Cosmic abundances of the elements

All chemical elements are present in about the same proportions in the Sun, in the nearby stars, and in the interstellar medium. Standing in contrast, planets have been deeply transformed by gravity and igneous differentiation. For this reason, their surfaces do not represent a fair sample of the cosmic abundances of the elements. However, there are still minor bodies in the Solar System (in particular in the asteroid belt) that have not been differentiated. Some of their fragments often reach the Earth; these primitive meteorites are called chondrites. Chondrites display the same elemental abundance ratios present in the Sun, at least for 60 elements of low volatility (loosely called “metals” by astronomers). The most volatile gases, such as hydrogen, helium, oxygen, and nitrogen, depleted in chondrites, were assumedly present in the same proportions as in the Sun, in the primitive mixture that formed the Sun and the planetary system 4.6 billion years ago.

The “cosmic abundances” are not essentially different elsewhere. About 98% of the total mass of the Universe seems to be 3/4 hydrogen and 1/4 helium. The next three most abundant elements are carbon, nitrogen, and oxygen; taken together, they make about one single percent of the mass. The other 87 elements, often called “metals” by astronomers, to the great dismay of chemists, represent a total of less than one percent of the mass.

The previous statement is an average, and there are small fluctuations. For instance, Snow and Witt (1995) review the evidence that carbon is more abundant by a factor of two in the Sun than in the nearby stars.

The primordial Earth

Four and a half billion years ago, the proto-Earth was completing its formation. During the last accretion phases, its growing gravity had increased the impact velocities, so that their energies had been transformed into more and more heat. Hence the proto-Earth became progressively covered with a thick layer of molten lava, possibly to a very great depth.

The large-scale differentiation that separated the denser iron core from the mantle of lighter silicates was triggered by this intense heat. The last large impact occurred somewhat later, notably the one which, by a tangential grazing collision, caused the appearance of a transient ring around the Earth that rapidly became the Moon. The smaller cometary impacts, however, persisted and ended by establishing, not only the atmosphere and the oceans, but also the minor differentiation that separated the terrestrial crust from the underlying mantle.

The chemical and isotopic evidence that the terrestrial crust formed so early on was an enigma for geologists. It seems to be resolved by the cometary bombardment, when chondritic silicates were plowed deeply into the surface of the Earth after the separation of the core from the mantle.

To understand cosmic evolution, it was necessary first to evaluate the immense times involved. It began with geology. To find the age of a rock, one method came out on top: that of measuring the time elapsed from the moment when a radioactive element was confined in the rock. Uranium-238 (238U) suits this particularly well, because it decays into lead-206 (206Pb) with a half-life of 4.5 billion years. This half-life is the time needed for half of the radioactive substance to decay. After two half-lives, there is only ¼ left; after three half-lives, ⅛, etc. This is what is called an exponential decay.

The ratio of 238U to 206Pb present in a rock is a direct measure of the age of solidification of this rock. When a rock solidifies, the radioactive clock is reset to start at zero, because there is no 206Pb in the uranium oxide crystal just formed (lead remains in the liquid state in the original magma or lava). The rate of radioactive decay is extraordinarily constant, and nothing short of destroying the rock can influence it. This stems from the fact that radioactive reactions call for much higher energies than do chemical reactions.

The oldest terrestrial rocks are 3.8 billion years old. NASA astronauts have brought back lunar rocks; the oldest of them are 4.1 billion years old. Most of the carbonaceous chondrites (coming from the asteroid belt) are all of the same age: 4.6 billion years to within 0.1 billion years.

Chirality is the property of those molecules that can exist into two symmetrical forms corresponding to mirror reflections, but cannot be superimposed on each other by a mere rotation in space. Left-hand and right-hand gloves are an example of chirality. Chiral objects must be three-dimensional, since two symmetrical plane objects can always be superimposed by a reversal in space.

Many of the molecules used by life are chiral. However, when they exist in non-living matter, most of the time one half is in the right-hand form and the other half is in the left-hand form. This is what is called a racemic mixture. In contrast, life nearly always chooses only one of these two forms. For instance, all proteins consist of left-hand amino acids, whereas RNA and DNA are always built up from right-handed sugars. When a living organism dies and decays, thermal fluctuations change molecular shapes at random, so that, in the long run, there is racemization. Since the opposite process does not exist, a mechanism was needed to trigger the emergence of life by selecting preferentially one of the two chiral forms. The continuity of life then becomes only a mere copying process.

Was the choice random? Two forms of life of different chirality could have emerged. Left-handed proteins could have eliminated righthanded proteins by a random evolutionary process. This matter does not seem fundamental for elucidating the origins of life, because all biochemical processes depend on chemistry; that is, on the electromagnetic interaction which is mirror-symmetric.

The plurality of inhabited worlds

Are there other worlds in the Universe that are inhabited by intelligent beings? This question has always fascinated thinkers and philosophers. In the absence of serious observational data, dreams and wishes nearly always prevail, and most answer yes to the question. The recurrent argument centers by and large on teleology: since the ‘reason for the existence of the Earth’ is to shelter the human race, the other planets would ‘serve no purpose’ if they were uninhabited.

In antiquity Lucretius said: ‘We have to believe that there are in other regions of space, other beings and other men’. In the sixteenth century, the Italian monk Giordano Bruno ‘explained’ the plurality of inhabited worlds as God's design and as the purpose of the infinite Universe; for Bruno had read Copernicus and rejected the ‘crystalline spheres’ of antiquity. He was burned at the stake only ten years before Galileo Galilei discovered the phases of Venus with his new telescope, establishing that planets are not stars, but are ‘worlds’ like the Earth since they reflect solar light like the Moon does.

When knowledge about the planets became less uncertain, the French man of letters Fontenelle published the famous Entretiens surla Pluralité des Mondes, in 1686. Later, the Dutch astronomer Christiaan Huyghens wrote Cosmotheoros on the same subject, published post humously in 1698.

Introduction

Even more than the Renaissance period, the twentieth century will be remembered in human memory as an extraordinary era in every regard. The awareness of our true position, and of our isolation, in an immense and mysterious Universe began nearly 400 years ago, but recently it has expanded enormously (see Figure 1.1 A and B).

At the end of the nineteenth century, we did not know where we were, or where we came from; we did not even realize that we did not know it. The vastness of space and time had always been thought to be beyond any possible observation or experiment; in a word, their study was considered to be a part of metaphysics. Metaphysics concerns everything that might exist, but which we have no means of detecting. In contrast, the physical world is made up of what we can see, touch, hear, taste and smell, i.e. observe. In this sense it can be said that angels are a part of metaphysics, whereas a chair is part of the physical world.

Over the last 300 years, we have invented new means of detection that have extended our senses and give them ‘feelers’. We have rolled back the limits of metaphysics more and more.

At the end of Chapter 1, it was mentioned that asymmetries in all the forces of nature disappear at extraordinary short distances, and that all force constants converge toward a single value.

Since the nuclear forces (strong and electroweak) are confined inside the atomic nucleus, the symmetry breaking of the forces must be produced by a phenomenon that takes place within the size of the nucleus (incidentally, this is what sets the nuclear size). The symmetry breakdown causes a change of state.

Changes of state, including familiar ones among solids, liquids and gases, imply a change in the symmetry properties. Ice forms crystals whose symmetry differs from that of water. Microscopic symmetries in the positions of atoms are not the same in liquid water and in steam. On the other hand, ice that turns into water absorbs heat without changing its temperature; it is the latent heat of the change of state. This latent heat arises from the entropy change coming from the symmetry change from ice to water. Moreover, while cooling, water often reaches a temperature below its freezing point without immediately solidifying: this is called supercooling.

Breaking of the original symmetry of all the forces has begun between rows 7 and 8 of Table E.1. About 10-35 seconds after the Big Bang, it can be assumed that the gravitational force had begun to fall in strength, followed by the decoupling of the strong nuclear force from the electroweak force.

Symmetries are features which are preserved after a specified operation. For instance, two figures are mirror-symmetrical when we can turn one of them over the other and check by transparency that it coincides with the original. We call this property an invariance of the mirror reflection.

In this case, there is invariance in the drawing when it is turned over. Circular symmetry arises from the invariance of the length used as the circle radius. Symmetry of the equilateral triangle comes from the invariance of the length chosen for the three sides.

It is possible to extend the idea of symmetry to time. An invariance in time is called a ‘conservation’. A mass that remains the same in the future as in the past comes from mass conservation, which expresses a time invariance, that is a symmetry when time flows. All conservation laws (of mass, energy, angular momentum, electric charge, etc.) are thus time symmetries.

An antisymmetry is also an invariance in absolute value, but with a change of sign. For example, a negative electric charge is antisymmetric to the same positive charge.

The symmetry properties of elementary particles, as well as those of the four distinct forces of nature, appear through particle interactions. These numerous symmetries are usually described as if they were geometrical symmetries in an abstract space of multiple dimensions.

A symmetry group is a set of properties that remain symmetric or antisymmetric over a specified type of operation.

The Universe grows old

Enormous stretches of time have elapsed since the Big Bang. The twilight of the first million years has been transformed into near complete darkness. The fossil radiation, a relic of the Big Bang, that was still dimly lighting the large cooling masses of gas, has diluted and shifted to the infrared, because the expansion of space goes on. This radiation soon becomes completely invisible. In the opaque night of the first billion years, the masses of gas become more and more patchy. This is because density fluctuations increased, and the aggregates of gas were more and more separated, first into superclusters, then clusters of galaxies, and finally into galaxies.

The ‘timeless night’ probably ends during the second billion years, because the quasars light up the central clusters of many galaxies. Their dazzling light hides the simultaneous appearance of many small bright dots that studded the galactic halos. The stars have just lit up, in the globular clusters and in the large central cluster of many galaxies.

The galaxies each evolve somewhat differently. They display a large diversity in sizes, and in angular momenta, which comes from the turbulence in the gas masses.

The origin of the biosphere

The biosphere is the ensemble of the life-supporting regions of the terrestrial globe. It is made up of the oceans and fresh waters, plus the atmosphere and the layer of soil (spread over the continents) that contains organic matter. Water is the predominant component of the biosphere, in which the atmosphere plays an important role, and where the many compounds of carbon are essential because they are needed by life. In the outer crust of the Earth, however, inorganic carbon is by far the most abundant component, in the form of carbonates (limestone, dolomite, etc.). Heat easily decomposes carbonates and frees carbon in the form of carbon dioxide (CO2); thus this process is the principal source of volcanic CO2.

For a long time, the origin of the biosphere remained a mystery, because no fossil trace exists from the first billion years of the Earth's evolution.

The nervous system

Living organisms learned very early on that the detection of changes happening in their environment was essential if they were to survive. Some photosynthetic algae had already learned how to move by wagging their flagellum, in order to look for places where lighting was optimal. The first multicellular organisms increased their chances of survival by detecting changes in their own body, and thus coordinate the response from their different cells.

Contact between one cell and its neighbors developed in the plants by means of enzyme exchange; that is, in a purely chemical way. It is a very slow process which leads to tropisms (such as the flower that turns toward the Sun, or the foliage that seeks light). But tropisms are too slow for animals; quick reactions for attack or defense are essential. A faster communication system appeared: some cells specialized in sending swift electrical impulses from one cell to another, as if along an electric wire. The nervous system began to emerge.

The life of the stars

At the time when the first quasars showed their dazzling brilliance, there were still no atoms of carbon, nitrogen, or oxygen, no metals in the Universe, nor any solid stuff (earth, rocks, etc.). It is tempting to think that the extreme temperatures reached in the accretion disks of quasars would have already produced new elements. But we must remember that the rings that reached a sufficiently high temperature were eventually absorbed by the black hole and disappeared from our Universe before having had a chance to make complex molecules.

The first stars formed out of a gaseous mixture of about 76% hydrogen and 24% helium, plus a few traces of rare light elements, such as lithium, or rare isotopes like deuterium or 3He. Table 3.1. Major thermonuclear reactions within stars, classified by increasing ignition temperature, from 10 million degrees for hydrogen, up to 6 billion degrees for iron

The minimum stellar mass able to reach this ignition temperature is indicated in solar mass units M⊙.

The grand beginning

Let us summarize the initial events in their chronological order. First, we can imagine a quantum fluctuation in the void, which began everything. The perfect symmetry of the little bubble of pure energy is unstable and breaks up spontaneously. We follow it at the instant when it is still smaller than a proton. It inflates exponentially while creating its space–time dimensions and, after 10-32 second, it is already larger than the present Solar System. This exponential ‘inflation’ (see Appendix F) creates all the matter and all the radiation still present in the Universe.

After that, the phase transition ends. The change of state has forever broken the initial symmetry. From now on, only the nuclear forces will remain confined between the quarks, whereas the forces of gravity and electromagnetism now act at a distance. The Universe will continue its expansion in an almost linear manner, restrained merely by gravitation, right up to the present.

But where did all this energy come from, with its ability to create the enormous bulk of matter and radiation that we see in the stars and the galaxies?