Time is rhythm: the insect rhythm of a warm humid night, brain ripple, breathing, the drum in my temple - these are our faithful timekeepers; and reason corrects the feverish beat.


What is time?

Time seems to be with me, within the very core of our being, all through my waking hours; and to all appearances, it is also  drifting silently and unhaltingly out there in the external world as well as. It is the most insubstantial element in human consciousness that is experienced very profoundly. Each one of  us tastes a slice of time and then suddenly drops out or strays away from its course.

When Saint Augustine declared, "If no one asks me, I know  it; if someone asks me, I know not." He was not talking about God, but about Time. Countless thinkers before and since have wondered about the nature and mystery of time. From the Upanishadic seers of ancient India and Pythagoras of reflective Greece through medieval scholastics to countless philosophers and scientists down to our own age, human minds have pondered on the nature and mystery of Time, and acquired but glimpses of its essence.

At the one extreme, thinkers have wondered and argued about the reality of time. Some have contended that time is mere illusion while others have insisted that it is as much an entity in the external world as the sun and the moon which help us measure it. No matter what, time is surely is an ever-present feature of perceived reality, powerful and useful in the scientific grasp and description of the world.

Time has been compared to a steady stream, gliding smoothly or rushing torrentially, for on occasion it seems to linger on, while on others we feel it  galloping away at undue speed. Slow or fast, in the phrase of a poet,  "there is no arresting the wheel of time."  Historians have referred to chunks of time as stagnant or tumultuous. Time has been called a robber of our possessions, a poison, the  dissolver and destroyer of all, for it seems to gobble up every thing and event and episode. Inimitable Shakespeare described time as "the king of men, he's both their parent, and he is their grave..." Yet time has also been called precious, and praised as a healer of heartache, a consoler in grief. In the words of Ovid, temporis ars medicina fere est: time is generally the best medicine.

We feel intuitively that it is time that keeps the world going, that it is time that makes things happen, for a world where time did not move  would be static and lifeless, more still  than a painted scene on canvass, more frozen than a sculptured bust.

Our minds cannot picture a moment beyond which there will be no moment, nor one before which no time there was. Unending time seems to have had no beginning either. Such at least is what the purely reflecting mind seems to suggest. Time, we are inclined to think, is eternal. Like expansive space and never-ending numbers, time is a baffling infinity.

Time reckoning and measuring

We have all been touched by the rising and setting of the sun, the waxing and waning of the moon. Some of us have even observed the changing configurations of constellations in the skies during different zodiacal periods. From the shedding of leaves and the blossoming of flowers we conclude that all nature is struck by seasonal changes, the ambient cold or warmth clearly provoking respite or activity. But it is not as obvious that the behavior patterns of some animals are affected by solar activity and lunar phases also. It has been well established, for instance, that oysters, even when in the depths of  water where there is no light,  open and close,  shell-dancing, as it were, with lunar phases [1].

Time is one of the first parameters of the physical world that came to be measured by the human mind.  Over the ages, in all societies and civilizations, time has been recognized, recorded and reckoned. Aside from the biorhythm that subtly governs our moods and potencies, periodic changes in our environment have provoked temporal units and insights into the nature of time.

It is interesting that linear time is registered with cyclic changes [2]. We have the hour, inspired by the rising of a star before daybreak [3]; the day, inspired by sunrise and the sunset;  the week, resulting from the naked-eye visibility of five planets, the sun, and the moon; the month, related to the periodic reappearance of the full moon; and the year, provoked by seasonal cycles [4]. Astronomers speak of the great year which consists of 26,000 years [5], while the civilization of ancient India defined still larger time units, stretching to the yuga  and the kalpa which span several million years [6].

At the other extreme, we have defined and measured mind-bogglingly small fractions of a second,  touching fleeting  periods of picosecond and nanosecond durations in our experiments [7]. Modern physics has tracked down elementary particles with pathetically brief lifetimes [8]. These breakthroughs would be impossible from mere speculative discourses on the ephemeral nature of experienced life. While philosophers debate about the reality of time, experimentalists, taking perceived reality as the starting point, go forward and accomplish the most fantastic things.  At the same time, at the conceptual level, modern cosmologists unhesitatingly talk of Planck time, whose magnitude, though simple to write out on a piece of paper, is beyond the visualization by  normal  human minds [9].

Countless measuring devices have been constructed for the measurement of time: from sundials and hour glasses to pendulum chronometers, spring watches, digital clocks and more. What is important to note is that all time measuring devices have one thing in common: change. One cannot measure time if there is no change.

This empirical intertwining of motion and time measurement is the origin of what is known as the relational theory of time, according to which the concept (and reality) of time is intimately related to changes in the world. Time, in this view, is merely "the order of succession of perceptions." This has been the source of endless arguments among philosophers: some have regarded time as no more than an impression created by a series of changes while others have given it a more independent status.

Homogeneity and continuity of time

              As with space, an important characteristic of time is its homogeneity. This simply means that all along its ceaseless flow the entity we call time is uniformly the same. There is no difference, qua  time,  between an hour or an instant some eons ago and the same in our temporal locality.  Using a spatial analogy, time is like an interminable line, any sector of which is identical in its essential nature to any other.

              We may also look upon time as a smooth and flawless highway that is being continuously created which in essence and rate of formation is the same at every inch or mile of the path, though a host of different entities may be seen all along it. Every instant of time has another whence it emerged, and yet another into which it merges.

              This implies that there was no beginning, nor will there be an end to time, for terminal points are, by definition, different from all others in being without a predecessor or successor. Even in the theological framework in which the universe had a moment of creation, that was a significant point in  time, rather than the starting point of time. God, the everlasting, is said to exist in Time.

              Recall that space has local inhomogeneity, but this is not the case with physical time. However, psychological time may be experientially non-homogeneous, some durations appearing to be denser (longer) than others.

              Like the spatial line again, time cannot be broken down to some ultimate indivisible unit. We speak of instants and points, but they all merge into neighboring dots in a smooth and inseparable continuity. That is why we have the image of time flowing, rather than dropping like a series of pebbles. However, it is important not to take the analogy between space points on a line and time-instants too far: such identification has led to some paradoxes in the history of human thought [10].

              Some theoretical physicists have toyed with the notion of a fundamental indivisible time interval, dubbing it the chronon [11]. Aside from some neat mathematical formulations, this has not led to any significant insight or verifiable result of consequence [12].

Absolute time

              Isaac Newton spoke of an  "absolute true and mathematical time," called duration, which flowed uniformly, and he distinguished this from "relative, apparent and vulgar time... estimated by the motions of bodies [13]." This is in accordance with our intuitive grasp of the world, for one is normally inclined to imagine an instant of time that is universally pervasive. Right now,  there is a fleeting moment in our conscious experience of the world corresponding to which, we imagine,  there is a moment that ticks away at every nook and corner of all the universe. It is as if there is a cosmic pulse, a steady stream of subtle seconds  flowing imperceptibly, carrying the  universe in its entirety along a single temporal course. It seems as if there is a cosmic simultaneity.

              The notion of absolute time through which an absolute space endures is an ancient philosophical predilection, based no doubt on our common-sense grasp of perceived reality, and it is sufficient for our everyday discourse. It has also served as a cornerstone on which three centuries classical physics rested. But, as happens so often in our  interpretation of the world, as we delve deeper into the roots of perceived reality, we find that there is no such thing as absolute time, though for many practical purposes one may assume such an entity. Physicists have discovered that the notion of absolute time crumbles down upon probing analysis, strengthened by careful observations of phenomena,.

              It is remarkable that so much of significance and certainty was achieved on what turned out to be an erroneous view of so fundamental an aspect of the world. It should be noted here that though physics has established with conceptual clarity and experimental certainty that there is no such thing absolute time, the notion is still useful in speaking about the age of the universe. For when current cosmology proclaims that the universe is some fifteen billion years old, an unspecified absolute reference system is implied.

              Theologically inclined writers in the past used to be more specific about the date and time of cosmic creation. Recall the memorable assertion of Bishop Usher that "The beginning of time fell on the beginning of the night which preceded the 23rd day of October, in the year 4004 B.C." The Bishop was merely echoing the with more specificity the belief of his age. He has his counterparts in other theological systems.  Modern defenders of ancient world views have tried to explain the Book of Genesis and its equivalents in other cultural contexts by suggesting that if we  appropriately transform reference systems, the fifteen billion years of current science could be made to correspond to a week and whatever in the scale of the divine creator [14].


Information transmission

              Our perception of reality requires sensory inputs, and light is a primary information messenger for the goings on in the world around. This is especially so when we take note of whatever is there in the skies above. When we fix our eyes on a star at night our first impulse is to think we are seeing it such as it is at the moment that flashes through our consciousness. But knowing that light takes time to travel a distance, and that the distance to travel is considerable here, we are reminded that what we see is a body such as it was a few years or a few hundred years ago. We are indeed looking into the distant past every time we cast our glance in stellar space.

              What this implies is that even if there was an absolute time, our knowledge and perception of events in the world depend on how far we are from the point or region where the events occur, for it takes time for light to travel the intervening distance.

              This insight into the nature of perceived reality would be impossible if we did not realize that light travels with a finite speed. If, as had once been imagined, light traveled with infinite speed, then there could be instantaneous transmission of information. Since it appears that nothing physical can travel with a speed exceeding that of light, instantaneous transmission of information becomes a physical impossibility [15].

              This is a matter of some significance in our understanding of the world. For it appears that, in principle, it will  take a finite interval of time, small or large, for information to pass from one entity to another. This has always been one of the fundamental tenets of physics. However, careful experiments with photons and electrons which have been conducted during the past two decades, based on the fundamental theories of 20th century physics, suggest that in certain microcosmic phenomena, an event in one point of space may affect the status at a distant point without any lapse of time [16].

              The possibility of instantaneous transmission of information, even between subatomic entities, opens up all kinds of possibilities [17]. Some have argued that this makes telepathy (the reading of one mind by another) more than magic-mongering on a stage, for perhaps these experiments show that minds can receive and send signals in instantaneous flashes. Scientific validation for telepathy has been sought by its practitioners and subscribers for a long time [18]. Some have regarded the results of these experiments as confirming mysticism, while others have described such interpretations as a "flurry of flap-doodle [19]."

              And yet, serious physicists have also been tempted to come up with models and processes in terms of which instantaneous information transmission would become a possibility. One such idea was proposed by the brilliant and unorthodox quantum physicist David Bohm who introduced the notion of implicate order which is best understood by means of his analogy. Consider a table standing on the floor. The universe we experience is analogous to what creatures constrained to the flat floor would feel: to them the four feet of the tables are unconnected, though in fact they are interconnected, via the table top. So too, suggested Bohm, every event in the space-time world is intrinsically linked to every other via dimensions beyond the modes of perceptual reality. Certainly not inconceivable, and perhaps not an impossibility, but still only in the realm of theoretical speculation.

Relativity of time

               The happier the time, the more quickly it passes.
                                                                                                     The Younger Pliny

              We have all experienced the truth in Pliny's words, but he was referring here only to psychological time. It turns out that, in a different sense, physical time also passes at different rates.

              One of the intellectual revolutions of our century is embodied in what is known as the special theory of relativity, mentioned earlier. This theory uncovered a fundamental error in the ancient view of space and time by which the two are separate and absolute. The theory of relativity revealed an intrinsic intertwining of space and time which results in the demolition of their independent absoluteness. What this means is that an instant or interval of time makes sense only in relation to a point in space. This discovery gave a death-blow to the classical notion of simultaneity.

              An important consequence of this fact is that durations of an event, that is to say, the time interval between two occurrences, will also depend on the space frame or reference system. This means that if two observers set their perfectly functioning watches synchronously, and one of them gets into a train which begins to move at a certain speed, then the moving observer's watch (i.e. time in the moving reference system) will be flowing at a slower rate than for the stationary observer, and vice versa! Physicists call this puzzling phenomenon time dilation. For this to be significant enough to be observable, however, the train should be zooming at nearly three hundred million kilometers a second which is a technological impossibility (as of now).  The veracity of time dilation is, nevertheless, an empirically verified consequence of Einstein's theory since physicists track down and measure particles that move with such uncommon speeds [19]. 

              Our understanding of the underlying link between space and time follows from the recognition that there is no such thing (in the observable sense) as absolute motion [20]. Every motion (or rest) that we can put into evidence by any observation, simple or sophisticated, is with respect to something else. An ant may be crawling on a table at rest, but the stationary table is moving along with the earth. The earth's motion is with respect to the sun, and the sun itself is voyaging with respect to our galactic center which in turn is receding with respect to other galaxies, and so on.

              The impossibility of absolute rest or motion leads to the non-existence of absolute space or time. Though intuitively we may picture the stars as moving in an absolutely stationary empty space, a crucial experiment performed in the last quarter of the 19th century, and repeated many times since, established beyond a reasonable doubt  that there is no observational evidence whatever for such a system at absolute rest [21].


              The intertwining of space and time leads to a new concept of the perceived universe. The basis of perceived reality is not simply space and time, but a complex of both which we call space-time. Thus, as Herman Minkowski stated, "space by itself, and time by itself must sink into the shadows, while only the union of the two preserves independence."

Since both space and time have a non-discrete character, we refer to the substratum of the physical world as the space-time continuum. We say that space-time has a dimension of three-plus-one, to emphasize the fact that time as a category is in essential respects different from space. The notion of space-time, introduced by Herman Minkowski, admits of an elegant mathematical formulation. To get a general idea of this, let us consider a pair of orthogonal  axes in which we take the horizontal axis to  represent space and the vertical one to represent time (both with respect to a specified frame of reference). Then, any point on the plane would correspond to a point in space at a specific time.  Rather than points in space and instants of time, we now describe the world in terms of space-time events. Time, to use a phrase that has become popular even in common parlance, is then the fourth dimension [22].

Imagine a line AB on this space-time graph [x: horizontal, t; vertical axes] would correspond to a particle which was at a space point x1 at an instant t1 and moved to x2 at time t2. A  horizontal line EF makes no sense since it implies that a particle moved from one point of space to another while time stood still. A particle that stands still during an interval of time would be represented by a vertical line like GH.

How, one may wonder, does this essential interconnection between space and time remain hidden from our normal perceptual modes? The answer to this question is to be found in the stupendous speed of light. Light travels at the incredible speed of three hundred million kilometers a second, a fantastic speed compared to anything we are familiar with. Furthermore, the formulas describing processes in the world when the space-time connection is taken into account, and those when the connection is ignored, become identical when ordinary speeds are involved [23].

In other words, if the universe had been designed ( or had evolved) with a much smaller value for the speed of light, or if we happened to be sentient beings buzzing around with speeds comparable to the speed of light, then right from our conscious stage in life we would have recognized the space-time nature of the physical world.

Asymmetry of time

There is an important difference between spatial extension and temporal evolution. Given a spatial line and direction one may move forward or backward with respect to the direction. But this seems to be impossible on  the temporal line. We always move from the present into  the future or the future is always transforming itself into the past, (whichever metaphor one wishes to choose), but never is the opposite true. There is an asymmetry in the flow of time. Shakespeare expressed the asymmetry of time with his inimitable power of words when he spoke of "the dark backward and abysm of time.

This has two consequences: On the one hand, we cannot move back in time. Whatever has transpired has left its relic, legacies, and records. No one can bring back yesteryear, or even yestersecond, for as Milton wrote [24] in his Paradise Lost,

               But past who can recall, or done undo?
               Not God Omnipotent.

Yet, in another meaning of the word recall, we all can and often do recall the past, for that is what memory is. Here we recognize an interesting aspect of mind and consciousness: they accomplish things that are impossible in the physical world. The scenes and events of days gone by can be brought back in an instant to the mind's eye;  even  ancient episodes of the distant past that we never witnessed are brought back to vivid reality through the powerful pages of history. "Oh, but this is mere imagery," one may object, "it is not the past that comes back, but only its visions." But then is not the present also a vision? True, it is tangible, but not for more than an instant. Perceived reality may be looked upon as  fleeting transformations of the subtle into the concrete, of the insubstantial into the tangible.

Like a myriad other things, sheer familiarity makes us feel that what has happened cannot unhappen. However, there is a problem: If we rely on the fundamental equations that articulate the laws governing the physical world, there is something unacceptable (at least logically) in this state of affairs, for it turns out that if we reverse the direction of time in these equations, naught is affected [25]. The most solid laws of physics, crystallized in their mathematical purity, assure us that the world can evolve along one direction just as easily as along the other!          

Today's cosmologists and particle physicists have been grappling with this paradox in ways that are different from their predecessors in another century [26]. Current thinking tries to link time's asymmetry with the initial conditions of the universe. A theoretical solution to the paradox comes from the application of  microcosmic physics (quantum mechanics) to the description the universe at large (cosmology). Though wrought with  conceptual complexities such as fuzzy time and time seeping into space, this theory, introduced by Stephen Hawking and James Hartle in the 1980s),  is more than an intellectual tour de force. It is a penetrating peep into the birth-throes of the universe, through ingenious interpretations of sophisticated mathematics that calculate singularities in black holes. The essence of the theory is that time itself had its origin with the big bang, and that  it was the starting direction that determined which would be the past and which the future [27].

Time and causality

Time going in the opposite direction is equivalent to the future occurring before the past. Thus, if you fall down and hurt your knee, the reverse order in the chain of events would be your knee bleeding first and then your falling. This is obviously  impossible, because the hurt knee is a consequence of the sudden fall. Falling is the cause of the hurt knee which is the effect. Two fundamental tenets of physics (indeed of all science) are (a) that  every effect has a cause;  and (b) that the cause invariably precedes the effect.

The word precedes drags in the notion of time in our conception. In other words, the forward march of time is intimately related to the notion of cause and effect, or as we also say, to the principle of causality. To imagine time moving in the backward direction is equivalent to imagining that an effect has occurred before its cause. It is like hearing what a person says before he or she has uttered a word.

Let us look a closer into something that was mentioned in the last section: namely, that  physical laws permit equally the forward and the backward surge of time. This is quite apparent in the case of the pendulum: if it swings one way, it does so with equal ease the opposite way too. However, this does not seem to be happening in all cases. A child grows into a full grown person, a full grown person does not revert back to a child, like the pendulum does. In the case of most phenomena, changes seem to occur only in one direction.

Mathematical analysis reveals that any source which emits electromagnetic waves must also be receiving them at the same rate. This is very perplexing because what it implies is that the antenna in the radio station is not only emitting waves, but also absorbing the same waves. The emerging waves are called retarded  because they take time to reach a destination;  and the incoming ones are known as advanced because they are arriving even before they were emitted from a source. What is intriguing is that according to mathematical reasoning both types of waves must be present.      

The paradox resulting from  the symmetry with respect to time in the mathematical  formulation of physical laws may be understood by means of an analogy. Suppose that you are continuously throwing upwards a series of balls. The balls keep falling down and you keep throwing them. Both processes are occurring and we find nothing strange in it. Suppose, however, that you keep throwing the balls, and none of them is falling back to the ground. Wouldn't this be very strange?

In the case of the electromagnetic waves, though one expects this from mathematical analysis, it would be very strange if advanced waves arrived, because that would be equivalent to effects preceding causes. The question then is, is there a mechanism in the physical world that makes this impossible though it is mathematically permissible and expected?

One explanation to the paradox was provided by the Wheeler-Feynman dissection of the problem [28]. These two physicists showed (by a technical analysis of the situation) that in fact both advanced and retarded waves are always present, but that because of the various masses distributed all over the universe, electromagnetic waves are reflected back from everywhere in such quantities that all advanced waves are (for all practical purposes) simply canceled out (by interference effects), hence never observed. It is as if some kind of a counter-process is continually taking place, instigated by matter all over the universe,  as if to prevent the future from materializing itself prematurely. In order for this to happen, however, there must be sufficiently large amounts of matter in the universe to absorb and radiate. This leads to the intriguing conclusion that the principle of causality is a natural consequence of the enormous quantity of matter in the universe!

The roots of perceived reality can indeed be very different from the superficial impressions it creates.


Que serÓ serÓ and precognition

     If you can look into the seeds of time,
     And say which grain will grow and which will not....

                                                           - SHAKESPEARE (Macbeth)

The second consequence of time's asymmetry is that, in the phrase of a popular song, "the future's not ours to see."  While we have footprints on the sands of time, there is no trace of things yet to come. To be told that one recognizes the marks (to be) left by events yet unborn smacks of psychic mumble-jumble, unacceptable, if not offensive, to rational modes.

While even an omnipotent being  may not be able to undo the past, an omniscient being can know the future. But here we may imagine two types of futures: One which is pre-ordained, and simply remains hidden from our view, time serving as the unveiler of events already determined. From this perspective, in the words of Omar Khayyam,

               The First Dawn of Creation wrote
               What the Last Day of Reckoning shall read.

From this perspective, we are only witnessing what was pre-ordained. If some religious traditions imagined a fate-etching God to have done the job of writing the script for the universe, mechanistic physics attributed the credits to its initial conditions. A ball projected in  air moves in accordance with the laws of gravity, but the particular path it follows depends very much on the speed and angle of projection. So too, the world evolves in accordance with immutable physical laws, but the specific modes by which its countless atoms and molecules move and interact were determined by the initial kick that each received.

This was the picture painted by physicists of the 18th and 19th centuries who, on the basis of their understanding of physical laws cast as differential equations, believed that the primordial push to the evolving universe determined once and for all times how every single atom and molecule would behave at every instant in the future. This implied that every aspect of the universe that is to emerge could be foreseen by a calculating super-intelligence that could track down the dynamic states of the constituents of the world. In a sense, such a view does away with time as a significant entity, for the phenomenal world is simply like the turning of the pages of a book since everything is already inscribed. Time does not play a part in the evolution of phenomena, it is a static course on which things appear to be happening. In this view, events in the world are like images on the walls of a long tunnel through which the train of consciousness is moving. Each of us, a passenger in the train, zooms past the images, experiencing and recording the scenes that come our way. In the process we feel as if the scenes are changing (i.e. that time is flowing) when, in fact it is the conscious spirit that is hurtling forward. 

This static view of time is mentioned by a character in a science fiction who says,  "...we think that time 'passes,' flows past us, but what if it is we who move forward, from past to future... [29]?"

In another view, however, the future may take unplanned turns, yet an omniscient mind can foresee what these would be. In a sacred book of Hinduism, the divine principle Krishna  reveals to a mere mortal events that were to transpire on the battlefield where they stood [30]. It is easy to imagine an all-knowing God who, by definition, knows the future also. But do human beings have this ability which is known as precognition? In 2600 BCE beautiful Nefertiti of ancient Egypt is said to have predicted that "A king shall come forth from Upper Egypt called Ameni, the son of a woman of the South [31]." Ancient Rome had its soothe-sayers too [32]. The prophesies of Nostradamus have impressed a great many [33]. All through history, knowledge of the future has ranged from the majestic spiritual splendor of religious mythology, through foretelling of royal undertakings to journalistic astrology spelling out occurrences in individual lives on the basis of birthdays [34].

Aside from revered prophets, paltry astrologers, and calculating physicists who can predict the precise spot where a missile will land or the precise time when a comet will reappear in the skies, there are some people who report flashes of recognition of events whose actual occurrence they themselves witness only later. In various forms, prophecy, divination, psychic powers, and the like have  held an appeal to the general public all through the ages and in all cultures.  Many honest people have had foreboding dreams, prescient insights, and dÚjÓ-vu experiences. Most, if not all, premonitions can be brushed off as fantasies and cute coincidences [35]. Yet, one continues to wonder whether  the human brain and the related consciousness have capacities of which we are as yet not fully aware [36].

Changes and the arrow of time

Let us pause to reflect over what I just noted: If there is no change, there can be no measure of time. The implication is profound. Contrary to general impression, it is not time that causes change, but it is change that causes time to flow! Here is a dramatic instance of cause and effect being mixed up. 

Heraclitus of Greece declared, "Everything flows, nothing stays the same [37]." And Terence the Latin poet said, "Omnium rerum, heus, vicissitudo  est! (Mark this, that there is change in all things.) This ancient wisdom has found a thousand reformulations among later philosophers and poets. But it was not until the 19th century that the connection between perpetual change and the direction of time was unraveled.

Careful observations put into evidence two kinds of changes. Consider first the falling of a stone from a table top or a child drinking a glass of milk. These are examples of irreversible change. Irreversible changes are changes which cannot spontaneously occur in the opposite direction. Thus, we cannot expect the stone to rise automatically back to the table top, nor the milk to pour back into the glass from the child's body. Indeed, if the transformation in an irreversible change happened backwards, it would be equivalent to time going in the opposite direction. This may be illustrated dramatically by running the film of a common event in the reverse. What appears on the screen will be the equivalent of how the world would appear if time were to change direction [38]. Thus we note that irreversible changes are what give time an arrow:  a direction of flow.

At first blush one might be inclined to think that if any brief event is filmed and projected on a screen one can always say if the film was running in the forward or in the reverse direction. A little reflection will reveal that this may not always be possible. Consider, for example, a pendulum swinging in an evacuated class case. If this change is displayed on a screen, one cannot be sure in which direction the movie is running. This is an example of a reversible change. Reversible changes are indifferent to time's arrow.

So if the notion of time arises only in the context of change, that of the direction of time makes sense only where change is irreversible. It turns out that irreversible changes are far more likely when large numbers are in any system undergoing change. In particular, since ordinary matter consists of unimaginably large numbers of atoms and molecules, all changes in which atomic/molecular constituents participate are irreversible. Hence in most natural phenomena that we observe on our scale, time does flow in one direction only.

If, however, we were to shrink down to atomic and subatomic dimensions and observe the changes which those individual entities undergo, where collective and mutual exchanges do not come into play, then we will be observing primarily reversible changes. In such a world time may flow either way, and it would make no difference.

Irreversibility and return: cyclic time

When irreversible changes are examined from the molecular perspective, another interesting insight emerges. This is best grasped through an analogy. Consider a deck of cards in which the component cards happen to be in a particular random sequence. Let us shuffle the deck, and the order becomes altered. As we shuffle more and more, say a hundred time, a series of different patterns of arrangement are generated after each shuffle. We are effecting an irreversible change, because it is impossible for the same set of configurations to arise during another hundred shuffles.

But is this really so? After all, the hundred shuffles correspond to a hundred different sequential configurations of the cards. Since we have only a finite number of cards, if we imagine performing the shuffling unceasingly, in principle, these very hundred sequential configurations  will be repeated again in one of our future exercises.

In Hindu thought there was the idea of periodic creation (by Brahma) and dissolution (by Shiva) of the cosmos: the cycle of birth and death was  not just for beings here below, but for the world at large too. This would take incredibly long time-spans called yugas. Heraclitus in ancient Greece spoke of cosmic conflagrations too, and the idea of eternal recurrence was given an extreme literal interpretation by some, as in the quote above. And Eudemus of Rhodes said:

Everything will eventually return in the self-same numerical order, and I shall converse with you staff in hand, and you will sit as you are sitting now, and so it will be in everything else, and it reasonable to assume that time too will be the same."

Physicists call this the ergodic hypothesis [39]. A rough analogy to this would be that if one keeps walking indefinitely in a park, sooner or later one will  trace back the paths one has already been through. In technical terminology the ergodic hypothesis states that every system will pass as closely as one may stipulate to every possible state. Using the mathematical theory of probability it is possible to calculate after how many attempts a given sequence of configurations will be repeated. This turns out to be a tremendously large number. And yet, as Bergson put it, "A group of elements which has gone through a state can ... always find its way back to that state... [40]

If now we replace the cards by the atoms, molecules and other  ultimate constituents of the material world, then the aspect of the universe at any instant would correspond to a particular card configuration. The processes in nature correspond to the shuffling. In principle, then, after a mind-boggling series of transformations, the same configuration can (and indeed must) re-emerge in principle! What this implies is that the universe will eventually revert back to any of its current states, after a sufficiently long (inconceivably large) lapse of time. In which case time reverts as in a cycle.

While this is very possible, even necessary in principle, in practice this is  beyond realistic recognition. For one thing, the time-span required for such a cosmic recurrence is unimaginable quintillions of times the age of the universe. Yet, that this is a possibility implies a radical departure from our traditional view of linear time: At the far, far distant future, time may turn back and bring the universe back to one of its way back when distant past state.

In the cosmological models that were developed during the 1920s, Friedmann and Einstein proposed a periodic model for the universe, by which the universe would expand and contract, then expand and contract again, etc. [41]. Such an oscillating universe could in a way be regarded as creating cyclic time, although it is also conceivable that after each oscillation the universe would begin to function under a quite different set of physical laws such as we cannot even imagine now. Such a circular model eliminates the paradox of the beginning and end of time [42].

Time ranges in the universe

It takes but a few minutes to glance through the papers, a hour perhaps to sit through a show, a few days or weeks to accomplish a task, a month for the moon to return to its shape, a year for the season to reappear, and so on. Things happen, events take place, episodes last in the phenomenal world  in varying durations of time. The range of time intervals, from the fleeting life-time of a fundamental particle, to the immense age of the cosmos itself, with human history and life-span in between, is impressive indeed.

We measure time in seconds or hours, in days or weeks or years, depending on the context. Each of these units is human-made, contrived for our convenience, provoked by our experience. In terms of these, we live for a hundred years at most, while our species itself has been around for a million years at least. But our recorded history is barely ten thousand years, and we may reflect upon the wonders and wasteful atrocities we have wrought in this relatively short opportunity we have had with civilization!

Mammals have been around for a few million years, and our planet itself appears to have been spinning around for a few billion years. And, by current reckoning, the age of the cosmos is between twelve and fifteen billion years.

All this is general knowledge, taught or should be taught in schools. We need to remember here as elsewhere as we read these pages that all this information - whether dependable or changeable - comes from an analysis of perceived reality with the aid of concepts, mathematics, and ingenious instruments.

Now is there, or more exactly, can we define a natural unit of time that is independent of human concerns and experiences? Yes, indeed we can. Consider some very small distance in the physical world, say the radius of the electron as it was pictured and measured by the beginning of this century. The time light takes to traverse this standard distance turns out to be 10-23 (human-defined) seconds. We may take this as the natural unit of time.

In terms of this unit, we live, not for a mere hundred years, but for about 1032 natural times units: an impressive figure, but not any longer than a hundred years. The universe, on this scale is about 1040 natural time units.


Transcending time

          You are the origin of the worlds and you are Time, their destroyer.


          No creature or thing we know of can disappear out of space, nor jump away from the temporal axis. The notion of anything beyond the  touch of time is simply  inconceivable. The whole universe, from minute matter to gigantic galaxies, is embraced in the arms of time, for who can imagine a world where time never ticks.

But would it be fair to say that what cannot be accommodated in the human mind does not or cannot exist?  An entity that is both particle and wave is a conceptual oxymoron, for a particle can be constrained to a  narrow nook in space, while a wave is smeared all over: yet the building bricks of the material universe are corporundals: particle-waves, or so they seem to be.

Are they then right, those mystic meditators who declare there is a reality  that transcends space and time? If change is what engenders time, if  time is a mere manifestation of change, then if there is something that is changeless, it must be beyond time. Now if we define, or envision the Divine as that which is  immutable, as the ever-unchanging principle behind the ceaselessly changing universe, then of course the Divine is bound to be beyond time.

However, it is not even necessary to go into esoteric mysticism to talk of transcendence beyond time. Fundamental physics, strengthened by hard core mathematics, has dragged us willy-nilly to states in this very tangible universe of ours where time as an entity naturally, not mysteriously, disappears. Yes, if anything should ever fall into the dismal depth of a black hole, technically known as a singularity, then, says a celebrated theorem of current cosmology,  it would be squeezed out of the temporal domain as well [44]! Unbelievable, inconceivable, fantastic, and whatever: but this is the translation into plain English of what the mathematical telescope unveils.

So, as with everything pertaining to the beginning and end of things, as with the ultimate essence of the most common experiences, time too is passive and serving us well when we are indifferent to it, but it becomes a teaser and baffling bully when we try to probe into its secrets.