The Enigma of Time

Daniel T. Johnson
Houston, Texas
2006 May 26


For what is time? Who can readily and briefly explain this? Who can even in

thought comprehend it, so as to utter a word about it? But what in

discourse do we mention more familiarly and knowingly, than time? And,

we understand, when we speak of it; we understand also, when we hear

it spoken of by another. What then is time? If no one asks me, I know:

if I wish to explain it to one that asketh, I know not: yet I say

boldly that I know, that if nothing passed away, time past were not;

and if nothing were coming, a time to come were not; and if nothing

were, time present were not. Those two times then, past and to come,

how are they, seeing the past now is not, and that to come is not yet?


 . . . Yet what do we measure, if not time in some space? For we do not

say, single, and double, and triple, and equal, or any other like

way that we speak of time, except of spaces of times. In what space

then do we measure time passing? In the future, whence it passeth

through? But what is not yet, we measure not. Or in the present, by

which it passes? but no space, we do not measure: or in the past, to

which it passes? But neither do we measure that, which now is not.


My soul is on fire to know this most intricate enigma.




We count time, and we can count on time to bring perplexity when we ask what it is  -- it is an enigma.  From ancient times people have pondered time and its nature, and the emergence of the modern concept of time is at the root of our culture.  The narrative flow of history is in the context of time as a connecting force and forward impetus, essential for progress toward modern science with the formalization of time in physics and mathematics. 


Physics tightens our everyday notions of time, and separates the intricacies of human life from the simplifying idealization of forces, energy, and particles in motion.  From Zeno's paradoxes to the infinitesimals of Newton's calculus, the analysis of motion crystallizes our intuition of time and exposes the enigmatic issues.  The invention of calculus by Newton and Leibniz in the 17th century essentially solved Zeno's arrow paradox of counting the instants as a body moves from one place to another [2], taming the continuum in a way that eluded ancient science and philosophy.  Newton's "absolute, true, and mathematical time" which "from its own nature, passes equably without relation to anything external, and thus without reference to any change or way of measuring of time" [3] clarified and extended common intuition about time, but led to new paradoxes as physics advanced.


While Newton's concept of time seems quite intuitive to us, at the end of the 19th century the unified theory of electromagnetism embodied in Maxwell's equations indicated that the speed of light doesn't depend on the speed of the observer.  Others had discovered how to reconcile the observations with theory, but the underlying reality wasn't reconceptualized until Albert Einstein's Special Relativity in 1905, giving us spacetime.  But Einstein's even greater achievement was General Relativity in 1919, in which measurements of time and space not only expand or contract uniformly but bend as well.  This resolves a troubling feature of Newton's gravity, which was an instantaneous force.


For 100 years now, Einstein's relativity has made time both more warped and more universal.  The framework of spacetime takes cosmology beyond old confines of speculation to a new frontier of scientific investigation.  Time is not what it used to be -- physics has transformed time, from the classical philosophical narrative to everyday digital synchronization enabled by esoteric theory.


The abstraction of time in physics makes explicit the connection between ultimate reality, God, and the unique events of our human experience, history.

Ancient Time

"Time is the number of motion."  So said Aristotle, in the 4th century B.C.E. [4]  Time as motion:  Aristotle sounds so ancient, yet so modern.  Far more obscure to us today are non-modern world views that "manage without this concept [pure time] completely," and where the key concept is "not time but process, . . . a structured sequence of events."  [5] Such an assertion sounds incredible enough if made about some unknown tribe, but the author, Sacha Stern, is a careful scholar and is talking about pre-medieval Judaism. 


How can Stern make this claim when we read the following passage in the Bible?


My days are like an evening shadow; I wither away like grass.  But thou, O LORD, art enthroned for ever; thy name endures to all generations.  Thou wilt arise and have pity on Zion; it is the time to favor her; the appointed time has come. . . .

Let this be recorded for a generation to come, so that a people yet unborn may praise the LORD:  that he looked down from his holy height, from heaven the LORD looked at the earth, to hear the groans of the prisoners, to set free those who were doomed to die; that men may declare in Zion the name of the LORD, and in Jerusalem his praise, when peoples gather together, and kingdoms, to worship the LORD.  He has broken my strength in mid-course; he has shortened my days.  "O my God," I say, "take me not hence in the midst of my days, thou whose years endure throughout all generations!"  Of old thou didst lay the foundation of the earth, and the heavens are the work of thy hands.  They will perish, but thou dost endure; they will all wear out like a garment. Thou changest them like raiment, and they pass away; but thou art the same, and thy years have no end. (RSV Psalm 102:11-13, 18-27)


Stern argues that nevertheless something is missing from pre-modern Judaism:  the abstraction of time in general, pure time in itself:


The dimension of time which we usually take for granted in our modern world view is not a tangible or concrete reality; it is not perceptible to the senses.  Much the same can be said, indeed, about the notion of 'pure', empty space, although this is outside our present scope.  All we experience around us are concrete objects, engaged in certain relations which we call 'events'; events, in turn, are structured in sequences which we call 'processes'.  Time is only an abstract measurement of processes:  it is, primarily, a way of expressing how long a process is.  The modern concept of time as a general category, an autonomous flow, an empty extension, or a structure and dimension of the universe, is only a generalization and synthesis of all the discrete time-measurements that can be made of the individual processes which we empirically experience.  Time itself, however, is not an empirical experience, nor a palpable reality:  it is only a generalized abstraction.  Inasmuch as we tend to treat it, in modern culture, as existing and real, time often becomes a reified abstraction. [6]


So how did the concept of time in itself emerge?  Stern finds perhaps the earliest traces in the Zoroastrian idea of "unlimited time", and even its deification.  He says "The concept of time as a cosmic power and entity in its own right, which we find to be common to ancient Greece, Iran, and India, may thus be identified as a specifically Indo-European tradition, which would stand in contrast with the ancient Semitic cultures of Mesopotamia and the Levant, where this concept appears not to have existed. . . . It was out of this ancient religious tradition that the modern Western concept of time eventually emerged." [7]

History of Time

Perhaps the best-known popularization of the history of time is Stephen Hawking's A Brief History of Time:  From the Big Bang to Black Holes (1998).  Hawking is so brief as to neglect the pre-modern world view, and begins with Aristotle and Augustine before getting to his specialty of spacetime in physics.  This ground is covered more thoroughly if more pedantically in Lawrence Fagg's The Becoming of Time:  Integrating Physical and Religious Time (2003). Fagg does explore the cultural and religious development of time, saying of the ancient Israelites "In effect they began worshipping a single God of evolving history instead of gods of cyclical nature."  Still, their "holy occasions were originally regarded as separate, temporally disconnected 'times' by the Israelites, who had no comprehension, as we do today, of a universal chronological time, proceeding independent of individual occurrences." Fagg attributes these insights to G. von Rad, but concurs with Stern that "the Hebrew language lacked a word for time in this sense, or for history." [8]


Both Fagg and Hawking consider time especially as it appears in physics, and the new discoveries this has brought, with relativity and quantum mechanics exposing the naiveté of some intuitive ideas about time.  A significant issue in physics is the arrow of time, the question of what distinguishes past and future with time advancing in only one direction, since the fundamental laws of physics are symmetric with respect to time.  There are three irreversible gauges of time:  cosmologic, thermodynamic, and psychological.  The universe is expanding from an initial Big Bang (cosmologic),  Spilt mike does not gather itself back in the bottle (thermodynamic), and we remember our past but are uncertain of the future (psychological).  Fagg links these to the religious sense of purpose and the ultimate.  The issue of the arrow of time is treated more fully in a volume edited by Steven F. Savitt, Time's Arrow Today:  Recent Physical and Philosophical Work on the Direction of Time (1995).


Time today is a topic of serious interdisciplinary scholarship, across physics, philosophy, and the humanities.  There is an International Society for the Study of Time,, which has organized triennial conferences since 1966 and publishes selected papers from proceedings as well as the ISST Journal KronoScope with this Mission Statement:


Time bears a unique and direct pertinence to all human concerns. Time is a fundamental feature of the physical universe, of the life process, of the functions of the mind, and of collective behavior. In humans, temporal experience is all pervasive, intimate and immediate. Life, death and time combine in a dynamic unity that has been of concern to all great philosophies and religions and to the arts and humanities.


Since 1966, the International Society for the Study of Time (ISST) has been providing a framework for an interdisciplinary dialogue about the nature of time. KronoScope, edited by an international board of scholars, carries forward the work of ISST. By offering an open-ended platform for the cross-fertilization of scholarly and scientific ideas, it helps professional men and women become acquainted with the nature of time as seen from their own and from other fields of knowing. As a journal, its goal is to accommodate the expanding concerns of the global community in search of understanding and meaning.


Popular publications are also serious about the topic of time, for example the recent Scientific American special edition A Matter of Time (2006) [9], whose editors say in their synopsis:


 . . . Our fundamental human drives have not changed from the Paleolithic era, hundreds of thousands of years ago. Much of what we are about centers on the same impulses to eat, procreate, fight or flee that motivated Fred Flintstone. Despite the constancy of these primal urges, human culture has experienced upheaval after upheaval in the period since our hunter-gatherer forebears roamed the savannas. Perhaps the most profound change in the long transition from Stone Age to information age revolves around our subjective experience of time.


But what is time? Physicists and philosophers have grappled with the question. So, too, have biologists and anthropologists. This special issue explores their musings.

Relative Time

One of the marvelous things about Einstein's Special Theory of Relativity is that it can be presented without calculus and so is accessible to people with no more than high school algebra.  The key feature is the Lorentz transformation, which relates measurements of time and distance for coordinate systems in motion relative to each other.  For example, moving at 98% of the speed of light gives a Lorentz dilation factor of 5, and an observer moving at this speed will see stationary clocks running 5 times too fast relative to his own.  This is often described as time slowing down for the moving system, and presented as an example of a space-traveling twin leaving at birth and returning to earth on his 10th birthday to find his twin 50 years old. 


But if motion is relative, who's to say who is moving?  Won't the twins both see the other's clocks as running fast?  This is often called the Twin Paradox, and the trick is the turnaround, since the traveling twin must turn around halfway and travel in the opposite direction to arrive back home, and this is where most of the time shift happens.  This is dissatisfying as a thought experiment, since the instantaneous boosts to near light speed at the start (and end), and the double boost backward at turnaround involve violent forces that real people could never survive.  This usually isn't discussed, and many presentations duck the question by saying that Special Relativity only deals with constant motion, not the accelerated motion involved in launching, turning around, or landing. 


However, this isn't so -- Special Relativity can handle acceleration, although calculus is needed and some of the mathematical tools of General Relativity help [10].  Even without equations, it seems much more satisfying to consider a twin travel case with human-scale acceleration, approximately the acceleration we feel at the earth's surface due to gravity, 1-g [11].  Instead of an instant boost to near light speed, the traveling twin would gradually pick up speed, reaching 98% of light speed only after almost 2.5 years, when he would stop accelerating.  Looking out the window, he can see that clocks at rest are running fast by a Lorentz dilation factor of more than 6, and if he measures his speed by timing how quickly he passes mileposts at rest he notices that his apparent speed is much faster than the speed of light, and if he also looks at the time shown by a clock at rest he can make the remarkable observation that his apparent superluminal speed is exactly what he'd calculate by classical physics using the rest time.  Having made these interesing observations, he begins slowing down at the same 1-g rate, reaching zero speed after another 2.5 years and, continuing to accelerate toward home, again reaches over 98% of light speed after a total of 7.5 years of travel, then slows for the last 2.5 years to gently land at rest back home after 10 years, experiencing nothing more violent than we all do every day with gravity.  Having spent most of the time at much less than the 98% of light speed in the first example, his twin will not have aged by nearly as much as five times more, but will still be much older, about 25 years old. 


Thinking further, it is interesting to consider what would happen if the traveling twin were away longer, say 20 years instead of 10 but again segmenting the trip into 4 parts with similar 1-g accelerations, which would reach a maximum of 99.99% of light speed and a peak time dilation Lorentz factor of 74.  Returning, almost 300 years would have elapsed on earth and he would not expect his twin brother to be alive.  But new generations of people would see him as a time traveler, not a paradoxical backward in time traveler, but as someone who has lived a very long time without the usual ravages of age.  Thinking even further, one can ask how old must such a 1-g traveler be to have come from a date in the past, like the year 1 CE.  The relative time increases almost exponentially near light speed, more than doubling with each passing year for the traveler, so a 28 year journey (4 segments of 7 years) could bring the twin of an early Roman emperor to us, but such a visitor from that era of the past couldn't be much younger than 28 without enduring inhuman acceleration.  Interestingly, a 1-g traveler from the beginning of time (14 billion years) would have to be about as old as the limit of human lifespan, 96 years.


Gödel and Einstein

Albert Einstein's discoveries in physics are legendary, and in the twentieth century the world of mathematics was also turned on its ear, by Kurt Gödel's incompleteness theorem.  Gödel and Einstein both left Germany for the United States and were close friends near the ends of their lives in Princeton, New Jersey, where they often walked home together from their offices at the Institute for Advanced Study.  The story of their friendship and its intellectual consequences is related by Palle Yourgrau in A World Without Time:  The Forgotten Legacy of Gödel and Einstein.


If Einstein had succeeded in transforming time into space, Gödel would perform a trick yet more magical:  He would make time disappear.  Having already rocked the mathematical world to its foundations with his incompleteness theorem, Gödel now took aim at Einstein and relativity.  Wasting no time, he announced in short order his discovery of new and unsuspected cosmological solutions to the field equations of general relativity, solutions in which time would undergo a shocking transformation.  The mathematics, the physics and the philosophy of Gödel's results were all new.  In the possible worlds governed by these new cosmological solutions, the so-called rotating or Gödel universes, it turned out that the spacetime structure is so greatly warped or curved by the distribution of matter that there exist timelike future-directed paths by which a spaceship, if it travels fast enough -- and Gödel worked out the precise speed and fuel requirements, omitting only the lunch menu -- can penetrate into any region of the past, present, or future.


Gödel, the union of Einstein and Kafka, had for the first time in human history proved, from the equations of relativity, that time travel was not a philosopher's fantasy but a scientific possibility.  Yet again he had somehow contrived, from within the very heart of mathematics, to drop a bomb into the laps of philosophers.  The fallout, however, from this mathematical bomb was even more perilous than that from the incompleteness theorem.  Gödel was quick to point out that if we can visit the past, then it never really "passed."  But a time that fails to pass is no time at all.  Einstein saw at once that if Gödel was right, he had not merely domesticated time:  he had killed it.  Time, "that mysterious and seemingly self-contradictory being," as Gödel put it, "which, on the other hand, seems to form the basis of the world's and our own existence," turned out in the end to be the world's greatest illusion.  In a word, if Einstein's relativity was real, time itself was merely ideal.  The father of relativity was shocked.  Though he praised Gödel for his great contributions to the theory of relativity, he was fully aware that time, that elusive prey, had once again slipped his net. [12]


Yourgrau's presentation of Gödel's solution to Einstein's equations and its consequences is not the common view, but neither is the incontrovertible history of the close personal relationship between these two intellectual giants.  One may expect that more is yet to come in the story of time.


1. The Project Gutenberg Etext the The Confessions of Saint Augustine is available at: This etext was prepared by Robert S. Munday from the 1921 Chatto & Windus edition, translated by Edward Bouverie Pusey.


2. Zeno's paradoxes from the 5th century BCE are classic arguments against common concepts of time and space.  See the Wikipedia article for more on the tortoise and hare, the arrow, and other paradoxes.


3. Isaac Newton's Philosophae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), was first published in 1687.  The quote is from the Scholium to the definitions in Philosophiae Naturalis Principia Mathematica, Bk. 1 (1689), see  This quote from Newton is widely repeated in books and articles on time.


4. Aristotle is quoted without specific attribution in the heading of Chapter 8, Time and Motion, of Lawrence W. Fagg's book, The Becoming of Time:  Integrating Physical and Religious Time, Duke University Press (2003).  Physics, By Aristotle, Written 350 B.C.E., Translated by R. P. Hardie and R. K. Gaye is available at:  The direct quote can be found in Book VIII part 1, although it seems to refer to a more extended discussion in Book IV part 11:  "When, therefore, we perceive the 'now' one, and neither as before and after in a motion nor as an identity but in relation to a 'before' and an 'after', no time is thought to have elapsed, because there has been no motion either. On the other hand, when we do perceive a 'before' and an 'after', then we say that there is time. For time is just this-number of motion in respect of 'before' and 'after'.   Hence time is not movement, but only movement in so far as it admits of enumeration. A proof of this: we discriminate the more or the less by number, but more or less movement by time. Time then is a kind of number."


5. Sacha Stern, Time and Process in Ancient Judaism, The Littman Library of Jewish Civilization, (2003), p. 2 and footnote.


6. ibid, p. 18.


7. ibid, p. 118-120.


8. Lawrence W. Fagg, The Becoming of Time:  Integrating Physical and Religious Time, Duke University Press (2003).  Chapter 6, Probing Beyond:  Spiritual Perceptions of Our Cocoon's Temporality, p. 86-87.


9. Scientific American special edition A Matter of Time (2006), in print and online, see


10. E. F. Taylor and J. A. Wheeler, Spacetime Physics (2nd edition), (1992).  Box 4-1 (p. 132), "Do we need general relativity? No!"


11. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation, (1973), Section 6.2 Hyperbolic Motion, and the suggestive Exercise 6.3.


12. Palle Yourgrau, A World Without Time:  The Forgotten Legacy of Gödel and Einstein, Basic Book (2005).  Chapter 1, p. 6-7.