PRINCIPLE OF EQUIVALENCE

Gravitational and inertial forces produce effects that are indistinguishable – this is the principle of equivalence. It serves as an essential stepping-stone to the theory of general relativity, and makes a basic connection between motion and gravity. It leads to a second stepping-stone: the realization that geometry and gravity have much in common. Then, in an inspired leap across the gulf of non-Euclidean geometry, we enter a country into which comparatively few explorers have ventured. No person entering the third millenium may claim to have a liberal education who has not glimpsed, however briefly, the universe of general relativity.

An inertial force, such as centrifugal force, exists when a body is accelerated. We recall from Newtonian theory that when a body is in free fall, and hence moves freely in space under the influence of gravity, it follows a path of such a kind that the sum of the inertial and gravitational forces is zero. With items of knowledge such as these, sufficient to land men on the Moon, we have made our first step toward the theory of general relativity.

NEW IDEAS FOR OLD

Old Ideas

Newtonian space and time were public property, which all observers shared in common. Its intervals of space and intervals of time separating events were absolute. They were the same for everybody. One person in an apple orchard would see an apple fall from a tree and take 1 second to drop 5 meters. Another person in motion relative to the tree also would see it drop 5 meters in 1 second, no matter how fast that person moved. Now things have changed. The old Newtonian universe, with its ideas on the fixity of intervals of space and time, is no longer the universe in which we live.

Space-and-time diagrams, displaying events and world lines, were used in the Middle Ages, and there is nothing particularly frightening or difficult about them. Until the beginning of this century they were a convenient graphical way of representing things in motion. Then came the theory of special relativity, and diagrams of this kind acquired a new physical meaning.

New ideas

The theory of special relativity emerged toward the end of the nineteenth century and was brought into final form in 1905 by the genius of Albert Einstein. It has withstood countless tests and is now in everyday use by physicists. Yet even nowadays, when we pause to reflect, the theory is as astonishing as when it first emerged.

THE UNIVERSE IN A NUTSHELL

Reflecting walls

We look out in space and back in time and the things seen at large distances are similar to things that existed in this part of the universe long ago. The scenery billions of light years away, as we see it, is the same as the scenery here billions of years ago. With a time machine that could travel back into the past we would have less need of large telescopes that strain to reach the limits of the observable universe.

This argument prompts the following thought. Things are very much the same everywhere at the same time, why not then confine our attention to a single region, concentrate on its history and ignore the rest of the universe? The history of what happens in this single region is the same as the history of what happens everywhere.

But this argument has an apparent drawback. Any chosen sample region is influenced by other regions near and far, how then can we afford to ignore the affect of these other regions? Light, for instance, travels great distances and influences what happens in the sample region. If we are to pay undivided attention to a single region, ignoring all other regions, we must in some way allow for their influence.

THE GREAT RIDDLE

An inferno of stars

There is a simple and important experiment in cosmology that almost everybody can perform. It consists of gazing at the night sky and noting its state of darkness. When we ask, why is the sky dark at night? (Figure 24.1) the natural response is the Sun is shining on the other side of the Earth and starlight is weaker than sunlight. It takes an unusual mind to realize that the relative weakness of starlight is of cosmological significance, and such a person was the astronomer Johannes Kepler, imperial mathematician to the emperor of the Holy Roman Empire.

In a forest (Figure 24.2), a line of sight in any horizontal direction must eventually intercept a tree trunk, and the distant view consists of a background of trees. Similarly, on looking away from Earth at night, we see a “forest” of stars (Figure 24.3). If the stars stretch away endlessly, a line of sight must eventually intercept the surface of a distant star. The distant view of the universe should consist of a continuous background of bright stars with no separating dark gaps.

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.