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Chapter 1


I. The Study of Space and Time

Our aim in this book is to trace the evolution of the concepts of physical space and time in Western thought from the Greeks to the contemporary developments in relativity theory.

We begin with some remarks about the relation between the concepts of space and time as they appear in modern physics and space and time as they are conceived in everyday life. Space and time, because they are so pervasive and so intangible, are hard to come to grips with. Our common experience is filled with objects in motion. That classical physics is the study of objects in motion and the forces that act upon them is easy to grasp. Of course, a moving object is just one which moves through space in a certain amount of time, so it should not be surprising that space and time are such fundamental physical concepts. What is not so obvious is that space and time, abstracted from any particular motions, might be objects which could be studied in their own right.

At a more mundane level, our everyday experience of space and time is focused on quite specific questions, such as

We resolve such issues quite well by focusing on public time and space markers which are independent of our psychological measures of time and distance. We synchronize our watches in the morning to be able to meet at noon for lunch. Modern man is extremely time conscious. We no longer wear "watches" but rather, "chronometers" of extreme sophistication and precision. Why we, in the West at least, are so obsessed with time is an interesting psycho-socio-political question. We confidently expect that our friend, if (s)he is reliable, will show up on time at the appointed place, and after engaging in our business, we can arrange to meet again somewhere else at a later time. Even if our private means of keeping time or keeping track of where we are breaks down, a phone call will establish the local time for us, and checking street markers or a map will tell us where we are. The system gets a little more complicated if we travel any distance. Then we have to make corrections for local time differences between distant places, but again the time-zone system provides a public means for us to do so.

Even so, our ordinary intuitions of space and time are perhaps best characterized as implying a "container" view of space and time. Space is like a container within which objects move and time is some thing through which objects endure. Were we to try to formalize these everyday intuitions of space and time, we might be led to the plausible view that space and time function as a back-ground framework within which the actions of everyday life occur. A key implicit, although often unacknowledged, feature of this framework is that it is "decoupled" from the activity of the objects for whose motion it serves as a frame of reference. That is, the motion of bodies does not affect the structure of space and time on this view.

This conception of space and time, which is the implicit foundation of the classical physics of Isaac Newton, while thoroughly adequate for everyday life in the 1980's, is not adequate to serve as the foundation of modern physical science. One of the major revolutions of twentieth century science was the discovery that the container view of space and time, while plausible, was incorrect. The Special Theory of Relativity (1905) and the General Theory of Relativity (1915), as developed by Albert Einstein and others, has shown that this picture is incorrect in at least two fundamental ways.

First, space and time themselves are coupled. In our everyday experiences and in the physical world as seen in the light of Newton's physics, space and time are pervasive but distinct features of the physical world. They are related to each other, through the phenomenon of motion, but they do not interact with one another. Of course, measurements of time involve spatial measurements, for example, a pendulum clock "measures" time by keeping track of the number of swings [through space] of the pendulum. Spatial measurements also involve time measurements, although usually only implicitly. For example, when one measures the length of an object, one must either know that the object has not changed its size over time or one must perform all the measurements simultaneously.

But, this is not what we mean by saying that space and time are coupled. One of the implications of the special theory of relativity, first recognized by Herman Minkowski in 1908, was that space and time were not distinct but were (or could be viewed as) two aspects of one interconnected framework that Minkowski called "spacetime." Another implication is that spatiotemporal measurements by an observer are a function of the stage of motion of the observer with respect to what is being measured. If two different observers are in different relative states of motion with respect to something being measured, then their respective measurements will not agree. A startling implication of the Special Theory of Relativity is that there is no "natural" way to say that one of them is right and the other wrong: in effect, both are right.

As an illustration, consider two twins, Jack and Jill, each with identical synchronized chronometers. First, let us suppose that, being somewhat lazy, they do not move for the rest of their lives. Assuming that their watches are perfect timekeepers, and ignoring a small but real effect which occurs whenever they move their arms (to check that their watches are, indeed, keeping perfect time), their watches will remain synchronized forever (assuming that their immediate environment does not change too radically). Even in this somewhat limited situation, we notice a deviation from the classical picture. We had to add qualifiers concerning arm motions and environmental changes to achieve constancy of synchronization.

No such qualifiers are needed in the classical picture. Were the classical picture true and were the watches indeed perfect timekeepers, then once synchronized they would have remained so forever regardless of arm motions and other changes in the environment.

Now suppose that one twin is more adventuresome than the other and decides to move about. Periodically, she returns to check on her more lackadaisical twin. Each time they meet, they check their watches. Whenever Jill moves with respect to Jack they notice (depending on the accuracy of their watches) that their watches are no longer synchronized.

The degree of lag is a function of the relative velocity of Jill with respect to Jack. This effect occurs with all timekeepers, not only watches. When Jack and Jill are moving with respect to one another, they age at different rates. Einstein showed that the stay-at-home twin would age more than the traveling twin during each trip.

Funny things happen to spatial measures as well. When Jack and Jill compare notes on how far Jill traveled each trip, they find that their measurements do not agree, even when they use identical instruments and techniques to make the measurements.

For example, on one trip let us assume that Jill traveled, more or less in a straight line, from Jack to Pluto. Jack measures the distance from himself to Pluto to be some distance, say d (ignoring complications due to the relative motion of Pluto with respect to Jack). When Jill is sitting relatively at rest near Jack, she makes a similar measurement and comes up with the same figure. While she is traveling, however, she makes another measurement and discovers that the distance from Jack to Pluto is some measure d', less than the distance d.

The special theory of relativity predicts, and experiment confirms, that space and time measurements are influenced by the state of motion of the observer with respect to what is being measured. This is in sharp contrast to the predictions of Newtonian physics and to our everyday experience. We do not normally notice these effects because they become appreciable only when the relative velocity between observer and observed is some appreciable fraction of the speed of light. Such high velocities are outside the range of our everyday experience.

The Special Theory of Relativity is "special" in that it ignores the effects of gravitation. Since every object in the universe is gravitationally attracted to every other, this might seem to be a severe limitation. In practice, however, one does not get into trouble unless one is making measurements in the vicinity of very massive objects like stars or "black holes." The General Theory of Relativity which takes gravitational effects into consideration, predicts that space and time measurements are influenced by the distribution of mass throughout the universe and the presence or absence of very massive objects in the immediate neighborhood of the measurements being made. Clocks near more massive objects tick more slowly than identical clocks near less massive objects, other things being equal.

Similar remarks hold for spatial measures. Measuring rods near more massive objects are longer than identical rods near less massive objects. (Note that to say that the clocks and rods are identical is to say that when they are situated near each other--ideally, when they are superimposed upon one another--then the clocks tick at the same rate and the rods are equally long). Again, the General Theory of Relativity predicts and experiment confirms that the spacetime background is "coupled" with the masses and their motions in spacetime. The advent of the theories of relativity thus marks two significant departures from the "container" view of space and time. First, the Special Theory suggests that space and time are not independent structures but are coupled with each other to form a unitary structure, spacetime. Second, the General Theory suggests that spacetime is itself coupled with the objects and interactions which, on the container view existed and took place "in" space-time. (The implications of these changes in perspective are discussed in detail in chapters 14-15).

These results seem strange and counterintuitive. But, what makes them so is that they conflict with our ordinary intuitions of physical space and time. Our ordinary intuitions seem so obvious that one might think that they are somehow "natural" ways of perceiving the world. Historical examination reveals, however, that these intuitions, although characteristic of Newton's 17th century physics, are not universal.

Before Newton, there was much dispute about how to characterize space and time, and about the role of space and time in physical theories. How did the 17th century picture of space and time come into being? How was it subsequently modified to produce the picture which underlies current r which determine the shape of this book.

We begin in earnest (in chapter 2) with the pre-Socratics of ancient Greece, because with them one sees the beginnings of what developed into the Western scientific tradition. However, the origins of speculations about space and time are to be found even earlier among the mythmaking peoples of the ancient Near East during the period from 1500 B.C. to 600 B.C. It is instructive to examine their views, however briefly, if only to make clear the radical effect that the (very different) Greek way of thinking had on the subsequent development of Western thought. We hardly recognize the mythopoeic views as serious speculations at all; yet the Greek views, however outlandish they may appear, at least seem, for the most part, to be moving in the right direction. While rejecting them as wrong or incomplete, we can still recognize them as distant ancestors of our own contemporary views about the nature of space and time.

II. Mythopoeic Views of Space and Time

The origins of speculation about the nature of space and time can be found in the traditions originally developed by the bronze-age cultures, i.e., cultures existing during the period ranging from 3800 B.C.-1500 B.C.. Vestiges of these views can still be found in the work of writers such as Homer and Hesiod (1100 B.C.-600 B.C.) as well as in some of the earlier pre-Socratics.

This is not the place to deal with myths in any great detail. We focus on some of the themes and features of mythic thought as they relate to space and time.

1. Mythological thinking tends to be poetic rather than analytical. This is exemplified in the tendency of myths to portray abstract ideas such as love, fate, justice and time in terms of concrete images. For example, one often finds love portrayed as a goddess; fate is represented, at least in early Greek thinking, as the Furies; in Homer, a transition figure from mythological to scientific ways of thinking, one finds in the Iliad Book I, for example, Rumor represented as a messenger from Zeus sent to spread dissension among the troops setting siege to Troy by whispering in one soldier's ear after another. Time itself is often depicted (in late mythopoeic thinking) as a self-generating god which yields offspring from his own seed (See West, 1971 for details).

This is however, a peculiar Middle-Eastern tradition. M.L. West writes:

Time is not personified by other peoples. Personification of months, seasons, etc., is fairly wide spread, but time in the abstract appears as a god only in the regions we are considering. In Greece and perhaps in India, it appears in the sixth century B.C. In Iran and at Sidon, it is established by the fourth century at the latest, and our evidence is so incomplete that there is no difficulty in the idea of its being a couple of centuries older. It appears in all four places in a remarkably similar form. The uniformity is the more remarkable in view of the fact that the progenitor Time appears combined with quite different natural traditions. (West, 1971, 35; cf. Thompson, 1966)

2. Mythological thinking has an emotional dimension which is lacking in later natural philosophy. The pre-Greek thinkers did not systematically separate the cognitive (information content, knowledge) function of language from the emotional function of language. In general, myths about natural processes differ from scientific theories insofar as the myths are often constructed not only to convey information but also to inculcate a certain attitude on the part of those hearing the story.

3. Mythological thinking tends to be ritualistic. Man is conceived not as a spectator, theorizing about nature (this is a typically Greek idea), but as a participant in nature. Thus, in order to grow crops, for example, it was thought not enough to plant seeds at the right time, certain rituals had to be followed as well. These rituals were not thought of as merely symbolic acts, but rather as acts whose performance was integral to the fulfillment of what ever was being invoked. The planting rituals were thought of as essential elements in setting in motion the natural forces which would insure a good harvest. Through participation in the rituals, men exerted control by being

like the gods (natural forces): in effect, men became gods. In becoming gods, they became efficacious in the fulfillment of whatever it was that the ritual was trying to achieve. This is a very different conception of the relationship between man and nature than that which was advanced by the Greeks and which is the foundation of our modern Western scientific world view. The key difference is that men do not participate in nature: their actions are neither necessary nor sufficient to change the laws of nature or to insure that nature follows its natural course. Classical physics is very much in the Greek vein in this respect. However, contemporary quantum theory reraises the question of the relationship between observer and observed (see Chapter 16).

4. Mythological thinking is characterized by a sense of immediacy. Thus, in myths, there is, in general, no distinction between the symbolic and the real, between subject and object, or between appearance and reality (See chapter 2 for a discussion of these distinctions in Greek thought). With respect to rituals, for example, similarity and identity are taken to be the same. The human actors in rituals are not like the forces of nature, they become the forces of nature.

A different kind of example of this can be found in cultures in which killing someone in a dream, for example, is the same as actually killing someone. There is no distinction drawn between what apparently is the case and what is really the case, or between what is symbolic and what is real.

This pattern of thinking is also exemplified in thinking about space and time. We tend to think of space geometrically, as a continuum each of whose points can be represented in terms of a global coordinate system. Such a perspective is alien to mythical thinking. For mythopoeic man, space was a set of concrete, particular localities which were distinguished not by coordinate positions but by emotional feel or significance. Similarity of emotional feel or significance constitutes identity of spatial location. For example, in the Egyptian creation myths, we find the story of a primeval hill which emerges from the flood and becomes the dry earth. All temples had a place which was this hillock, no matter where (in our sense) the temple was. All such sacred places were, for the Egyptians, the same place. (Such a conception is hopeless for practical everyday enterprises, for example, where to ship this load of grain. But nothing is known, as far as we know, about the views of space (or time) of the ordinary Egyptians.) An important moral which emerges from this example is that what one considers as the same place or spatial position is not something which is given to us naturally, but is something which reflects basic cultural conventions.

A similar story can be given for the mythological concept of time. Mythological people tend to think of time in terms of qualitative characteristics, i.e., in terms of concrete events. Each harvest, for example, was the same, because it represented an important function which was periodically repeated. Similarly, each planting was the same as those which, in our sense at least, had come before. This is connected with the ritualistic emphasis of mythological thinking: everything must be done exactly according to ritual or else there is no crop.

Another characteristic doctrine of mythological thought is that of cyclical time. This view is known as the doctrine of Eternal Return. The basic idea is that every event is repeated an infinite number of times in a never ending cycle. Each re-occurrence of an event is identified with all the other re-occurrences of that same event in the cycle (See Newton-Smith, 1980, chapter III for some contemporary speculation about the intelligibility of this view).

In classical Greece, the doctrine takes the form of postulating what was called a Great Year, a period of 36,000 years (according to one tradition) which, once endured, was repeated over and over again. Most ancient views of time were cyclical. The exception seems to have been the Hebraic doctrine of linear time. From the Hebrews comes the idea of progress, and the idea of one unique creation, which leads to the idea of a Messiah who will come but once.

Mircea Eliade, in Cosmos and History, gives an example, the Babylonian new year celebration (Akitu), of how the doctrine works. Akitu occupies twelve days and is, in effect a re-creation of the creation of the world. The Babylonian creation myth is called the Enuma Elish, and represents the creation of the world as a battle between two gods, Marduk and Tiamat. According to the mythological frame of mind, the participants in the new year celebration are actually recreating the original event at the moment the celebration is going on. It is, in essence, a festival of the fates, a recreation of the twelve months of the year. In the ceremony, the original state of chaos is recreated. The social order is upset. Slaves become masters. A carnival king is crowned. At the end of the celebration, the normal order is restored. Thus, the creation of the world (and of time) is reactualized each year.

Despite the prevalence of cyclical views of time, the Egyptians and the Babylonians were sensitive to the problem of keeping track of time. This is probably because certain yearly tasks were a matter of life and death to these people, e.g., when to plant and when to harvest the crops. Thus, we find the Egyptians and the Babylonians in antiquity, and the Mayans somewhat later in the new world, developing sophisticated calendars. The Mayan calendar is even more accurate than the Gregorian calendar which was instituted in 1582 and still in general use today. The Gregorian calendar is 3 days long in 10,000 years; The Mayan calendar is 2 days short in 10,000 years. (See Thompson, 1966, for information about the Mayans; Neugebauer, 1957, for information about the Egyptian and the Babylonian calendars). These remarks must be tempered by the observation that although the Egyptians, Babylonians and Mayans did develop sophisticated calendars, they did not see time as playing an essential role in the understanding of nature; rather, they saw time as having a purely religious or ritualistic significance.

5. Mythological thinking tends to be uncritical. By this one does not necessarily mean to suggest that they are irrational or illogical: myths tend to be uncritical in that mythopoeic thinkers rarely strive to make conflicting myths consistent with one another. Thus, in Egyptian mythology, for example, one finds two different creation stories standing side by side, each of which is inconsistent with the other. Instead of seeing a conflict that needed to be resolved, the Egyptians saw this as evidence of the diversity and wondrousness of nature. In Mesopotamian mythology, one finds examples of similar patterns of thought. Thus, some of the early myths deal with what we might consider potential conflicts, for example, how the same god can have two different natures. They account for this by creating stories which detail the dramatic events by means of which the two natures came to be in the same individual (see Frankfurt et. al., 1946 for details).

6. In mythological thinking, nature tends to be personalized. What we would consider to be natural objects or natural phenomena are conceived of as personalities with wills of their own. Time, as we have seen, was often personalized by Near Eastern traditions and particular parts of time like days or months or years are personalized by many traditions. Coming to grips with nature, for mythological thinkers, meant coming to grips with willful beings. The portrayal of events in nature are often seen as dramatic conflicts between these willful beings. These conflicts tend to be violent in Mesopotamian myths, and calm and ordered in Egyptian myths.

The important point for our purposes is that neither tradition developed a concept of nature as a unified cosmos, operating in accord with general laws. For example, causality was conceived in the mythopoeic tradition as purposeful,personal, and particular. What we would today consider as events with one constant cause (perhaps complex), e.g., two floods or two storms, is conceived in the mythopoeic tradition as due to the different whims of (perhaps) different gods. The modern view, which sees floods and storms, e.g., as the results of natural forces which can be understood in terms of universal laws, first began to be developed by the Greeks after 500 B.C. by the Greeks after 500 B.C..

This brief introduction to mythopoeic patterns of thinking is designed to establish the existence of a tradition, which, although the source of our own, is in sharp contrast to one we are acquainted with. With respect to space and time, what we find, for the most part, are attempts to characterize space and time in terms of concrete, particularistic and qualitative features of the environment. In contrast to our modern quantitative and geometrical approach, the mythopoeic views focus on the emotional and religious significance of places and times. The distance from these views to modern relativity theory is vast indeed.

In this book, we trace the conceptual evolution which leads from the one to the other.

III. The Organization of This Book.

In our introductory remarks, we have argued that the concepts of physical space and time which are characteristic of an age are a function not only of the "facts" but also of cultural considerations. Different eras raise and try to answer different questions. A historical and philosophical analysis which attempts to string together the contributions of various authors from various periods into a coherent picture of the development of a concept runs the risk of distorting the past in the light of the present. The result is a "Whiggish" interpretation of the history of science, which sees earlier thinkers as precursors to later ones. On the other hand, to treat each era sui generis threatens to produce an account which fails to do justice to the continuity of development which does exist. Our work tries to steer between these two extremes. We do this through the use of two techniques: (1) the development of a set of categories which recur throughout the historical development of the concepts of space and time. These allow us to construct comparative profiles of the prevalent views of space and time from different historical stages; (2) the exploitation of the event point of view which is characteristic of some presentations of relativity theory to "reconstruct" the views of Aristotle, Galilei, and Newton; this facilitates their comparison with current theories in terms of a common framework.

The first approach focuses on the theories as they were historically developed and attempts to deal with them in the light of their own times and concerns. We cannot see Aristotle on Newton as somehow paving the way for relativity theory from this point of view. The second approach focuses on the present and, looking backwards, tries to see to what extent the earlier theories were anticipations of or provided the basis for current theories.

(I) A number of themes reappear in the succession of views about space and time. These themes serve as a framework in terms of which we can compare and contrast the different views.

Since we are dealing with the evolution of ideas, the very categorical properties may vary in significance from period to period. Nevertheless, we think that there is sufficient continuity to make this approach informative. We focus on 8 basic categorical properties.

(1) Homogeneity: Space is homogeneous just in case two positions in space are not different simply in virtue of their difference in position. Time is homogeneous just in case two moments in time are not different simply in virtue of the fact that they are different moments. Homogeneity comes down to qualitative indistinguishability. Suppose we lived in a world where places had characteristic colors. Then we could distinguish places on the basis of their color, and space would be qualitatively heterogeneous.

Suppose, in addition, that different times were associated with different color intensities, e.g., that the color associated with a place were lighter in the morning than in the afternoon, continuously varying throughout the day from a peak darkness to a peak lightness. Then we could distinguish different moments in time by their color intensity, and time would be qualitatively heterogeneous. All of the views we discuss take time to be homogeneous, but some take space to be heterogeneous and some take space to be homogeneous.

(2) Finitude: The issue here is whether space and time are infinite or finite. With respect to space, Plato, and Aristotle hold that space is finite. Einstein's General Theory of Relativity is compatible with the finitude of space, but it is also compatible with space being infinite. For both Newton and Leibniz, space is infinite. Einstein's Special Theory of Relativity holds space to be infinite as well. The question of the infinitude of time is tied up with the question of the creation of the world. Some who think the universe was created a finite time ago, think that time was created in that act as well; others argue that even if the universe was created a finite time ago, time itself is uncreated, and hence, that the past is infinite is extent.

(3) Continuity: Continuity is a concept whose meaning has changed significantly over the course of history. For the Greeks, continuity meant infinite divisibility or what modern mathematicians call "denseness." The Greek continuum was not pointlike, but rather consisted of intervals which could be divided indefinitely. For modern mathematicians, a continuum is composed of points. An example of a l-dimensional continuum is something which has the structure of the real number line. This structure is not only dense (with elements corresponding to the integers and rational fractions), but it also contains elements which correspond to "irrational" numbers. An example of a 3-dimensional continuum is the ordinary 3-dimensional space of solid Euclidean geometry. The modern concept of continuity was first formalized in the l9th century. For pre-19th century thinkers, when we say that they held space (time) to be continuous, we mean they took it to be dense or infinitely divisible. The alternative is that space (time) is discrete. Most major pre-19th century thinkers held space and time to be continuous. For 20th century thinkers, we say that space (time) is continuous just in case it has the structure (locally, at least) of 3-dimensional Euclidean space (of the real line). For these 20th century thinkers, three alternatives exist:

(a) space (time) is continuous in the modern sense;

(b) space (time) is dense, but not continuous in the modern sense;

(c) space (time) is discrete.

Those who are concerned with the empirical verifiability of spatio-temporal facts may opt for (b) rather than (a), on the grounds that all actual measurements involve rational but not real numbers. Those concerned with the possible implications of quantum limitations on measurement might opt for (c) rather than for (a) or (b) on the grounds that the quantum theory entails the ultimate discreteness of spatial and temporal intervals. The possible implications of quantum considerations on the structure of space and time are just beginning to be explored (see chapter 16).

(4) Isotropy: Space is isotropic if there are no preferred directions, anisotropic if there are. When Aristotle says "not any chance direction is up," he commits himself to the anisotropy of space.

Time, as experienced, seems to have a built in anisotropy. Time, insofar as it appears as a variable in the mathematical formulation of the laws of physics, seems to be isotropic, that is, the laws of physics are the same whether the time variable is given a plus sign or a minus sign. The source of the anisotropy of experienced time is a matter of some controversy (see Grunbaum (1967), Reichenbach (1956), Mehlberg (1979), and Gale (1967) for further discussion of these points). All the theories we consider in this book take time to be anisotropic.

(5) Object dependence: Space is said to be object dependent if the existence of space is dependent upon the existence of objects. Space is object independent if it is held to exist independently of the existence of objects. The basic question here is: Can space be absolutely empty? If the answer is yes, then space is object independent, if no, then space is object dependent. Plato, Newton and Einstein (in both the Special and the General Theory) hold that space is object independent. Aristotle and Leibniz hold space to be object dependent.

Time is said to be object dependent if the existence of time is dependent on the existence of objects in motion, i.e., processes; object independent if it is not. The basic question here is: Can absolutely empty times exist? If the answer is yes, then time is object independent, if no, then time is object dependent. Newton and Einstein hold time to be object independent: Plato, Aristotle and Leibniz hold time to be object dependent.

A related issue is whether space is taken to be "absolute" or "relational." These terms can signify a number of different distinctions (see Hinckfuss (1975) and Newton-Smith (1980) for a discussion of some of them). In this book, we will usually take the term "absolute" to signify that space (or time) is a structure which can exist on its own, independently of the presence or absence of object or processes. We take the term "relational" to signify that space (or time) is a structure which exists only insofar as something else exists (in the case of space, this something else is usually a collection of objects of some sort; in the case of time, a group of processes). A simple example of what we have in mind is afforded by the term "husband." Suppose John is the husband of Mary. Being a husband is a relational property that John has in virtue of some relation he bears to Mary. Were Mary not to exist or were the relationship to be severed, then John would cease to be a husband but he himself would not cease to exist, we might say that being a husband is dependent on John's being a man (and other things as well). Similarly, those who hold a relational theory of space or time are taking space and time to be, in some sense analogous to the case we have just considered, dependent on objects or processes. If no men or women existed, then no husbands or wives would exist either (but not vice verse; that is what makes only the one dependent on the other). Just so, for a relationalist, if no objects (processes) existed then space (time) would not exist either. We will return to these questions in greater detail in chapters 7 and 8.

(6) Mind dependence: Space is said to be mind dependent if the existence of space is dependent on the existence of conscious minds which are aware of it. None of the writers considered in this book hold this view. One candidate for holding such a view is Immanual Kant. Time is said to be mind dependent if the existence of time is dependent on the existence of conscious minds which are aware of it. This view is held by many Idealist philosophers. Of the thinkers

discussed in this book only Augustine, and perhaps Plotinus are clearly committed to this position, although an ambiguous remark by Aristotle has led some to attribute this position to him (For Aristotle, see the discussion in chapter 5 below; for Augustine and Plotinus, who hold a similar view, see chapter 6.) To the extent that Quantum Mechanics calls into question the relation between observer and observed, the issue of the possible mind dependence of space and time is, once again, a live issue.

(7) Mutability: Space (time) is said to be mutable insofar as it changes over time (evolves) or changes as a function of who makes the measurements. Space and time have both an ordinal and a metrical structure. The ordinal structure relates to the relative ordering of positions of space or moments of time. The metrical structure deals with measurements of spatial or temporal intervals. Until the advent of the theories of relativity, the general consensus was that the physical structure of space and time was constant for all observers and did not evolve over time. The Special Theory of Relativity entails, however, that the temporal order of events, the duration of temporal intervals, and the extent of spatial intervals are a function of the state of motion of the observer with respect to the events being observed. The geometrical structure of spacetime, however. is the same for each observer and does not change over time. The General Theory of Relativity allows, however, that, at a given time, observers at different locations find the local geometric structure of spacetime to be different, and that, over time, an observer who takes himself to be at rest, may find that the local geometric structure of spacetime changes.

The theories of relativity, thus, have opened up a whole new range of possibilities with respect to our understanding of space and time (see Chapters 11-16 for further details).

(8) Causal Activity: Space or time is said to be causally active if it interacts with the object and processes which are contained within it. On some readings of Aristotle, he is committed to the causal activity of space and time. Similarly for Plato with respect to space. Newton and Leibniz both hold space and time to be causally inert as does Einstein in the Special Theory of Relativity. Einstein, in the General Theory of Relativity, in virtue of the "coupling" effect discussed above, is committed to the causal activity of space-time.

These eight characteristics serve as a framework by which we can compare and contrast the alternative theories of space and time as put forward by Plato, Aristotle, Newton, Leibniz and Einstein. For some, the textual evidence is too sparse to allow a complete profile, e.g., for Plato. For others, we must make inferences, based on the available evidence, as to what an author might have said, had he considered the issue at hand.

(II) Halfway through the book, preparatory to a discussion of the theories of relativity, we introduce a second approach which takes "events" as the basic elements of the universe and construes space and time as structures which are imposed on the set of events. Such an approach has developed in the 20th century (although there are hints of it in Leibniz) in conjunction with the development of the theories of relativity. Using it, we reconstruct (in chapter 9) the historical views of Aristotle, Galilei, and Newton in such a way that the evolution of spacetime theories from Aristotle to Einstein can be viewed in terms of the imposition and relaxation of various structures on the set of events. The conceptual similarities and differences between contemporary physical theories of spacetime and the "essence" (from the modern point of view) of the views of Aristotle, Galilei, Newton and the others stand out quite clearly given this approach.

We then go on to use the event approach to discuss Einstein's Theories of Relativity. As we have mentioned earlier, until the 20th century, space and time were conceived of as distinct non-interacting, although all pervasive structures. Einstein's Special Theory of Relativity paved the way for a consideration of a new structure, spacetime, which appears to be more fundamental than either space or time by itself. Spacetime, in turn, can be (locally, at least) construed as a causal structure on the set of events. The discussion of the Special and General Theories of Relativity turns out to be elegant from the event point of view.

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