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.

Our story of holes in space and time would not be complete if we failed to mention their wonderful property of continuously releasing energy. This feature is one of the manifestations of the as yet undeciphered relationship between time and energy. This relationship manifests itself clearly when quantum properties of matter begin to dominate.

However, I should start very briefly with empty space and its quantum properties.

According to current notions, the vacuum is not absolute emptiness, the ‘perfect nothingness’. It is a sea of so-called virtual particles and antiparticles which do not emerge as real particles. However, the vacuum is the place where pairs of virtual particles and antiparticles are constantly created for a very short moment, only to disappear immediately. They cannot transform into real particles because this would mean the creation of real energy from emptiness. The so-called uncertainty relation of quantum physics allows these particles to appear for a fleeting moment; this relation states that the product of the lifetime of a pair of virtual particles and their energy is of the order of Planck's constant. Real particles can always be removed from a volume while virtual particles cannot be removed - in principle.

Such are the properties of the vacuum. If some strong field is applied to the vacuum, then some virtual particles may ‘pick up’ sufficient energy in this field to become real; they extract the energy for that from the external field.

Albert Einstein created general relativity theory using a minimum number of experimental data on gravitation; he selected this set of data with the intuition of a genius. Over the many decades since the creation of the theory, all its predictions that allowed observational or experimental verification were invariably proved correct.

Tiny corrections to the motion of the planets of the Solar System, predicted by the theory, were detected and then carefully measured. In 1919 Arthur Eddington discovered the bending of light rays in the gravitational field of the Sun, in agreement with Einstein's prediction.

Then the reddening of light emerging from higher gravitational fields was discovered, which again confirmed Einstein's prediction.

Finally, black holes, those exotic objects that are like nothing else in nature, were discovered - with a high degree of certainty - in the 1970s. In this case, relativity theory manifests itself not in some small corrections to well-known processes but in full-blown effects that drastically change the geometry of space and the properties of time.

Not a single fact that would throw a shadow of doubt on relativity theory was found in all these years. Taken together, the entire experience of science in the 20th century makes one treat seriously the other predictions of the theory, those that have not yet been confirmed by experiment or astrophysical observations. We have seen that modern physics, which describes the most profound structure of matter, evolves in the direction outlined by Albert Einstein.

Ever since I started reading popular science books on physics, I have regarded it as self–evident that time is synonymous with empty duration, that it flows like a river and carries in this flow all events without exception. This stream is unalterable and unstoppable, going in a never–changing direction: from the past to the future.

It seemed that this interpretation, given our knowledge about the surrounding world, was unavoidable.

I learnt only many years later that people had not always held such or similar intuitive notions - far from it.

Heraclitus of Ephesus, a philosopher in ancient Greece who lived at the end of the 6th century bc, appears to have been one of the first thinkers of antiquity who set forth a belief that everything in the world changes and that this changeability is the highest law of nature (all things are in process and nothing stays still). Heraclitus set out his view in the book About Nature, of which only a few fragments survived and reached us (Cosmic Fragments).

Heraclitus taught that the world is full of contradictions and variability. All things undergo changes. Time flows relentlessly, and everything that exists moves with this unstoppable stream. The skies move, physical bodies move, a human's feelings and consciencemove as well. ‘You cannot enter twice into one and the same river’ said he, ‘because its water is constantly renewed.’ Things come to replace other things.

Introduction

The determination of physical constants and the definition of the units with which they are measured is a specialised and, to many, hidden branch of science.

A quantity with dimensions is one whose value must be expressed relative to one or more standard units. In the spirit of the rest of the book, this section is based around the International System of units (SI). This system uses seven base units (the number is somewhat arbitrary), such as the kilogram and the second, and defines their magnitudes in terms of physical laws or, in the case of the kilogram, an object called the “international prototype of the kilogram” kept in Paris. For convenience there are also a number of derived standards, such as the volt, which are defined as set combinations of the basic seven. Most of the physical observables we regard as being in some sense fundamental, such as the charge on an electron, are now known to a relative standard uncertainty, ur, of less than 10–7. The least well determined is the Newtonian constant of gravitation, presently standing at a rather lamentable ur of 1.5 – 10–3, and the best is the Rydberg constant (ur = 7.6 – 10–12). The dimensionless electron g-factor, representing twice the magnetic moment of an electron measured in Bohr magnetons, is now known to a relative uncertainty of only 4.1 – 10–12.

No matter which base units are used, physical quantities are expressed as the product of a numerical value and a unit. These two components have more-or-less equal standing and can be manipulated by following the usual rules of algebra.