THE PROBLEMS OF SPACE AND TIME

INTRODUCTION.
Before the theory of relativity, space and time were treated as separate concepts.
THE PROBLEM OF SPACE.
1. STATEMENT OF THE PROBLEM: What is space?
2. ANALYSIS OF THE PROBLEM:
  Historical analysis:
  1. In ancient Greek philosophy of the fifth century, B.C., there are two different concepts of space: the plenum and the void. Democritus (460-370 B.C.) held that space is the void in which atoms move. On the other hand, the Eleatic philosophers, Parmenides (c.515-c.450 B.C.) and Melissus of Samos, held that there could not be empty space or void, since, as Parmenides' follower Zeno of Elea (490-430 B.C.) argued, the concept is contradictory; empty space is Non-Being. Parmenides contrasted "Non-Being" [to me on] with the eternal and indestructible "Full Being" [pampleres on]. Full Being exists and Non-Being dose not exist; Non-Being is simply nothingness. Being is ungenerated and indestructible. It cannot come into being out of what does not exist. Neither can it cease to be, since being is not non-being. Hence being is eternal and unchanging. Change is impossible; for if anything changes, it ceases to be what it is and becomes what it is not; and since being cannot cease to be and non-being does not exist, change is impossible. And also movement is impossible; for if anything moves, it must occupy empty space where it was not; and since empty space is non-being and does not exist, movement is not possible. And there can be only one being. For if there were more than one being, these beings would have to be separated by empty space; since empty space is non-being and does not exist, they cannot be separated and thus they must occupy the same space; thus the many are one and being is one. Finally being is homogeneous and simple, not having parts; for if it has parts, then it would be many; but since being is one, it has no parts and thus is it simple and homogeneous. From this homogeneity Parmenides argued that being is finite. Since being is homogeneous, being must be solid and, like the surface of a sphere, being is "perfected on every side", equally distance from its center at every point. Thus being is finite. Parmenides' student, Mellisus of Samos (5th cent. B.C.), rejected his teacher's conclusion that being is finite; being must be spatially and temporally infinite. For if being is finite, then beyond it there would be empty space; but since empty space is nothing, non-being, it does not exist and thus being occupies all space. Thus being is spatially infinite. Full Being occupied all of space, since Non-Being is nothingness. Thus being is spatially infinite. Mellisus, like Parmenides, rejected a void or vacuum, empty space, as impossible and non-existent, "for what is empty is nothing. What is nothing cannot be". Thus Parmenides viewed space as a plenum or fulness, which made motion impossible.
  2. The fifth century, B.C., Atomist philosophers, Leucippus and Democritus, accepted the Eleatic term to me on (Non-Being) but not its meaning. In order to solve the paradoxes of the Eleatic philosopher Zeno, Leucippus assumed that the void had some kind of existence - a kind of existence that belongs to empty space, necessary for the reality of motion and diversity. Democritus, taking advantage of the subtle distinction between the two Greek negatives, coined his own term for space, "not Being" [to ouk on]. He thus avoided the meaning that the Eleatics had given to Non-Being, "non-existence" or "nothingness", and gave it the meaning "not having anything in it", that is, the void or empty space. But they gave to matter itself the properties of the Eleatic Full Being, immutability and simplicity, having no parts, that is, the "uncuttable" atom. And in order to explain change they assumed this Being is not One, but Many, many atoms in motion. And the atoms could combine with each other to form the things moving in space or the void. Space is not completely empty but is occupied by things with empty space between them.
  3. Plato (428-348 B.C.) in his Timaeus held that space is a "receptacle" in which the Ideas or Forms become individual things and particular instances of the universal Ideas by the Demiurge, the divine craftsman. Matter is in this receptacle which is empty space. This "Platonic matter" has been interpreted to be either a kind of body lacking all quality (Stoics, Plutarch, Hegel) or the mere possibility of corporeality (Chalcidius, Neoplatonists). Critical analysis seems to show that Plato intended to identify the world of physical bodies with world of geometric forms. Thus with Plato physics became geometry as with the Pythagoreans it became arithmetic. The four elements are assigned spatial form; the icosahedron (twenty congruent faces) to water, the octahedron (eight congruent faces) to air, the regular pyramid (four triangular faces) to fire, and the cube (six square faces) to earth, which is most immovable of the four, having the most stable bases. Therefore, it is only natural that the element earth is found at the center of the universe. The other elements are embedded in layers according to their increasing mobility which is due to their shape and size.
  4. In his Neoplatonic philosophy, Plotinus (A.D. 205-270) taught that the second emanation out of the One is the World-Soul, which is the principle of motion. This World-Soul is like the demiurge of Plato that forms the chaotic world of change. Looking back to the first emanation, the Nous or Ideas, she forms and moves the third emanation, Hyle or Matter. Extending herself, she leaves a "shadow" behind (IV. 3, 9, 45, sqq.) and this is "Space". There is no Absolute Space; space is a function of the World-Soul.
  5. Aristotle (384-322 B.C.), in order to refute the Atomist, assumed that space is not empty but is full. He defined space as a plenum, that is, fully occuping space, in contrast to the void and empty space. This space is unchanging and full, and was logically prior to its material content. Space was necessary for material existence and the existence of material things are contingent upon space; without space they could not exist. Aristotle rejected the Platonic and Democritian conceptions of space. Space is neither a receptacle nor void. The void, conceived by Aristotle as the privation of all conceivable properties, cannot by its very definition be a substance differentiated by its properties. On this basis Aristotle repudiated the void or vacuum and he insisted repeatedly that the containing body has to be everywhere in contact with the contained. Also if matter is indefinitely divisible and continuous, then the atoms or the indivisibles are not possible. Aristotle expounds his theory of space in his Categories and Physics. In his Categories Aristotle remarks that quantity is either discrete or continuous. "Space" belongs to the category of quantity and is a continuous quantity. He conceived of "space" as the sum total of all places occupied by bodies, and "place" (Greek, topos) is conceived as that part of space whose limits coincide with the limits of the occupying body. Thus Aristotle viewed space in terms of place, which he defined as the inner or adjacent boundary of the containing body or receptacle. Space is the sum total of all places.
    In his Physics, Aristotle attempts to define place by reference to the cosmos as a whole. He thought of the cosmos as a system of concentric spheres with its center at the center of the earth, and the outermost sphere would define all other places in relation to it. In this cosmology the various elements tend toward their place: bodies containing the element earth would tend toward the center of the earth, as the center of universe; water above it on the surface of the earth; air above the water; and fire tended up through the air to its place above the air. This "up" and "down" motion is "natural motion" of these four elements: air and fire "up," and earth and water "down." The outermost sphere is the region of the fixed stars, which rotates about the center of the universe. In his De Caelo (On the Heavens) he identifies the substance of this heavenly sphere as the fifth element, "fifth body," aether (later called the "quintessence") whose natural motion is circular, which explains the movement of the stars, which are composed of aether. Beyond the stars is the prime mover that is itself unmoved but has the power to move by acting as the object of desire. Aristotle held that this prime mover is eternal, infinite and non-material and it moves the outermost heavens as the first-moved object. The unmoved mover is necessarily at rest, in order to avoid an infinite regression of movers.
  6. The later atomists, Epicurus (341-270 B.C.) and Lucretius (c.99-55 B.C.), continued the interpretation of space as the void. But Aristotle's view of space as the plenum came to be held in the Middle Ages after the 12th century.
  7. Pierre Gassendi (1592-1655), Professor at the College de France in Paris, a follower of Copernicus and Galileo, re-introduced the views of the ancient atomist, namely that the universe is formed of material atoms, eternal and unchangeable, moving about in a space which except for them is empty. The most formidable objection to this new view was that it was associated with the moral and theological views of Epicurus and Lucretius. Gassendi, who was himself a priest, worked hard to show that atomism had no necessary connection with religious error, and that it could be accepted as a basis for physics by Christian men. After a sharp controversy with Descartes in 1641-1646, he was successful and his views were accepted by Newton, and became later the theory of matter in Chemistry. The theory had the advantage that space need not be considered as a plenum, and there was no need for moving particles to form closed chains and to form the Cartesian vortices.
  8. The Cambridge Neoplatonist, Henry More (1614-1687), placed himself in strong opposition both to ancient Greek atomism and to the Cartesian identification of matter and extension. Both seemed to him to lead inevitable to materialism and atheism. He argued that extension is not the distinguishing attribute of matter; matter also has the attribute of impenetrability or "solidity," as it was called at that time. Impenetrability (and the related tangibility) is the criterium differentionis between matter and spirit. In order to understand mutual interaction between the spirit and matter it is necessary to find a common ground between them. More maintained that this common ground is extension. Extension characteristizes spirit as well as matter. In a word, extension is not the distinguishing attribute of matter, but belongs to both spirit and matter. He argued that space is real. He rejected Descartes' plenum, accepting the existence of space as such. To both thinkers empty space does not exist; but if space may be empty as far as matter is concerned, it is yet, according to More, always filled with spirit. He argued that the reality of space is guaranteed by its very measurability. That is, space has indubitably the attribute of measurability, even when empty of all matter; as there are no attributes without substance, measurability as an attribute demonstrates the substantiality and reality of space. Also this substance is incorporeal, since it has the attributes of immobility and penetrability, which are not attributes of matter. More also contended with regard to this "subtle" substance that it exists necessarily, even if all matter were annihilated. This lead More finally to identify space with God. Since God and space have both the attribute of necessary existence, they are therefore one and the same.
  9. Classical modern science understood space as a homogeneous medium existing objectively and independently of it physical content, whose rigid and timeless structure had been described by the postulates, axioms and theorems of Euclidean geometry. This space, that was self-sufficent and independence of the matter which it contains, was clearly defined by Issac Newton (1642-1727) in his Principia:
    "Absolute space, in its own nature, without regard to anything external, remains always similar and immovable."
    Newton was not the first to formulate this definition of Absolute Space, even though it is commonly held that he formulated it. Pierre Gassendi, Henry More, and several Renaisance philosophers, Telesio, Patrizzi, Bruno, and Campanella used it. They rejected Aristotle's concept of space as the plenum, as occupied space, but retained the immutability of space, considering space as the void, or empty space, and matter as occupying space. With the Greek Atomists, they stressed this separability of space and matter, holding that space is absolute and independent of what occupies it.
    Closely related to the independence and immutability of space is its homogeneity ("the quality of being the same in nature or kind"). In fact, its independence and immutability logically comes from its homogeneity. Since no place in space is different from any other place, space is independent of what is at any place in space. Though the content at any place in space may change the underlying space is immutable. Though Newton historically does not start with the homogeneity of space in his definition of Absolute Space, he silently assumed it, though it is not mentioned by him explicitly. The tacit assumption of the homogeneity of space was made as soon as space was separated from its physical content; and this was done by the Greek atomist. In their veiw all qualitative diversity in the physical world was due to the various position, shapes, and motion of the atoms, not to the instrinsic differentation of space itself, as belived by Aristotle and his followers. Aristotle's idea of "natural place" for the different elements implied the qualitative heterogeneity of space. This feature was explicitly rejected by the modern seventeenth century atomist. In a conscious return to the ancient Greek ideas of the atomist, the homogeneity of space was explicitly expressed.
    Two other features of Absolute Space follow directly from its homogeneity: its infinity and mathematical continuity (infinite divisibility). Space has no limit, since any boundary of space must be located in space, and cannot be the end of space. Aristotle's elaborate proofs that outside the sphere of the fixed stars there is no space are therefore unconvincing. The homogeneity of space also implies its infinite divisibility. Space is homogeneious because it is made up of points that are all alike. And all of these points are so related to each other such that between any two points there is always another point between them. This juxtaposition of points means that no matter how small a spatial segment may be, it is always possible to divide it into two further segments, and so infinitium. In other words, no matter how small the segment may be, there must be a segment separating two points, each of which are external to each other.
    To claim that certain intervals of space are indivisible means that it is impossible to discern within them any juxtaposition parts; but since juxtaposition is the very essence of spatiality, this would mean that such segments are themselves devoid of spatiality. Thus this thesis of the indivisible spatial intervals is self-destructive; while it denies the possibility of "zero lengths" (points), it at the same time reintroduces their existence when it speaks of atomic intervals separating two very near points.
    With respect to matter, Absolute Space had the same attributes that had traditionally been assigned to the Supreme Being by the scholastics. This was observed by Henry More in his Enchiridion Metphysicum (1671):
    "Unum, Simplex, Immobile, Aeternium, Completum, Independens, A se existens, Per se subsistens, Incorruptibile, Necessarium, Immensum, Increatum, Incircumscriptum, Incomprehensibile, Omnipresens, Incorporeum, Omnia permeans et complectans, Ens per essentiam, Ens actu, Purus actus."
    ["One, simple, immovable, eternal, complete, independent, existing by itself, existing through itself, incorruptible, necessary, measureless, uncreated, unbounded, incomprehensible, omnipresent, incorporeal, all-prevading and all-embracing, Being in essence, Being in act, Pure act."]
    That this divinization of space infuenced Newton's philosophy of Nature is well known. But he regarded this Absolute Space as an attribute of God, the sensorsium Dei, by which the divine omnipresence as well as the divine knowledge of the totality of things is made possible. Of course, Newton believed that God created everything in that Absolute Space, the heavens and the earth. The Absolute Space is eternal but not the things in Absolute Space. They were created by God. But the logical, if not the temporal, priority of space to its physical content was a dogma that few dared doubt, especially in England. For Newton as for Gassendi and More, this priority was temporal as well; Absolute Space, being the attribute of God, naturally had to exist prior the creation of the world. There was nothing absurd about this belief, although the coeternity of space and matter was equally compatible with the Newtonian laws of physics. But in France where a rejection of Roman Catholic theology and Thomistic philosophy took place, this second alternative, logically simpler, was adopted. The co-eternity of space and matter appeared to be logically simpler and more elegant view of reality than the arbitrary creation of matter at a definite date in the past. This lead many philosophers to return to ancient atomistic materialism or the pantheism of Spinoza, which appeared to be more satisfactory than the synthesis of Lucretian metaphysics and Christian theism as found in Gassendi and Newton.
  10. Whether space and matter were to be regarded as coeternal or not was a question to be debated, but the absoluteness of space, that is, its independence of matter, had hardly been questioned. There were a few who rejected the absoluteness of space: Leibniz, Huygens, and Berkeley are a few of the most well known. In the case of the difference between Newtonian philosophy and the rival Cartesian philosophy, on this point the difference was more apparent than real. Rene Descartes (1596-1650) had insisted on the inseparability of matter and space, the plenum, and would apparently have challenged the logical priority of space asserted by Newton. But Descartes made his philosophy of nature ambiguous by retaining only the geometrical property of matter, extension. In what intelligible sense can space be called a plenum? Descartes' answer is that all space is filled with a medium which, though imperceptible to the senses, is capable of transmitting force, and exerting effects on the material bodies immersed in it, the aether, as it was called. Before Descartes, the word was used for Aristotle's fifth element, the quintessense, of which the planets, the sun, and stars were made; Descartes was the first to introduce aether into science, and give to it mechanical properties. In his view, it was regarded as the solitary tenant of the universe, occupying all space except for that small fraction occupied by ordinary matter. Descartes assumed that the aether particles are in continual motion. And since there was no empty space for the aether particles to move into, he inferred that they moved by taking place vacated by other aether particles which are also in motion. Thus the movement of a single particle of the aether involved the motion of an entire closed chain of particles; and the motion of these closed chains constituted vortices, which performed the important function in his picture of the cosmos of moving the heavenly bodies. Holding, then, to the view that the effects produced by means of contacts and collisions of the aether particles in motion was the simplest and most intelligible explanation of phenomena in the external world, Descartes would not admit any other agencies. Descartes is thus the originator of the Mechanical Philosophy, Mechanism, that is, the doctrine that the external inanimate world may be considered for scientific purposes as an automatic mechanism, and that it is possible and desirable to explain every physical phenomena by a mechanical model.
    But in certain sense the Cartesian philosophy of nature was even more Newtonian than that of Newton; while for Newton space was the primary reality, for Descartes space was the only true reality in the physical world. It is not surprising that Spinoza, and to a certain extent Malebranche, who owed much to Descartes, arrived at nearly the same divinization of space as Newton; for them, also, extension was an attribute of God. It was the absoluteness of space that led to its divinization.
  11. The German philosopher, Gottfried Wilhelm Leibniz (1646-1716), opposed Decartes' concept of space and put forth a relational view of space; space was in no sense a substance or stuff, but merely a system of relations in which indivisible substances, or "Monads", stand to each other. Few philosophers have accepted Leibniz' theory of monads but his relational theory of space, slightly modified, has continued to be the rival of absolute theory of space.
  12. The German philosopher, Immanuel Kant (1724-1804), argued against the theory of Absolute Space and the relational theory of space. He held that space is something merely subjective (or "phenomenal") where in sensation the subject arranges non-spatial "things-in-themselves" (or "noumena") spatially. That is, to the raw data of sensation the knowing subject contributes the forms of space and time. He regarded space as the a priori or innate form which the sensibility imposes upon its sensations; it is innate in the senses themselves and is not a property of things in themselves independent of the sensibility. It is not an innate idea in the mind in the Cartesian sense, but an innate form of perception.
  13. The theoretical physicist, Albert Einstein (1879-1955), developed the concept of the relativity of space, dropping the Newtonian concept of Absolute Space. In his Special Theory of Relativity, Einstein showed that the length of physical objects will contract in the direction of their motion as the relative uniform speed of their frames of reference approaches the speed of light, c. That is, space is relative to the frame of reference of the observer.
THE PROBLEM OF TIME.
1. STATEMENT OF THE PROBLEM: What is time?
2. ANALYSIS OF THE PROBLEM:
  Historical analysis:
  1. In an early view, time was identified with cyclical movement. Heraclitus (c.540-475 B.C.) calculated the length of the world year or great year (the period in which the cycle of existence would come to an end and begin again to repeat itself) to be the period of 10,800 years = 360 thirty-year generations.
  2. The Eleatic Greek philosophers, Parmenides (c.525-c.450 B.C.) and Zeno of Elea (490-430 B.C.), indirectly argued against the reality of time, on the grounds that change and motion are unreal.
  3. The Greek philosopher, Plato (428-348 B.C.), defines time as the moving image of eternity. Time appears through the agency of the demiurge, the divine craftman, who embodied the eternal forms or ideas in the receptacle of space.
  4. The Greek philosopher, Aristotle (384-322 B.C.), defined time as the numbering of motion with respect to before and after. On the grounds that every "now" implies a "before", Aristotle concluded that time has no beginning.
  5. For the Graeco-Roman school of philosophy, Stoicism, (founded in 108 B.C. in Athens by Zeno of Citium), things do not happen in time; time is a dimension of things. The eternal course of the universe is, by the nature of things, cyclical, not progressive or regressive. Each cycle is called a periodos [period], or magnus annus [great year], and every periodos begins with the logos, or the creative fire, passing through the creation and organization of the four elements (earth, water, air, and fire), and ends with a conflagration, a return to the fire to begin again. Every periodos is identical in all details with every other one; there is an eternal recurrence of all things. Time being what it is and the logos spermatickos, or life-giving word, containing its own purposes and powers, these changes are autonomous, not stimulated or bounded from without, since space, like time, is only a dimension of body. This means that all change is immanent in God and unchanging in its laws.
  6. Neoplatonism, as presented by the the Egypto-Roman philosopher Plotinus (A.D. 205-270) in his Enneads, followed Plato interpreting the demiurge as the World-Soul, who imposes the forms of the infinite fulness of the Nous or Ideas on the material world, Hyle or Matter. The World-Soul mediates between what is Eternity and what is Time (III, 7, 13). What is the cause of Time? Not the One nor the first emanation, the Nous or Ideas; the One is the undifferentiated principle of unity out of whose eternal (timeless) being all temporal order arise by emanation. Emanation is not temporal, but logical and occurs by the refulgence of the One. Neither is the Nous the cause of Time; the Nous is not thinking, but the objects of thinking, the ideas, and these ideas are paradeigmata (models) of the sensible things. Since the psyche (soul) is the principle of motion, the World-Soul, reflecting on the divine Ideas, eternally moves on the infinitely, indefinite void, forming it into the things of the world. Since she is the principle of motion, the World-Soul is the cause of Time.
  7. Augustine (A.D. 354-430), confessing that he knows what time is when no one asks, and that he does not know what it is when anyone does ask, held that God is timeless and has created the world with time, having a beginning. He was fully aware of the paradox of this view. All that we really know about time is that time is in us, measuring time as before and after, the memory of the past and the anticipation of the future. Augustine as young man found himself incapable to understand Christian theism until he had learned and discovered in Neoplatonism the basis for the existence of immaterial entities (the Ideas). He finally concluded that these eternal ideas, or rationes aeternas, existed in the mind of God. From Neoplatonism he derived his basic understanding of God. With regard to God's nature, Augustine with Newoplatonism affirms God's perfection, eternity, infinity, incomprehensibility, simplicity and unity. Augustine's understanding of God as "the inexhausible light" or "intelligible light" was derived from the Neoplatonic understanding that intelligible light is original, and physical light is derivative, the former causing the latter. The Neoplatonic theory of emanation was based on the metaphor of light radiating and enlightening all. Augustine rejected the Neoplatonic theory of emanations and held to the Christian doctrine of creation ex nihilo ("out of nothing") at the moment chosen by God. The world and time thus had a definite beginning. But what God wills to create is determined by what God's knowledge has determined to be good. God's intellect is the primary motive to create. From Neoplatonism he also derived his conception of God as timeless. The One is unchanging, therefore, timeless. God is not only eternal, having no beginning nor end, but He is without time, no past nor future, but just an eternal "now". In this eternal "Now", God sees all the past, present, future of the world that He will and has created. According to Augustine eternity is motionless, no succession; everything is present at once; there is no past nor future. Time was created by God out of nothing, ex nihilo. It is not an independent principle nor a being, the Receptacle, nor non-Being, the void.
  8. Against Aristotle, medieval Schoolman following Augustine believed time had a beginning. Between eternity, the Res Tota Simul, and time, is the Aevum, or everlastingness, of heavenly bodies and of angels.
  9. The English philosopher, Thomas Hobbes (1588-1679), held that the present has its being in nature, the past is memory, and the future has no being at all.
  10. The Jewish philosopher, Baruch (Benedict) Spinoza (1632-1677), held that eternity was more basic than time. God as the "absolutely infinite being" is the whole of reality that exists necessarily, eternal not temporal, its essence implying its existence. It is its own cause, causa immanens and causa sui. An absolutely infinite being will have an infinite number of attributes, of which man knows two, thought and extension. The modes of thought and extension apply to the things of this world. Time is an inadequate perception by man of a limited reality. Reality seen, or conceived, fully is eternal. Thus the temporal dimension is in some sense illusory, or partially so.
  11. The English physicist, Isaac Newton (1642-1727), demonstrated, at least to his own satisfaction, that, like space, there is Absolute Time, in addition to its relativities. He defined time as duration, which flows equably without any relation to anything external. As space in classical physics is regarded as a three-dimensional manifold of co-existing homogenious points, so time was regarded as one-dimensional manifold of successive instances. As the basic relation in space is juxtaposition, so the basic relation of time is succession. As the points in space are beside one another, so the instances of time follow one another. Both space and time were regarded as a manifold, and both were believed to be homogeneous. As in the case of space, the basic attributes of time follow from its homogeneity: its independence from its physical content, its infinity, its continuity, and its uniformity. The uniformity of time is the counterpart of the immutability of space; it might be more expressively designated uniform fluidity. Time flows uniformly. The independence of time in regard to concrete changes which take place in it was explicitly formulated by Newton:
    "Absolute time and mathematical time, of itself and by its own nature, flows uniformly, without regard to any thing external. It is called duration. Relative, apparent and vulgar time, is some sensible and external measure of absolute time (duration), estimated by the motions of bodies, whether accurate or unequable, and is commonly used instead if true time; such as an hour, a day, a month, a week." [1]
    According to this view, time flows no matter whether something changes or not; in its own nature time is empty and is only filled in an accessory and contingent way by changes. Changes are in time; they are not time itself. This distinction between time and concrete becoming is at the very foundations of classical physics. As space does not imply matter, so time does not imply motion nor change in general. This was clearly said by Isaac Barrow, the teacher and predecessor of Newton, whose influence on the formation of Newton's concept of time was as important as the influence of Henry More was on Newton's concept of space. He wrote,
    "But does time imply motion? Not at all, I reply, as far as its absolute, intrinsic nature is concerned; no more than rest; the quantity of time depends on neither essentially; whether things run or stand still, whether we sleep or wake, time flows in its even tenor. Imagine all the stars to have remained fixed from their birth; nothing would have been lost to time; as long would that stillness have endured as has continued the flow of this motion. Before, after, at the same time (as far as concerns the rise and disappearance of things), even in that tranquil state would have had their proper existence, and might by a more perfect mind have been perceived." [2]
  12. The German philosopher, Immanuel Kant (1724-1804), held that time is something merely subjective (or "phenomenal") wherein sensation in the subject arranges non-temporal "things-in-themselves" (or "noumena") temporally. He regarded time like space as the a priori or innate form which the perceptibility imposes upon its sensations; it is innate in the senses themselves and is not a property of things in themselves independent of the sensibility. It is not an innate idea in the Cartesian sense, but an innate form of perception.
  13. The French philosopher, Henri Bergson (1859-1941), defined time as qualitative change, involving an irreversible becoming, and having its own inner duration. He held that reason "spatializes" time, and that intuition is therefore a more adequate means of apprehending it.
  14. The English philosopher, Alfred North Whitehead (1861-1947), thought of time under the category of becoming, the movement from potentiality to actuality of events which thereafter retain an "objective immortality."
  15. The theoretical physicist, Albert Einstein (1879-1955), developed the concept of the relativity of time, dropping the Newtonian concept of Absolute Time. In his Special Theory of Relativity, Einstein showed that the interval between two events will increase or dilate as the relative uniform speed of the frames of reference in which they are measured approaches the speed of light, c. That is, the clocks in two different inertial frame of reference will slow down as the relative uniform speed of the frames of reference approaches the speed of light. The relativity of time means that the simultaneity of events can be determined only within a given inertial frame of reference, and will not be same for another inertial frame of reference moving relative to the given system.
THE PROBLEM OF SPACE-TIME.
The theory of relativity replaced the separate concepts of space and of time of classical or Newtonian theory by a unified concept of space-time.
1. STATEMENT OF THE PROBLEM: What is space-time?
2. ANALYSIS OF THE PROBLEM:
  Historical analysis:
  1. The German mathematican and physicist Hermann Minkowski (1864-1909) joined the three dimensions of space to the dimension of time to form a four dimensional space-time continuum, with time as the fourth dimension. In particular he showed that the Lorentz transformations of special relativity correspond to a rotation of axes in space-time. He showed how natural the kinematics of special relativity seem, as opposed to Newtonian kinematics, in which the time axis is rotated without correspondingly rotating the space axis. Space-time is the four-dimensional continuum which includes the three dimensions of space (length, width and height) and the one of time to form the unity of space and time. Minkowski contended that nothing can exist or be conceived of as physical apart from space-time; for every physical object must not only have length, width, and height but also duration of time. As a result, a complete description and location of an object must be given in terms of the four coordinates. Space-time is mathematically grounded in world-points, or durationless geometrical points, and become world-lines, or geometrical lines, because of their temporal dimension, that cut across the four dimensions of space-time. An enduring geometrical point becomes a geometrical line (or possibly a curve) in space-time. The universe of four dimensions (it could be called omniverse) includes space with all its events and objects as well as time with its changes and motions.
  2. Einstein accepted the Minkowski space-time continuum as the basis of his Special Theory of Relativity. In his General Theory of Relativity, gravitation is reduced to or is the effect of space-time curvature and depends upon the masses distributed through out the universe. Thus the Newtonian concept of action-at-a-distance is discarded.
    Isaac Newton had held to an absolute theory of space and of time, whereas his contemporary Leibniz argued that space and time are merely sets of relations between things which are "in" space and time. The Special Theory of Relativity has made it impossible to consider time as something absolute; rather, space and time are both relative to the motion of the observer. This view stands neutrally between the absolute and relational theories of space-time. According to the General Theory of Relativity the structure of space-time is dependent on the distribution of matter in the universe. A curvature is attributed to space-time, even in the absence of matter, and the inertia of a body depends in part on this cosmological distribution to the local metrical field and hence not solely on the total mass of the universe, as in a purely relational theory would require.
  3. The English philosophers C. Lloyd Morgan (1852-1936) and Samuel Alexander (1859-1938) held that space-time is the ultimate matrix from which everything else has evolved.
    Morgan believed that everything emerges from an original space-time matrix, including matter itself. He held that evolution occurs at all levels of natural history, not continuously but by discontinuity, in which "emergents" abruptly appear, moving from lower to higher forms of life. God is not an emergent, but directs the course of evolution, expressing His purpose in the entire course of events.
    Alexander, beginning with the idea that a thing as a complexus of motion, he identified space-time as pure motion, and views space-time as the source and origin of all existing things. But motion is one among a number of properties of space-time. These properties he called the categories. The primordial properties of space-time will also characterize whatever emerges from space-time. Besides motion his categories are substance, quantity, number, existence, universality, relation, and order. Alexander took the process of emergent evolution as his basic metaphysical principle. Where the ancient philosophers and modern classical physical sciences took matter and motion as the original stuff, after Minkowski, Einstein, Lorentz, and others, it became indivisible space-time, instead of space and time. Thus nature begins as a four-dimensional matrix in which it is the moving principle. Materiality, the secondary qualities, life, mentality are all emergent modifications of proto-space-time. Alexander thought of the deity as the next highest level to be emerged out of a given level. Thus for things on the level of life, mind is deity, but for beings possessing minds there is a nisus or urge toward a still higher quality. To such beings that dimly felt quality is deity. The quality next above any given level is deity to the beings on that level; thus on level of a dog, man is deity. For men deity has not yet emerged, but there is a nisus toward its emergence.
  4. The British mathematican and philosopher Alfred North Whitehead (1861-1947) published in 1920 a criticism of the General Theory of Relativity in the Times Educational Supplement. [3] He criticized the non-isotropic character of space-time, that is, that space does not have the same properties in all directions. He wrote, "I doubt the possibility of measurement in space which is heterogeneous as to its properties in different parts. I do not understand how the fixed conditions for measurement are to be obtain." He followed up this idea by devising an alternate theory which he set forth in his book, The Principle of Relativity in 1922. "I maintain the old-fashioned belief in the fundamental character of simultaneity. But I adapt it to the novel outlook by the qualification that the meaning of simultaneity may be different in different individual experiences." [4] With this statement Whitehead admits the relativity theory of Poincare and Lorentz, but it is not compatible with the General Theory of Relativity, in which the observer's domain of simultaneity is confined to a small region of the observer's neighborhood. Whitehead therefore postulated two fields of natural relations; one of them (namely, space and time relations) being isotropic, is universally uniform and not condition by physical circumstances; the other, comprising the physical relations expressed by natural laws, which are contingent.
    Whitehead considered events, and the objects related to each other, as occurring in a four-dimensional space-time manifold, which he called the extensive continuum. The geometrical properties of this field are defined by the method of extensive abstraction. That is, points, lines, planes, and other geometrical objects, are ideal limits of converging classes of appropriate kinds. For example, squares and circles converge to a point, while rectangles converge to a line segment. These routes of approximation toward an ideal limit involve time as well as space. According to Whitehead, the character of space is dependent upon the character of time, and the routes of approximation of geometrical objects are fixed by the intersections of alternate time-systems. The ultimate elements of the space-time manifold are event-particles. An event-particle is an instantaneous point-flash, or a point of instantaneous space, as much an instant of time as a point of space. Geometrical objects can thus be described as the loci of the complete sets of event-particles covered by appropriately intersecting moments of of different time-systems.
    The theory of Whitehead offers a veiw of space-time somewhere between the extremes of the Newtonian theory of absolute space and time, on the one hand, and the General Theory of Relativity on the other. The theory conforms to the requirements of the Lorentz invariance (thus overcoming the major criticism of Newtonian theory), but it does not reinstate the concept of force, with its equality of action reaction, so that its range of applicabiliy is lower than that of Newtonian mechanics. But it does free the theorist from the nearly impossible task of solving (without a computer) a system of non-linear partial differential equations whenever dealing with gravitational fields. It is not a field theory, but an action-at-distance theory, propagated at the speed of light, c. Whitehead's theory, though totally different from Einstein's general theory, may be described as fitting the laws of Special Relativity into a flat space-time. But no observational test has hitherto been proposed to decide between the two theories. Philosophically, Whitehead's theory of relativity differed from that of Einstein by its grounding in philosophical realism rather than operationalism, which grounds and defines scientific concepts in terms of operations by which they are measured, and meaning of those concepts are identical to the operations entering into those definition.
THE CLUE TO THE SOLUTION:
There is no definition of time given in the Bible.
In the Bible time is mentioned, but not defined. The Bible does not view time abstractly as a problem, but concretely as the region in which God accomplishes his purposes.
Linguistic analysis:
There are two Greek words commonly translated "time": "chronos" and "kairos"; there are also other Greek words that are used to refer to time: "aion", "aionios", "ephapax" and "nun".
1. The Greek noun "chronos" is the word used for time in Hellenistic literature and it is used in the Greek New Testament for measured time, a period of time, whether short or long (Matt. 2:7; Mark 9:21; Luke 1:57; Acts 3:21; 7:17, 23; 13:18; 17:30; 27:9; I Pet. 1:17; 4:3; Gal. 4:4; Rev. 10:6 [delay]).
2. The Greek noun "kairos" is used in Hellenistic literature and the Greek New Testament for the time in which a significant event occurs or a given activity is accomplished (Mark 1:15; Luke 21:8; Acts 24:25; Rom. 8:18; 13:11; II Cor. 6:2; Eph. 5:16; Col. 4:5; I Pet. 1:5, 11; Rev. 1:3).
3. The Greek noun "aion" is used in Hellenistic literature of a period of time, for a lifetime, a generation, a period of history, and in the Greek New Testament it is used for an indefinitely long period of time, an age, eternity, usually with the preposition "eis": "unto the ages of ages" ("forever", Matt. 6:13; Rom. 16:27; Eph. 3:21; I Pet. 5:11; II Pet. 3:18; Jude 25). And with a double negative, it also means "never again" (Matt. 21:19), and "never" (John 4:14; 8:51; 11:26). It is also used for the sum of all periods of time, including all that is manifested in them ("world", Heb. 1:2; 11:3), or for sum of all the ages or world-periods that make up eternity (I Tim. 1:17). It is also used of the present age (Matt. 12:32; 13:22; Luke 20:34; Gal. 1:4; I Tim. 6:17) and of the time after Christ returns (Matt. 12:32; Luke 20:35; Mark 10:30).
4. The Greek adjective "aionios" is used in the Greek New Testament to mean age-long, or eternal, of that which is without beginning or end (Rom. 16:27; Heb. 9:14), or of that which is without end (John 3:16; 4:14: 5:24; 6:47, 68; 10:28; 17:3; II Thess. 1:9; 2:16; Heb. 6:2; 9:12, 15; 13:20; Rev. 14:6). It is also used with "chronos" for very long periods of time ("times of the ages", Rom. 16:25; "before the times of the ages" [pro chronon aionion] II Tim. 1:9; Titus 1:2 [which the NIV incorrectly translates "before the beginning of time"; the NAS translates it as "from all eternity" and "long ages ago", the RSV as "ages ago", and the KJV as "before the world began".]).
5. The Greek adverb "ephapax" is used in the Greek New Testament to mean "once for all" (Rom. 6:10; Heb. 7:27; 9:12; 10:10) or "at once" (I Cor. 15:6).
6. The Greek adverb "nun" is used in the Greek New Testament to mean "now", that is, at the present time, as opposed to the past (John 4:18; Acts 7:52; Rom. 13:11; II Cor. 6:2; 7:9; Col. 1:24; II Thess. 2:6; etc.). With an article, it is a noun that means "the present" ("now time", Rom. 3:26; Gal. 4:25; "the now age", I Tim. 6:17; Titus 2:12, etc.). Sometimes it is used of logical sequence, "therefore, however, as it is" (Luke 11:39; John 8:40; 9:41: 15:22, 24; 18:36; Acts 3:17; 7:34; I Cor. 5:11; 7:14; 12:20; I John 2:28).
The Bible not only mentions time, but also makes statements about time.
"But let this one thing be not concealed from you, beloved,
that one day with the Lord is as a thousand years,
and a thousand years as one day."
(II Pet. 3:8 ERS).
"For a thousand years in your sight are like a day that has gone by,
or like a watch in the night."
(Psalms 90:4 NIV).
"I am the Alpha and the Omega,
the first and the last,
the beginning and the end."
(Rev. 22:13 NAS; see also Rev. 1:8; 4:8).
THE SOLUTION:
From the previous analysis there are two problems:
(1) the nature of time and of space, and
(2) God's relation to time and space.
To the first problem, the Special Theory of Relativity has shown that space and time are relative to the motion of the observer and that space and time are are related though different. In addition to the three dimensions of space, time is a fourth dimension, but is not a fourth dimension of space. This concept of space-time is shown in the equation that gives the relation of space to time.
r² = x² + y² + z² + (ict)²,
where x, y, and z are the spatial coordinates, t is the time coordinates, and c is the speed of light, and i is the imaginary unit = √-1. This imaginary unit does not mean that time is unreal but indicates that time is different from the spatial coordinates, but yet related to them. This equation gives the coordinates of an events in space-time and r is the relation of this event to the origin of the space-time frame of reference. An event takes place at a certain place in space (x, y, z) at a certain time t as indicated with reference to space-time frame of reference. In the General Theory of Relativity the flat space-time of Special Relativity is replaced with a curved space-time, and the curvature of space-time depends upon the distribution of matter-energy. Newtonian Law of Gravity is explained as due to the curvature of space-time.
As to the second problem of God's relation to time and space, Augustine's solution has dominated Christian theology; that is, that God is timeless, beyond time and space, and that time with space was created by God when in the beginning He created the heavens and the earth. This solution is only partially correct; God created time and space (space-time) when He created the heavens and the earth. But as we saw above, Augustine borrowed the Neo-Platonic concept of God (the one Being) as timeless, and interpreted it as an "eternal now", without a before or after, without a beginning or end. This solution of Augustine's has raised many problems: for example, if God is timeless, then how could the Son of God (the second person of the Trinity) become a man and enter into time? And how could God make a decision of His will to create the heavens and the earth? ("Worthy art thou, our Lord and God, to receive glory and honor and power, for thou didst create all things, and by the will they existed and were created." Rev. 4:10) In any decision of the will, there is a before and an after the decision. If God is timeless, then how can there be a before and after the decision to create? To these complications of Augustine's solution of God's relation to time that God is timeless, Christian theology has usually declared that they are mysteries beyond our human understanding. But instead of retreating into mysteries, why didn't Christian theology recognize that these complications were produced by the Greek and Neo-Platonic philosophical view of God as timeless, and to reject this view of God and Its relation to time? Again, the Greek view of God is a Super-It, and things, even super-its, can not make decisions because they do not have wills. Persons do have wills, and in fact their existence is in their decisions. "I choose, therefore I am." Choices involve time; there is a before the decision, the now of the decision, and an after the decision. Since God has revealed Himself as three persons, the Father, the Son, and the Holy Spirit, time must exist in God; God is not timeless. But God's time is not our created time. The statement of II Pet. 3:8 makes this clear. "...that one day with the Lord is as a thousand years, and a thousand years as one day." This language is not metaphorical but is a statement of reality. God has time, but His time is not our created time. God's uncreated time is absolute time; it has no beginning nor end. But it is not our created relative time. Just as God created space (the heavens and the earth), He created time. Newton's mistake was that he identified relative created time with God's absolute time. What the theory of relativity shows us is the true character of created time as relative and Newton's mistake in absolutizing it. The complications introduced by Augustine's view of God as timeless are thus now removed. When God decided to create the heavens and the earth, there was in God's time a before and after the execution of the decision to create, but that act of creation was the beginning of our created relative time. And in the incarnation, the Son of God decided in His absolute time (in eternity) to take upon Himself our relative created time.

END NOTES

[1] Isaac Newton, Mathematical Principles of Natural Philosophy, scholuim I.

[2]Mathematical Works of Isaac Barrow D.D., Whewell edition
(Cambridge, 1860), Vol. II, pp. 160f.

[3] Times Educational Supplement, 12 Feb. 1920, p. 83.

[4] A. N. Whitehead, The Principle of Relativity,
with applications to physical science
(Cambridge University Press, 1922)