Contemporary science has uncovered the relation between time and physical processes, making it possible to ‘grope’ for the first links of the time chain in the past and to project its properties to the distant future.

But what does modern science say about why time flows at all, and why only from the past to the future? I should immediately say that experts still lack an exhaustive, clear and generally accepted answer to this question. Nevertheless, a great deal has been achieved in this field, too, and we will have a quick look at some fragments of the achievement of the science of time.

In the post-Newtonian era, physicists have always emphasized a surprising property of the laws of nature: they do not in any way single out the direction of time flow from the past to the future.

We easily recognize this fact by looking at the simplest problems in mechanics. For example, let a ball roll along a surface, hit a wall at a certain angle, rebound and continue rolling. Now we can, in our minds, reverse the direction of time and imagine the ball rolling in the opposite direction, going through all the points of its trajectory in the opposite order. It is as if we had filmed the experiment and then projected the film beginning with the last frame. All laws of mechanics describe the motion of the ball equally well both in the forward and the reversed directions of time flow.

Here unfolds the story of the momentous achievements of science in the 20th century. I would say that the most impressive discovery was made at the very beginning of the century by Albert Einstein when he created relativity theory. He showed that there does not exist any ‘absolute time’, no unified unchangeable river of time which impartially carries all events occurring in the Universe.

Academician A. Alexandrov of the Academy of Sciences of the USSR wrote: ‘Einstein's greatest discovery which became the cornerstone of relativity theory and a turning point in the general physical and philosophical interpretation of space and time was the revelation that nature knows no absolute time.’

Evidently, time behaves as a river with constant, unchangeable flowrate only in the habitual conditions of relatively slow motions and not very high interaction energies. Its properties are very different under very unconventional conditions! We will discuss this later in great detail.

The discovery of the relative nature of time is contained in relativity theory that Einstein created in 1905. An enormous number of books have been written about Einstein, definitely more than about any other physicist. Several factors explain this. I will quote the opinions of several well–known scientists who knew Einstein personally, and also Einstein himself; these sources may help, to some extent, to reconstruct the image of this personality and to understand the causes of his immense popularity.

Which of us was not immersed in our youth in Herbert Wells' famous short novel The Time Machine? The protagonist of this story uses a device that can travel in time to visit a very remote future of the Earth. Wells also imparted to this device the property of reverse motion into the past.

A large number of books have been written which fantasized about the possibility of freely visiting the past and the future. In all likelihood, their authors were never in doubt that their inventions belonged to pure imagination and treated this as nothing more than a literary stratagem.

The entire experience of mankind and scientific knowledge have made inevitable the conclusion that travel in time is impossible. Space is where motion is allowed. Say, travel on the Earth is possible in different directions and one can also return to the starting point. On the contrary, we are seemingly unable to choose the direction of motion in time, we are bound to ‘float’ passively in this flow. It was assumed that here lies the dramatic difference between time and space.

Einstein's discovery of the surprising properties of time in 1905 demonstrated the fallacy of the view that we are ‘captives’ of the river of time and thus cannot ‘steer’ on it; it was seen as a fruit of not knowing, as a consequence of the limited possibilities that mankind had during its preceding history. But does this mean that we are free to roam in time?

I began preparations to publish this book in English at the end of 1991; for a number of reasons, this stage stretched to several years. An oriental adage says: ‘Hours tick away, days run away but years fly away.’ These words are a reflection of our subjective perception of time intervals in the past, of what we remember of them. For most people, the feeling of the flight of time is considerably intensified when one turns in one's mind's eye to larger and larger blocks of time which one has lived through. I distinctly feel now that it was virtually yesterday that I was writing this book, even though several years separate me from those days and so much has happened and so much has changed. In that period, I began working in a new place, as astrophysics professor of Copenhagen University. My native country, the former USSR, the former enormous empire, broke into pieces and is trying, in untold hardship for its peoples, to claw its way out of the frightening historical abyss into which it had been plunged. Even though I continue to head the Department of Theoretical Astrophysics of the Petr Lebedev Physics Institute in Moscow, my settled life beyond the borders of my native land, in a very different world, has definitely changed my perception of life, although to a considerably lesser degree than I could have predicted. It involves my attitude to this book as well.

Despite all this, in spite of all the progress, the nature of time remains to a large extent a mystery for us. Regardless of the millennia counted by the history of science, we are only at the very beginning of the way to comprehend the essential meaning of time flow.

Our knowledge about this ‘grand river’ was gleaned very slowly. The science of the ancient Greeks defined the concept of time as an independent category, as a universal property inherent in all objects and phenomena of the material world. It also established that time does not move in circles, that it is not cyclic, that it moves inexorably from the past to the future.

The laws of classical physics, which found their exhaustive expression in Newton's work, assigned to time the role of empty duration, without beginning or end, flowing eternally at a constant rate, regardless of what events take place in the world.

The revolution in physics that began a century ago, and the subsequent relentless progress in this science produced, numerous overwhelming discoveries. We now know that the rate of flow of the river of time can indeed be influenced. In principle, a ‘flight’ can be made to the very distant future, and, who knows, one may be able to move ‘upstream’ on the ‘time river’, that is, into the past; technically, of course, both sorts of time travel remain unfeasible at present.

We have thus far discovered that time can flow very differently. The river of time has estuaries and sinks. However, does it have a source?

Now that it is clear that the properties of time are a function of the physical processes that go on in nature, this question no longer seems to be so absurd. Philosophers pondered this problem for quite a long time. However, the striking successes of Newtonian mechanics and, as a result, the universally accepted Newtonian concept of eternal and unchanged time accustomed them to thinking that the source of time was in the infinite past.

Time was thought of as a uniform river or a never changing road which stretched from the past to the future. In fact, scientists had to face the problem of the beginning of time again, and quite dramatically, in the 20th century. This happened after the discovery of the expansion of the Universe. A detailed description of this achievement is given in the book Edwin Hubble: the Discoverer of the Big Bang Universe, that A. Sharov and I wrote in 1989. (An expanded version in English translation was published in 1993 by Cambridge University Press.) Here I will only trace the main points on this road.

It all began at the end of the 19th century. A rich American astronomer Percival Lowell had a private observatory built for him in the Arizona desert.

When we were discussing the vacuum - the emptiness - in the chapter on ‘Energy extracted from black holes’, we emphasized that virtual particles are constantly created and annihilated in it. The emptiness proved to be a complex entity. The vacuum is a very complicated state of ‘boiling’ virtual particles of most different species.

The reader may not be too surprised by the statement that the properties of this state - the vacuum - depend on the recipe of its preparation. This implies that different vacua are possible; different types of emptiness!

In what follows, we will see examples of possible vacua. Now we will try to answer the following question: can the activity of the vacuum (its ‘boiling’) result in the formation of some energy density owing to the interaction of virtual particles?

Energy density can indeed appear. Zeldovich emphasized this fact in the 1960s. Each energy corresponds to a certain mass. Therefore, mass density will arise together with vacuum energy density. The reader may ask here: does it mean that some sort of universal medium, a new ‘ether’ is emerging in our notions? If this is true, such a medium can restore the concept of absolute rest and absolute motion. Indeed, the motion relative to this medium would be the motion with respect to the emptiness, in other words, with respect to the absolute space. It may seem that if we move relative to this new ‘ether’, we should feel the flow going against us, the ‘ether wind’ blowing in our face.

The Renaissance that came to replace the somber Medieval centuries brought outstanding discoveries in natural sciences. This was the time when Nicolaus Copernicus (1473–1543) developed his theory which was to produce a dramatic transformation in people's view of the world. First of all, this new concept eliminated the impenetrable barrier between the terrestrial and the celestial. Before, everything celestial was a symbol of perfection, of eternity, and of ideals. Heavenly bodies were ideal, as was their uniform motion along circular orbits. This perfection was in opposition with the rough terrestrial matter and its chaotic irregular motion. Copernicus' model showed the Earth to be an ordinary planet which revolves, just as other planets, around the Sun.

Nicolaus Copernicus became a canon of a Catholic church in Frauenberg [Frombork], a small town on the banks of the Vistula in Poland, in 1510. In quiet solitude, he worked on his astronomy. In fact, he spent his free hours on other things as well. He treated patients for no fee. A new monetary system was introduced in Poland following his proposal. He designed and constructed a hydraulic machine to supply water to households.

Copernicus was very careful about publishing his results; he clearly recognized the contradiction with the church's teaching of the singular position of the Earth and man in the Universe. His treatise, On the Revolution of Celestial Spheres, dedicated to Pope Paul III (this was agreed upon with the Holy See) was printed in 1543, not long before Copernicus' death.

When I began to study general relativity seriously (which was in the late fifties), no one knew well what a black hole would be. Even the term itself did not appear in either strictly scientific or popular science publications. This is a stark contrast with what we see today, when almost everyone has read or at least heard about them. The black hole is a product of gigantic gravitational forces. Black holes are born when the gravitational field, growing in the course of catastrophic contraction of a very large mass of matter, becomes so strong that it ceases to let out anything, even light. An object can only fall into a black hole, pulled by its huge gravitational force, but there is simply no way out.

I first read a description of very strong gravitational fields in the Landau and Lifshitz monograph that I have already mentioned. I studied it while still a student, under Zelmanov's guidance. The book gave a very brief but extremely clear presentation of the properties of the gravitational field of a strongly compressed spherical mass. The solution of Einstein's equations for this case was found by the German astronomer Karl Schwarzschild; consequently, this gravitational field is known as the Schwarzschild field.

I remember that this subsection left me rather indifferent. Nevertheless, I did make some evaluations, using the formulas in the book and the knowledge gained from talking to Abram Zelmanov.

We are now departing on a voyage to the very sources of the river of time. What was it that happened at the very beginning of time? What triggered the expansion of the Universe?

We have seen in the chapter ‘Towards the sources of the river of time’ that the huge pressure of hot matter at time zero cannot be the cause of the high velocities of recession of matter, because the uniform Universe has no pressure drop, which is the only cause of force driving an expansion. What then was the cause of the expansion?

The key to understanding the ‘primeval push’ lies in the existence of the special vacuum-like state of matter at high densities and temperatures.

We have already looked at several vacuum-like states in the chapter dealing with Grand Unification. Theorists believe that a unique vacuum-like state with enormous energy density and the corresponding gigantic mass density is formed at the temperature of ‘superunification’. This density in grams per cubic centimeter is written as unity with ninety four zeros (!). The enormity of this number defies imagination. We have already mentioned in the preceding chapter that any vacuum possessing non-zero mass density must have huge negative pressure.

In accordance with Einstein's theory of gravitation, gravitation is produced not only by mass but by pressure as well. Pressure is usually not high and so the gravitation connected with it is negligibly small.

I found this epigraph in Paul Nahin's book Time Machines (New York: AIP) published in 1993 and kindly mailed to me. Another quotation from this book that impressed me with its precision of analysis is:

Indeed, if a chance to visit the past is available, it seems that by modifying this past we could modify the lot of some individuals, the fate of mankind or even the evolution of the entire Universe. Is this true?

The argument that is especially popular in debates of this sort is the so–called ‘grandfather paradox’. It goes roughly like this: ‘If I could go back into the past in which my grandfather was very young, I could kill him and thereby make my own birth impossible’. Or another version of the same paradox: ‘I return into my own past, meet myself in my youth and kill my younger version.’

In both cases this unnatural homicide generates complete nonsense. Should we infer that such an event is impossible? But why? I have my ‘free will’, don't I? Hence I can realize this ‘free will’, at least in principle.

The person to whom I owe my fate was my grandmother. My parents were not there to take part in bringing me up, so my first consciously made steps in life grew from her love and care. Once she found for me an exciting book: Brer Rabbit's Adventures, translated into Russian. I learnt to read with this book. It was my grandmother again who bought for me, on a flea–market,my first popular book about science. It was a very difficult time, the Second World War was raging and the family was evacuated to the town of Krasnokamsk on the Volga. People thought about food first, books were very secondary. But my grandmother — mind you, she had no education whatsoever — felt, perhaps, that food for thought was just as necessary for kids as food for the stomach. The book that she bought (or swapped?) was marvelous; I will never forget it. It was Children's Encyclopaedia, a pre–1917 book, with wonderful color prints. As far as I can remember, their quality was far superior to the often smeared and bleak illustrations that I find nowadays in some editions of books that I write.

That book had a chapter about astronomy. Browsing for the first time through the volume (as for any other kid, this was the first thing to do with a new book), I was amazed by a drawing of a gigantic fountain of fire, with a small globe of our Earth alongside.

I was not quite correct when saying that only motion at relatively modest velocities was known in Isaac Newton's time. Of course, this would be true if only the motion of physical bodies was meant. However, from time immemorial mankind knew a process which propagates at a truly fantastic speed. I mean light. What is it?

Suggestions that light consists of particles which are emitted by a glowing body were made in ancient Greece. Aristotle held this opinion and Newton also shared this point of view. Aristotle assumed the velocity of light propagation to be infinitely high. The same point of view was prevalent until the middle of the 17th century. This belief was shared by the great scientists Johannes Kepler, René Déscartes and others. Galileo was the first to attempt an experimental determination of the speed of light in 1688. He placed two torches on top of two hills at a distance of less than one mile from each other. First the shutter of one torch was opened and when the beam of light reached the observer at the other hill, the latter opened the shutter of his torch. The observer with the first torch was to measure the time between the opening of its shutter and the moment when he saw the flash of the second torch. This was meant to measure the time of travel of light to the second hill and back again.

Everyone knows that the space of the Universe is three-dimensional. This means that space is characterized by length, width and height. The same is true for any body. Somewhat differently, the position of a point in space is characterized by three numbers known as coordinates. If we draw straight lines or planes or complicated curves through space, their properties are described by the laws of geometry. These laws have been known to man since ancient times and were compiled by Euclid in the 3rd century bc. Euclidean geometry is studied in schools as a harmonious system of axioms and theorems that describe all properties of lines, surfaces and solids.

If we wish to study not only the spatial position but also processes occurring in three-dimensional space, we need to add time as well. An event taking place at some point is characterized by the position of this point, that is, by indicating three numbers, and by a fourth number, that is, the moment of time at which the event occurred. For the event the time is its fourth coordinate. In this sense we say that our world is four-dimensional.

All this is well known, of course. Then why wasn't this formulation of four-dimensionality treated as serious and fraught with new knowledge before the theory of relativity was born? The catch lay in the fact that the properties of space and time seemed to be too dissimilar.