The origin of life, as with any other process of structure formation, should have been accompanied by a loss of entropy. Since the second law of thermodynamics states that the entropy of an isolated system tends to increase, any self-organizing system must exchange free energy (closed system) and/or matter (open system) with its environment in order that the overall entropy increases (Kondepudi and Prigogine, 1998). This simple observation emphasizes the importance of energy transfers in the origin and development of early life. As far as biochemical systems are concerned, energy exchanges mostly involve chemical energy that is brought about by ‘high-energy’ carriers so that energy flows through metabolic pathways from free energy-rich compounds towards low-energy molecules, the difference being released in the environment as heat. When the occurrence of a thermodynamically unfavourable reaction makes it necessary, fresh energy is provided to the system through coupled reactions involving a free-energy carrier such as ATP. The principle that energy is brought about by ‘high-energy’ carriers applies to most metabolic pathways, though some of them do not simply follow this rule. An example is the process of energy collection leading to ATP synthesis, in which ‘chemical’ energy is generated from a ‘physico–chemical’ source: a gradient of concentration between two compartments separated by the plasma–cell membrane (Mitchell, 1961).

Introduction

The first two thirds of the history of life on Earth are dominated by single-celled microorganisms with prokaryotes characterizing the time period up to at least the Palaeoproterozoic Period (from 2.5 to about 1.8 billion years (Ga) ago). The oldest recognizable eukaryotes appear in the Mesoproterozoic Era (and are dated at between 1.6 to 1.8 Ga (Javaux et al., 2001, 2004; see also review in Knoll et al., 2006). This chapter on early life will concentrate on the traces of life contained in the oldest crustal rocks potentially capable of hosting well-preserved biosignatures, i.e. Early to Mid-Archaean, 3.5 to 3.0 Ga-old sediments and volcanic rocks from greenstone belts in both the Pilbara (NW Australia) and the Barberton (East South Africa) Greenstone Belts. The fossil traces of early microorganisms in these rocks resemble prokaryotes in terms of their morphology, metabolic processes and interactions with the environment. Life is directly influenced by its environment and, reciprocally, it can also influence its immediate environment. On the microbial scale, this influence is in proportion to the size of the microbial colonies, biofilms or mats, which can range from tens of microns to several metres or more (sometimes up to kilometres) for well-developed mats. For instance, if one takes into consideration the probable microbial control on the rise of oxygen in the atmosphere (between 2.4 and 2.0 Ga; Bekker et al., 2004; Canfield, 2005), this influence also reaches the planetary scale.

Introduction

In a paper entitled ‘The prospect of alien life in exotic forms on other worlds’ published in 2006, the authors write:

Similar comments can be found in several papers (Bains, 2004).

We are not planning to address the possibility of an alien life, but wish to focus on the issue of the solvent in order to try to demonstrate that water is an essential component of all living systems. Living systems are complex both at the molecular and supra-molecular levels (Schulze-Makuch and Irwin, 2006). Water plays, at both these levels, a role which is crucial for the structure, the stability and the biological function of all molecules that are essential for life, a role that cannot be played by any other solvent or any other molecule.

A solvent is never an inert medium and always interacts with the solute molecules. These interactions affect not only the solute but also the solvent. Water is a unique solvent because solute-induced modifications are very important in this medium.

As mentioned in the first chapter, astrophysical applications played a crucial role in the development of atomic physics. In their 1925 paper, Russell and Saunders [2] derived the rules for spectroscopic designations of various atomic states based on the coupling of orbital angular momenta of all electrons into a total L, and the coupling of all spin momenta into a total S, called the LS coupling scheme. Each atomic state is thus labelled according to the total L and S.

Atomic structure refers to the organization of electrons in various shells and subshells. Theoretically it means the determinations of electron energies and wavefunctions of bound (and quasi-bound) states of all electrons in the atom, ion or atomic system (such as electron–ion). As fermions, unlike bosons, electrons form structured arrangements bound by the attractive potential of the nucleus. Different atomic states arise from quantization of motion, orbital and spin angular momenta of all electrons. Transitions among those states involve photons, and are seen as lines in observed spectra.

This chapter first describes the quantization of individual electron orbital and spin angular momenta as quantum numbers l and s, and the principal quantum number n, related to the total energy E of the hydrogen atom. The dynamic state of an atom or ion is described by the Schrödinger equation. For hydrogen, the total energy is the sum of electron kinetic energy and the potential energy in the electric field of the proton.

As we will see throughout this book, Hamiltonian formulations provide important insights, especially for gauge theories such as general relativity with its underlying symmetry principle of general covariance. Canonical structures play a role for a general analysis of the systems of dynamical equations encountered in this setting, for the issue of observables, for the specific types of equation as they occur in cosmology or the physics of black holes, for a numerical investigation of solutions, and, last but not least, for diverse sets of issues forming the basis of quantum gravity.

Several different Hamiltonian formulations of general relativity exist. In his comprehensive analysis, Dirac (1969), based on Dirac (1958a) and Dirac (1958b) and in parallel with Anderson and Bergmann (1951), developed much of the general framework of constrained systems as they are realized for gauge theories. (Earlier versions of Hamiltonian equations for gravity were developed by Pirani and Schild (1950) and Pirani et al. (1953). In many of these papers, the canonical analysis is presented as a mere prelude to canonical quantization. It is now clear that quantum gravity entails much more, as indicated in Chapter 6, but also that a Hamiltonian formulation of gravity has its own merits for classical purposes.) The most widely used canonical formulation in metric variables is named after Arnowitt, Deser and Misner (Arnowitt et al. (1962)) who first undertook the lengthy derivations in coordinate-independent form.

In general relativity, the space-time metric provides the physical field of gravity and is subject to dynamical laws. For a complete and uniform fundamental description of nature, the gravitational force, and thus space-time, is to be quantized by implementing the usual features of quantum states, endowing it with quantum fluctuations and imposing the superposition principle. Only then do we obtain a fully consistent description of nature, since matter as well as the non-gravitational forces are quantum, described by quantum stress-energy which can couple to gravity only via some quantum version of the Einstein tensor.

An implementation of this program requires a clear distinction of the different concepts used in general relativity. One normally works with the line element for metric purposes, but this is a combination of metric tensor components and coordinate differentials (separating events from each other). Only the geometry is dynamical, not the coordinates. After quantization, we may have a representation for geometrical observables such as the sizes of physically characterized regions, but not for coordinates or distances between mathematical points as mere auxiliary ingredients. Metrics or other tensors may arise in an effective form from quantum gravity, but they are not the basic object. One has to dig deeper, similarly to hydrodynamics where the continuous fluid flow is not suitable for a fundamental quantum theory, which must, rather, be based on an atomic picture.

Hyperbolicity, as verified for general relativity in Chapter 3.4.2, guarantees the existence of local solutions in terms of initial data, but not the existence of global ones at all times. When evolving for long time intervals, singularities can develop in the solution and prevent it from being extendable further. We have already seen examples in homogeneous solutions of Bianchi models and the simpler isotropic solutions of FLRW models. In these cases, for matter satisfying the strong energy condition, there were always reasonable initial values which led to solutions with a diverging Hubble parameter and expansion rate at some time in the future or the past. The Hubble parameter corresponds to the expansion of the family of timelike geodesics followed by comoving Eulerian observers, a concept which presents a useful perspective in the context of singularities. When this expansion parameter diverges, the geodesic family no longer defines a smooth submanifold of space-time but develops a caustic or focal point where, in a homogeneous geometry, all geodesics intersect. For every spatial point on a non-singular slice, there is exactly one such geodesic intersecting it; when all these geodesics simultaneously intersect at the singular slice, it means that the whole space collapses into a single point after a finite amount of proper time. At this time, the initial value problem breaks down and space-time cannot be extended further.