and other distinctive attributes of the rock. Layered, sedimentary rocks (strata) are the most widely used, and during the nineteenth century allowed geologists to establish a relative geological timescale. The scale used strata with their contained fossils, and applied four fundamental principles of relative time: (1) original horizontality, (2) superposition, (3) original lateral continuity, and (4) fossil succession. Fossil succession refers to the particular vertical (stacked) order that fossils occur in strata. William Smith recognized this in 1799 and employed it to great effect in his geological map of England and Wales published in 1815. The other three principles were established much earlier by the Danish scholar Nicolaus Steno (1669). Original horizontality states that sediments are originally laid down in a horizontal or nearly horizontal manner. Superposition means that the oldest stratum is at the bottom and the youngest at the top. Original lateral continuity refers to the way strata extend laterally in all directions. The geometric relationship of bodies of rock to one another is also used; for example, an intrusion that cuts layered rock is younger than the layered rock it cuts.

The emerging field of astrobiology encompasses a daunting variety of specialties, from astronomy to microbiology, from biochemistry to geology, from planetary sciences to phylogenetics. This is both exciting and frustrating – exciting because the potential astrobiologist is continually exposed to entirely new ways to look at the world, and frustrating because it is difficult to understand new results when venturing outside the confines of one's own specialty. There are now many excellent popular books on astrobiology, but a scientist wants more details and more sophistication than these afford. Where can an astronomer without any formal biology since high school learn the basics of cellular metabolism? Or the principles of evolution? Or notions about alternative forms of life? And where can a microbiologist with little physics and no astronomy learn the basics of how a planetary atmosphere works? Or how the Earth formed? Or how planets are detected around other stars? This book is designed to fill these needs.

We have endeavored to cover all the important aspects of astrobiology at an advanced level, yet such that most of the contents in every chapter should be understandable to anyone versed in any relevant science discipline. We envision our youngest readers to be science majors near the end of undergraduate study or the beginning of graduate study. And at the other extreme, we aim to serve scientists who haven't taken an academic course for forty years, but are intrigued by the nascent field of astrobiology.

From Lamarck to Darwin to the central dogma

The basic notion of evolution is that inherited changes in populations of organisms result in expressed differences over time – these differences are at the gene level (the genotype) and/or expression of the gene into an identifiable characteristic (the phenotype). The important underlying fact of evolution is that all organisms share a common inheritance, or, put more dramatically, all extant organisms on Earth evolved from a common ancestor. We see this in the universal nature of the genetic code and in the unity of biochemistry: (a) all organisms share the same biochemical tools to translate the universal information code from genes to proteins, (b) all proteins are composed of the same twenty essential amino acids, and (c) all organisms derive energy for metabolic, catalytic, and biosynthetic processes from the same high-energy organic compounds such as adenosine triphosphate (ATP).

In On the Origin of Species Charles Darwin (1859) (Fig. 10.1) built his theory of evolution using evidence that included an ancient Earth thought at the time by many geologists to have an age in millions of years. He also took the extinction of species to be a real phenomenon since fossils existed that were without living representatives.

A new synthesis: the Biological Universe

A remarkable shift in our scientific world picture is taking place, potentially as fundamental in its consequences as the new views put forth by Copernicus in the sixteenth century, or by Darwin in the nineteenth. Although astronomers have long been involved with the prospects for extraterrestrial life, their fundamental task since Newton has been to apply physics to a lifeless Universe. On the other hand, biologists have pursued their studies for centuries in cosmic isolation, meaning that biology considered life on Earth, with no attention paid to its cosmic context. Today, however, both camps are recognizing fruitful and exciting avenues of research created by a new synthesis. Biology is vastly enriched when attention is paid to a broader context for life as we know it, as well as the possibilities for other origins of life. And astronomy is coming to realize that the themes of cosmic, galactic, stellar, and planetary evolution, which have become central over the past century, must now also incorporate biological origin(s) and evolution(s). Historian of science Steven Dick (1996) has hailed this new synthesis as the Biological Universe. Although astronomy and biology are its two primary poles, many other disciplines are also vital components, in particular Earth and planetary sciences.

Introduction

Ice is the “natural state” or predominant form of water in our Solar System. The surfaces of most planets and moons are currently at temperatures well below the freezing point of pure water, including two of the more promising sites in the search for traces of extraterrestrial life, Mars and Europa. The amount of water-ice on Europa exceeds the volume of liquid water on Earth. Comets, considered potential vectors for precursors or early stages of life, are also icy bodies (Chapter 3). Even Earth may have undergone a series of complete (or near-complete) glaciations in its recent history, earning the title “Snowball Earth” (Section 4.2.4).

The presence of the liquid phase of water, however, is essential to the prospering of life as we know it. In order to study where liquid water can occur, we must understand scales ranging from the structure of the water molecule to the temperatures possible on a planetary surface or subsurface. In our Solar System, only Earth allows for a planetary surface with abundant liquid water (Chapter 4). Mars, however, may well have some liquid water in permafrost (perennially frozen soil) beneath its surface today (Section 18.4.1), and the evidence is strong that Europa and perhaps other moons of Jupiter have water oceans below their icy crusts (Chapter 19).

In this chapter we define semianalytic structures and draw conclusions from those which are important for the uniqueness of the kinematical representation of LQG. Semianalytic structures are intuitively the same thing as piecewise analytic structures, that is, objects such as paths or surfaces are analytic on generic subsets but analyticity may be violated on lower-dimensional subsets. On those subsets there is again a notion of semianalyticity. This enables one to take advantage of analyticity while making the constructions local: for instance, strictly analytical paths are determined everywhere on their analytic extension once they are known on an open set, thus making them very non-local. If we make it semianalytic then these data only determine the path up to the next point where analyticity is reduced to Cn, n > 0. This is important because we need to make sure that certain local constructions do not have an impact on regions far away from the region of interest. We will see this explicitly in the uniqueness proof.

We will now develop elements of semianalytic differential geometry in analogy to Chapter 19. We begin with ℝn with its canonical analytic structure. For general manifolds M we will assume that they are differential manifolds with given smooth structure and that a compatible analytic structure has been fixed. An introduction to semianalytical notions can be found in [888].

In this chapter we are going to address the famous ‘problem of time’ which has become the headline for all the physical interpretational problems of the mathematical formalism. Roughly speaking the problem of time is that there is none in GR: at least in the spatially compact case without boundaries the Hamiltonian vanishes on the physical, constraint surface. This is physically relevant because we seem to live in a universe with precisely that spatial topology. Since the Hamiltonian generates time translations in any canonical theory we arrive at the conclusion that ‘nothing moves’ in GR, which is in obvious contradiction to experiment. Since there is no time also the usual interpretation of quantum mechanical measurements at given moments of time breaks down. One can fill books about this issue and we will not even try to cover a substantial amount of the existing literature. A superb source of information on these conceptual problems is Carlo Rovelli's book [3]. Rather, what we will do in what follows is to collect various proposals for solutions to the problem of time taken from other authors, especially Rovelli's relational approach to classical and quantum physics and Hartle et al.'s consistent history interpretation, and combine them into a consistent picture. We do not want to suggest that the resulting picture is to be accepted, rather we want to draw attention to the problems involved and to develop a working hypothesis. The discussion on the interpretation of quantum mechanics is very alive and some authors such as Penrose [243] not only propose to alter the interpretational aspect of quantum mechanics but also the mathematical framework.