Space and Time

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Space and Time

Archeological excavations of ancient temples and tombs have shown that solar seasonal movements were known in neolithic times. Such knowledge depends on a recognition of former events as being in the past and an expectation of events to come as being in the future and, therefore, presupposes awareness of time. Prehistoric peoples must also have appreciated time sequence in the rhythm of the seasons, in plant growth and decay, and in the cycle of birth, life, and death. These cycles of heavenly and earthly events would have suggested that time itself perpetually recurred; to prehistoric peoples, a sense of temporal rhythm was more important than temporal sequence.

Time and religions

It has been suggested that religion originated from human awareness of the inevitable cycle of events. Rites and sacrifices were performed on specific occasions and these were often associated with particular phases of the moon or solar solstices. Other heavenly bodies, as well as the sun and moon, were often regarded as gods. The gods had superhuman powers, but they were thought to have desires and emotions analogous to those of humans, so that they were amenable to entreaty and flattery through propitiation ceremonies. Those who conducted these ceremonies were accorded high status in society: They were priests and often priest-kings. Priests observed the rhythms and movements of heavenly bodies and could predict their positions in the heavens. Babylonian priests, who could predict eclipses of both the sun and the moon, kept continuous records by the first millennium b.c.e.

A theory of time. For ancient civilizations, astronomical knowledge was practical rather than theoretical. The ancient Greeks were the first to develop a more abstract concept of time and its relation to space. Plato (c. 427–347 b.c.e.) and Aristotle (348–322 b.c.e.) had the most profound influence on later Western religious thought. Plato held that the creation of the cosmos was the work of a divine craftsman, the demiurge. The demiurge was not to be conceived as a god in the sense of a powerful spirit, but to be regarded as a principle of reason, who imposed order on the formless and chaotic raw materials of the world. Plato's ideal cosmos was a nonmaterial mathematical model that was immobile, immaterial, eternal, and timeless. But the created material universe was subject to change, a change manifested in the revolutions of the heavenly bodies that Plato identified as time. Therefore, at the creation, the demiurge had produced time as well as space.

Both Plato and Aristotle were influenced by cyclical theories and thought that the circle was a perfect figure because it had no end; it was a symbol of eternity and of a changeless immutable reality. Circular motion, apparent in the revolutions of the heavenly bodies, also displayed this perfection and need have no end. By contrast, motion in a straight line could not continue indefinitely unless the line were of infinite length, and Aristotle did not believe that there could be such a line. Whereas the cyclical theory of events in time ended with Christianity, the almost mystical view of the circle and of perfect, potentially eternal, circular motion permeated and strongly influenced philosophical and religious thought until the seventeenth century.

The Christian concept of time. Plato's postulate of an original chaos from which the demiurge created space and time is unique because he took the material universe to be but a pale reflection of an immaterial, eternal, and changeless reality. The idea of a universe formed from chaos, however, is a feature of many creation myths. It is echoed in-Genesis: "In the beginning God created the heaven and the Earth. And the Earth was without form, and void" (Gen. 1:1–2).

The early Christian saint Augustine of Hippo (354–430 c.e.) agreed with Plato that there could be no time without a created universe and that people were aware of time as the sequence of events in the created world. "I know that if nothing passed, there would be no past time; if nothing were going to happen there would be no future time; and if nothing were, there would be no present time" (p. 261). God was the creator of time, though God was outside time. Addressing God, Augustine wrote "although you are before time, it is not in time that you precede it. If this were so you would not be before all time. It is in eternity, which is supreme over time because it is a neverending present, that you are at once before all past time and after all future time. For what is now the future, once it comes will become the past, whereas you are unchanging, your years can never fail" (p. 263). But Augustine disagreed with Plato's identification of time with the motions of the heavenly bodies. He argued, as had Aristotle, that time measures motion and therefore had to be distinguished from motion. Other Christian philosophers also disagreed with earlier views about the cyclical nature of time. For Christians the crucifixion was a unique event, and time had to be thought of as a unidirectional linear progression from the past, through the present, and on to the future. Though God was aware of past, present, and future in eternity, humans could only proceed forward in time.

Aristotle and the Christian cosmology. After the rediscovery of Aristotle's writings and their evaluation by the Christian saint Thomas Aquinas (1224–1274), Aristotle's cosmology became part of Christian doctrine and also played a major part in philosophical and scientific thought. Aristotle's cosmos was a closed and complicated system of transparent crystalline spheres revolving round the central immobile Earth. In all there were fifty-five such spheres. The moon, the sun, and each of the five planets were embedded in a separate sphere and each was carried round the Earth as its particular sphere rotated in its circular orbit. The fixed stars were all embedded, rather like lights in a ceiling, in an eighth sphere beyond these and beyond that penultimate sphere was the outermost sphere, the sphere of the unmoved mover. Circular motion was perfect and eternal and, for Aristotle, it was the natural motion of the heavens. Aristotle's account was developed further by Claudius Ptolemy (90–168 c.e.), who constructed a table, the Almagest, which provided a basis for predicting the positions of the planets in the sky. It was used in navigation, to foretell eclipses, and to calculate the dates of the equinoxes and the date of Easter.

For medieval Christians, Aristotle's cosmology had a religious significance that went far beyond its role in calculating the date of Easter. They regarded the system of spheres as a heavenly hierarchy. Aristotle's ninth sphere, the sphere of the unmoved mover was, for them, the sphere of God in glory. As well as being incorporated into Christian doctrine, the Aristotelian cosmos played an important role in medieval and renaissance literature. In the Paradise of his Divine Comedy, the Italian poet Dante (1265–1321) described his ascension outward to higher and higher spheres. For though they were all heavenly, the higher (outer) spheres were considered nearer perfection and the abode of God. This cosmos was closed and finite; there might be disturbances and disarray on Earth but above the sphere of the moon the heavens were an ordered hierarchy showing eternal, regular unchanging circular motion, and creating heavenly harmony: the music of the spheres. More than two centuries after Dante, William Shakespeare described this music in The Merchant of Venice:

Look how the floor of heaven
Is thick inlaid with patines of bright gold;
There's not the smallest orb which thou behold'st
But in his motion like an angel sings,
Still quiring to the young-eyed cherubims;
Such harmony is in immortal souls;
But whilst this muddy vesture of decay
Doth grossly close it in, we cannot hear it. (5.1)

A new cosmology

By the early sixteenth century, navigators voyaging to America and around Southern Africa to India and the Spice Islands found the Almagest inadequate; it was also proving unsatisfactory in fixing the date of Easter. Nicolaus Copernicus (1473–1543) was one of several distinguished mathematician astronomers asked to revise and improve on Ptolemy's work. In 1543, the year of his death, Copernicus published his new cosmology placing an immobile sun at the center of the universe and displacing the Earth, which now orbited the sun along with the planets. Copernicus did not think his theory was revolutionary. He regarded it as a modification of the Aristotelian and Ptolemaic cosmos. Copernicus's universe still consisted of concentric crystalline spheres and was closed and finite. However, as a physical account it was incompatible with contemporary (Aristotelian) physics, and it also seemed to flout common sense. In addition there were grave theological objections. Aristotle's cosmology had become part of religious dogma and could not be rejected without firm evidence. Moreover in the early seventeenth century there was an alternative cosmology, that of the Danish astronomer Tycho Brahe (1546–1601), that retained a central immobile Earth and accounted for new observations equally well.

The cosmos of classical physics. In 1543, the crystalline spheres had seemed essential in order to carry the heavenly bodies and to keep them in their orbits. In proposing a Copernican-type cosmos (with a central sun but with no spheres) Galileo Galilei (1564–1642) had to explain how those spheres could be dispensed with. He asserted that all bodies had a natural (inertial) circular motion bestowed by God that would continue indefinitely. This was in accord with the universal belief in the perfection of the circle and of circular motion, a belief that had to be abandoned after Johannes Kepler (1571–1630) showed that the planets revolved in elliptical orbits. But the important change in the cosmology was that the universe, and therefore space, was no longer closed and finite. Copernicus himself had postulated a much larger universe but, for him, it was still closed. After Galileo the universe was seen as potentially infinite. Moreover, since there was no sphere of the moon separating the Earth from the heavenly bodies, the same physical laws that were beginning to be established on Earth also ruled in the heavens. The French philosopher and mathematician René Descartes (1596–1650) was the first to call them the laws of nature. Later he formulated the principle of inertial motion in a straight line. Descartes justified the principle partly by appeal to direct human experience of motion but also by appeal to religious belief. He affirmed that God must be the ultimate cause of all motion and that the amount of motion in the universe must remain constant, an implicit reference to God's perfection and consequent immutability.

Absolute space. Isaac Newton (1642–1737), who developed what is known as classical physics, took the principle of inertial motion in a straight line and, using his laws of force and of gravitational attraction, he was able to confirm Kepler's theory of elliptical orbits. More importantly, Newton established the classical concepts of absolute space and time and distinguished these from relative space and relative time.

If one assumes a homogeneous space extending indefinitely in all directions, then the position of a lone object can not be specified because position has to be related to something, for example another object. Likewise the concept of change of position can have no significance for a lone object. If one assumes just two objects, then if their relative positions change can it be said that only one object moves? If so, which one? Or do both of them move? The answer depends entirely on what one decides to adopt as a point of reference. In everyday experience there are an indefinitely large number of objects in space, and people take reference points that suit their purposes. But is there an absolute reference point? Can space itself provide a reference so that in principle even the position of a lone object could be established? Newton conceived of space itself as having an absolute position, so that any portion of space (as opposed to any body in space) was fixed. For him, space was sensorium-Dei (a sense organ of God) and was a manifestation of God. Thus space was eternal and changeless and, therefore, there were absolute, as opposed to relative, positions in space. But only God could know these; Newton appreciated that human beings could not distinguish the parts of space and so had to be content with the relative positions of objects in space.

Absolute time. There is an analogous problem in relation to the measure of time. If nothing whatever were to change, not only would one be unable to measure time, one would not be aware of time passing; time would stand still. Galileo is said, wrongly as it happens, to have used his pulse to time the swings of the pendulum in the cathedral at Pisa. This would not have been an accurate measure because pulses are not completely regular. But how is this known? By comparing pulse rates with a more regular sequence. The most regular sequence is shown to be the most regular because it consistently correlates all other time intervals: This is the only way regularity can be tested. Like Augustine's concept, the mathematical/scientific concept of time in classical physics was that of a steady stream in which "the present," the flow of events, moved forward at a constant rate. Without events and therefore without any change, people could not be aware of time, it would have no empirical significance.

Is it then legitimate to assume an absolute and perfectly regular flow of time? Newton took the existence of absolute time as a fundamental metaphysical postulate: "Absolute time and mathematical time, of itself and from its own nature, flows equably without relation to anything external" (Koyré, p. 7). Newton appreciated that absolute time had to be distinguished from the time that could be measured; he called the latter "relative time," "apparent time" or "common time," and he realized that there was no way to know how close "sensible measures" were to measuring the absolute flow of time. He based his metaphysical assumption on appeal to God. Like absolute space, absolute time was a manifestation of God.

Relativity and the geometry of space

During the fourth century b.c.e., the Greek mathematician Euclid elucidated the nature of space. His geometry consisted of a system of theorems logically deduced from five axioms. The axioms were held to be self-evident and so constituted a set of indubitable premises. Euclidean geometry specified the properties of Euclidean space and these properties were assumed to be logically certain. This was the space of the Greeks, medieval space, and the space of classical physics. During the nineteenth century two mathematicians, Georg Friedrich Bernhard Riemann (1826–1866) and Hermann Minkowski (1864–1909), suggested two different geometries for two theoretical spaces that could be devised by changing Euclid's fifth axiom. That axiom is: Through a point not on a given line there can be only one line that will not cross the given line. Riemann, and later Minkowski, offered alternatives: There is no line that will not cross the given line, or there are an indefinitely large number of lines that will not cross the given line. The changed axioms defined two different non-Euclidean spaces, but when first formulated they were regarded as nothing more than mathematical speculations that did not apply to the real world.

In the nineteenth century no one questioned the assumption that space was Euclidean space and that measurements of space and measurements of time were independent of the motion of the observer. Parallel lines did not meet, distances remained constant, and clocks ran at a constant rate. It was these assumptions that were to be undermined by Albert Einstein (1879–1955). Einstein's new physics arose from his study of problems relating to the transmission of light and other electromagnetic vibrations. To solve the problems, Einstein had to postulate that the velocity of light was constant in all so-called inertial frames of reference so that it would remain the same for two or more observers moving at different velocities relative to each other. Such a postulate would have been nonsensical in classical physics and entailed a fundamental reassessment of assumptions about time, space, and motion.

In his reassessment. Einstein did not jettison common sense; rather he invited his colleagues to consider fundamental concepts on the basis of a common-sense analysis of the significance of familiar and ordinary terms. Einstein argued that the crucial element in a person's notion of time was that of simultaneity because any judgment made of time and the time of an event must be a judgment of the simultaneity of that event with another event. For example, to say that a train arrives at seven o'clock is equivalent to saying that it arrives when the small clock hand points to seven; the two events are claimed to be simultaneous. Einstein was the first to point out that there had to be a finite time for the light conveying the information about the position of the clock hand to reach a site a finite distance from the clock, and that clocks must be calibrated to allow for this. Calibration is possible if the clock and the observer are in the same frame of reference. But because light travels at the same velocity for observers in different frames of reference (e.g., traveling in cars toward the station) calibration is not possible. It follows that there can be no agreement about simultaneity and therefore no agreement about the time of the train. Of course because light travels millions of times faster than any car, the disagreement would not be noticed, but a discrepancy can be detected in careful experiments. Einstein was able to show that as the velocity of a frame of reference increased relative to an observer outside the frame, the bodies within the moving frame would appear to contract. Observers in the moving system would see no change and to them the objects in the "stationary" frame of reference would seem to shrivel. Thus time and space could not be regarded as absolutes: They were observation-frame-dependent. A further consequence of Einstein's new physics was that space and time themselves were distorted by mass and were to be described by the geometry of Riemann or Minkowski rather than that of Euclid.

Minkowski had been Einstein's teacher and he proposed a way to establish independence of the frame of reference. In a lecture "Space and Time," given in 1908, Minkowski suggested that events should be identified and described by their positions in space-time. This would allow objective measurements but it would entail making space and time interdependent because the "time axis" would be as necessary for a description as the three space axes. Unfortunately, people find it very difficult to envisage events in four (as opposed to three) dimensions, and Minkowski's suggestion removes physical accounts of objects and events from common-sense intuitions. Space-time is a concept that can be regarded as providing a different metaphysical framework that could replace the two Newtonian concepts of absolute space and absolute time. However, within any given frame of reference, one can use classical physics and it can apply in a different frame with velocities that are small compared to the velocity of light. This is the case in most situations, and why classical physical laws still hold. But these laws are approximation, and one must concede that classical (and indeed intuitive) concepts of time and space are flawed.

Metaphysics and religious belief

Although this account has been primarily concerned with Christianity, the nature of the religious beliefs of Copernicus, Galileo, Kepler, Descartes, Newton, and many others was grounded in a mystical acceptance of a higher power rather than in Christian doctrine. Underlying their heterodox and even heretical opinions was the faith that human reason was a gift of God and it was adequate to the task of explaining events in the world.

By the end of the twentieth century, science rarely made direct appeal to religious faith. The theoretical physicist Stephen Hawking (b. 1942) allows for the need to appeal to some power transcending human capacities to account for creation. In a chapter significantly called "The Origin and Fate of the Universe," in his popular book A Brief History of Time (1988), Hawking reveals a Cartesian concept of laws of nature, and though, unlike Descartes, he does not postulate that they are divine decrees, he does entertain the notion. Hawking argues that events cannot be random and, whether they be divine or no, there must be laws of nature. He appears reasonably confident that human beings will arrive at a complete explanation (a unified theory) "within the lifetime of some of us" (p. 156). But his confidence may be misplaced, not only because evidence from the past gives greater grounds for pessimism than Hawking is prepared to acknowledge, but because it remains an open question as to whether the laws of nature are not human constructions. What Hawking does clearly reveal is the necessity for metaphysical and possibly religious beliefs. His expositions show that the basic metaphysical assumptions of Aristotle, the medieval scholars, the founders of classical physics, and the founders of modern physics are still in play. The assumption is that there is an objective order and that humanity is capable of discovering that order.

See also Aristotle; Augustine; Einstein, Albert; Galileo Galilei; Geometry: Philosophical Aspects; Geometry, Modern: Theological Aspects; Newton, Isaac; Plato; Relativity, General Theory of; Thomas Aquinas