September 16, 2006

“THERE was a young lady named Bright/ Whose speed was far faster than light/ She set out one day, in a relative way/ And returned on the previous night.”

We usually have an intuitive perception of time but when we are asked to explain what it is, we find ourselves at a loss to describe it consistently. According to Paul Davies (About Time, pp 16, 17, 53): “People often ask: ‘what is time?’ Many centuries ago, St Augustine of Hippo, one of the world’s most intellectual thinkers on the nature of time, gave a perceptive, if enigmatic, reply to the question: ‘if no one asks me, I know; but if any person should require me to tell him, I cannot’.”

We are in no better condition now than St Augustine. Lee Smolin (http://members.fortunecity.com/templarser/whattime. html.), a prominent physicist of our times, expressed himself similarly when he wrote, “I have been studying the question of what time is for much of my adult life. But I must admit at the beginning that I am no closer to an answer now than I was then. Indeed, after all this study, I do not think we can answer even the simple question: ‘What sort of thing is time?’” It however does not mean that we have not made any headway in understanding time over the last centuries.

We become conscious of time when we observe changes in the state of things and phenomena around us. We notice the changes in seasons and their periodicity. Winter invariably gives way to spring that leads us into summer and then the fall and the cycle is repeated endlessly. Naturally, we start pondering how long winter lasted compared with the summer season. The “how long” in this perspective can only be answered with any degree of satisfaction in terms of some ‘measure of time.’ We are led to think similarly by the alternation of day and night. The waning and waxing of the moon gave people a measure of time in terms of the “moons”. For example, such and such thing happened so many moons ago. Although this is quite a crude measure of time yet it provided an elementary kind of awareness of it.

Galileo’s observation of the swinging of a pendulum gave an incentive for measuring time more accurately. He “timed” the swinging of a hanging lamp in his church with the beating of his pulse in his wrist and concluded that the time period of a pendulum swing was independent of its amplitude (width of the swing). In order to measure time more accurately for verifying his experiment and the motion of moving objects, mechanical clocks were invented.

A philosophical prelude

People have been philosophising ever since the history of human intellectual endeavours was recorded and various philosophers thought of time in their own respective ways. Often they gave metaphysical descriptions of time which defy precise and accurate comprehension. The idea of time was more often associated with God in one way or the other and that was not unnatural either. The story of the creation of the universe and mankind narrated in the Bible and the Quran is intricately woven in the fabric of time. According to the Bible, God created the universe – including our planet Earth, humankind and all of the other animal and plant life – in six days. Thus, the creation of space (universe) and time was almost simultaneous. This is also in accord with the Quran (29:59). According to the Bible, after creating the universe in six days, God rested on the seventh.

Many philosophers had difficulties in comprehending time and they came to the conclusion that time was unreal. For instance, Richard Morris (The Big Questions, p.11) wrote, “The problem of nature of time is not an easy one. Contemplating it has caused some philosophers, such as Parmenides, Plato, Spinoza, and Hegel, to conclude that the concept of time contained serious contradictions, and that, therefore, time couldn’t be real.” He then commented on this view as follows: “I don’t know about you, but I can’t help but feel that this is an evasion. Or at least an attempt to solve a problem by making the claim that the thing that is problematic doesn’t really exist.”

Many philosophers believe that perception of time is subjective and mental. That is fine but if time cannot exist independent of our mental states, does it mean there was no time before human beings came into existence. Cosmology tells us that our universe came into existence some 14 billions years ago and our earth is some six billion years old. Homo sapiens are quite recent, that is, only a few hundreds of thousands years. If time is all mental and subjective, should we conclude that time began with the advent of homo sapiens? What about the origin of the universe which began 14 billion years ago? We are in the same kind of dilemma here as of the belief that the moon does not exist until we look at it. This kind of time conception is not very helpful and does not have a place in science.

Physical time

We became conscious of physical time with the inception of empirical science. The mechanics of moving bodies could not be comprehended without the concept of physical time. For instance, speed (velocity) which is a fundamental concept in physics is defined as the rate of change of position of a moving body. The rate of change can only be understood if we measure the change of position from, say, point A to another point B in time. In Galileo’s time, there were no clocks so he timed the swing of a lamp with the beats of his pulse.

For centuries, time was considered as absolute and universal. Newton believed time to be “absolute, true and mathematical, which of itself, and from its own nature, flows equably without relation to anything external.” Time perceived as flowing uniformly like a river is unidirectional like the flight of an arrow.

The directionality of time implied that it is irreversible. Once you have made an omelet from an egg, you can not reconstitute the egg by reversing the process. If you made a movie of the process of making an omelet and ran it backwards, you can watch the omelet turning into an egg but it does not happen in real life.

The mathematical equations describing the fundamental laws of physics are however symmetrical (reversible in time meaning that we can change the sign of time, say from positive to negative and still recover the original equations). Richard Morris described it differently. He wrote (The Big Questions, p.13), “If a videotape were made of the motion of the planets in some distant star system, for example, you would not be able to tell whether the tape was being played forward or backwards, no matter how much physics you knew: If the planets were moving backwards in time, their motion would still be accurately described by the same laws of gravity.”

Commenting on the reversibility of time, Richard Feynman (Six Not-So-Easy Pieces, p.29) wrote, “But if we look at the individual atoms themselves, the laws look completely reversible…apparently it is true that the fundamental physical laws, on a microscopic and fundamental level, are completely reversible in time. However, “…all obvious phenomena are irreversible on a large scale,” wrote Feynman. According to Omar Khayyam (quoted by Feynman): “The moving finger writes, and having writ, moves on.”

Time is not absolute

Newton’s equations of motion were in conformance with an absolute nature of time as was commonly believed for a couple of centuries. Discrepancies began showing when they were applied to bodies moving at a very high speed, close to that of light, for example. Whereas motion was known to be relative with time considered absolute in Newton’s mechanics, when the bodies moving at very high speed were considered relative to a beam of light, anomalies appeared. These anomalies were “fixed” on an ad hoc basis by using the Lorentz transformation formulas but there was no reasonable explanation for them. Einstein’s revolutionary contribution for resolving these anomalies was that he regarded both time and space as relative entities. According to him, the only absolute entity in the whole universe was the speed of light. With whatever frame of reference you measure it, it remains constant. If for instance, a spaceship is moving at 0.5c, where c is the speed of light, speed of light should appear to be equal to 0.5c to an observer riding the spaceship, according to the usual method of calculating the relative velocities. But according to Einstein, it still is equal to c. How can that be? Einstein suggested that it is so because time is slowed down for the observer riding the spaceship. Time in this sense is not absolute but relative. Without going into any mathematical details, I want to state that the relativistic time is absolutely consistent with the mathematical formulation.

This created several paradoxes (twin paradox is one of them) but all of them are satisfactorily explained by Einstein’s theory of relativity. According to Paul Davies, “The major upshot of his new theory of relativity, then, was the prediction that time and space are not, as Newton had proclaimed, simply ‘there,’ fixed once and for all in an absolute and universal way for all observers to share. Instead, they are in some sense malleable, able to stretch and shrink according to the observer’s motion.”

Is this the end of the story? By no means.

Time before big bang?

The theory of the big bang was formulated in the middle of the 20th century. It holds its ground even now but some other notions and ideas have also appeared. The big bang was conceived by playing the movie of the evolution of the universe backwards. It was then believed that originally the universe must have started from a singular point (at t = 0) at which the density of the matter and temperature were infinite. The point in universe then exploded with a big bang and started expanding and cooling. According to this theory, there was a beginning of the universe; it came into existence at a certain time which we say was the origin of the universe. The universe began some 14 billion years ago. According to this theory, time and space were created simultaneously. There was no time “before” the big bang; talking of a “before” is meaningless in the sense of the big bang theory.

But this may not be true because extrapolation of Einstein’s equations of general relativity to times smaller than the Planck time is not correct because his theory is not valid in that region. You can thus not extrapolate to t = 0. It is the theory of quantum mechanics which applies at the subatomic scale. So it’s not very certain that time did not exist before the big bang. The string theory was devised to avoid the singularity (at t = 0) which is a consequence of applying theory of general relativity at t = 0. According to the string theory, there was no singularity and the universe began from an infinitely small but a finite string. The universe may indeed be cyclic, starting from a small string; expanding and expanding, and then start contracting and reaching the infinitely small string again. These cycles might go on for ever and ever.

There are many theories regarding events close to or even earlier than the big bang. For example, “According to Hawking and Hartle, time originally resembled a dimension of space (this is what Hawking means when he speaks of ‘imaginary time’), so that initially there were four space-like dimensions, and nothing resembling time as we know it. According to this hypothesis, the universe had no beginning in time. Time came into existence only when the space-like imaginary time evolved into the dimension of time that we know” (Richard Morris, pp 29).

Andre Linde has formulated the theory of chaotic inflation according to which numerous big bangs occur every instant of time creating numerous new universes. There are, thus, theories and conjectures about the origination of the (mega)universe or multiverse, none of which can be empirically tested yet with the available technology. A Harvard physicist Cumrun Vafa believes that time may be two-dimensional.

It is hoped that when we have a “Theory of Everything” (Toe), we shall gain better understanding as to how the universe began. Toe will hopefully tie all the loose ends and provide a deep insight into all the cosmic mysteries. Or, so we hope and anticipate. This will change our knowledge and perspective of physical time also.

The writer akramgill@yahoo.com is a US-based engineer who did his PhD from London University

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