THE DECLINE OF ARISTOTELIAN SCIENCE

Aristotle's law of motion

In Aristotle's day, ideas on space and time were vague and had yet to be sharpened into their modern forms. Space was associated with the distribution of things directly observed. Things distributed in time, however, were not directly observed, and generally intervals of time were not easily measured. How to define motion by combining intervals of space and time was not at all clear, and motion was poorly distinguished from other forms of change.

Aristotle's law of motion may be expressed by the relation

applied force = resistance × speed.

But really he had no general formula, and no precise way of measuring force, resistance, and speed. He argued qualitatively, reasoning from the everyday experience that effort is needed to maintain a state of motion, and the faster the motion, the bigger the effort needed to maintain that motion. “A body will move through a given medium in a given time, and through the same distance in a thinner medium in a shorter time,” said Aristotle, and “will move through air faster than through water by so much as air is thinner and less corporeal than water.” Guided by this principle, it seemed natural to conclude that bodies of unequal weight fall through air at different speeds.

INTRODUCTION

Facts about the heavens

We begin on a philosophical note by quoting Arthur Eddington from his book The Expanding Universe: “For the reader resolved to eschew theory and admit only definite observational facts, all astronomical books are banned. There are no purely observational facts about the heavenly bodies. Astronomical measurements are, without exception, measurements of phenomena occurring in a terrestrial observatory or station; it is only by theory that they are translated into knowledge of a universe outside.” Without books and theories our observations of the heavens lack content and significance.

We construct universes that are models of the true Universe. Our longing for absolute truth tempts us to believe that the current universe of our society is the Universe. Each society has its own universe (ours is the physical universe whose principles are discussed in Chapter 8), and each society interprets its observations in accord with the principles of that universe.

This second edition of Cosmology: The Science of the Universe revises and extends the first edition published in 1981. Much has happened since the first edition; many developments have occurred, and cosmology has become a wider field of research.

As before, the treatment is elementary yet broad in scope, and the aim is to present an outline that appeals to the thoughtful person at a level not requiring an advanced knowledge in the natural sciences. Cosmology has many faces, scientific and nonscientific; in this work the primary emphasis is on cosmology as a science, but the important historical, philosophical, and theological aspects are not ignored. Mathematics is avoided except in a few places, mostly at the end of chapters, and the treatment is varied enough to meet the needs of both those who enjoy and do not enjoy mathematics.

At the end of each chapter are two sections entitled Reflections and Projects. The Reflections section presents topics for reflection and discussion. The Projects section raises questions and issues that a challenged reader might care to tackle. Cosmology impels us to ask deep questions, read widely, and think deeply. It is not the sort of subject that lends itself readily to simple yes and no answers. On most issues there are conflicting arguments to be investigated, weighed, rejected, accepted, or modified according to one's personal tastes and beliefs.

THE UNIVERSE

From the outset we must decide whether to use Universe or universe. This is not so trivial a matter as it might seem. We know of only one planet called Earth; similarly, we know of only one Universe. Surely then the proper word is Universe?

The Universe is everything and includes us thinking about what to call it. But what is the Universe? Do we truly know? It has many faces and means many different things to different people. To religious people it is a theistically created world ruled by supernatural forces; to artists it is an exquisite world revealed by sensitive perceptions; to professional philosophers it is a logical world of analytic and synthetic structures; and to scientists it is a world of controlled observations elucidated by natural forces. Or it may be all these things at different times. Even more diverse are the worlds or cosmic pictures held by people of different societies, such as the Australian aboriginals, Chinese, Eskimos, Hindus, Hopi, Maoris, Navajo, Polynesians, Zulus. Cosmic pictures evolve because cultures influence one another, and because knowledge advances. Thus in Europe the medieval picture, influenced by the rise of Islam, evolved into the Cartesian, then Newtonian, Victorian, and finally Einsteinian pictures.

THE GREAT DISCOVERY

Doppler effect

From a historical viewpoint the Doppler effect paved the way to the discovery of the expanding universe. Nowadays we do not use the Doppler effect in cosmology, except in its classical Fizeau–Doppler form as a rough and ready guide. We examine the Doppler effect briefly and defer to Chapter 15 a more searching inquiry.

The spectrum of light from a luminous source contains bright andd ark narrow regions, as shown in Figure 14.1, that are the emission (bright) and absorption (dark) lines produced by atoms. When a luminous source such as a candle or a star moves away from an observer, all wavelengths of its emitted radiation, as seen by the observer, are increased. Its spectral lines are moved toward the longer wavelength (redder) end of the spectrum and it is said to have a redshift. This redshift is detected by comparing the spectrum of the luminous source with the spectrum of a similar source that is stationary relative to the observer. The source may move away from the observer, or the observer may move away from the source, and in either case the separating distance increases and there is an observed redshift.

SPACE

Dressed and undressed space

From the Heroic Age of Greece until modern times we see the development, side by side, of two views on the nature of space: “dressed space” and “undressed space.”

Space as a void – undressed, existing in its own right, independent of the things it contains – was at first a lofty abstraction that many persons could not take seriously. It seemed more natural to think of space as dressed and made real with a continuous covering of material and ethereal substances. Aristotle, who believed in dressed space, regarded the notion of a vacuum as nonsense and said that a vacuum is nothing and what is nothing does not exist. This enabled him to argue in favor of a finite universe. The ether – the fifth element – ended at the sphere of fixed stars. Beyond the sphere of stars, because there was no ether, there could be no space. At first this was the view of scholars in the Middle Ages who later succeeded in extending space beyond the sphere of fixed stars by inhabiting it with God.

PROLOGUE

Cosmology, the science of the universe, attracts and fascinates us all. In one sense, it is the science of the large-scale structure of the universe: of the realm of extragalactic nebulae, of distant and receding horizons, and of the dynamic curvature of cosmic space and time. In another sense, it seeks to assemble all knowledge into a unifying cosmic picture. Most sciences tear things apart into smaller and smaller constituents in order to examine the world in ever greater detail, whereas cosmology is the one science that puts the pieces together into a “mighty frame.” In yet another sense, it is the history of mankind's search for understanding of the universe, a quest that began long ago at the dawn of the human race. We cannot study cosmology in the broadest sense without heeding the many cosmic pictures of the past that have shaped human history. We trace the rise of the scientific method and how it has increased our understanding of the physical universe. Which brings us to the major aim of this book: gaining an elementary understanding of the physical universe of modern times.

COSMIC REDSHIFTS

Wavelength stretching

In the previous chapter we saw how the Fizeau–Doppler (known more briefly as the Doppler) formula played a vital role in the discovery of the expansion of the universe. Distant galaxies have redshifted spectra, and their redshifts were interpreted to mean the galaxies are rushing away from us. Then in the late 1920s and early 1930s Georges Lemaître, Howard Robertson, and other cosmologists discovered a totally new interpretation of extragalactic redshifts based on the expanding space paradigm.

The new expanding space redshift is simple and very easy to understand. We suppose that all galaxies are comoving and their emitted light is received by observers who are also comoving. Light leaves a galaxy, which is stationary in its local region of space, and is eventually received by observers who are stationary in their own local region of space. Between the galaxy and the observer, light travels through vast regions of expanding space. As a result, all wavelengths of the light are stretched by the expansion of space (see Figure 15.1). It is as simple as that.

A light ray, emitted by a distant galaxy, travels across expanding space and is received by the observer. If, while the light ray travels, all comoving distances are doubled, it follows that all wavelengths of the light ray are also doubled.

THE CONTAINMENT PRINCIPLE

Much of cosmology in the past has been concerned with the center and edge of the universe (see Figure 8.1), and our attitude nowadays on these matters is expressed by the principles of location and containment. Broadly speaking, the location principle (previous chapter) involves issues concerning the cosmic center, and the containment principle (this chapter) involves issues concerning the cosmic edge. Both principles help us to avoid pitfalls that trapped earlier cosmologists.

The containment principle of the physical universe states: the physical universe contains everything that is physical and nothing else. It is the battle cry of the physical sciences (chemistry and physics). To some persons the principle seems so elementary and obvious that it hardly deserves mentioning, to others it is a declaration of an outrageous philosophy. Before condemning the principle as too elementary or too outrageous, we must look more fully at what it means.

Modern scientific cosmology explores a physical universe that includes all that is physical and excludes all that is nonphysical. The definition of physical is sweeping and at first sight exceeds what common sense deems proper. It includes all things that are measurable and are related by concepts that are vulnerable to disproof. Atoms and galaxies, cells and stars, organisms and planets are physical things that belong to the physical world.

CONSTANTS OF NATURE

Natural units

We measure distances in units such as meters and light years, intervals of time in units such as seconds and years, and masses in units such as grams and kilograms. There is nothing sacred about these units, which are determined by our history, environment, and physiology. If we communicate with beings in another planetary system and inform them that something has a size of so many meters, an age of so many seconds, and a mass of so many kilograms, they will not understand because their units of measurement are undoubtedly different. But they will understand if we say the size is so many times that of a hydrogen atom, the age is so many times that of a certain atomic period, and the mass is so many times that of a hydrogen atom, simply because their atoms are the same as ours (if they were not, it would be an incoherent universe, incomprehensible, and we might not be able to communicate with them). The basic uniformity of the universe provides us all with the same set of natural units of measurement.

WHAT ARE COSMOLOGICAL HORIZONS?

Horizons

We look out in space and back in time and do not see the galaxies stretching away endlessly to an infinite distance in an infinite past. Instead, we look out a finite distance and see only things within the “observable universe.” Like the sea-watching folk in Robert Frost's poem, we “cannot look out far” and “cannot look in deep.”

The observable universe is normally only a portion of the whole universe. We are at the center of our observable universe; its distant boundary acts as a cosmic horizon beyond which lie things that cannot be observed. Observers in other galaxies are located at the centers of their observable universes that are also bounded by horizons. A person on a ship far from land, who sees the sea stretching away to a horizon, is at the center of an “observable sea.” People on other ships are at the centers of their own observable seas that are bounded by horizons. Despite this analogy the horizons of the universe are not as simple as the horizons of the sea.

GRAVITATIONAL COLLAPSE

Stars are luminous globes of gas in which the inward pull of gravity matches the outward push of pressure. The nuclear energy released in the interior at high temperature is radiated from the surface at low temperature and this low-temperature radiation sustains the chemistry of planetary life.

But to each star comes a day of reckoning. Its central reservoir of hydrogen approaches exhaustion and the star begins to die. The tireless pull of gravity causes the central regions to contract to higher densities and temperatures, and as a consequence the outer regions swell up and the star becomes a red giant. A star like the Sun then evolves into a white dwarf in which most of its matter is compressed into a sphere roughly the size of Earth. Many stars end as white dwarfs, slowly cooling, supported internally against gravity by the pressure of electron waves (as in ordinary metals).

More massive stars do not give up the game so easily. Gravity is stronger in these stars and their central regions continue to contract to even higher densities and temperatures, thus enabling them to draw on the last reserves of nuclear energy. These stars become luminous giants squandering energy at a prodigious rate. Soon their reserves of nuclear energy are exhausted. Only gravitational energy remains with its fatal price of continual contraction.

THE PRIMEVAL ATOM

The universe expands, and naturally we conclude that in the past the universe was in a more condensed state than at present. If we journeyed back in time we would expect to see the universe get steadily denser. Ultimately, we would arrive at the very high-density state popularly called the “big bang.” This conclusion seems unavoidable. It might be a mistake, however, to forget entirely the many debates among cosmologists concerning the reality of a big bang beginning. Eddington was firmly against the idea of a universe that begins in a dense state, and many persons – particularly those who were drawn to science by Eddington's popular works – have felt disinclined to set his views aside lightly. The steady–state theory of an expanding universe, proposed in the late 1940s, attracted many who were united in their dislike of the big bang idea, and even now, as the 20th century closes, a few cosmologists continue to think that a big bang interpretation of the observations is mistaken.

What do we mean by the expression “big bang?” The actual singularity of maximum density at the origin of time? Or an early period in cosmic history? If the latter, how long a period?

Introduction

The first ring system to be observed in the solar system was discovered around Saturn by Galileo in 1610. Unsure of the nature of the phenomenon he had observed, he originally interpreted the ring ansae as two moons, one on each side of the planet. In a Latin anagram sent to fellow scientists he announced, “I have observed the most distant planet to have a triple form”. Galileo was surprised to find that the phenomenon had disappeared by 1612, only to reappear again soon afterwards. Huygens (1659) correctly attributed the varying appearance as being due to the different views of a thin disk of material surrounding Saturn. It was Maxwell (1859) who provided a mathematical proof that the rings could not be solid; they had to be composed of individual particles orbiting the planet.

The rings of Uranus were detected serendipitously in March 1977 by astronomers observing an occultation of a star by the planet. The Voyager spacecraft detected a faint ring around Jupiter (Smith et al. 1979a), and occultations of stars by Neptune led to the discovery of the ring arcs of Neptune, subsequently shown to be the optically thicker parts of a faint ring system. The flybys of the outer planets by the Voyager spacecraft and the continuing ground- and space-based observations of the ring systems have provided evidence of a wide variety of dynamical phenomena, which provide an ideal testing ground for some of the concepts covered in this book.

We are living in a new age of discovery. The major voyages of exploration in the fifteenth and sixteenth centuries have modern parallels in the interplanetary spacecraft missions that have “discovered” our solar system. The data from these spacecraft combined with ground-based observations have revealed a solar system that is more than a collection of planets, satellites, asteroids, comets, and dust distributed in some arbitrary fashion: It has an intricate dynamical structure, which can be largely understood by the application of a simple inverse square law of force to its constituent bodies. To understand the dynamical structure and evolution of the solar system we must therefore understand the qualitative and quantitative effects of the universal law of gravitation.

We consider solar system dynamics to be the application of the techniques of celestial mechanics to solve real problems in planetary science. There are several classical texts on celestial mechanics and many are still in use today. These include the books by Plummer (1918), Brown & Shook (1933), Brouwer & Clemence, (1961) and, more recently Danby (1988). The books by Hagihara (1970, 1972a,b, 1974a,b, 1975a,b, 1976a,b) are authoritative works of reference but make little attempt to convey understanding.