Introduction

While the notion of worlds beyond our Earth is ancient, the specific idea of planets orbiting distant stars is relatively new. Over two millennia ago Epicurus stated “there are infinite worlds both like and unlike this world of ours,” but he was not speaking of Earth-like planets orbiting Sun-like stars. Indeed, planets orbiting stars would have been a meaningless issue to the Greeks, as the Sun was not recognized as a star, nor the Earth as a planet (Chapter 1).

One of the earliest and most eloquent spokespersons for what is now called astrobiology, and among the first to grasp the implications of the Sun being a star and the Earth a planet, was the mystical Roman Catholic monk Giordano Bruno. In On the Infinite Universe and Worlds (1584) he wrote:

Bruno then concludes with the revolutionary slogan:

Bruno's reward for this prescience and for other heresies was condemnation by the Church, followed by immolation in a public square in Rome in 1600.

Introduction

Prokaryotic microorganisms were the only form of life for at least 80 percent of our evolutionary history (Schopf and Packer, 1987). Multicellular organisms including plants, animals and fungi evolved a mere 0.5–1.0 Ga from single-celled eukaryotic ancestors. Geologists and paleontologists debate the age of life on this planet and when the major microbial lineages first diverged (see Chapter 12 for details). Cyanobacterium-like fossils suggest that life emerged at least 3.45 Ga (Schopf et al., 2002; Schopf and Packer, 1987), but the biogenic origins of these structures are contested (Brasier et al., 2002; Section 12.2.1). The chemical record documents prokaryotic metabolisms that may have existed 3.47–3.85 Ga (Mojzsis et al., 1996) and eukaryotic biosignatures that may be as old as 2.7 Gyr (Brocks et al., 1999). Yet, these are still imprecise interpretations (some might be more recent microbial contamination) and do not set absolute limits on the possible origins of life on Earth. Early periods of heavy bombardment between 4.1 and 3.8 Ga might constrain when life first appeared on Earth, although microorganisms living off chemical energy at kilometer depths could have survived even the largest impact events.

By the standards of multicellular plants and animals, single-cell organisms look relatively simple (Patterson and Sogin, 1993), yet they transformed the atmosphere, the waters, the surface, and the subsurface of the Earth.

In this chapter we will describe the so-called kinematical geometrical operators of Loop Quantum Gravity. These are gauge-invariant operators which measure the length, area and volume respectively of coordinate curves, surfaces and volumes for D = 3. The area and volume operators were first considered by Smolin in [660] and then formalised by Rovelli and Smolin in the loop representation [425]. In [575] Loll discovered that the volume operator vanishes on gauge-invariant states with at most trivalent vertices and used area and volume operators in her lattice theoretic framework [661–663]. Ashtekar and Lewandowski [427] used the connection representation defined in previous chapters and could derive the full spectrum of the area operator, while their volume operator differs from that of Rovelli and Smolin on graphs with vertices of valence higher than three, which can be seen as the result of using different diffeomorphism classes of regularisations. In [664] de Pietri and Rovelli computed the matrix elements of the RS volume operator in the loop representation and de Pietri created a computer code for the actual case-by-case evaluation of the eigenvalues. In [559] the connection representation was used in order to obtain the complete set of matrix elements of the AL volume operator.

Area and volume operators could be quantised using only the known quantisations of the electric flux of Section 6.3 but the construction of the length operator [424] required the new quantisation technique of using Poisson brackets with the volume operator, which was first employed for the Hamiltonian constraint, see Chapter 10. To the same category of operators also belong the ADM energy surface integral [442], angle operators [429, 430] and other similar operators that test components of the three-metric tensors.

Introduction

Picture a future triumph in robotic space exploration: in a complex mission to Mars, a sample has been collected from the martian subsurface near a newly discovered hydrothermally active site at 30°N latitude. Ten years in the detailed planning and execution, the mission's Earth return capsule with its sample canister has landed in the Utah desert. The sample is now under extensive analysis and testing in an ultra-clean containment facility – and initial observations have shown positive indications that it contains life. Only after later testing is completed, checked, rechecked, and repeated is it shown unequivocally that the lifeform contained within the sample is a soil bacterium common to the dirt of an old Soviet launch facility in Baikonur, Kazakhstan, and which has apparently been alive on Mars since a spacecraft crash-landed there in 1972 …

Or picture, as did novelist Michael Crichton (1969) in the very year of the first lunar sample-return mission (Apollo 11), a spacecraft returning to Earth containing a dangerous extraterrestrial organism – The Andromeda Strain – not related in any way to Earth-life and operating by rules scarcely understood even after hundreds of humans have met their grisly demise …

Once you have those events in mind, you are developing a feel for what planetary protection might be, and what it is meant to prevent.

Introduction

How does life begin? Can life arise elsewhere than the Earth? These questions are among the most fundamental and challenging in all of biology. Charles Darwin once wrote to a friend, “It is mere rubbish, thinking at present of the origin of life; one might as well think of the origin of matter.” (Letter to J. D. Hooker, March 29, 1863.) Darwin made this comment when the knowledge required to think about the origin of life and matter simply did not exist. Now, 150 years later, we understand much more. We know that new elements are constantly being synthesized by nuclear fusion of hydrogen and helium in the interiors of stars, then expelled into interstellar space when stars reach the ends of their lives. This matter is the source of new stars and planetary systems, and it is literally true that planets like the Earth and the biogenic elements that give rise to life are composed of “star dust” (Chapter 3). We also know that liquid water once existed on Mars, and perhaps still does beneath the martian surface, suggesting that microbial life may exist elsewhere than on the Earth. Probably most important is that we understand living cells in unprecedented detail, even to the point of knowing the entire sequence of three billion nucleotide bases in the human genome, and we have begun to manipulate the genetic blueprint of life.

Beyond merely checking whether we have a quantum theory of the correct classical theory, namely General Relativity coupled to all known matter, quantum gravity has certainly a huge impact on the whole structure of physics. For instance, if the picture drawn in Chapter 12 is correct, then one must do quantum field theory on one-dimensional polymer-like structures rather than in a higher-dimensional manifold, presumably the ultraviolet divergences disappear and while there are still bare and renormalised charges, masses, etc., the bare charges will presumably be finite while the renormalised charges should better be called effective charges because they simply take into account physical screening effects.

Quantum gravity effects are notoriously difficult to measure because the Planck length is so incredibly tiny. It may therefore come as a surprise that recently physicists have started to seriously discuss the possibility of measuring quantum gravity effects, mostly from astrophysical data and gravitational wave detectors [503–506]. See also the discussion in the extremely beautiful review by Carlip [9] and references therein. Those who laugh at these ideas are recommended to have a look at the historical remarks in [872], which draws an analogy with the situation at the end of the nineteenth century when it was widely believed that it would never be possible to detect atomic effects. Einstein showed that the atomic structure of matter was not directly, but indirectly, visible through collective effects, in this case Brownian motion, and what we are about to describe goes in the same direction.

The challenge is of course to compute quantum gravity effects within Quantum General Relativity or more specifically LQG.

Quantum General Relativity (QGR) or Quantum Gravity for short is, by definition, a Quantum (Field) Theory of Einstein's geometrical interpretation of gravity which he himself called General Relativity (GR). It is a theory which synthesises the two fundamental building blocks of modern physics, that is, (1) the generally relativistic principle of background independence, sometimes called general covariance and (2) the uncertainty principle of quantum mechanics.

The search for a viable QGR theory is almost as old as Quantum Mechanics and GR themselves, however, despite an enormous effort of work by a vast amount of physicists over the past 70 years, we still do not have a credible QGR theory. Since the problem is so hard, QGR is sometimes called the ‘holy grail of physics’. Indeed, it is to be expected that the discovery of a QGR theory revolutionises our current understanding of nature in a way as radical as both General Relativity and Quantum Mechanics did.

What we do have today are candidate theories which display some promising features that one intuitively expects from a quantum theory of gravity. They are so far candidates only because for each of them one still has to show, at the end of the construction of the theory, that it reduces to the presently known standard model of matter and classical General Relativity at low energies, which is the minimal test that any QGR theory must pass.

One of these candidates is Loop Quantum Gravity (LQG). LQG is a modern version of the canonical or Hamiltonian approach to Quantum Gravity, originally introduced by Dirac, Bergmann, Komar, Wheeler, DeWitt, Arnowitt, Deser and Misner.

Introduction

Habitable planets are those bodies that provide environments, materials and processes that are advantageous for the formation and long-term evolution of life. Understanding the processes that lead to the formation of such planets is a central issue in astrobiology. We are of course handicapped in this quest since Earth is the only example of a planet with proven habitability – the only one known to have provided thermal, chemical, and other physical conditions that allowed life to form and survive for ~3.5 Gyr.

This chapter emphasizes the formation of Earth-like planets, those with environments capable of supporting complex life comparable to Earth's plants and animals. The focus on life comparable to Earth's multicellular organisms is partly due to the practical consideration that we better understand the environmental constraints of such life. Despite this restricted focus, note that most astrobiologists consider that the dominant form of life in the Universe, as it has been on Earth over most of its history, is probably far simpler and more rugged, analogous to Earth's bacteria and archaea (Section 3.2).

This interpretation of habitability is highly Earth-centric and assumes that life elsewhere is similar to terrestrial life and requires environments similar to those of terrestrial organisms. The actual cosmic limits of life are of course unknown, but the Earth-centric view is a reasonable, albeit conservative, place to start. Until there are detailed data on other inhabited planets, discussions of extraterrestrial life would be prudently biased by what is known from our Earth experience.

Normally, when constructing a perturbative quantum field theory on Minkowski space or any other background spacetime one never doubts that the resulting theory has the correct classical limit. One is satisfied with having found a Fock representation and a definition of the S-matrix, that is, matrix elements of powers of a normal ordered Hamiltonian operator. In fact it is clear from the outset that a theory written in terms of (an infinite number of) annihilation and creation operators has the correct classical limit because one can construct the usual coherent states for the underlying free field theory and then one knows that operators written in terms of the annihilation and creation operators have expectation values very close to the classical values that the corresponding classical function takes at the point in phase space where the coherent state is peaked.

In a constrained, non-perturbative quantum field theory without background structure the question about the classical limit is much less trivial. First of all, since we are using a non-perturbative approach we cannot expand around a free field theory and hence cannot use Fock space (coherent state) techniques. Secondly, since we must work without a background spacetime we are forced to use completely new types of Hilbert spaces for which no semiclassical techniques have been developed so far. Thirdly, the theory is highly non-linear: for example, the constraint operators are simply not polynomials of the basic variables A, E for which one would hope to be able to construct semiclassical states which approximate those.

Why is this question important?

In observing our vast Universe thus far, we have encountered life only on or near the surface of our home planet. Yet life in its properties and behavior is so different from the barren realms that we have surveyed elsewhere, that we cannot help but wonder how it first took root here, and whether things that we would consider alive exist elsewhere. The fossil record on Earth appears to extend to 3.5 Gyr (Schopf et al., 2002) and isotopic evidence suggests the presence of life several hundred million years earlier than that. Recently, however, this evidence has come into question (Brasier et al., 2002), so caution should be used in relying on these conclusions (Section 12.2.1). No hard evidence exists at all, however, concerning the mechanism by which life first began here.

Every human culture has felt the need to address this question, considering its importance in defining our place in the cosmos. In the absence of firm evidence, the door has been left open to a variety of answers from science, mythology, and religion, each defining our place in the Universe in different ways. I will follow a scheme put forward by the scientist and philosopher Paul Davies (1995: 21) and separate the competing points of view into three groups, called Biblical–Creationist, Improbable Event, and Cosmic Evolution.