penrosebook Physics > History and Philosophy of Physics Historical Approach to Physics according to Kant, Einstein, and Hegel Y. S. Kim (Submitted on 25 Jan 2013) It is known that Einstein's conceptual base for his theory of relativity was the philosophy formulated by Immanuel Kant. Things appear differently to observers in different frames. However, Kant's Ding-an-Sich leads to the existence of the absolute reference frame which is not acceptable in Einstein's theory. It is possible to avoid this conflict using the ancient Chinese philosophy of Taoism where two different views can co-exist in harmony. This is not enough to explain Einstein's discovery of the mass-energy relation. The energy-momentum relations for slow and ultra-fast particles take different forms. Einstein was able to synthesize these two formulas to create his energy-mass relation. Indeed, this is what Hegelianism is about in physics. Isaac Newton synthesized open orbits for comets and closed orbits for planets to create his second law of motion. Maxwell combined electricity and magnetism to create his four equations to the present-day wireless world. In order to synthesize wave and particle views of matter, Heisenberg formulated his uncertainty principle. Relativity and quantum mechanics are the two greatest theories formulated in the 20th Century. Efforts to synthesize these two theories are discussed in detail. Comments: Latex 10 pages with 6 figures, based on an invited presented at the 32nd Congress of the Italian Society of Historians of Physics and Astronomy (Rome, Italy, September 2012) Subjects: History and Philosophy of Physics (physics.hist-ph); Popular Physics (physics.pop-ph) Cite as: arXiv:1301.6091 [physics.hist-ph] (or arXiv:1301.6091v1 [physics.hist-ph] for this version) Submission history https://www.marxist.com/science-old/relativitytheory.html Relativity Theory What is Time? Time and Philosophy Newton and Hegel Relativity The General Theory of Relativity Relations Between Things The Measurement of Time Problem Not Resolved Idealist Interpretations Mach and Positivism Boltzman and Time Relativity and Black Holes Few ideas have penetrated the human consciousness as profoundly as that of time. The idea of time and space has occupied human thought for thousands of years. These things at first sight seem simple and easy to grasp, because they are close to everyday experience. Everything exists in time and space, so they appear as familiar conceptions. However, what is familiar is not necessarily understood. On closer examination, time and space are not so easily grasped. In the 5th century, St. Augustine remarked: "What, then, is time? If no one asks me, I know what time is. If I wish to explain it to him who asks me, I do not know." The dictionary is not much help here. Time is defined as a "a period," and a period is defined as "time." This does not get us very far! In reality, the nature of time and space is quite a complex philosophical problem. Men and women clearly distinguish between past and future. A sense of time is, however, not unique to humans or even animals. Organisms often have a kind of "internal clock," like plants which turn one way during the day and another at night. Time is an objective expression of the changing state of matter. This is revealed even by the way we talk about it. It is common to say that time "flows." In fact, only material fluids can flow. The very choice of metaphor shows that time is inseparable from matter. It is not only a subjective thing. It is the way we express an actual process that exists in the physical world. Time is thus just an expression of the fact that all matter exists in a state of constant change. It is the destiny and necessity of all material things to change into something other than what they are. "Everything that exists deserves to perish." A sense of rhythm underlies everything: the heart-beat of a human, the rhythms of speech, the movement of the stars and planets, the rise and fall of the tides, the alternations of the seasons. These are deeply engraved upon the human consciousness, not as arbitrary imaginings, but as real phenomena expressing a profound truth about the universe. Here human intuition is not in error. Time is a way of expressing change of state and motion which are inseparable features of matter in all its forms. In language we have tense, future, present and past. This colossal conquest of the mind enabled humankind to free itself from the slavery of the moment, to rise above the concrete situation and be "present," not just in the here and now, but in the past and the future, at least in the mind. Time and movement are inseparable concepts. They are essential to all life and all knowledge of the world, including every manifestation of thought and imagination. Measurement, the corner-stone of all science, would be impossible without time and space. Music and dance are based upon time. Art itself attempts to convey a sense of time and movement, which are present not just in representations of physical energy, but in design. The colours, shapes and lines of a painting guide the eye across the surface in a particular rhythm and tempo. This is what gives rise to the particular mood, idea and emotion conveyed by the work of art. Timelessness is a word that is often used to describe works of art, but really expresses the opposite of what is intended. We cannot conceive of the absence of time, since time is present in everything. There is a difference between time and space. Space can also express change, as change of position. Matter exists and moves through space. But the number of ways that this can occur is infinite: forward, backward, up or down, to any degree. Movement in space is reversible. Movement in time is irreversible. They are two different (and indeed contradictory) ways of expressing the same fundamental property of matter—change. This is the only Absolute that exists. Space is the "otherness" of matter, to use Hegel’s terminology, whereas time is the process whereby matter (and energy, which is the same thing) constantly changes into something other than what it is. Time—"the fire in which we are all consumed"—is commonly seen as a destructive agent. But it is equally the expression of a permanent process of self-creation, whereby matter is constantly transformed into and endless number of forms. This process can be seen quite clearly in non-organic matter, above all at the subatomic level. The notion of change, as expressed in the passing of time, deeply permeates human consciousness. It is the basis of the tragic element in literature, the feeling of sadness at the passing of life, which reaches its most beautiful expression in the sonnets of Shakespeare, like this one which vividly conveys a sense of the restless movement of time : "Like as the waves make toward the pebbled shore, So do our minutes hasten to their end; Each changing place with that which goes before, In sequent toil all forward do contend." The irreversibility of time does not only exist for living beings. Not only humans, but stars and galaxies are born and perish. Changes affects all, but not only in a negative way. Alongside death there is life, and order arises spontaneously out of chaos. The two sides of the contradiction are inseparable. Without death, life itself would be impossible. Every man and woman is not only aware of themselves, but also the negation of themselves, their limit. We come from nature and will return to nature. Mortals understand that as finite beings their lives must end in death. As the Book of Job reminds us: "Man that is born of woman is of a few days, and full of trouble. He cometh forth like a flower, and is cut down; he fleeth also as a shadow, and continueth not." (29) Animals do not fear death in the same way because they have no knowledge of it. Human beings have attempted to escape their destiny by establishing a privileged communion with an imaginary supernatural existence after death. The idea of everlasting life is present in almost all religions in one form or another. It is the motive-force behind the egotistical thirsting for an imaginary immortality in a non-existent Heaven, which is supposed to provide a consolation for the "Vale of Tears" on this sinful earth. Thus, for countless centuries men and women have been taught to submit meekly to suffering and privation on earth in expectation of a life of happiness—once they are dead. That every individual must pass away is well known. In the future, human life will be prolonged far beyond its "natural" span; nevertheless the end must come. But what is true for particular men and women is not true of the species. We live on through our children, through the memories of our friends, and through the contribution we make to the good of humanity. This is the only immortality to which we are entitled to aspire. Generations pass away, but are replaced by new generations, which develop and enrich the scope of human activity and knowledge. Humanity can conquer the earth and reach out its hands to the heavens. The real search for immortality is realised in this endless process of human development and perfection, as men and women make themselves anew on a higher basis than before. The highest goal we can set ourselves is thus not to long for an imaginary paradise in the beyond, but to fight to attain the real social conditions for the building of a paradise in this world. From our earliest experiences, we come to an understanding of the importance of time. So it is surprising that some have thought time to be an illusion, a mere invention of the mind. This idea has persisted down to the present In fact, the idea that time and change are mere illusions is not new. It is present in ancient religions like Buddhism, and also in idealist philosophies like that of Pythagoras, Plato and Plotinus. The aspirations of Buddhism was to reach Nirvana, a state where time ceased to exist. It was Heraclitus, the father of dialectics, who understood correctly the nature of time and change, when he wrote that "everything is and is not because everything is in flux" and "we step and do not step in the same stream, we are and are not." The idea of change as cyclical is the product of an agricultural society utterly dependent upon the change of seasons. The static way of life rooted in the mode of production of former societies found its expression in static philosophies. The Catholic Church could not stomach the cosmology of Copernicus and Galileo because it challenged the existing view of the world and society. Only in capitalist society has the development of industry disrupted the old, slow rhythms of peasant life. Not only is the difference between the seasons abolished in production, but even the difference between night and day, as machines run for 24 hours a day, seven days a week, fifty two weeks a year, under the glare of artificial lights. Capitalism has revolutionised the means of production, and with it the minds of men and women. However, the progress of the latter has proved to be far slower than the former. The conservatism of the mind is revealed in the constant attempt to cling to outworn ideas, old certainties whose time has long past, and, ultimately, the age-old hope for a life after death. The idea that universe must have a beginning and an end has been revived in recent decades by the cosmological theories of the big bang. This inevitably involves a supernatural being who creates the world according to some unfathomable plan from nothing, and keeps it going for as long as He considers it necessary. The old religious cosmology of Moses, Isaiah, Tertullian and Plato’s Timaeus, incredibly resurfaces in the writings of some modern cosmologists and theoretical physicists. There is nothing new in this. Every social system which enters into a phase of irreversible decline always presents its own demise as the end of the world, or, better still, the universe. Yet the universe still carries on, indifferent to the destiny of this or that temporary social formation on earth. Humankind continues to live, to fight and, despite all reverses, to develop and progress. So that every period sets out on a higher level than before. And there is, in principle, no limit to this process. Time and Philosophy The Ancient Greeks actually had a far deeper insight into the meaning of time, space and motion than the moderns. Not only Heraclitus, the greatest dialectician of Antiquity, but also the Eleatic philosophers (Parmenides, Zeno) arrived at a very scientific conception of these phenomena. The Greek atomists already put forward the picture of a universe which required no Creator, no beginning and no end. Space and matter are generally seen as opposites, as conveyed by the idea of "full" and "empty." In practice, however, the one cannot exist without the other. They presuppose each other, determine, limit and define each other. The unity of space and matter is the most fundamental unity of opposites of all. This was already understood by the Greek atomists who visualised the universe as being composed of only two things—the "atoms" and the "void." In essence, this view of the universe is correct. Relativism has been observed many times in the history of philosophy. The sophists held that "man is the measure of all things." They were relativists par excellence. Denying the possibility of absolute truth, they inclined towards extreme subjectivism. The sophists nowadays have a bad name, but in fact they represented a step forward in the history of philosophy. While there were many charlatans in their ranks, they also had a number of talented dialecticians like Protagoras. The dialectic of sophism was based on the correct idea that truth is many sided. A thing can be shown to have many properties. It is necessary to have the ability to see a given phenomenon from different sides. For the undialectical thinker, the world is a very simple place, made up of things existing separately, one after the other. Every "thing" enjoy a solid existence in time and space. It is before me "here" and "now." However, closer observation reveals these simple and familiar words to be one-sided abstractions. Aristotle as in so many other fields, dealt with space, time and motion with great rigour and profundity. He wrote that only two things are imperishable: time and change, which he rightly considers identical: "It is impossible, however, that motion should be generable or perishable; it must always have existed. Nor can time come into being or cease to be; for there cannot be a ‘before’ or ‘after’ where there is no time. Movement, then, is also continuous in the sense in which time is, for time is either the same thing as motion or an attribute of it; so than motion must be continuous as time is, and if so it must be local and circular." Elsewhere he says that "Movement can neither come into being nor cease to be: nor can time come into being, or cease to be." (30) How much wiser were the great thinkers of the Ancient World than those who now write about "the beginning of time," and without even smiling! The German idealist philosopher Emmanuel Kant was the man who, after Aristotle, investigated the question of the nature of time and space most fully, although his solutions were ultimately unsatisfactory. Every material thing is an assemblage of many properties. If we take away all these concrete properties, we are left with only two abstractions: time and space. The idea of time and space as really existing metaphysical entities was given a philosophical basis by Kant, who claimed that space and time were "phenomenally real," but could not be known "in themselves." Time and space are properties of matter, and cannot be conceived separately from matter. In his book The Critique of Pure Reason, Kant claimed that time and space were not objective concepts drawn from observation of the real world, but were somehow inborn. In point of fact, all the concepts of geometry are derived from observations of material objects. One of the achievements of Einstein’s general theory of relativity was precisely to develop geometry as an empirical science, the axioms of which are inferred from actual measurements, and which differ from the axioms of classical Euclidean geometry, which were (incorrectly) supposed to have been the products of pure reason, deduced from logic alone. Kant attempted to justify his claims in the famous section in his Critique of Pure Reason known as the Antinomies. which deal with the contradictory phenomena of the natural world, including space and time. The first four of Kant’s (cosmological) antinomies deal with this question. Kant had the merit of posing the existence of such contradictions, but his explanation was at best incomplete. It fell to the great dialectician Hegel to resolve the contradiction in The Science of Logic. Throughout the 18th century, science was dominated by the theories of classical mechanics, and one man set his stamp on the whole epoch. The poet Alexander Pope sums up the adulatory attitude of contemporaries to Newton in his verse: "Nature and Nature’s laws lay hid in night: God said ‘Let Newton be!’ and all was light." Newton envisaged time as flowing in a straight line everywhere. Even if there was no matter, there would be a fixed frame of space and time would still flow "through" it. Newton’s absolute spatial frame was supposed to be filled with a hypothetical "ether" through which light waves flowed. Newton thought that time was like a gigantic "container" inside which everything exists and changes. In this idea, time is conceived as having an existence separate and apart from the natural universe. Time would exist, even if the universe did not. This is characteristic of the mechanical (and idealist) method in which time, space, matter and motion are regarded as absolutely separate. In reality, it is impossible to separate them. Newtonian physics was conditioned by mechanics which In the 18th century was the most advanced of the sciences. It was also convenient for the new ruling class because it presented an essentially static, timeless, unchanging view of the universe, in which all contradiction were smoothed out—no sudden leaps, no revolutions, but a perfect harmony, in which everything sooner or later returned to equilibrium, just as the British parliament had reached a satisfactory equilibrium with the Monarchy under William of Orange. The 20th century has pitilessly destroyed this view of the world. One after the other, the old rigid, static mechanism has been displaced. The new science has been characterised by restless change, fantastic speed, contradictions and paradoxes at all levels. Newton distinguished between absolute time and "relative, apparent and common time," as it appears in earthly clocks. He advanced the notion of absolute time, an ideal time scale which simplified the laws of mechanics. These abstractions of time and space proved to be powerful ideas which have greatly advanced our understanding of the universe. They were held to be absolute for a long time. However, upon closer examination, the "absolute truths" of classical Newtonian mechanics proved to be—relative. They were true only within certain limits. Newton and Hegel The mechanistic theories which dominated science for two centuries after Newton, were first seriously challenged in the field of biology by the revolutionary discoveries of Charles Darwin. Darwin’s theory of evolution showed that life could originate and develop without the need for Divine intervention, on the basis of the laws of nature. At the end of the 19th century, the idea of the "arrow of time" was put forward by Ludwig Boltzmann in the second law of thermodynamics. This striking image no longer presents time as a never-ending cycle, but as an arrow moving in a single direction. These theories assume that time is real and that the universe is in a continual process of change, as old Heraclitus had foreseen. Almost half a century before Darwin’s epoch making work, Hegel had anticipated not only him, but many other discoveries of modern science. Boldly challenging the assumption of the prevailing Newtonian mechanics, Hegel advanced a dynamic view of the world, based on processes and change through contradiction. The brilliant anticipations of Heraclitus were transformed by Hegel into a completely elaborated system of dialectical thought. There is no doubt that, had Hegel been taken more seriously, the process of science would have advanced far more rapidly than it did. The greatness of Einstein was to get beyond these abstractions and reveal their relative character. The relative aspect of time was, however, not new. It was thoroughly analysed by Hegel. In his early work The Phenomenology of Mind, he explains the relative content of words like "here" and "now." These ideas which seem quite simple and straightforward turn out to be very complex and contradictory. "To the question, What is the Now? we reply, for example, the Now is night-time. To test the truth of this certainty of sense, a simple experiment is all we need: write that truth down. A truth cannot lose anything by being written down, and just as little by our preserving and keeping it. If we look again at the truth we have written down, look at it now, at his noon-time, we shall have to say it has turned stale and become out of date." (31) It is a very simple matter to dismiss Hegel (or Engels) because their writings on science were necessarily limited by the actual state of science of the day. What is remarkable, however, is how advanced Hegel’s views on science actually were. In their book Order out of Chaos, Prigogine and Stengers point out that Hegel rejected the mechanistic method of classical Newtonian physics, at a time when Newton’s ideas were universally sacrosanct: "The Hegelian philosophy of nature systematically incorporates all that is denied by Newtonian science. In particular, it rests on the qualitative difference between the simple behaviour described by mechanics and the behaviour of more complex entities such as living beings. It denies the possibility of reducing those levels, rejecting the idea that differences are merely apparent and that nature is basically homogeneous and simple. It affirms the existence of a hierarchy, each level of which presupposes the preceding ones." (32) Hegel wrote scornfully about the allegedly absolute truths of Newtonian mechanics. He was the first one to subject the mechanistic approach of the 18th century to a thorough criticism, although the limitations of the science of his day did not allow him to put forward a worked-out alternative. For Hegel, every finite thing was mediated, that is, relative to something else. Moreover, this relationship was not merely a formal juxtaposition, but a living process: everything was limited, conditioned and determined by everything else. Thus, cause and effect only hold good in relation to isolated relations (such as we find in classical mechanics), but not if we regard things as processes, in which everything is the result of universal interrelations and interactions. Time is the form of existence of matter. Mathematics and formal logic cannot really deal with time, but treat it merely as a quantitative relation. Now there is no doubt about the importance of quantitative relations for understanding reality, since every finite thing can be approached from a quantitative point of view. Without a grasp of quantitative relationships, science would be impossible. But in and of themselves, they cannot adequately express the complexity of life and movement, the restless process of change in which gradual, smooth developments suddenly give rise to chaotic transformations. Purely quantitative relations, to use Hegel’s terminology, present the real processes of nature "only in an arrested paralysed form." (33) The universe is an infinite, self-moving whole, which is self-establishing and contains life within itself. Movement is a contradictory phenomenon, containing both positive and negative. This is one of the fundamental propositions of dialectics, which are closer to the real nature of things than the axioms of classical mathematics. Only in classical geometry is it possible to conceive of completely empty space. It is yet another mathematical abstraction, which plays an important role, but only approximately represents reality. Geometry essentially compares different spatial magnitudes. Contrary to what Kant believed, the abstractions of mathematics are not "a priori" and inborn, but derived from observations of the material world. Hegel shows that the Greeks had already understood the limitedness of purely quantitative descriptions of nature, and comments: "How much further had they progressed in thought than those who in our day, when some put in the place of determinations of thought number and determinations of numbers (like powers), next the infinitely great and the infinitely small, one divided by infinity, and other such determinations, which often are a perverted mathematical formalism, take the return to this impotent childishness for something praiseworthy and even for something thorough and profound." (34) These lines are even more appropriate today than when they were written. It really is incredible when certain cosmologists and mathematicians make the most preposterous claims about the nature of the universe without the slightest attempt to prove them on the basis of observed facts, and then appeal to the alleged beauty and simplicity of their equations as the final authority. The cult of mathematics is greater today than at any time since Pythagoras who thought that "all things are Number." And, as with Pythagoras, there are similarly mystical overtones. Mathematics leaves aside all qualitative determinations except number. It ignores the real content, and applies its rules externally to things. None of these abstractions have real existence. Only the material world exists. This fact is all too frequently overlooked with disastrous results. Relativity Albert Einstein was undoubtedly one of the great geniuses of our time. Between his twenty first and thirty eighth birthdays he completed a revolution in science, with profound repercussions at many levels. The two great breakthroughs were the Special Theory of Relativity (1905) and the General Theory of Relativity (1915). Special relativity deals with high speeds, general relativity with gravity. Despite their extremely abstract character, Einstein’s theories were ultimately derived from experiments, and were successfully given practical applications, which confirmed their correctness time and again. Einstein set out from the famous Michelson-Morley experiment, "the greatest negative experiment of the history of science" (Bernal), which exposed an inner contradiction in 19th century physics. This experiment attempted to generalise the electromagnetic theory of light by demonstrating that the apparent velocity of light was dependent upon the rate at which the observer travelled through the supposedly fixed "ether." In the end, no difference was found in the velocity of light, in whatever direction the observer was travelling. J. J. Thomson later showed that the velocity of electrons in high electrical fields was slower than predicted by the classical Newtonian physics. These contradictions in 19th century physics were resolved by the special theory of relativity. The old physics was unable to explain the phenomenon of radioactivity. Einstein explained this as the release of a tiny part of the enormous amount of energy trapped in "inert" matter. In 1905, Einstein developed his special theory of relativity in his spare time, while working as a clerk in a Swiss patent office. Setting out from the discoveries of the new quantum mechanics, he showed that light travels through space in a quantum form (as bundles of energy). This was clearly in contradiction to the previously accepted theory of light as a wave. In effect, Einstein revived the old corpuscular theory of light, but in an entirely different way. Here light was shown as a new kind of particle, with a contradictory character, simultaneously displaying the properties of a particle and a wave. This startling theory made possible the retention of all the great discoveries of 19th century optics, including spectroscopes, as well as Maxwell’s equation. But it killed stone-dead the old idea that light requires a special vehicle, the "ether," to travel through space. Special relativity starts from the assumption that the speed of light in a vacuum will always be measured at the same constant value, irrespective of the speed of the light source relative to the observer. From this it is deduced that the speed of light represents the limiting speed for anything in the universe. In addition, special relativity states that energy and mass are in reality equivalents. This is a striking confirmation of the fundamental philosophical postulate of dialectical materialism—the inseparable character of matter and energy the idea that motion ("energy") is the mode of existence of matter. Einstein’s discovery of the law of equivalence of mass and energy is expressed in his famous equation E = mc2, which expresses the colossal energies locked up in the atom. This is the source of all the concentrated energy in the universe. The symbol e represents energy (in ergs), m stands for mass (in grams) and c is the speed of light (in centimetres per second). The actual value of c2 is 900 billion billion. That is to say, the conversion of one gram of energy locked up in matter will produce a staggering 900 billion billion ergs. To give a concrete example of what this means, the energy contained in a single gram of matter is equivalent to the energy produced by burning 2,000 tons of petrol. Mass and energy are not just "interchangeable," as dollars are interchangeable with Deutschmarks, they are one and the same substance, which Einstein characterised as "mass-energy." This idea goes far deeper and is more precise than the old mechanical concept whereby, for example, friction is transformed into heat. Here, matter is just a particular form of "frozen" energy, while every other form of energy (including light), has mass associated with it. For this reason, it is quite wrong to say that matter "disappears" when it is changed into energy. Einstein’s law displaced the old law of the conservation of mass, worked out by Lavoisier, which says that matter, understood as mass, can neither be created nor destroyed. In fact, every chemical reaction that releases energy converts a small amount of mass into energy. This could not be measured in the kind of chemical reaction known to the 19th century, such as the burning of coal. But nuclear reaction releases sufficient energy to reveal a measurable loss of mass. All matter, even when at "rest," contains staggering amounts of energy. However, as this cannot be observed, it was not understood until Einstein explained it. Far from overthrowing materialism, Einstein’s theory establishes it on a firmer basis. In place of the old mechanical law of the "conservation of mass," we have the far more scientific and more general laws of the conservation of mass-energy, which expresses the first law of thermodynamics in an universal and unassailable form. The mass does not "disappear" at all, but is converted into energy. The total amount of mass-energy remains the same. Not a single particle of matter can be created or destroyed. The second idea is the special limiting character of the speed of light: the assertion that no particle can travel faster than the speed of light, since as it approaches this critical velocity, its mass approaches infinity, so that it becomes harder and harder to go faster. These ideas seem abstract and difficult to grasp. They challenge the assumptions of "sound common sense." The relationship between "common sense" and science was summed up by the Soviet scientist Professor L. D. Landau in the following lines: "So-called common sense represents nothing but a simple generalisation of the notions and habits that have grown up in our daily life. It is a definite level of understanding reflecting a particular level of experiment." And he adds: "Science is not afraid of clashes with so-called common sense. It is only afraid of disagreement between existing ideas and new experimental facts and if such disagreement occurs science relentlessly smashes the ideas it has previously built up and raises our knowledge to a higher level." (35) How can a moving object increase its mass? Such a notion contradicts our everyday experience. A spinning top does not visibly gain in mass while revolving. In point of fact, it does, but the increase is so infinitesimal that it may be discounted for all practical purposes. The effects of special relativity cannot be observed on the level of everyday phenomena. However, under extreme conditions, for example, at very high speeds approaching the speed of light, relativistic effects begin to come into play. Einstein predicted that the mass of a moving object would increase at very high speeds. This law can be ignored when dealing with normal speeds. Nevertheless, subatomic particles move at speeds of nearly 10,000 miles per second or more, and at such speeds as these relativistic effects appear. The discoveries of quantum mechanics demonstrated the correctness of the special theory of relativity, not only qualitatively, but quantitatively. An electron gains in mass as it moves at 9/10th the speed of light; moreover, the gain in mass is 3 1/6th times, precisely as Einstein’s theory predicted. Since then, special relativity has been tested many times, and so far it has always given correct results. Electrons emerge from a powerful particle accelerator about 40,000 times heavier than when they started, the extra mass representing energy of motion. At far higher velocities the increase in mass becomes noticeable. And modern physics deals precisely with extremely high velocities, such as the speed of sum-atomic particles, which approach the speed of light. Here the classical laws of mechanics, which adequately describe everyday phenomena, cannot be applied. To common sense the mass of an object never changes. Therefore a spinning-top has the same weight as a still one. In this way a law was invented which states that mass is constant irrespective of speed. Later, this law was shown to be incorrect. It was found that mass increases with velocity. Yet, since the increase only becomes appreciable near the speed of light, we take it as constant. The correct law would be: "If an object moves with a speed of less than 100 miles per second, the mass is consistent to within one part in a million." For everyday purposes, we can assume that mass is constant irrespective of speed. But for high speeds, this is false, and the higher the speed, the falser is the assertion. Like thinking based on formal logic, it is accepted as valid for practical purposes. Feynman points out: "…Philosophically, we are completely wrong with the approximate law. Our entire picture of the world has to be altered even though the mass changes only by a little bit. This is a very peculiar thing about the philosophy, or the ideas, behind the laws. Even a very small effect sometimes requires profound changes in our ideas." (36) The predictions of special relativity have been shown to correspond to the observed facts. Scientists discovered by experiment that gamma-rays could produce atomic particles, transforming the energy of light into matter. They also found that the minimum energy required to create a particle depended on its rest-energy, as predicted by Einstein. In point of fact not one, but two particles were produced: a particle and its opposite, the "anti-particle." In the gamma-ray experiment, we get an electron and an anti-electron (positron). The reverse process also takes place: when a positron meets an electron, they annihilate each other, producing gamma rays. Thus, energy is transformed into matter, and matter into energy. Einstein’s discovery provided the basis for a far more profound understanding of the workings of the universe. It provided an explanation of the source of the sun’s energy, which had been a mystery throughout the ages. The immense storehouse of energy turned out to be—matter itself. The awesome power of the energy locked up in matter was revealed to the world in August 1945 at Hiroshima and Nagasaki. All this is contained in the deceptively simple formula E = mc2. The General Theory of Relativity Special relativity is quite adequate when dealing with an object moving at constant speed and direction in relation to the observer. However, in practice motion is never constant. There are always forces which cause variations in the speed and direction of moving objects. Since subatomic particles move at immense speeds over short distances, they do not have time to accelerate much, and special relativity can be applied. Nevertheless, in the motion of planets and stars, special relativity proved insufficient. Here we are dealing with large accelerations caused by huge gravitational fields. It is once again a case of quantity and quality. At the subatomic level, gravitation is insignificant in comparison with other forces, and can be ignored. In the everyday world, on the contrary, all other forces except gravity can be ignored. Einstein attempted to apply relativity to motion in general, not just to constant motion. Thus we arrive at the general theory of relativity, which deals with gravity. It marks a break, not only with the classical physics of Newton, with its absolute mechanical universe, but with the equally absolute classical geometry of Euclid. Einstein showed that Euclidean geometry only applied to "empty space," an ideally-conceived abstraction. In reality, space is not "empty." Space is inseparable from matter. Einstein maintained that space itself is conditioned by the presence of material bodies. In his general theory, this idea is conveyed by the seemingly paradoxical assertion that, near heavy bodies, "space is curved." The real, i.e., material, universe is not at all like the world of Euclidean geometry, with the perfect circles, absolutely straight lines, and so on. The real world is full of irregularities. It is not straight, but precisely "warped." On the other hand, space is not something which exists separate and apart from matter. The curvature of space is just another way of expressing the curvature of matter which "fills" space. For example, it has been proved that light rays bend under the influence of the gravitational fields of bodies in space. The general theory of relativity is essentially of a geometrical character, but this geometry is completely different to the classical Euclidean kind. In Euclidean geometry, for instance, parallel lines never meet or diverge, and the angles of a triangle always add up to 180°. Einstein’s space-time (actually first developed by the Russian-German mathematician, Hermann Minkowski, one of Einstein’s teachers, in 1907) represents a synthesis of three dimensional space (height, breadth and length) with time. This four-dimensional geometry deals with curved surfaces ("curved space-time"). Here the angles of a triangle may not add up to 180°, and parallel lines can cross or diverge. In Euclidean geometry, as Engels points out, we meet a whole series of abstractions which do not at all correspond to the real world: a dimensionless point which becomes a straight line, which, in turn, becomes a perfectly flat surface, and so on and so forth. Among all these abstractions we have the emptiest abstraction of all, that of "empty space." Space, in spite of what Kant believed, cannot exist without something to fill it, and that something is precisely matter (and energy, which is the same thing). The geometry of space is determined by the matter which it contains. That is the real meaning of "curved space." It is merely a way of expressing the real properties of matter. The issue is only confused by inappropriate metaphors contained in popularisations of Einstein: "Think of space as a rubber sheet," or "Think of space as glass," and so on. In reality, the idea that must be kept in mind at all times is the indissoluble unity of time, space, matter and motion. The moment this unity is forgotten, we instantly slide into idealist mystification. If we conceive space as a Thing-in-Itself, empty space, as in Euclid, clearly it cannot be curved. It is "nothing." However, as Hegel put it, there is nothing in the universe which does not contain both being and not-being. Space and matter are not two diametrically opposed, mutually exclusive phenomena. Space contains matter, and matter contains space. They are completely inseparable. The dialectical unity of matter and space is precisely what the universe is. In a most profound way, the general theory of relativity conveys this dialectical idea of the unity of space and matter. In the same way in mathematics zero itself is not "nothing," but expresses a real quantity, and plays a determining role. Einstein presents gravitation as a property of space rather than a "force" acting upon bodies. According to this view space itself curves as a result of the presence of matter. This is a rather singular way of expressing the unity of space and matter, and one that is open to serious misinterpretations. Space itself, of course, cannot curve if it is understood as "empty space." The point is that it is impossible to conceive of space without matter. It is an inseparable unity. What we are considering is a definite relationship of space to matter. The Greek atomists long ago pointed out that atoms existed in the "void." The two things cannot exist without each other. Matter without space is the same as space without matter. A totally empty void is just nothing. But so is matter without any boundaries. Space and matter, then, are opposites which presuppose each other, define each other, limit each other, and cannot exist without each other. The general theory served to explain at least one phenomenon which could not be explained by Newton’s classical theory. As the planet Mercury approaches its closest point to the sun, its revolutions display a peculiar irregularity, which had been previously attributed to the perturbations caused by the gravity of other planets. However, even when these were taken into account, it did not explain the phenomenon. The deviation of Mercury’s orbit around the sun ("perihelion") was very small, but enough to upset the astronomers’ calculations. Einstein’s general theory predicted that the perihelion of any revolving body should have a motion beyond that prescribed by Newton’s law. This was shown to be correct for Mercury, and later also for Venus. He also predicted that a gravitational field would bend light-rays. Thus, he claimed, a light ray passing close to the surface of the sun would be bent out of a straight line by 1.75 seconds of arc. In 1919 an astronomic observation of an eclipse of the sun showed this to be correct. Einstein’s brilliant theory was demonstrated in practice. It was able to explain the apparent shift in the position of stars near the sun by the bending of their rays, and also the irregular motion of the planet Mercury, which could not be accounted for by Newton’s theories. Newton worked out the laws governing the movement of objects, according to which the strength of gravitational pull depends upon mass. He also maintained that any force exerted upon an object produces acceleration in inverse proportion to the mass of the object. Resistance to acceleration is called inertia. All masses are measured either through gravitational effects or inertial effects. Direct observation has shown that inertial mass and gravitational mass are, in fact, identical to within one part in one trillion. Einstein began his theory of general relativity by assuming that inertial mass and gravitational mass are exactly equal, because they are essentially the same thing. The apparently motionless stars are moving at colossal speeds. Einstein’s cosmic equations of 1917 implied that the universe itself was not fixed for all time, but could be expanding. The galaxies are moving away from us at speeds of about 700 miles a second. The stars and galaxies are constantly changing, coming into being and passing away. The whole universe is a vast arena where the drama of birth and death of stars and galaxies is played out across eternity. These are truly revolutionary events! Exploding galaxies, supernovas, catastrophic collisions between stars, black holes with a density billions of times greater than our sun greedily devouring entire clusters of stars. These things put in the shade the imaginings of the poets. Relations Between Things Many notions are purely relative in character. For example, if one is asked to say whether a road is on the right or left side of a house, it is impossible to answer. It depends on which direction one is moving relative to the house. On the other hand, it is possible to speak of the right bank of a river, because the current determines the direction of the river. Similarly, we can say that cars keep to the left (at least in Britain!) because the movement of a car singles out one of the two possible directions along the road. In all these examples, however, the notions "left" and "right" are shown to be relative, since they only acquire meaning after the direction by which they are defined as indicated. In the same way, if we ask "Is it night or day?" the answer will depend on where we are. In London it is day, but in Australia it is night. Day and night are relative notions, determined by our position on the globe. An object will appear bigger or smaller depending upon its distance from a given point of observation. "Up" and "down" are also relative notions, which changed when it was discovered that the world is round, not flat. Even to this day, it is hard for "common sense" to accept that people in Australia can walk "upside down." Yet there is no contradiction if we understand that the notion of the vertical is not absolute but relative. For all practical purposes, we can take the earth’s surface to be "flat" and therefore all verticals to be parallel, when dealing for instance, with two houses in one town. But when dealing with far larger distances, involving the whole earth’s surface, we find that the attempt to make use of an absolute vertical leads to absurdities and contradictions. By extension, the position of a planetary body is necessarily relative to the position of others. It is impossible to fix the position of an object without reference to other objects. The notion of "displacement" of a body in space means no more than that it changed its position relative to other bodies. A number of important laws of nature have a relativistic character, for example the principle of the relativity of motion and the law of inertia. The latter sates that an object on which no external force acts can only be not only in a state of rest but also in a state of uniform straight line motion. This fundamental law of physics was discovered by Galileo. In practice, we know that objects upon which no external force is applied tend to come to rest, at least in everyday life. In the real world, the conditions for the law of inertia to apply, namely the total absence of external forces acting on the body, cannot exist. Forces such as friction act on the body to bring it to a halt. However, by constantly improving the condition of the experiment, it is possible to get closer and closer to the ideal conditions envisaged by the law of inertia, and thus show that it is valid even for the motions observed in everyday life. The relative (quantitative) aspect of time was perfectly expressed in Einstein’s theories, which conveyed it far more profoundly than the classical theories of Newton. Gravity is not a "force," but a relation between real objects. To a man falling off a high building, it seems that the ground is "rushing towards him." From the standpoint of relativity, that observation is not wrong. Only if we adopt the mechanistic and one-sided concept of "force" do we view this process as the earth’s gravity pulling the man downwards, instead of seeing that it is precisely the interaction of two bodies upon each other. For "normal" conditions, Newton’s theory of gravity agrees with Einstein’s. But in extreme conditions, they completely disagree. In effect, Newton’s theory is contradicted by the general theory of relativity in the same way as formal logic is contradicted by dialectics. And, to date, the evidence shows that both relativity and dialectics are correct. As Hegel explained, every measurement is really the statement of a ratio. However, since every measurement is really a comparison, there must be one standard which cannot be compared with anything but itself. In general, we can only understand things by comparing them to other things. This expresses the dialectical concept of universal interconnections. To analyse things in their movement, development and relationships is precisely the essence of the dialectical method. It is the exact antithesis of the mechanical mode of thought (the "metaphysical" method in the sense of the word used by Marx and Engels) which views things as static and absolute. This was precisely the defect of the old classical Newtonian view of the universe, which, for all its achievements, never escaped from the one-sidedness which characterised the mechanistic world outlook. The properties of a thing are not the result of relations to other things, but can only manifest themselves in relations to other things. Hegel refers to these relations in general as "reflex-categories." The concept of relativity is an important one, and was already fully developed by Hegel in the first volume of his masterpiece The Science of Logic. We see this, for example, in social institutions such as kingship. "Naïve minds," Trotsky observed, "think that the office of kingship lodges in the king himself, in his ermine cloak and his crown, in his flesh and bones. As a matter of fact, the office of kingship is an interrelation between people. The king is king only because the interests and prejudices of millions of people are refracted through his person. When the flood of development sweeps away these interrelations, then the king appears to be only a washed-out man with a flabby lower lip. He who was once called Alfonso XIII could discourse upon this from fresh impressions. "The leader by will of the people differs from the leader by will of God in that the former is compelled to clear the road for himself or, at any rate, to assist the conjuncture of events in discovering him. Nevertheless, the leader is always a relation between people, the individual supply to meet the collective demand. The controversy over Hitler’s personality becomes the sharper the more the secret of his success is sought in himself. In the meantime, another political figure would be difficult to find that is in the same measure the focus of anonymous historic forces. Not every exasperated petty bourgeois could have become Hitler, but a particle of Hitler is lodged in every exasperated petty bourgeois." (37) In Capital, Marx shown how concrete human labour becomes the medium for expressing abstract human labour. It is the form under which its opposite, abstract human labour, manifests itself. Value is not a material thing which can be derived from the physical properties of a commodity. In fact, it is an abstraction of the mind. But it is not on that account an arbitrary invention. In fact, it is an expression of an objective process, and is determined by the amount of socially necessary labour power expended in production. In the same way, time is an abstraction which, although it cannot be seen, heard or touched, and can only be expressed in relative terms as measurement, nevertheless denotes an objective physical process. Space and time are abstractions which enable us to measure and understand the material world. All measurement is related to space and time. Gravity, chemical properties, sound, light, are all analysed from these two points of view. Thus, the speed of light is 186,000 feet per second, while sound is determined by the number of vibrations per second. The sound of a stringed instrument, for instance, is determined by the time in which a certain number of vibrations occur and the spatial elements (length and thickness) of the vibrating body. That harmony which appeals to the aesthetic feelings of the mind is also another manifestation of ratio, measurement and therefore time. Time cannot be expressed except in a relative way. In the same way, the magnitude value of a commodity can only be expressed relative to other commodities. Yet value is intrinsic to commodities, and time is an objective feature of matter in general. The idea that time itself is merely subjective, that is to say an illusion of the human mind, is reminiscent of the prejudice that money is merely a symbol, with no objective significance. The attempt to "demonetise" gold, which flowed from this false premise, led to inflation every time it was attempted. In the Roman Empire, the value of money was fixed by imperial decree, and it was forbidden to treat money as a commodity. The result was a continuous debasement of the currency. A similar phenomenon has taken place in modern capitalism, particularly since the Second World War. In economics, as in cosmology, the confusion of measurement with the nature of the thing itself leads to disaster in practice. The Measurement of Time While defining what time is presents a difficulty, measuring it does not. Scientists themselves do not explain what time is, but confine themselves to the measurement of time. From the mixing up of these two concepts endless confusion arises. Thus, Feynman: "Maybe it is just as well if we face the fact that time is one of the things we cannot define (in the dictionary sense), and just say that it is what we already know it to be: it is how long we wait! What really matters anyway is not how we define time, but how we measure it." (38) The measurement of time necessarily involves a frame of reference, and any phenomenon which entails change with time—e.g., the rotation of the earth or the swing of a pendulum. The earth’s daily rotation on its axis provides a time scale. The decay of radioactive elements can be used for measuring long time intervals. The measurement of time involves a subjective element. The Egyptians divided day and night into twelfths. The Sumerians had a numerical system based on 60, and thus divided the hour into 60 minutes and the minute into 60 seconds. The metre was defined as one 10 millionth of the distance from the earth’s pole to the equator (although this is not strictly accurate). The centimetre is 100th of a metre, and so on. At the beginning of this century, the investigation of the subatomic world led to the discovery of two natural units of measurement: the speed of light, c, and Planck’s constant, h. These are not directly mass, length, or time, but the unity of all three. There is an international agreement that the metre is defined as the distance between two scratches on a bar kept in a laboratory in France. More recently, it has been realised that this definition is neither as precise as would be useful, nor as permanent or universal as one would like. It is currently being considered that a new definition be adopted, an agreed-upon (arbitrary) number of wavelengths of a chosen spectral line. On the other hand, the measurement of time varies according to the scale and life-span of the objects under consideration. It is clear that the concept of time will vary according to the frame of reference. A year on earth is not the same as a year on Jupiter. Nor is the idea of time and space the same for a human being as for a mosquito with a life-span of a few days, or a subatomic particle with a life span of a trillionth of a second (assuming, of course, that such entities could possess a concept of anything at all). What we are referring to here is the way time is perceived in different contexts. If we accept the given frame of references the way in which time would be seen would be different. Even in practice this can be seen, to some extent. For example, normal methods of measuring time cannot be applied to the measurement of the life-span of subatomic particles, and different standards must also be used for measuring "geological time." From this point of view, time can be said to be relative. Measurement necessarily involves relationships. Human thought contains many concepts which are essentially relative, for example relative magnitudes, such as "big" and "small." A man is small compared to an elephant, but big in comparison to an ant. Smallness and bigness, in themselves, have no meaning. A millionth of a second, in ordinary terms, seems a very short length of time, yet at the subatomic level it is an extremely long time. At the other extreme, a million years is an extremely short time on the cosmological level. All ideas of space, time and motion depend on our observations of the relations and changes in the material world. However, the measurement of time varies considerably when we consider different kinds of matter. The measurement of space and time is inevitably relative to some frame of reference—the earth, the sun, or any other static point—to which events of the universe can relate. Now it is clear that matter undergoes all kinds of different change: change of position, which, in turn, involves different velocities, change of state, involving different energy states, birth, decay and death, organisation and disorganisation, and many other transformations, all of which can be expressed and measured in terms of time. In Einstein, time and space are not regarded as isolated phenomena, and indeed it is impossible to regard them as "things in themselves." Einstein advanced the view that time depends on the movement of a system and that the intervals of time change in such a way that the speed of light in the given system does not vary according to the movement. Spatial scales are also subject to change. The old classical Newtonian theories are still valid for everyday purposes, and even as a good approximation of the general workings of the universe. Newtonian mechanics still applies in a very wide branch of sciences, not only astronomy, but also practical sciences such as engineering. At low speeds, the effects of special relativity can be ignored. For example, the error involved in considering the behaviour of a plane moving at 250 mile an hour would be about ten billionth of one percent. However, beyond certain limits it breaks down. At the kind of speeds that we find in particle acceleration, for example, it is necessary to take into account Einstein’s prediction that mass is not constant, but increases with velocity. From the point of view of our normal everyday notion of the measurement of time, the extremely short life-span of certain subatomic particles cannot be adequately expressed. A pi-meson, for instance, has a life-span of only about 10–16 of a second, before it disintegrates. Likewise, the period of a nuclear vibration, or the life-time of a strange resonance particle, is 10–24 second, approximately the time needed for light to cross the nucleus of a hydrogen atom. Another scale of measurement is necessary. Very short times, say 10–12 second, are measured by an electron beam oscilloscope. Even shorter times can be calibrated by means of laser techniques. At the other end of the scale, very long periods can be measured by a radioactive "clock." In a sense, every atom in the universe is a clock, because it absorbs light (that is, electromagnetic rays) and emits it at precisely defined frequencies. Since 1967, the official internationally recognised standard of time is based on the atomic (caesium) clock. One second is defined as 9,192,631,770 vibrations of the microwave radiation from caesium-133 atoms during a specified atomic rearrangement. Even this highly accurate clock is not absolutely perfect. Different readings are taken from atomic clocks in about 80 different countries, and agreement is reached, "weighting" the time in favour of the steadiest clocks. By such means it is possible to arrive at accurate time-measurement to one millionth of a second per day, or even less. For everyday purposes, "normal" time keeping, based on the rotation of the earth and the apparent movements of the sun and stars, is sufficient. But for a whole series of operations in the field of modern advanced technology, such as certain radio navigational aids in ships and aeroplanes, it becomes inadequate, leading to serious errors. It is at these kind of levels that the effects of relativity begin to make themselves felt. Experiments have shown that atomic clocks run slower at ground level than at high altitudes, where the gravitational effect is weaker. Atomic clocks, flown at an altitude of 30,000 feet, gained about three billionth of a second an hour. This conforms to Einstein’s prediction to within one percent. Problem Not Resolved The special theory of relativity was one of the greatest achievements of science. It has revolutionised the way we look at the universe to such an extent that it has been compared with the discovery that the earth is round. Gigantic strides forward have been made possible by the fact that relativity established a far more accurate method of measurement than the old Newtonian laws it partially displaced. The philosophical question of time has, however, not been removed by Einstein’s theory of relativity. If anything, it is more acute than ever. That there is something subjective and even arbitrary in the measurement of time is evident, as we have already commented. But this does not lead to the conclusion that time is purely a subjective thing. Einstein’s entire life was spent in the pursuit of the objective laws of nature. The question is whether the laws of nature, including time, are the same for everyone, regardless of the place in which they are and the speed at which they are moving. On this question, Einstein vacillated. At times, he seemed to accept it, but elsewhere he rejected it. The objective processes of nature are not determined by whether they are observed or not. They exist in and for themselves. The universe, and therefore time, existed before there were human beings to observe it, and will continue to exist long after there are no humans to concern themselves about it. The material universe is eternal, infinite, and constantly changing. However, in order that human minds may grasp the infinite universe, it is necessary to translate it into finite terms, to analyse and quantify it, so that it can become a reality for us. The way we observe the universe does not change it (unless it involves physical processes which interfere with what is being observed). But the way it appears to us can indeed change. From our standpoint, the earth appears to be at rest. But to an astronaut flying past our planet, it seems to be hurtling past him at a great speed. Einstein, who seems to have had a very dry sense of humour, apparently once asked an astonished ticket inspector: "What time does Oxford stop at this train?" Einstein was determined to re-write the laws of physics in such a way that the predictions would always be correct, irrespective of the motions of different bodies, or the "points of view" which derive from them. From the standpoint of relativity, steady motion on a straight line is indistinguishable from being at rest. When two objects pass each other at a constant speed, it is equally possible to say that A is passing B, or that B is passing A. Thus, we arrive at the apparent contradiction that the earth is both at rest and moving at the same time. In the example of the astronaut, "it has to be simultaneously correct to say that the earth has great energy of motion and no energy and motion; the astronaut’s point of view is just as valid as the view of learned men on earth." (39) Although it seems straightforward, the measurement of time nevertheless presents a problem, because the rate of change of time must be compared to something else. If there is some absolute time, then this in turn must flow, and therefore must be measured against some other time, and so on ad infinitum. It is important to realise, however, that this problem presents itself only in relation to the measurement of time. The philosophical question of the nature of time itself does not enter into it. For the practical purposes of calculation and measurement, it is essential that a specific frame of reference by defined. We must know the position of the observer relative to the observed phenomena. Relativity theory shows that such statement as "at one and the same place" and "at one and the same time" are, in fact, meaningless. The theory of relativity involves a contradiction. It implies that simultaneity is relative to a frame of axes. If one frame of axes is moving relative to another, then events that are simultaneous relative to the first are not simultaneous relative to the second, and vice versa. This fact, which flies in the face of common sense, has been experimentally demonstrated. Unfortunately, it can lend itself to an idealist interpretation of time, for instance, the assertion that there can be a variety of "presents." Moreover, the future can be portrayed as things and processes "that come into being" as four-dimensional solids that have as earliest temporal cross section or "time slice." Unless this question is settled, all kinds of mistakes can be made: for example, the idea that the future already exists, and suddenly materialises in the "now," as a submerged rock suddenly appears when a wave breaks over it. In point of fact, both the past and the future are combined in the present. The future is being-in-potential. The past is what has already been. The "now" is the unity of both. It is actual being as opposed to potential being. Precisely for this reason, it is usual to feel regret for the past and fear for the future, not vice versa. The feeling of regret flows from the realisation, corroborated by all human experience, that the past is lost forever, whereas the future is uncertain, consisting in a great number of potential states. Benjamin Franklin once observed that there are only two things certain in this life—death and taxes, and the Germans have a proverb: "Man muss nur sterben"—"one only has to die," meaning that everything else is optional. Of course, this is not actually true. Many more things are inevitable than death, or even taxes. Out of an infinitely large number of potential states, in practice we know that only a certain number are really possible. Out of these, fewer still are probable at a given moment. And of the latter, in the end, only one will actually arise. The exact way in which this process unfolds is precisely the task of the different sciences to uncover. But this task will prove to be impossible if we do not accept that events and processes unfold in time, and that time is an objective phenomenon which expresses the most fundamental fact of all forms of matter and energy—change. The material world is in a constant state of change, and therefore it "is and is not." This is the fundamental proposition of dialectics. Philosophers like the Anglo-American Alfred North Whitehead and the French intuitionist Henry Begson believed that the flow of time was a metaphysical fact which could only be grasped by non-scientific intuition. "Process philosophers" like these, despite their mystical overtones, at least are correct in saying that the future is open or indeterminate whereas the past is unchangeable, fixed and determinate. It is "congealed time." On the other hand we have the "philosophers of the manifold" who maintain that future events may exist but not be connected in a sufficiently lawlike way with past events. Pursuing a philosophically incorrect view of time, we end up with sheer mysticism, as in the notion of the "multiverse"—an infinite number of "parallel" universes (if that is the right word, since they do not exist in space "as we know it") existing simultaneously (if that is the right word, since they do not exist in time "as we know it"). Such is the confusion that arises from the idealist interpretation of relativity. Idealist Interpretations "There was a young lady named Bright Whose speed was faster than light; She set out one day In a relative way And returned home the previous night." (A. Buller, Punch, 19th December 1923) As with quantum mechanics, relativity has been seized upon by those who wish to introduce mysticism into science. "Relativity" is taken to mean that we cannot really know the world. As J. D. Bernal explains: "It is, however, equally true that the effect of Einstein’s work, outside the narrow specialist fields where it can be applied, was one of general mystification. It was eagerly seized on by the disillusioned intellectuals after the First World War to help them in refusing to face realities. They only needed to use the word ‘relativity’ and say ‘Everything is relative,’ or ‘It depends on what you mean.’" (40) This is a complete misinterpretation of Einstein’s ideas. In point of fact, the very word "relativity" is a misnomer. Einstein himself preferred the name invariance theory which gives a far better idea of what he intended—the exact opposite of the vulgar idea of relativity theory. It is quite untrue that for Einstein, "everything is relative." To begin with, rest energy (that is, the unity of matter and energy) is one of the absolutes of the theory of relativity. The limiting speed of light is another. Far from an arbitrary, subjective interpretation of reality, in which one opinion is as good as another, and "it all depends how you look at it," Einstein "discovered what was ‘absolute’ and reliable despite the apparent confusions, illusions and contradictions produced by relative motions or the action of gravity." (41) The universe exists in a constant state of change. In that sense, nothing is "absolute" or eternal. The only absolute is motion and change, the basic mode of existence of matter—something which Einstein demonstrated conclusively in 1905. Time and space, as the mode of existence of matter are objective phenomena. They are not merely abstractions or arbitrary notions invented by humans (or gods) for their own convenience, but fundamental properties of matter, expressing the universality of matter. Space is three dimensional, but time has only one dimension. With apologies to the makers of films in which it is possible to "go back to the future," it is only possible to travel in one direction in time, from the past to the future. There is no more danger of a spaceman returning to earth before he was born, or of a man marrying his great grandmother, than there is of any of the other amusing but idiotic fantasies of Hollywood. Time is irreversible, which is to say, every material process develops in only one direction—from the past to the future. Time is merely a way of expressing the real movement and changing state of matter. Matter, motion, time and space are inseparable. The shortcoming of Newton’s theory was to regard space and time as separate entities, one alongside the other, independent of matter and motion. Up till the 20th century, scientists identified space with a vacuum (a "nothing"), which was seen as something absolute, that is, always and everywhere the same, changeless "thing." These empty abstractions have been discredited by modern physics, which has demonstrated the profound relation between time, space, matter and motion. Einstein’s relativity theory firmly establishes that time and space do not exist in and of themselves, in isolation from matter, but are part of a universal interrelation of phenomena. This is conveyed by the concept of the integral and indivisible space-time, of which time and space are seen as relative aspects. A controversial idea here is the prediction that a clock in motion will keep time more slowly than one that is stationary. However, it is important to understand that this effect only becomes noticeable at extraordinarily high speeds, approaching the speed of light. If Einstein’s general theory of relativity is correct, then the theoretical possibility would exist in the future of travelling unimaginable distances through space. Theoretically, it would be possible for a human being to survive thousands of years into the future. The whole question hinges upon whether the changes observed in rates of atomic clocks also apply to the rate of life itself. Under the effect of strong gravity, atomic clocks run slower than in empty space. The question is whether the complex interrelations of molecules which constitute life can behave in the same way. Isaac Asimov, who knew a thing or two about science fiction, wrote: "If time really slows down in motion, one might journey even to a distant star in one’s own lifetime. But of course one would have to say good-bye to one’s own generation and return to the world of the future." (42) The argument for this is that the rates of living processes are determined by the rates of atomic action. Thus, under strong gravity, the heart will beat more slowly, and the brain impulses will also slow down. In fact, all energy diminishes in the presence of gravity. If processes slow down, they also take longer in time. If a space-ship were able to travel close to the speed of light, the universe would be seen flashing past it, while for those inside, time would continue as "normal," i.e., at a much slower rate. The impression would be that time outside would be speeded up. Is that correct? Would he in fact be living in the future, relative to people on earth, or not? Einstein seems to answer in the affirmative. All kinds of mystical notions arise from such speculation—for example about hopping into a black hole and entering another universe. If a black hole exists, and that is still not definitely proven, all that would be at the centre would be the collapsed remains of a gigantic star, not another universe. Any real person who entered it would be instantly torn apart and converted into pure energy. If that is what is considered as passing into another universe, then those who advocate such ideas are most welcome to make the first excursion! In reality, this is pure speculation, however entertaining it may be. The whole idea of "time-travel" inevitably lands one in a mass of contradictions, not of dialectical but of the absurd variety. Einstein would have been shocked at the mystical interpretation of his theories which involve notions such as shuttling back and forth in time, altering the future, and nonsense of that sort. But he himself must bear some responsibility for this situation because of the idealist element in his outlook, particularly on the question of time. Let us grant that an atomic clock at a high altitude runs faster at high altitudes than on the ground, because of the effect of gravitation. Let us also grant that, when this clock returns to earth, it is found to be, say, 50 billionth of a second older than equivalent clocks which had never left the ground. Does that mean that a man travelling in the same flight has equally aged? The process of ageing is dependent upon the rate of metabolism. This is partly influenced by gravitation, but also by many other factors. It is a complex biological process, and it is not easy to see how it could be fundamentally affected either by velocity or gravitation, except that extremes of either can cause material damage to living organisms. If it were possible to slow down the rate of metabolism in the way predicted, so that, for example, the heart-beat would slow to one every twenty minutes, the process of ageing would presumably be correspondingly slower. It is, in fact, possible to slow down metabolism, for example, by freezing. Whether this would be the effect of travelling at very high speeds, without killing the organism, is open to doubt. According to the well-known theory, such a relativistic space-man, if he succeeded on returning to earth, would come back after, say 10,000 years, and to pursue the usual analogy, would presumably be in a position to marry his own remote descendants. But he would never be able to return to his "own" time. Experiments conducted with subatomic particles (muons) indicate that particles travelling at 99.94 per cent of the speed of light extended their life by nearly thirty times, precisely as predicted by Einstein. However, whether these conclusions can be applied to matter on a larger scale, and living matter in particular, is an issue which remains to be seen. Many serious mistakes have been made by attempting to apply the results derived from one sphere to another, entirely different, area. In the future, space-travel at very high speeds—maybe one-tenth of the speed of light—may become possible. At such speed, a journey of five light-years would take fifty years (though according to Einstein, it would take three months less for those travelling). Will it ever be possible to travel at the speed of light, thus enabling human beings to reach the stars? At this moment in time, such a prospect seems remote. But then, a hundred years ago—a mere blink in history—the idea of travelling to the moon was still confined to the novels of Jules Verne. Mach and Positivism "The object, however, is the real truth, is the essential reality; it is, quite indifferent to whether it is known or not; it remains and stands even though it is not known, while the knowledge does not exist it the object is not there." (Hegel) (43) The existence of past, present and future is deeply engraved on the human consciousness. We live now, but we can remember past events, and, to some extent, foresee future ones. There is a "before" and an "after." Yet some philosophers and scientists dispute this. They regard time as a product of the mind, an illusion. In their view, in the absence of human observers, there is no time, no past, present or future. This is the standpoint of subjective idealism, an entirely irrational and anti-scientific outlook which nevertheless has attempted for the last hundred years to base itself in the discoveries of physics to lend respectability to what is essentially a mystical view of the world. It seems ironical that the school of philosophy which has had the biggest impact upon science in the 20th century, logical positivism, is precisely a branch of subjective idealism. Positivism is a narrow view which holds that science should confine itself to the "observed facts." The founders of this school were reluctant to refer to theories as true or false, but preferred to describe them as more or less "useful." It is interesting to note that Ernst Mach, the real spiritual father of neo-positivism, opposed the atomist theory of physics and chemistry. This was the natural consequence of the narrow empiricism of the positivist outlook. Since the atom could not be seen, how could it exist? It was regarded by them at best as a convenient fiction, and at worst as an unacceptable ad hoc hypothesis. One of Mach’s co-thinkers, Wilhelm Ostwald actually attempted to derive the basic laws of chemistry without the help of the atomic hypothesis! Boltzmann sharply criticised Mach and the Positivists, as did Max Planck, the father of quantum physics. Lenin subjected the views of Mach and Richard Avenarius, the founder of the school of Empirio-criticism, to a devastating criticism in his book Materialism and Empirio-criticism, (1908). Nevertheless, the views of Mach had a big impact and, among others, impressed the young Albert Einstein. Setting out from the view of that all ideas must be derived from "the given," that is, from the information provided immediately by our senses, they went on to deny the existence of the natural world, independent of human sense-perception. Mach and Avenarius referred to physical objects as "complexes of sensation." Thus, for example, this table is no more than a collection of sense-impressions such as hardness, colour, mass and so on. Without these, they maintained, nothing would be left. Therefore, the idea of matter (in the philosophical sense, that is, the objective world given to us in sense-perception) was declared to be meaningless. As we have already pointed out, these ideas lead directly to solipsism—the idea that only "I" exist. If I close my eyes, the world ceases to exist. Mach attacked Newton’s idea that space and time are absolute and real entities, but he did so from the standpoint of subjective idealism. Incredibly, the most influential school of modern philosophy (and the one that had the biggest influence on scientists) was derived from the subjective idealism of Mach and Avenarius. The obsession with "the observer" which is a thread running through the whole of 20th century theoretical physics is derived from the subjective idealist philosophy of Ernst Mach. Taking his starting-point from the empiricist argument that "all our knowledge is derived from immediate sense-perception," Mach argued that objects cannot exist independently of our consciousness. Carried to its logical conclusion, this would mean that, for example, the world could not have existed before there were people present to observe it. As a matter of fact, it could not have existed before I was present, since I can only know my own sensations, and cannot therefore be sure that any other consciousness exists. The important thing is that Einstein himself was initially impressed by these arguments, which left their mark on his early writings on relativity. This has, beyond doubt, exercised the most harmful influence upon modern science. Whereas Einstein was capable of realising his mistake, and attempted to correct it, those who have slavishly followed the master, have been incapable of sorting out the chaff from the grain. As often happens, over-eager disciples become dogmatic. They are more Papist than the Pope! In his autobiography, Karl Popper shows clearly that in his later years Einstein regretted his earlier subjective idealism, or "operationalism," which demanded the presence of an observer to determine natural processes: "It is an interesting fact that Einstein himself was for years a dogmatic positivist and operationalist. He later rejected this interpretation: he told me in 1950 that he regretted no mistake he ever made as much as this mistake. The mistake assumed a really serious form in his popular book, Relativity: The Special and the General Theory. There he says ‘I would ask the reader not to proceed farther until he is fully convinced on this point.’ The point is, briefly, that ‘simultaneity’ must be defined— and defined in an operational way—since otherwise ‘I allow myself to be deceived…when I imagine that I am able to attach a meaning to the statement of simultaneity.’ Or in other words, a term has to be operationally defined or else it is meaningless. (Here in a nutshell is the positivism later developed by the Vienna Circle under the influence of Wittgenstein’s Tractatus, and in a very dogmatic form)." This is important, because it shows that Einstein in the end rejected the subjectivist interpretation of relativity theory. All the nonsense about "the observer" as a determining factor was not an essential part of the theory, but merely the reflection of a philosophical mistake, as Einstein frankly confirmed. That, unfortunately, did not prevent the followers of Einstein from taking over the mistake, and blowing it up to the point where it appeared to be a fundamental cornerstone of relativity. It is here that we find the real origin of Heisenberg’s subjective idealism: "But many excellent physicists," Popper continues, "were greatly impressed by Einstein’s operationalism, which they regarded (as did Einstein himself for a long time) as an integral part of relativity. And so it happened that operationalism became the inspiration of Heisenberg’s paper of 1925, and of his widely accepted suggestion that the concept of the track of an electron, or of its classical position-cum-momentum, was meaningless." (44) The fact that time is an objective phenomenon, reflecting real processes in nature was first demonstrated by the laws of thermodynamics, which were worked out in the 19th century and which still play a central role in modern physics. These laws, particularly as developed by Boltzmann, firmly establish the idea not only that time exists objectively, but that it flows in only one direction, from past to future. Time cannot be reversed, nor is it dependent upon any "observer." Boltzmann and Time The fundamental question which has to be addressed is: Is time an objective feature of the physical universe? Or is it something purely subjective, an illusion of the mind, or merely a convenient way of describing things to which it has no real relationship? The latter position has been held, in one or other degree, by a number of different schools of thought, all of them closely related to the philosophy of subjective idealism. Mach, as we have seen, introduced this subjectivism into science. It was decisively answered towards the end of the 19th century by the pioneer of the science of thermodynamics, Ludwig Boltzmann. Einstein, under the influence of Ernst Mach, treated time as something subjective, which depended on the observer, at least in the beginning before he realised the harmful consequences of this approach. In 1905, his paper on the special theory of relativity introduced the notion of a "local time" associated with each separate observer. The concept of time here contains an idea carried over from classical physics, namely that time is reversible. This is really quite an extraordinary notion, and one which flies in the face of all experience. Film directors often resort to a trick photography, in which the camera is put into reverse, whereupon the most peculiar events occur: milk flows from the glass back into the bottle, buses and cars run backwards, eggs return to their shells, and so on. Our reaction to all this is to laugh, which is what is intended. We laugh because we know that what we are seeing is not just impossible, but absurdly so. We know that the processes which we are seeing cannot be reversed. Boltzmann understood this, and the concept of irreversible time lies at the heart of his famous theory of the arrow of time. The laws of thermodynamics represented a major breakthrough in science, but were controversial. These laws could not be reconciled with the existing laws of physics at the end of the 19th century. The second law cannot be derived from the laws of mechanics or quantum mechanics, and, in effect, marks a sharp break with the theories of previous physical science. It says that entropy increases in the direction of the future, not the past. It denotes a change in state over time, which is irreversible. The notion of a tendency towards dissipation clashed with the accepted idea that the essential task of physics was to reduce the complexity of nature to simple laws of motion. The idea of entropy, which is usually understood as a the tendency of things towards greater disorganisation and decay with the passing of time, entirely bears out what people have always believed: that time exists objectively and that it is a one-way process. The two laws of thermodynamics imply the existence of the phenomenon known as entropy that is conserved in all irreversible processes. Its definition is based on another property known as available energy. The entropy of an isolated system may remain constant or increase, but it cannot decrease. One of the results of this is the impossibility of a "perpetual motion machine." Einstein considered the idea of irreversible time to be an illusion that had no place in physics. In Max Planck’s words, the second law of thermodynamics expresses the idea that there exists in nature a quantity which changes always in the same sense in all natural processes. This does not depend on the observer, but is an objective process. But Planck’s view was in a small minority. The great majority of scientists, like Einstein, attributed it to subjective factors. Einstein’s position on this question shows up the central weakness of his standpoint in making objective processes depend upon a non-existent "observer." This was undoubtedly the weakest element in his entire outlook, and, for that very reason, is the part which has proved most popular with his successors, who do not seem aware of the fact that Einstein himself changed his mind on this towards the end of his life. In physics and mathematics the expression of time is reversible. A "time-reversal invariant" implies that the same laws of physics apply equally well in both situations. The second event is indistinguishable from the first and the flow of time does not have any preferred direction in the case of fundamental interactions. For example, a film of two billiard balls colliding can be run forward or backward, without giving any idea of the true time sequence of the event. The same was assumed to be true of interactions at the sub atomic level, but evidence to the contrary was found in 1964 in weak nuclear interactions. For a long time it was believed that the fundamental laws of nature were "charge symmetrical." For example, an antiproton and a positron behave like a proton and an electron. Experiments have now shown that the laws of nature are symmetrical if three basic things are combined—time, charge and parity. This is known as a "CPT mirror." In dynamics, the direction of a given trajectory was irrelevant. For example, a ball bouncing on the ground would return to its initial position. Any system can thus "go backwards in time," if all the points involved in it are reversed. All the states it previously went through would simply be retraced. In classical dynamics, changes such as time reversal (t —> –t) and velocity reversal (v —> –v) are treated as mathematically equivalent. This kind of calculation works well for simple closed systems, where there are no interactions. In reality, however, every system is subject to many interactions. One of the most important problems in physics is the "three-body" problem, for example, the moon’s motion is influenced by the sun and the earth. In classical dynamics, a system changes according to a trajectory that is given once and for all, the starting point of which is never forgotten. Initial conditions determine the trajectory for all time. The trajectories of classical physics were simple and deterministic. But there are other trajectories that are not so easy to pin down, for example, a rigid pendulum, where an infinitesimal disturbance would be enough to set it rotating or oscillating. The importance of Boltzmann’s work was that he dealt with the physics of processes rather than the physics of things. His greatest achievement was to show how the properties of atoms (mass, charge, structure) determine the visible properties of matter (viscosity, thermal conductivity, diffusion, etc.). His ideas were viciously attacked during his lifetime, but vindicated by the discoveries of atomic physics shortly before 1900, and the realisation that the random movements of microscopic particles suspended in a fluid ("Brownian motion") could only be explained in terms of the statistical mechanics invented by Boltzmann. The bell-shaped Gauss curve describes the random motion of molecules in a gas. An increased temperature leads to an increase in the average velocity of the molecules and the energy associated with their motion. Whereas Clausius and Maxwell approached this question from the standpoint of the trajectories of individual molecules, Boltzmann considered the population of molecules. His kinetic equations play an important role in the physics of gases. It was a major advance in the physics of processes. Boltzmann was a great pioneer, who was treated as a madman by the scientific establishment. He was finally driven to suicide in 1906, having previously been compelled to retreat from his attempt to establish the irreversible nature of time as an objective feature of nature. Whereas in the theory of classical mechanics, the events in the film earlier described are perfectly possible, in practice, they are not. In the theory of dynamics, for example, we have an ideal world in which such things as friction and collision do not exist. In this ideal world, all the invariants involved in a given motion are fixed at the start. Nothing could happen to alter its course. By these means, we arrive at a completely static view of the universe, where everything is reduced to smooth, linear equations. Despite the revolutionary advances made possible by relativity theory, Einstein, at heart, remained wedded to the idea of a static, harmonious universe—just like Newton. The equations of motion of Newtonian or for that matter quantum mechanics have no built-in irreversibility. It is possible to run a movie film forward or backwards. But this is not true of nature in general. The second law of thermodynamics predicts an irreversible tendency towards disorder. It states that randomness always increases in time. Until recently, it was thought that the fundamental laws of nature are symmetrical in time. Time is asymmetrical and moves only in one direction, from past to future. We see fossils, footprints, photographs and hear recordings of things from the past, but never from the future. It is easy to mix eggs to make an omelette or put milk and sugar into a cup of coffee, but not to reverse these processes. The water in the bath transfers its heat to the surrounding air, but not vice versa. The second law of thermodynamics is the "arrow of time." The subjectivists objected that irreversible processes like chemical affinity, heat conduction, viscosity, etc., would depend on the "observer." In reality, they are objective processes that take place in nature, and this is clear to everyone in relation to life and death. A pendulum (at least in an ideal state) can swing back to its initial position. But everyone knows that the life of an individual moves in only one direction, from the cradle to the grave. It is an irreversible process. Ilya Prigogine, one of the leading theorists of chaos theory, has devoted a lot of attention to the question of time. When he first began to study physics as a student in Brussels, Prigogine recalls that he was "astonished by the fact that science had so little to say about time, especially since his earlier education had centred mainly around history and archaeology." In relation to the conflict between classical mechanics (dynamics) and thermodynamics, Prigogine and Stengers write: "To a certain extent, there is an analogy between this conflict and the one that gave rise to dialectical materialism. We have described…a nature that might be called "historical"—that is, capable of development and innovation. The idea of a history of nature as an integral part of materialism was asserted by Marx and, in greater detail, by Engels. Contemporary developments in physics, the discovery of the constructive role played by irreversibility, have thus raised within the natural sciences a question that has long been asked by materialists. For them, understanding nature meant understanding it as being capable of producing man and his societies. "Moreover, at the time Engels wrote his Dialectics of Nature, the physical sciences seemed to have rejected the mechanistic world view and drawn close to the idea of an historical development of nature. Engels mentions three fundamental discoveries: energy and the laws governing its qualitative transformations, the cell as the basic constituent of life, and Darwin’s discovery of the evolution of species. In view of these great discoveries, Engels came to the conclusion that the mechanistic world view was dead." Against the subjective interpretation of time, the authors conclude: "Time flows in a single direction, from past to future. We cannot manipulate time, we cannot travel back to the past." (45) Relativity and Black Holes In Einstein’s view, unlike that of Newton, gravity affects time because it affects light. If one could imagine a particle of light poised on the edge of a black hole, it would be suspended indefinitely, neither advancing nor retreating, neither losing energy, nor gaining it. In such a state, it is possible to argue that "time stands still." This is the argument of the relativist proponents of the black hole and its properties. What this boils down to is that if all motion were to cease, then there would be no change either of state or position, and therefore no time in any meaningful sense of the word. Such a situation is alleged to exist at the edge of a black hole. This, however, seems a highly speculative and mystical interpretation of a phenomenon, the existence of which is, in itself, unproved. All matter exists in a constant state of change and motion, and therefore, all that is being said here is that if matter and motion are eliminated, there is no time either, which is a complete tautology. It is like saying—if there is no matter, there is no matter, or if there is no time, there is no time. Because both statements mean just the same thing. Strangely enough, one would seek in vain in the theory of relativity for a definition of what time and space are. Einstein certainly found it difficult to explain. However, he came close to it when he explained the difference between his geometry and the classical geometry of Euclid. He said that one could imagine a universe in which space was not warped, but it would be completely devoid of matter. This points clearly in the right direction. After all the fuss about black holes, you may also be surprised to discover that this subject was not even mentioned by Einstein. He relied upon a rigorous approach, mainly based on very complicated mathematics, and made predictions which could be verified by observation and experiment. The physics of black holes, in the absence of clearly established empirical data, has an extremely speculative character. Despite its successes, it is still possible that the general theory of relativity may be wrong. Unlike special relativity, the experimental tests which have been carried out on it are not very many. There is no conclusive proof, although up to the present time no conflict has been found between the theory and the observed facts. It is not even ruled out that the assertion of special relativity, that nothing can move faster than the speed of light, may be shown to be incorrect in the future*. Alternative theories of relativity have been put forward, for example, by Robert Dicke. Dicke’s theory predicted a deflection of the moon’s orbit of several feet towards the sun. Using advanced laser technology, the McDonald observatory in Texas found no trace of this displacement. However, there is no reason to suppose that the last word has been spoken. So far, Einstein’s theories have been borne out by repeated experiment. But the constant probing of extreme conditions must sooner or later reveal a set of circumstances that are not covered by the equations, preparing the way for new epoch-making discoveries. The theory of relativity cannot be the end of the line, any more than Newtonian mechanics, Maxwell’s theory of electromagnetism, or any previous theory. For two hundred years, the theories of Newton were held to be absolutely valid. His authority could not be challenged. After his death, Laplace and others carried his theories to an extreme where they became absurd. The radical break with the old mechanistic Absolutes was a necessary condition for the further advance of physics in the 20th century. It was the proud boast of the new physics that they had forever killed off the ogre of the Absolute. Suddenly thought was free to move into hitherto unheard of realms. These were heady times! Unfortunately, such happiness cannot last forever. In the words of Robert Burns: "But pleasures are like poppies spread: You seize the flow’r, its bloom is shed." The new physics solved many problems, but only at the cost of creating new contradictions, which remain unresolved even at the present time. For most of the present century, physics has been dominated by two imposing theories: quantum mechanics and relativity. What is not generally realised is that the two theories are at variance. In fact, they are incompatible. The general theory of relativity takes no account whatever of the uncertainty principle. Einstein spent the last years of his life attempting to resolve this contradiction, but failed to do so. Relativity theory was a great and revolutionary theory. So was Newtonian mechanics in its day. Yet it is the fate of all such theories to become transformed into orthodoxies, to suffer a kind of hardening of the arteries, until they are no longer able to answer the questions posed by the march of science. For a long time, theoretical physicists have been content to rest on the discoveries of Einstein, in the same way that an earlier generation were content to swear by Newton. And in just the same way, they are guilty of bringing general relativity into disrepute by reading into it the most absurd and fantastic notions, which its author never even dreamed of. Singularities, black holes where time stands still, multiverses, a time before time began, about which no questions must be asked—one can imagine Einstein clutching his head! All this is supposed to flow inevitably from general relativity, and anyone who raised the slightest doubt about it is immediately confronted with the authority of the great Einstein. This is not one whit better than the situation before relativity, when the authority of Newton was similarly wielded in defence of the existing orthodoxy. The only difference is that the fantastic notions of Laplace seem extremely sensible alongside the mystical gobbledygook written by some physicists today. And even less than Newton can Einstein be made responsible for the outlandish flights of fancy of his successors, which represent the reductio ad absurdum of the original theory. These senseless and arbitrary speculations are the best proof that the theoretical framework of modern physics is in need of a complete overhaul. For the problem here is one of method. It is not just that they provide no answers. The problem is that they do not even know how to ask the right questions. This is not so much a scientific as a philosophical question. If everything is possible, then one arbitrary theory (more correctly, guess) is as good as the next. The whole system has been pushed near to breaking-point. And to cover up the fact, they resort to a mystical kind of language, in which the obscurity of expression does not disguise the complete lack of any real content. This state of affairs is clearly intolerable, and has led a section of scientists to begin to question the basic assumptions on which science has been operating. David Bohm’s investigations into the theory of quantum mechanics, Ilya Prigogine’s new interpretation of the Second Law of Thermodynamics, Hannes Alfvén’s attempt to work out an alternative to the orthodox cosmology of the big bang, above all, the spectacular rise of chaos and complexity theory—all this indicates the existence of a ferment in science. While it is too early to predict the exact outcome of this, it seems likely that we are entering into one of those exciting periods in the history of science, when an entirely new approach will emerge. There is every reason to suppose that eventually the theories of Einstein will be surpassed by a new and broader-based theory, which, while preserving all that is viable in relativity, will correct and amplify it. In the process, we shall certainly arrive at a truer and more balanced understanding of the questions relating to the nature of time, space and causality. This does not signify a return to the old mechanical physics, any more than the fact that we can now achieve the transformation of the elements means a return to the ideas of the alchemists. As we have seen, the history of science frequently involves an apparent return to earlier positions, but on a qualitatively higher level. One thing we can predict with absolute confidence: when the new physics finally emerges from the present chaos there will be no place in it for time-travel, multiverses, or singularities which compress the whole of the universe into a single point, about which no questions are allowed to be asked. This will sadly make it much more difficult to win big cash prizes for providing the Almighty with scientific credentials, a fact which some may regret, but which, in the long term, may not be a bad thing for the progress of science! * This prediction appears to have been confirmed far sooner than we expected. Before the book was sent to the printers, reports appeared in the press of an experiment conducted by American scientists which appear to indicate that photons can travel faster than the speed of light. The experiment is a complicated one, based on a peculiar phenomenon known as "quantum tunnelling." If it is shown to be correct, this will demand a fundamental rethinking of the whole concept of relativity.

http://lipn.univ-paris13.fr/~duchamp/Books&more/Penrose/Road_to_Reality-CAPE_JONATHAN_(RAND)(2004).pdf

Physics > History and Philosophy of Physics

Historical Approach to Physics according to Kant, Einstein, and Hegel

Y. S. Kim

(Submitted on 25 Jan 2013)

It is known that Einstein's conceptual base for his theory of relativity was the philosophy formulated by Immanuel Kant. Things appear differently to observers in different frames. However, Kant's Ding-an-Sich leads to the existence of the absolute reference frame which is not acceptable in Einstein's theory. It is possible to avoid this conflict using the ancient Chinese philosophy of Taoism where two different views can co-exist in harmony. This is not enough to explain Einstein's discovery of the mass-energy relation. The energy-momentum relations for slow and ultra-fast particles take different forms. Einstein was able to synthesize these two formulas to create his energy-mass relation. Indeed, this is what Hegelianism is about in physics. Isaac Newton synthesized open orbits for comets and closed orbits for planets to create his second law of motion. Maxwell combined electricity and magnetism to create his four equations to the present-day wireless world. In order to synthesize wave and particle views of matter, Heisenberg formulated his uncertainty principle. Relativity and quantum mechanics are the two greatest theories formulated in the 20th Century. Efforts to synthesize these two theories are discussed in detail.

Comments:	Latex 10 pages with 6 figures, based on an invited presented at the 32nd Congress of the Italian Society of Historians of Physics and Astronomy (Rome, Italy, September 2012)
Subjects:	History and Philosophy of Physics (physics.hist-ph); Popular Physics (physics.pop-ph)
Cite as:	arXiv:1301.6091 [physics.hist-ph]
	(or arXiv:1301.6091v1 [physics.hist-ph] for this version)

Submission history

https://www.marxist.com/science-old/relativitytheory.html

Relativity Theory

What is Time?
Time and Philosophy
Newton and Hegel
Relativity
The General Theory of Relativity
Relations Between Things
The Measurement of Time
Problem Not Resolved
Idealist Interpretations
Mach and Positivism
Boltzman and Time
Relativity and Black Holes

Few ideas have penetrated the human consciousness as profoundly as that of time. The idea of time and space has occupied human thought for thousands of years. These things at first sight seem simple and easy to grasp, because they are close to everyday experience. Everything exists in time and space, so they appear as familiar conceptions. However, what is familiar is not necessarily understood. On closer examination, time and space are not so easily grasped. In the 5th century, St. Augustine remarked: "What, then, is time? If no one asks me, I know what time is. If I wish to explain it to him who asks me, I do not know." The dictionary is not much help here. Time is defined as a "a period," and a period is defined as "time." This does not get us very far! In reality, the nature of time and space is quite a complex philosophical problem.

Men and women clearly distinguish between past and future. A sense of time is, however, not unique to humans or even animals. Organisms often have a kind of "internal clock," like plants which turn one way during the day and another at night. Time is an objective expression of the changing state of matter. This is revealed even by the way we talk about it. It is common to say that time "flows." In fact, only material fluids can flow. The very choice of metaphor shows that time is inseparable from matter. It is not only a subjective thing. It is the way we express an actual process that exists in the physical world. Time is thus just an expression of the fact that all matter exists in a state of constant change. It is the destiny and necessity of all material things to change into something other than what they are. "Everything that exists deserves to perish."

A sense of rhythm underlies everything: the heart-beat of a human, the rhythms of speech, the movement of the stars and planets, the rise and fall of the tides, the alternations of the seasons. These are deeply engraved upon the human consciousness, not as arbitrary imaginings, but as real phenomena expressing a profound truth about the universe. Here human intuition is not in error. Time is a way of expressing change of state and motion which are inseparable features of matter in all its forms. In language we have tense, future, present and past. This colossal conquest of the mind enabled humankind to free itself from the slavery of the moment, to rise above the concrete situation and be "present," not just in the here and now, but in the past and the future, at least in the mind.

Time and movement are inseparable concepts. They are essential to all life and all knowledge of the world, including every manifestation of thought and imagination. Measurement, the corner-stone of all science, would be impossible without time and space. Music and dance are based upon time. Art itself attempts to convey a sense of time and movement, which are present not just in representations of physical energy, but in design. The colours, shapes and lines of a painting guide the eye across the surface in a particular rhythm and tempo. This is what gives rise to the particular mood, idea and emotion conveyed by the work of art. Timelessness is a word that is often used to describe works of art, but really expresses the opposite of what is intended. We cannot conceive of the absence of time, since time is present in everything.

There is a difference between time and space. Space can also express change, as change of position. Matter exists and moves through space. But the number of ways that this can occur is infinite: forward, backward, up or down, to any degree. Movement in space is reversible. Movement in time is irreversible. They are two different (and indeed contradictory) ways of expressing the same fundamental property of matter—change. This is the only Absolute that exists.

Space is the "otherness" of matter, to use Hegel’s terminology, whereas time is the process whereby matter (and energy, which is the same thing) constantly changes into something other than what it is. Time—"the fire in which we are all consumed"—is commonly seen as a destructive agent. But it is equally the expression of a permanent process of self-creation, whereby matter is constantly transformed into and endless number of forms. This process can be seen quite clearly in non-organic matter, above all at the subatomic level.

The notion of change, as expressed in the passing of time, deeply permeates human consciousness. It is the basis of the tragic element in literature, the feeling of sadness at the passing of life, which reaches its most beautiful expression in the sonnets of Shakespeare, like this one which vividly conveys a sense of the restless movement of time :

"Like as the waves make toward the pebbled shore,
So do our minutes hasten to their end;
Each changing place with that which goes before,
In sequent toil all forward do contend."

The irreversibility of time does not only exist for living beings. Not only humans, but stars and galaxies are born and perish. Changes affects all, but not only in a negative way. Alongside death there is life, and order arises spontaneously out of chaos. The two sides of the contradiction are inseparable. Without death, life itself would be impossible. Every man and woman is not only aware of themselves, but also the negation of themselves, their limit. We come from nature and will return to nature.

Mortals understand that as finite beings their lives must end in death. As the Book of Job reminds us: "Man that is born of woman is of a few days, and full of trouble. He cometh forth like a flower, and is cut down; he fleeth also as a shadow, and continueth not." (29) Animals do not fear death in the same way because they have no knowledge of it. Human beings have attempted to escape their destiny by establishing a privileged communion with an imaginary supernatural existence after death. The idea of everlasting life is present in almost all religions in one form or another. It is the motive-force behind the egotistical thirsting for an imaginary immortality in a non-existent Heaven, which is supposed to provide a consolation for the "Vale of Tears" on this sinful earth. Thus, for countless centuries men and women have been taught to submit meekly to suffering and privation on earth in expectation of a life of happiness—once they are dead.

That every individual must pass away is well known. In the future, human life will be prolonged far beyond its "natural" span; nevertheless the end must come. But what is true for particular men and women is not true of the species. We live on through our children, through the memories of our friends, and through the contribution we make to the good of humanity. This is the only immortality to which we are entitled to aspire. Generations pass away, but are replaced by new generations, which develop and enrich the scope of human activity and knowledge. Humanity can conquer the earth and reach out its hands to the heavens. The real search for immortality is realised in this endless process of human development and perfection, as men and women make themselves anew on a higher basis than before. The highest goal we can set ourselves is thus not to long for an imaginary paradise in the beyond, but to fight to attain the real social conditions for the building of a paradise in this world.

From our earliest experiences, we come to an understanding of the importance of time. So it is surprising that some have thought time to be an illusion, a mere invention of the mind. This idea has persisted down to the present In fact, the idea that time and change are mere illusions is not new. It is present in ancient religions like Buddhism, and also in idealist philosophies like that of Pythagoras, Plato and Plotinus. The aspirations of Buddhism was to reach Nirvana, a state where time ceased to exist. It was Heraclitus, the father of dialectics, who understood correctly the nature of time and change, when he wrote that "everything is and is not because everything is in flux" and "we step and do not step in the same stream, we are and are not."

The idea of change as cyclical is the product of an agricultural society utterly dependent upon the change of seasons. The static way of life rooted in the mode of production of former societies found its expression in static philosophies. The Catholic Church could not stomach the cosmology of Copernicus and Galileo because it challenged the existing view of the world and society. Only in capitalist society has the development of industry disrupted the old, slow rhythms of peasant life. Not only is the difference between the seasons abolished in production, but even the difference between night and day, as machines run for 24 hours a day, seven days a week, fifty two weeks a year, under the glare of artificial lights. Capitalism has revolutionised the means of production, and with it the minds of men and women. However, the progress of the latter has proved to be far slower than the former. The conservatism of the mind is revealed in the constant attempt to cling to outworn ideas, old certainties whose time has long past, and, ultimately, the age-old hope for a life after death.

The idea that universe must have a beginning and an end has been revived in recent decades by the cosmological theories of the big bang. This inevitably involves a supernatural being who creates the world according to some unfathomable plan from nothing, and keeps it going for as long as He considers it necessary. The old religious cosmology of Moses, Isaiah, Tertullian and Plato’s Timaeus, incredibly resurfaces in the writings of some modern cosmologists and theoretical physicists. There is nothing new in this. Every social system which enters into a phase of irreversible decline always presents its own demise as the end of the world, or, better still, the universe. Yet the universe still carries on, indifferent to the destiny of this or that temporary social formation on earth. Humankind continues to live, to fight and, despite all reverses, to develop and progress. So that every period sets out on a higher level than before. And there is, in principle, no limit to this process.

Time and Philosophy

The Ancient Greeks actually had a far deeper insight into the meaning of time, space and motion than the moderns. Not only Heraclitus, the greatest dialectician of Antiquity, but also the Eleatic philosophers (Parmenides, Zeno) arrived at a very scientific conception of these phenomena. The Greek atomists already put forward the picture of a universe which required no Creator, no beginning and no end. Space and matter are generally seen as opposites, as conveyed by the idea of "full" and "empty." In practice, however, the one cannot exist without the other. They presuppose each other, determine, limit and define each other. The unity of space and matter is the most fundamental unity of opposites of all. This was already understood by the Greek atomists who visualised the universe as being composed of only two things—the "atoms" and the "void." In essence, this view of the universe is correct.

Relativism has been observed many times in the history of philosophy. The sophists held that "man is the measure of all things." They were relativists par excellence. Denying the possibility of absolute truth, they inclined towards extreme subjectivism. The sophists nowadays have a bad name, but in fact they represented a step forward in the history of philosophy. While there were many charlatans in their ranks, they also had a number of talented dialecticians like Protagoras. The dialectic of sophism was based on the correct idea that truth is many sided. A thing can be shown to have many properties. It is necessary to have the ability to see a given phenomenon from different sides. For the undialectical thinker, the world is a very simple place, made up of things existing separately, one after the other. Every "thing" enjoy a solid existence in time and space. It is before me "here" and "now." However, closer observation reveals these simple and familiar words to be one-sided abstractions.

Aristotle as in so many other fields, dealt with space, time and motion with great rigour and profundity. He wrote that only two things are imperishable: time and change, which he rightly considers identical:

"It is impossible, however, that motion should be generable or perishable; it must always have existed. Nor can time come into being or cease to be; for there cannot be a ‘before’ or ‘after’ where there is no time. Movement, then, is also continuous in the sense in which time is, for time is either the same thing as motion or an attribute of it; so than motion must be continuous as time is, and if so it must be local and circular." Elsewhere he says that "Movement can neither come into being nor cease to be: nor can time come into being, or cease to be." (30) How much wiser were the great thinkers of the Ancient World than those who now write about "the beginning of time," and without even smiling!

The German idealist philosopher Emmanuel Kant was the man who, after Aristotle, investigated the question of the nature of time and space most fully, although his solutions were ultimately unsatisfactory. Every material thing is an assemblage of many properties. If we take away all these concrete properties, we are left with only two abstractions: time and space. The idea of time and space as really existing metaphysical entities was given a philosophical basis by Kant, who claimed that space and time were "phenomenally real," but could not be known "in themselves."

Time and space are properties of matter, and cannot be conceived separately from matter. In his book The Critique of Pure Reason, Kant claimed that time and space were not objective concepts drawn from observation of the real world, but were somehow inborn. In point of fact, all the concepts of geometry are derived from observations of material objects. One of the achievements of Einstein’s general theory of relativity was precisely to develop geometry as an empirical science, the axioms of which are inferred from actual measurements, and which differ from the axioms of classical Euclidean geometry, which were (incorrectly) supposed to have been the products of pure reason, deduced from logic alone.

Kant attempted to justify his claims in the famous section in his Critique of Pure Reason known as the Antinomies. which deal with the contradictory phenomena of the natural world, including space and time. The first four of Kant’s (cosmological) antinomies deal with this question. Kant had the merit of posing the existence of such contradictions, but his explanation was at best incomplete. It fell to the great dialectician Hegel to resolve the contradiction in The Science of Logic.

Throughout the 18th century, science was dominated by the theories of classical mechanics, and one man set his stamp on the whole epoch. The poet Alexander Pope sums up the adulatory attitude of contemporaries to Newton in his verse:

"Nature and Nature’s laws lay hid in night:
God said ‘Let Newton be!’ and all was light."

Newton envisaged time as flowing in a straight line everywhere. Even if there was no matter, there would be a fixed frame of space and time would still flow "through" it. Newton’s absolute spatial frame was supposed to be filled with a hypothetical "ether" through which light waves flowed. Newton thought that time was like a gigantic "container" inside which everything exists and changes. In this idea, time is conceived as having an existence separate and apart from the natural universe. Time would exist, even if the universe did not. This is characteristic of the mechanical (and idealist) method in which time, space, matter and motion are regarded as absolutely separate. In reality, it is impossible to separate them.

Newtonian physics was conditioned by mechanics which In the 18th century was the most advanced of the sciences. It was also convenient for the new ruling class because it presented an essentially static, timeless, unchanging view of the universe, in which all contradiction were smoothed out—no sudden leaps, no revolutions, but a perfect harmony, in which everything sooner or later returned to equilibrium, just as the British parliament had reached a satisfactory equilibrium with the Monarchy under William of Orange. The 20th century has pitilessly destroyed this view of the world. One after the other, the old rigid, static mechanism has been displaced. The new science has been characterised by restless change, fantastic speed, contradictions and paradoxes at all levels.

Newton distinguished between absolute time and "relative, apparent and common time," as it appears in earthly clocks. He advanced the notion of absolute time, an ideal time scale which simplified the laws of mechanics. These abstractions of time and space proved to be powerful ideas which have greatly advanced our understanding of the universe. They were held to be absolute for a long time. However, upon closer examination, the "absolute truths" of classical Newtonian mechanics proved to be—relative. They were true only within certain limits.

Newton and Hegel

The mechanistic theories which dominated science for two centuries after Newton, were first seriously challenged in the field of biology by the revolutionary discoveries of Charles Darwin. Darwin’s theory of evolution showed that life could originate and develop without the need for Divine intervention, on the basis of the laws of nature. At the end of the 19th century, the idea of the "arrow of time" was put forward by Ludwig Boltzmann in the second law of thermodynamics. This striking image no longer presents time as a never-ending cycle, but as an arrow moving in a single direction. These theories assume that time is real and that the universe is in a continual process of change, as old Heraclitus had foreseen.

Almost half a century before Darwin’s epoch making work, Hegel had anticipated not only him, but many other discoveries of modern science. Boldly challenging the assumption of the prevailing Newtonian mechanics, Hegel advanced a dynamic view of the world, based on processes and change through contradiction. The brilliant anticipations of Heraclitus were transformed by Hegel into a completely elaborated system of dialectical thought. There is no doubt that, had Hegel been taken more seriously, the process of science would have advanced far more rapidly than it did.

The greatness of Einstein was to get beyond these abstractions and reveal their relative character. The relative aspect of time was, however, not new. It was thoroughly analysed by Hegel. In his early work The Phenomenology of Mind, he explains the relative content of words like "here" and "now." These ideas which seem quite simple and straightforward turn out to be very complex and contradictory. "To the question, What is the Now? we reply, for example, the Now is night-time. To test the truth of this certainty of sense, a simple experiment is all we need: write that truth down. A truth cannot lose anything by being written down, and just as little by our preserving and keeping it. If we look again at the truth we have written down, look at it now, at his noon-time, we shall have to say it has turned stale and become out of date." (31)

It is a very simple matter to dismiss Hegel (or Engels) because their writings on science were necessarily limited by the actual state of science of the day. What is remarkable, however, is how advanced Hegel’s views on science actually were. In their book Order out of Chaos, Prigogine and Stengers point out that Hegel rejected the mechanistic method of classical Newtonian physics, at a time when Newton’s ideas were universally sacrosanct:

"The Hegelian philosophy of nature systematically incorporates all that is denied by Newtonian science. In particular, it rests on the qualitative difference between the simple behaviour described by mechanics and the behaviour of more complex entities such as living beings. It denies the possibility of reducing those levels, rejecting the idea that differences are merely apparent and that nature is basically homogeneous and simple. It affirms the existence of a hierarchy, each level of which presupposes the preceding ones." (32)

Hegel wrote scornfully about the allegedly absolute truths of Newtonian mechanics. He was the first one to subject the mechanistic approach of the 18th century to a thorough criticism, although the limitations of the science of his day did not allow him to put forward a worked-out alternative. For Hegel, every finite thing was mediated, that is, relative to something else. Moreover, this relationship was not merely a formal juxtaposition, but a living process: everything was limited, conditioned and determined by everything else. Thus, cause and effect only hold good in relation to isolated relations (such as we find in classical mechanics), but not if we regard things as processes, in which everything is the result of universal interrelations and interactions.

Time is the form of existence of matter. Mathematics and formal logic cannot really deal with time, but treat it merely as a quantitative relation. Now there is no doubt about the importance of quantitative relations for understanding reality, since every finite thing can be approached from a quantitative point of view. Without a grasp of quantitative relationships, science would be impossible. But in and of themselves, they cannot adequately express the complexity of life and movement, the restless process of change in which gradual, smooth developments suddenly give rise to chaotic transformations.

Purely quantitative relations, to use Hegel’s terminology, present the real processes of nature "only in an arrested paralysed form." (33) The universe is an infinite, self-moving whole, which is self-establishing and contains life within itself. Movement is a contradictory phenomenon, containing both positive and negative. This is one of the fundamental propositions of dialectics, which are closer to the real nature of things than the axioms of classical mathematics.

Only in classical geometry is it possible to conceive of completely empty space. It is yet another mathematical abstraction, which plays an important role, but only approximately represents reality. Geometry essentially compares different spatial magnitudes. Contrary to what Kant believed, the abstractions of mathematics are not "a priori" and inborn, but derived from observations of the material world. Hegel shows that the Greeks had already understood the limitedness of purely quantitative descriptions of nature, and comments:

"How much further had they progressed in thought than those who in our day, when some put in the place of determinations of thought number and determinations of numbers (like powers), next the infinitely great and the infinitely small, one divided by infinity, and other such determinations, which often are a perverted mathematical formalism, take the return to this impotent childishness for something praiseworthy and even for something thorough and profound." (34)

These lines are even more appropriate today than when they were written. It really is incredible when certain cosmologists and mathematicians make the most preposterous claims about the nature of the universe without the slightest attempt to prove them on the basis of observed facts, and then appeal to the alleged beauty and simplicity of their equations as the final authority. The cult of mathematics is greater today than at any time since Pythagoras who thought that "all things are Number." And, as with Pythagoras, there are similarly mystical overtones. Mathematics leaves aside all qualitative determinations except number. It ignores the real content, and applies its rules externally to things. None of these abstractions have real existence. Only the material world exists. This fact is all too frequently overlooked with disastrous results.

Relativity

Albert Einstein was undoubtedly one of the great geniuses of our time. Between his twenty first and thirty eighth birthdays he completed a revolution in science, with profound repercussions at many levels. The two great breakthroughs were the Special Theory of Relativity (1905) and the General Theory of Relativity (1915). Special relativity deals with high speeds, general relativity with gravity.

Despite their extremely abstract character, Einstein’s theories were ultimately derived from experiments, and were successfully given practical applications, which confirmed their correctness time and again. Einstein set out from the famous Michelson-Morley experiment, "the greatest negative experiment of the history of science" (Bernal), which exposed an inner contradiction in 19th century physics. This experiment attempted to generalise the electromagnetic theory of light by demonstrating that the apparent velocity of light was dependent upon the rate at which the observer travelled through the supposedly fixed "ether." In the end, no difference was found in the velocity of light, in whatever direction the observer was travelling.

J. J. Thomson later showed that the velocity of electrons in high electrical fields was slower than predicted by the classical Newtonian physics. These contradictions in 19th century physics were resolved by the special theory of relativity. The old physics was unable to explain the phenomenon of radioactivity. Einstein explained this as the release of a tiny part of the enormous amount of energy trapped in "inert" matter.

In 1905, Einstein developed his special theory of relativity in his spare time, while working as a clerk in a Swiss patent office. Setting out from the discoveries of the new quantum mechanics, he showed that light travels through space in a quantum form (as bundles of energy). This was clearly in contradiction to the previously accepted theory of light as a wave. In effect, Einstein revived the old corpuscular theory of light, but in an entirely different way. Here light was shown as a new kind of particle, with a contradictory character, simultaneously displaying the properties of a particle and a wave. This startling theory made possible the retention of all the great discoveries of 19th century optics, including spectroscopes, as well as Maxwell’s equation. But it killed stone-dead the old idea that light requires a special vehicle, the "ether," to travel through space.

Special relativity starts from the assumption that the speed of light in a vacuum will always be measured at the same constant value, irrespective of the speed of the light source relative to the observer. From this it is deduced that the speed of light represents the limiting speed for anything in the universe. In addition, special relativity states that energy and mass are in reality equivalents. This is a striking confirmation of the fundamental philosophical postulate of dialectical materialism—the inseparable character of matter and energy the idea that motion ("energy") is the mode of existence of matter.

Einstein’s discovery of the law of equivalence of mass and energy is expressed in his famous equation E = mc2, which expresses the colossal energies locked up in the atom. This is the source of all the concentrated energy in the universe. The symbol e represents energy (in ergs), m stands for mass (in grams) and c is the speed of light (in centimetres per second). The actual value of c2 is 900 billion billion. That is to say, the conversion of one gram of energy locked up in matter will produce a staggering 900 billion billion ergs. To give a concrete example of what this means, the energy contained in a single gram of matter is equivalent to the energy produced by burning 2,000 tons of petrol.

Mass and energy are not just "interchangeable," as dollars are interchangeable with Deutschmarks, they are one and the same substance, which Einstein characterised as "mass-energy." This idea goes far deeper and is more precise than the old mechanical concept whereby, for example, friction is transformed into heat. Here, matter is just a particular form of "frozen" energy, while every other form of energy (including light), has mass associated with it. For this reason, it is quite wrong to say that matter "disappears" when it is changed into energy.

Einstein’s law displaced the old law of the conservation of mass, worked out by Lavoisier, which says that matter, understood as mass, can neither be created nor destroyed. In fact, every chemical reaction that releases energy converts a small amount of mass into energy. This could not be measured in the kind of chemical reaction known to the 19th century, such as the burning of coal. But nuclear reaction releases sufficient energy to reveal a measurable loss of mass. All matter, even when at "rest," contains staggering amounts of energy. However, as this cannot be observed, it was not understood until Einstein explained it.

Far from overthrowing materialism, Einstein’s theory establishes it on a firmer basis. In place of the old mechanical law of the "conservation of mass," we have the far more scientific and more general laws of the conservation of mass-energy, which expresses the first law of thermodynamics in an universal and unassailable form. The mass does not "disappear" at all, but is converted into energy. The total amount of mass-energy remains the same. Not a single particle of matter can be created or destroyed. The second idea is the special limiting character of the speed of light: the assertion that no particle can travel faster than the speed of light, since as it approaches this critical velocity, its mass approaches infinity, so that it becomes harder and harder to go faster. These ideas seem abstract and difficult to grasp. They challenge the assumptions of "sound common sense." The relationship between "common sense" and science was summed up by the Soviet scientist Professor L. D. Landau in the following lines:

"So-called common sense represents nothing but a simple generalisation of the notions and habits that have grown up in our daily life. It is a definite level of understanding reflecting a particular level of experiment." And he adds: "Science is not afraid of clashes with so-called common sense. It is only afraid of disagreement between existing ideas and new experimental facts and if such disagreement occurs science relentlessly smashes the ideas it has previously built up and raises our knowledge to a higher level." (35) How can a moving object increase its mass? Such a notion contradicts our everyday experience. A spinning top does not visibly gain in mass while revolving. In point of fact, it does, but the increase is so infinitesimal that it may be discounted for all practical purposes. The effects of special relativity cannot be observed on the level of everyday phenomena. However, under extreme conditions, for example, at very high speeds approaching the speed of light, relativistic effects begin to come into play.

Einstein predicted that the mass of a moving object would increase at very high speeds. This law can be ignored when dealing with normal speeds. Nevertheless, subatomic particles move at speeds of nearly 10,000 miles per second or more, and at such speeds as these relativistic effects appear. The discoveries of quantum mechanics demonstrated the correctness of the special theory of relativity, not only qualitatively, but quantitatively. An electron gains in mass as it moves at 9/10th the speed of light; moreover, the gain in mass is 3 1/6th times, precisely as Einstein’s theory predicted. Since then, special relativity has been tested many times, and so far it has always given correct results. Electrons emerge from a powerful particle accelerator about 40,000 times heavier than when they started, the extra mass representing energy of motion.

At far higher velocities the increase in mass becomes noticeable. And modern physics deals precisely with extremely high velocities, such as the speed of sum-atomic particles, which approach the speed of light. Here the classical laws of mechanics, which adequately describe everyday phenomena, cannot be applied. To common sense the mass of an object never changes. Therefore a spinning-top has the same weight as a still one. In this way a law was invented which states that mass is constant irrespective of speed.

Later, this law was shown to be incorrect. It was found that mass increases with velocity. Yet, since the increase only becomes appreciable near the speed of light, we take it as constant. The correct law would be: "If an object moves with a speed of less than 100 miles per second, the mass is consistent to within one part in a million." For everyday purposes, we can assume that mass is constant irrespective of speed. But for high speeds, this is false, and the higher the speed, the falser is the assertion. Like thinking based on formal logic, it is accepted as valid for practical purposes. Feynman points out:

"…Philosophically, we are completely wrong with the approximate law. Our entire picture of the world has to be altered even though the mass changes only by a little bit. This is a very peculiar thing about the philosophy, or the ideas, behind the laws. Even a very small effect sometimes requires profound changes in our ideas." (36)

The predictions of special relativity have been shown to correspond to the observed facts. Scientists discovered by experiment that gamma-rays could produce atomic particles, transforming the energy of light into matter. They also found that the minimum energy required to create a particle depended on its rest-energy, as predicted by Einstein. In point of fact not one, but two particles were produced: a particle and its opposite, the "anti-particle." In the gamma-ray experiment, we get an electron and an anti-electron (positron). The reverse process also takes place: when a positron meets an electron, they annihilate each other, producing gamma rays. Thus, energy is transformed into matter, and matter into energy. Einstein’s discovery provided the basis for a far more profound understanding of the workings of the universe. It provided an explanation of the source of the sun’s energy, which had been a mystery throughout the ages. The immense storehouse of energy turned out to be—matter itself. The awesome power of the energy locked up in matter was revealed to the world in August 1945 at Hiroshima and Nagasaki. All this is contained in the deceptively simple formula E = mc2.

The General Theory of Relativity

Special relativity is quite adequate when dealing with an object moving at constant speed and direction in relation to the observer. However, in practice motion is never constant. There are always forces which cause variations in the speed and direction of moving objects. Since subatomic particles move at immense speeds over short distances, they do not have time to accelerate much, and special relativity can be applied. Nevertheless, in the motion of planets and stars, special relativity proved insufficient. Here we are dealing with large accelerations caused by huge gravitational fields. It is once again a case of quantity and quality. At the subatomic level, gravitation is insignificant in comparison with other forces, and can be ignored. In the everyday world, on the contrary, all other forces except gravity can be ignored.

Einstein attempted to apply relativity to motion in general, not just to constant motion. Thus we arrive at the general theory of relativity, which deals with gravity. It marks a break, not only with the classical physics of Newton, with its absolute mechanical universe, but with the equally absolute classical geometry of Euclid. Einstein showed that Euclidean geometry only applied to "empty space," an ideally-conceived abstraction. In reality, space is not "empty." Space is inseparable from matter. Einstein maintained that space itself is conditioned by the presence of material bodies. In his general theory, this idea is conveyed by the seemingly paradoxical assertion that, near heavy bodies, "space is curved."

The real, i.e., material, universe is not at all like the world of Euclidean geometry, with the perfect circles, absolutely straight lines, and so on. The real world is full of irregularities. It is not straight, but precisely "warped." On the other hand, space is not something which exists separate and apart from matter. The curvature of space is just another way of expressing the curvature of matter which "fills" space. For example, it has been proved that light rays bend under the influence of the gravitational fields of bodies in space.

The general theory of relativity is essentially of a geometrical character, but this geometry is completely different to the classical Euclidean kind. In Euclidean geometry, for instance, parallel lines never meet or diverge, and the angles of a triangle always add up to 180°. Einstein’s space-time (actually first developed by the Russian-German mathematician, Hermann Minkowski, one of Einstein’s teachers, in 1907) represents a synthesis of three dimensional space (height, breadth and length) with time. This four-dimensional geometry deals with curved surfaces ("curved space-time"). Here the angles of a triangle may not add up to 180°, and parallel lines can cross or diverge.

In Euclidean geometry, as Engels points out, we meet a whole series of abstractions which do not at all correspond to the real world: a dimensionless point which becomes a straight line, which, in turn, becomes a perfectly flat surface, and so on and so forth. Among all these abstractions we have the emptiest abstraction of all, that of "empty space." Space, in spite of what Kant believed, cannot exist without something to fill it, and that something is precisely matter (and energy, which is the same thing). The geometry of space is determined by the matter which it contains. That is the real meaning of "curved space." It is merely a way of expressing the real properties of matter. The issue is only confused by inappropriate metaphors contained in popularisations of Einstein: "Think of space as a rubber sheet," or "Think of space as glass," and so on. In reality, the idea that must be kept in mind at all times is the indissoluble unity of time, space, matter and motion. The moment this unity is forgotten, we instantly slide into idealist mystification.

If we conceive space as a Thing-in-Itself, empty space, as in Euclid, clearly it cannot be curved. It is "nothing." However, as Hegel put it, there is nothing in the universe which does not contain both being and not-being. Space and matter are not two diametrically opposed, mutually exclusive phenomena. Space contains matter, and matter contains space. They are completely inseparable. The dialectical unity of matter and space is precisely what the universe is. In a most profound way, the general theory of relativity conveys this dialectical idea of the unity of space and matter. In the same way in mathematics zero itself is not "nothing," but expresses a real quantity, and plays a determining role.

Einstein presents gravitation as a property of space rather than a "force" acting upon bodies. According to this view space itself curves as a result of the presence of matter. This is a rather singular way of expressing the unity of space and matter, and one that is open to serious misinterpretations. Space itself, of course, cannot curve if it is understood as "empty space." The point is that it is impossible to conceive of space without matter. It is an inseparable unity. What we are considering is a definite relationship of space to matter. The Greek atomists long ago pointed out that atoms existed in the "void." The two things cannot exist without each other. Matter without space is the same as space without matter. A totally empty void is just nothing. But so is matter without any boundaries. Space and matter, then, are opposites which presuppose each other, define each other, limit each other, and cannot exist without each other.

The general theory served to explain at least one phenomenon which could not be explained by Newton’s classical theory. As the planet Mercury approaches its closest point to the sun, its revolutions display a peculiar irregularity, which had been previously attributed to the perturbations caused by the gravity of other planets. However, even when these were taken into account, it did not explain the phenomenon. The deviation of Mercury’s orbit around the sun ("perihelion") was very small, but enough to upset the astronomers’ calculations. Einstein’s general theory predicted that the perihelion of any revolving body should have a motion beyond that prescribed by Newton’s law. This was shown to be correct for Mercury, and later also for Venus.

He also predicted that a gravitational field would bend light-rays. Thus, he claimed, a light ray passing close to the surface of the sun would be bent out of a straight line by 1.75 seconds of arc. In 1919 an astronomic observation of an eclipse of the sun showed this to be correct. Einstein’s brilliant theory was demonstrated in practice. It was able to explain the apparent shift in the position of stars near the sun by the bending of their rays, and also the irregular motion of the planet Mercury, which could not be accounted for by Newton’s theories.

Newton worked out the laws governing the movement of objects, according to which the strength of gravitational pull depends upon mass. He also maintained that any force exerted upon an object produces acceleration in inverse proportion to the mass of the object. Resistance to acceleration is called inertia. All masses are measured either through gravitational effects or inertial effects. Direct observation has shown that inertial mass and gravitational mass are, in fact, identical to within one part in one trillion. Einstein began his theory of general relativity by assuming that inertial mass and gravitational mass are exactly equal, because they are essentially the same thing.

The apparently motionless stars are moving at colossal speeds. Einstein’s cosmic equations of 1917 implied that the universe itself was not fixed for all time, but could be expanding. The galaxies are moving away from us at speeds of about 700 miles a second. The stars and galaxies are constantly changing, coming into being and passing away. The whole universe is a vast arena where the drama of birth and death of stars and galaxies is played out across eternity. These are truly revolutionary events! Exploding galaxies, supernovas, catastrophic collisions between stars, black holes with a density billions of times greater than our sun greedily devouring entire clusters of stars. These things put in the shade the imaginings of the poets.

Relations Between Things

Many notions are purely relative in character. For example, if one is asked to say whether a road is on the right or left side of a house, it is impossible to answer. It depends on which direction one is moving relative to the house. On the other hand, it is possible to speak of the right bank of a river, because the current determines the direction of the river. Similarly, we can say that cars keep to the left (at least in Britain!) because the movement of a car singles out one of the two possible directions along the road. In all these examples, however, the notions "left" and "right" are shown to be relative, since they only acquire meaning after the direction by which they are defined as indicated.

In the same way, if we ask "Is it night or day?" the answer will depend on where we are. In London it is day, but in Australia it is night. Day and night are relative notions, determined by our position on the globe. An object will appear bigger or smaller depending upon its distance from a given point of observation. "Up" and "down" are also relative notions, which changed when it was discovered that the world is round, not flat. Even to this day, it is hard for "common sense" to accept that people in Australia can walk "upside down." Yet there is no contradiction if we understand that the notion of the vertical is not absolute but relative. For all practical purposes, we can take the earth’s surface to be "flat" and therefore all verticals to be parallel, when dealing for instance, with two houses in one town. But when dealing with far larger distances, involving the whole earth’s surface, we find that the attempt to make use of an absolute vertical leads to absurdities and contradictions.

By extension, the position of a planetary body is necessarily relative to the position of others. It is impossible to fix the position of an object without reference to other objects. The notion of "displacement" of a body in space means no more than that it changed its position relative to other bodies. A number of important laws of nature have a relativistic character, for example the principle of the relativity of motion and the law of inertia. The latter sates that an object on which no external force acts can only be not only in a state of rest but also in a state of uniform straight line motion. This fundamental law of physics was discovered by Galileo.

In practice, we know that objects upon which no external force is applied tend to come to rest, at least in everyday life. In the real world, the conditions for the law of inertia to apply, namely the total absence of external forces acting on the body, cannot exist. Forces such as friction act on the body to bring it to a halt. However, by constantly improving the condition of the experiment, it is possible to get closer and closer to the ideal conditions envisaged by the law of inertia, and thus show that it is valid even for the motions observed in everyday life. The relative (quantitative) aspect of time was perfectly expressed in Einstein’s theories, which conveyed it far more profoundly than the classical theories of Newton.

Gravity is not a "force," but a relation between real objects. To a man falling off a high building, it seems that the ground is "rushing towards him." From the standpoint of relativity, that observation is not wrong. Only if we adopt the mechanistic and one-sided concept of "force" do we view this process as the earth’s gravity pulling the man downwards, instead of seeing that it is precisely the interaction of two bodies upon each other. For "normal" conditions, Newton’s theory of gravity agrees with Einstein’s. But in extreme conditions, they completely disagree. In effect, Newton’s theory is contradicted by the general theory of relativity in the same way as formal logic is contradicted by dialectics. And, to date, the evidence shows that both relativity and dialectics are correct.

As Hegel explained, every measurement is really the statement of a ratio. However, since every measurement is really a comparison, there must be one standard which cannot be compared with anything but itself. In general, we can only understand things by comparing them to other things. This expresses the dialectical concept of universal interconnections. To analyse things in their movement, development and relationships is precisely the essence of the dialectical method. It is the exact antithesis of the mechanical mode of thought (the "metaphysical" method in the sense of the word used by Marx and Engels) which views things as static and absolute. This was precisely the defect of the old classical Newtonian view of the universe, which, for all its achievements, never escaped from the one-sidedness which characterised the mechanistic world outlook.

The properties of a thing are not the result of relations to other things, but can only manifest themselves in relations to other things. Hegel refers to these relations in general as "reflex-categories." The concept of relativity is an important one, and was already fully developed by Hegel in the first volume of his masterpiece The Science of Logic.

We see this, for example, in social institutions such as kingship.

"Naïve minds," Trotsky observed, "think that the office of kingship lodges in the king himself, in his ermine cloak and his crown, in his flesh and bones. As a matter of fact, the office of kingship is an interrelation between people. The king is king only because the interests and prejudices of millions of people are refracted through his person. When the flood of development sweeps away these interrelations, then the king appears to be only a washed-out man with a flabby lower lip. He who was once called Alfonso XIII could discourse upon this from fresh impressions.

"The leader by will of the people differs from the leader by will of God in that the former is compelled to clear the road for himself or, at any rate, to assist the conjuncture of events in discovering him. Nevertheless, the leader is always a relation between people, the individual supply to meet the collective demand. The controversy over Hitler’s personality becomes the sharper the more the secret of his success is sought in himself. In the meantime, another political figure would be difficult to find that is in the same measure the focus of anonymous historic forces. Not every exasperated petty bourgeois could have become Hitler, but a particle of Hitler is lodged in every exasperated petty bourgeois." (37)

In Capital, Marx shown how concrete human labour becomes the medium for expressing abstract human labour. It is the form under which its opposite, abstract human labour, manifests itself. Value is not a material thing which can be derived from the physical properties of a commodity. In fact, it is an abstraction of the mind. But it is not on that account an arbitrary invention. In fact, it is an expression of an objective process, and is determined by the amount of socially necessary labour power expended in production. In the same way, time is an abstraction which, although it cannot be seen, heard or touched, and can only be expressed in relative terms as measurement, nevertheless denotes an objective physical process.

Space and time are abstractions which enable us to measure and understand the material world. All measurement is related to space and time. Gravity, chemical properties, sound, light, are all analysed from these two points of view. Thus, the speed of light is 186,000 feet per second, while sound is determined by the number of vibrations per second. The sound of a stringed instrument, for instance, is determined by the time in which a certain number of vibrations occur and the spatial elements (length and thickness) of the vibrating body. That harmony which appeals to the aesthetic feelings of the mind is also another manifestation of ratio, measurement and therefore time.

Time cannot be expressed except in a relative way. In the same way, the magnitude value of a commodity can only be expressed relative to other commodities. Yet value is intrinsic to commodities, and time is an objective feature of matter in general. The idea that time itself is merely subjective, that is to say an illusion of the human mind, is reminiscent of the prejudice that money is merely a symbol, with no objective significance. The attempt to "demonetise" gold, which flowed from this false premise, led to inflation every time it was attempted. In the Roman Empire, the value of money was fixed by imperial decree, and it was forbidden to treat money as a commodity. The result was a continuous debasement of the currency. A similar phenomenon has taken place in modern capitalism, particularly since the Second World War. In economics, as in cosmology, the confusion of measurement with the nature of the thing itself leads to disaster in practice.

The Measurement of Time

While defining what time is presents a difficulty, measuring it does not. Scientists themselves do not explain what time is, but confine themselves to the measurement of time. From the mixing up of these two concepts endless confusion arises. Thus, Feynman:

"Maybe it is just as well if we face the fact that time is one of the things we cannot define (in the dictionary sense), and just say that it is what we already know it to be: it is how long we wait! What really matters anyway is not how we define time, but how we measure it." (38)

The measurement of time necessarily involves a frame of reference, and any phenomenon which entails change with time—e.g., the rotation of the earth or the swing of a pendulum. The earth’s daily rotation on its axis provides a time scale. The decay of radioactive elements can be used for measuring long time intervals. The measurement of time involves a subjective element. The Egyptians divided day and night into twelfths. The Sumerians had a numerical system based on 60, and thus divided the hour into 60 minutes and the minute into 60 seconds. The metre was defined as one 10 millionth of the distance from the earth’s pole to the equator (although this is not strictly accurate). The centimetre is 100th of a metre, and so on. At the beginning of this century, the investigation of the subatomic world led to the discovery of two natural units of measurement: the speed of light, c, and Planck’s constant, h. These are not directly mass, length, or time, but the unity of all three.

There is an international agreement that the metre is defined as the distance between two scratches on a bar kept in a laboratory in France. More recently, it has been realised that this definition is neither as precise as would be useful, nor as permanent or universal as one would like. It is currently being considered that a new definition be adopted, an agreed-upon (arbitrary) number of wavelengths of a chosen spectral line. On the other hand, the measurement of time varies according to the scale and life-span of the objects under consideration.

It is clear that the concept of time will vary according to the frame of reference. A year on earth is not the same as a year on Jupiter. Nor is the idea of time and space the same for a human being as for a mosquito with a life-span of a few days, or a subatomic particle with a life span of a trillionth of a second (assuming, of course, that such entities could possess a concept of anything at all). What we are referring to here is the way time is perceived in different contexts. If we accept the given frame of references the way in which time would be seen would be different. Even in practice this can be seen, to some extent. For example, normal methods of measuring time cannot be applied to the measurement of the life-span of subatomic particles, and different standards must also be used for measuring "geological time."

From this point of view, time can be said to be relative. Measurement necessarily involves relationships. Human thought contains many concepts which are essentially relative, for example relative magnitudes, such as "big" and "small." A man is small compared to an elephant, but big in comparison to an ant. Smallness and bigness, in themselves, have no meaning. A millionth of a second, in ordinary terms, seems a very short length of time, yet at the subatomic level it is an extremely long time. At the other extreme, a million years is an extremely short time on the cosmological level.

All ideas of space, time and motion depend on our observations of the relations and changes in the material world. However, the measurement of time varies considerably when we consider different kinds of matter. The measurement of space and time is inevitably relative to some frame of reference—the earth, the sun, or any other static point—to which events of the universe can relate. Now it is clear that matter undergoes all kinds of different change: change of position, which, in turn, involves different velocities, change of state, involving different energy states, birth, decay and death, organisation and disorganisation, and many other transformations, all of which can be expressed and measured in terms of time.

In Einstein, time and space are not regarded as isolated phenomena, and indeed it is impossible to regard them as "things in themselves." Einstein advanced the view that time depends on the movement of a system and that the intervals of time change in such a way that the speed of light in the given system does not vary according to the movement. Spatial scales are also subject to change. The old classical Newtonian theories are still valid for everyday purposes, and even as a good approximation of the general workings of the universe. Newtonian mechanics still applies in a very wide branch of sciences, not only astronomy, but also practical sciences such as engineering. At low speeds, the effects of special relativity can be ignored. For example, the error involved in considering the behaviour of a plane moving at 250 mile an hour would be about ten billionth of one percent. However, beyond certain limits it breaks down. At the kind of speeds that we find in particle acceleration, for example, it is necessary to take into account Einstein’s prediction that mass is not constant, but increases with velocity.

From the point of view of our normal everyday notion of the measurement of time, the extremely short life-span of certain subatomic particles cannot be adequately expressed. A pi-meson, for instance, has a life-span of only about 10–16 of a second, before it disintegrates. Likewise, the period of a nuclear vibration, or the life-time of a strange resonance particle, is 10–24 second, approximately the time needed for light to cross the nucleus of a hydrogen atom. Another scale of measurement is necessary. Very short times, say 10–12 second, are measured by an electron beam oscilloscope. Even shorter times can be calibrated by means of laser techniques. At the other end of the scale, very long periods can be measured by a radioactive "clock."

In a sense, every atom in the universe is a clock, because it absorbs light (that is, electromagnetic rays) and emits it at precisely defined frequencies. Since 1967, the official internationally recognised standard of time is based on the atomic (caesium) clock. One second is defined as 9,192,631,770 vibrations of the microwave radiation from caesium-133 atoms during a specified atomic rearrangement. Even this highly accurate clock is not absolutely perfect. Different readings are taken from atomic clocks in about 80 different countries, and agreement is reached, "weighting" the time in favour of the steadiest clocks. By such means it is possible to arrive at accurate time-measurement to one millionth of a second per day, or even less.

For everyday purposes, "normal" time keeping, based on the rotation of the earth and the apparent movements of the sun and stars, is sufficient. But for a whole series of operations in the field of modern advanced technology, such as certain radio navigational aids in ships and aeroplanes, it becomes inadequate, leading to serious errors. It is at these kind of levels that the effects of relativity begin to make themselves felt. Experiments have shown that atomic clocks run slower at ground level than at high altitudes, where the gravitational effect is weaker. Atomic clocks, flown at an altitude of 30,000 feet, gained about three billionth of a second an hour. This conforms to Einstein’s prediction to within one percent.

Problem Not Resolved

The special theory of relativity was one of the greatest achievements of science. It has revolutionised the way we look at the universe to such an extent that it has been compared with the discovery that the earth is round. Gigantic strides forward have been made possible by the fact that relativity established a far more accurate method of measurement than the old Newtonian laws it partially displaced. The philosophical question of time has, however, not been removed by Einstein’s theory of relativity. If anything, it is more acute than ever. That there is something subjective and even arbitrary in the measurement of time is evident, as we have already commented. But this does not lead to the conclusion that time is purely a subjective thing. Einstein’s entire life was spent in the pursuit of the objective laws of nature. The question is whether the laws of nature, including time, are the same for everyone, regardless of the place in which they are and the speed at which they are moving. On this question, Einstein vacillated. At times, he seemed to accept it, but elsewhere he rejected it.

The objective processes of nature are not determined by whether they are observed or not. They exist in and for themselves. The universe, and therefore time, existed before there were human beings to observe it, and will continue to exist long after there are no humans to concern themselves about it. The material universe is eternal, infinite, and constantly changing. However, in order that human minds may grasp the infinite universe, it is necessary to translate it into finite terms, to analyse and quantify it, so that it can become a reality for us. The way we observe the universe does not change it (unless it involves physical processes which interfere with what is being observed). But the way it appears to us can indeed change. From our standpoint, the earth appears to be at rest. But to an astronaut flying past our planet, it seems to be hurtling past him at a great speed. Einstein, who seems to have had a very dry sense of humour, apparently once asked an astonished ticket inspector: "What time does Oxford stop at this train?"

Einstein was determined to re-write the laws of physics in such a way that the predictions would always be correct, irrespective of the motions of different bodies, or the "points of view" which derive from them. From the standpoint of relativity, steady motion on a straight line is indistinguishable from being at rest. When two objects pass each other at a constant speed, it is equally possible to say that A is passing B, or that B is passing A. Thus, we arrive at the apparent contradiction that the earth is both at rest and moving at the same time. In the example of the astronaut, "it has to be simultaneously correct to say that the earth has great energy of motion and no energy and motion; the astronaut’s point of view is just as valid as the view of learned men on earth." (39)

Although it seems straightforward, the measurement of time nevertheless presents a problem, because the rate of change of time must be compared to something else. If there is some absolute time, then this in turn must flow, and therefore must be measured against some other time, and so on ad infinitum. It is important to realise, however, that this problem presents itself only in relation to the measurement of time. The philosophical question of the nature of time itself does not enter into it. For the practical purposes of calculation and measurement, it is essential that a specific frame of reference by defined. We must know the position of the observer relative to the observed phenomena. Relativity theory shows that such statement as "at one and the same place" and "at one and the same time" are, in fact, meaningless.

The theory of relativity involves a contradiction. It implies that simultaneity is relative to a frame of axes. If one frame of axes is moving relative to another, then events that are simultaneous relative to the first are not simultaneous relative to the second, and vice versa. This fact, which flies in the face of common sense, has been experimentally demonstrated. Unfortunately, it can lend itself to an idealist interpretation of time, for instance, the assertion that there can be a variety of "presents." Moreover, the future can be portrayed as things and processes "that come into being" as four-dimensional solids that have as earliest temporal cross section or "time slice."

Unless this question is settled, all kinds of mistakes can be made: for example, the idea that the future already exists, and suddenly materialises in the "now," as a submerged rock suddenly appears when a wave breaks over it. In point of fact, both the past and the future are combined in the present. The future is being-in-potential. The past is what has already been. The "now" is the unity of both. It is actual being as opposed to potential being. Precisely for this reason, it is usual to feel regret for the past and fear for the future, not vice versa. The feeling of regret flows from the realisation, corroborated by all human experience, that the past is lost forever, whereas the future is uncertain, consisting in a great number of potential states.

Benjamin Franklin once observed that there are only two things certain in this life—death and taxes, and the Germans have a proverb: "Man muss nur sterben"—"one only has to die," meaning that everything else is optional. Of course, this is not actually true. Many more things are inevitable than death, or even taxes. Out of an infinitely large number of potential states, in practice we know that only a certain number are really possible. Out of these, fewer still are probable at a given moment. And of the latter, in the end, only one will actually arise. The exact way in which this process unfolds is precisely the task of the different sciences to uncover. But this task will prove to be impossible if we do not accept that events and processes unfold in time, and that time is an objective phenomenon which expresses the most fundamental fact of all forms of matter and energy—change.

The material world is in a constant state of change, and therefore it "is and is not." This is the fundamental proposition of dialectics. Philosophers like the Anglo-American Alfred North Whitehead and the French intuitionist Henry Begson believed that the flow of time was a metaphysical fact which could only be grasped by non-scientific intuition. "Process philosophers" like these, despite their mystical overtones, at least are correct in saying that the future is open or indeterminate whereas the past is unchangeable, fixed and determinate. It is "congealed time." On the other hand we have the "philosophers of the manifold" who maintain that future events may exist but not be connected in a sufficiently lawlike way with past events. Pursuing a philosophically incorrect view of time, we end up with sheer mysticism, as in the notion of the "multiverse"—an infinite number of "parallel" universes (if that is the right word, since they do not exist in space "as we know it") existing simultaneously (if that is the right word, since they do not exist in time "as we know it"). Such is the confusion that arises from the idealist interpretation of relativity.

Idealist Interpretations

"There was a young lady named Bright
Whose speed was faster than light;
She set out one day
In a relative way
And returned home the previous night."
(A. Buller, Punch, 19th December 1923)

As with quantum mechanics, relativity has been seized upon by those who wish to introduce mysticism into science. "Relativity" is taken to mean that we cannot really know the world. As J. D. Bernal explains:

"It is, however, equally true that the effect of Einstein’s work, outside the narrow specialist fields where it can be applied, was one of general mystification. It was eagerly seized on by the disillusioned intellectuals after the First World War to help them in refusing to face realities. They only needed to use the word ‘relativity’ and say ‘Everything is relative,’ or ‘It depends on what you mean.’" (40)

This is a complete misinterpretation of Einstein’s ideas. In point of fact, the very word "relativity" is a misnomer. Einstein himself preferred the name invariance theory which gives a far better idea of what he intended—the exact opposite of the vulgar idea of relativity theory. It is quite untrue that for Einstein, "everything is relative." To begin with, rest energy (that is, the unity of matter and energy) is one of the absolutes of the theory of relativity. The limiting speed of light is another. Far from an arbitrary, subjective interpretation of reality, in which one opinion is as good as another, and "it all depends how you look at it," Einstein "discovered what was ‘absolute’ and reliable despite the apparent confusions, illusions and contradictions produced by relative motions or the action of gravity." (41)

The universe exists in a constant state of change. In that sense, nothing is "absolute" or eternal. The only absolute is motion and change, the basic mode of existence of matter—something which Einstein demonstrated conclusively in 1905. Time and space, as the mode of existence of matter are objective phenomena. They are not merely abstractions or arbitrary notions invented by humans (or gods) for their own convenience, but fundamental properties of matter, expressing the universality of matter.

Space is three dimensional, but time has only one dimension. With apologies to the makers of films in which it is possible to "go back to the future," it is only possible to travel in one direction in time, from the past to the future. There is no more danger of a spaceman returning to earth before he was born, or of a man marrying his great grandmother, than there is of any of the other amusing but idiotic fantasies of Hollywood. Time is irreversible, which is to say, every material process develops in only one direction—from the past to the future. Time is merely a way of expressing the real movement and changing state of matter. Matter, motion, time and space are inseparable.

The shortcoming of Newton’s theory was to regard space and time as separate entities, one alongside the other, independent of matter and motion. Up till the 20th century, scientists identified space with a vacuum (a "nothing"), which was seen as something absolute, that is, always and everywhere the same, changeless "thing." These empty abstractions have been discredited by modern physics, which has demonstrated the profound relation between time, space, matter and motion. Einstein’s relativity theory firmly establishes that time and space do not exist in and of themselves, in isolation from matter, but are part of a universal interrelation of phenomena. This is conveyed by the concept of the integral and indivisible space-time, of which time and space are seen as relative aspects. A controversial idea here is the prediction that a clock in motion will keep time more slowly than one that is stationary. However, it is important to understand that this effect only becomes noticeable at extraordinarily high speeds, approaching the speed of light.

If Einstein’s general theory of relativity is correct, then the theoretical possibility would exist in the future of travelling unimaginable distances through space. Theoretically, it would be possible for a human being to survive thousands of years into the future. The whole question hinges upon whether the changes observed in rates of atomic clocks also apply to the rate of life itself. Under the effect of strong gravity, atomic clocks run slower than in empty space. The question is whether the complex interrelations of molecules which constitute life can behave in the same way. Isaac Asimov, who knew a thing or two about science fiction, wrote: "If time really slows down in motion, one might journey even to a distant star in one’s own lifetime. But of course one would have to say good-bye to one’s own generation and return to the world of the future." (42)

The argument for this is that the rates of living processes are determined by the rates of atomic action. Thus, under strong gravity, the heart will beat more slowly, and the brain impulses will also slow down. In fact, all energy diminishes in the presence of gravity. If processes slow down, they also take longer in time. If a space-ship were able to travel close to the speed of light, the universe would be seen flashing past it, while for those inside, time would continue as "normal," i.e., at a much slower rate. The impression would be that time outside would be speeded up. Is that correct? Would he in fact be living in the future, relative to people on earth, or not? Einstein seems to answer in the affirmative.

All kinds of mystical notions arise from such speculation—for example about hopping into a black hole and entering another universe. If a black hole exists, and that is still not definitely proven, all that would be at the centre would be the collapsed remains of a gigantic star, not another universe. Any real person who entered it would be instantly torn apart and converted into pure energy. If that is what is considered as passing into another universe, then those who advocate such ideas are most welcome to make the first excursion! In reality, this is pure speculation, however entertaining it may be. The whole idea of "time-travel" inevitably lands one in a mass of contradictions, not of dialectical but of the absurd variety. Einstein would have been shocked at the mystical interpretation of his theories which involve notions such as shuttling back and forth in time, altering the future, and nonsense of that sort. But he himself must bear some responsibility for this situation because of the idealist element in his outlook, particularly on the question of time.

Let us grant that an atomic clock at a high altitude runs faster at high altitudes than on the ground, because of the effect of gravitation. Let us also grant that, when this clock returns to earth, it is found to be, say, 50 billionth of a second older than equivalent clocks which had never left the ground. Does that mean that a man travelling in the same flight has equally aged? The process of ageing is dependent upon the rate of metabolism. This is partly influenced by gravitation, but also by many other factors. It is a complex biological process, and it is not easy to see how it could be fundamentally affected either by velocity or gravitation, except that extremes of either can cause material damage to living organisms.

If it were possible to slow down the rate of metabolism in the way predicted, so that, for example, the heart-beat would slow to one every twenty minutes, the process of ageing would presumably be correspondingly slower. It is, in fact, possible to slow down metabolism, for example, by freezing. Whether this would be the effect of travelling at very high speeds, without killing the organism, is open to doubt. According to the well-known theory, such a relativistic space-man, if he succeeded on returning to earth, would come back after, say 10,000 years, and to pursue the usual analogy, would presumably be in a position to marry his own remote descendants. But he would never be able to return to his "own" time.

Experiments conducted with subatomic particles (muons) indicate that particles travelling at 99.94 per cent of the speed of light extended their life by nearly thirty times, precisely as predicted by Einstein. However, whether these conclusions can be applied to matter on a larger scale, and living matter in particular, is an issue which remains to be seen. Many serious mistakes have been made by attempting to apply the results derived from one sphere to another, entirely different, area. In the future, space-travel at very high speeds—maybe one-tenth of the speed of light—may become possible. At such speed, a journey of five light-years would take fifty years (though according to Einstein, it would take three months less for those travelling). Will it ever be possible to travel at the speed of light, thus enabling human beings to reach the stars? At this moment in time, such a prospect seems remote. But then, a hundred years ago—a mere blink in history—the idea of travelling to the moon was still confined to the novels of Jules Verne.

Mach and Positivism

"The object, however, is the real truth, is the essential reality; it is, quite indifferent to whether it is known or not; it remains and stands even though it is not known, while the knowledge does not exist it the object is not there." (Hegel) (43)

The existence of past, present and future is deeply engraved on the human consciousness. We live now, but we can remember past events, and, to some extent, foresee future ones. There is a "before" and an "after." Yet some philosophers and scientists dispute this. They regard time as a product of the mind, an illusion. In their view, in the absence of human observers, there is no time, no past, present or future. This is the standpoint of subjective idealism, an entirely irrational and anti-scientific outlook which nevertheless has attempted for the last hundred years to base itself in the discoveries of physics to lend respectability to what is essentially a mystical view of the world. It seems ironical that the school of philosophy which has had the biggest impact upon science in the 20th century, logical positivism, is precisely a branch of subjective idealism.

Positivism is a narrow view which holds that science should confine itself to the "observed facts." The founders of this school were reluctant to refer to theories as true or false, but preferred to describe them as more or less "useful." It is interesting to note that Ernst Mach, the real spiritual father of neo-positivism, opposed the atomist theory of physics and chemistry. This was the natural consequence of the narrow empiricism of the positivist outlook. Since the atom could not be seen, how could it exist? It was regarded by them at best as a convenient fiction, and at worst as an unacceptable ad hoc hypothesis. One of Mach’s co-thinkers, Wilhelm Ostwald actually attempted to derive the basic laws of chemistry without the help of the atomic hypothesis!

Boltzmann sharply criticised Mach and the Positivists, as did Max Planck, the father of quantum physics. Lenin subjected the views of Mach and Richard Avenarius, the founder of the school of Empirio-criticism, to a devastating criticism in his book Materialism and Empirio-criticism, (1908). Nevertheless, the views of Mach had a big impact and, among others, impressed the young Albert Einstein. Setting out from the view of that all ideas must be derived from "the given," that is, from the information provided immediately by our senses, they went on to deny the existence of the natural world, independent of human sense-perception. Mach and Avenarius referred to physical objects as "complexes of sensation." Thus, for example, this table is no more than a collection of sense-impressions such as hardness, colour, mass and so on. Without these, they maintained, nothing would be left. Therefore, the idea of matter (in the philosophical sense, that is, the objective world given to us in sense-perception) was declared to be meaningless.

As we have already pointed out, these ideas lead directly to solipsism—the idea that only "I" exist. If I close my eyes, the world ceases to exist. Mach attacked Newton’s idea that space and time are absolute and real entities, but he did so from the standpoint of subjective idealism. Incredibly, the most influential school of modern philosophy (and the one that had the biggest influence on scientists) was derived from the subjective idealism of Mach and Avenarius.

The obsession with "the observer" which is a thread running through the whole of 20th century theoretical physics is derived from the subjective idealist philosophy of Ernst Mach. Taking his starting-point from the empiricist argument that "all our knowledge is derived from immediate sense-perception," Mach argued that objects cannot exist independently of our consciousness. Carried to its logical conclusion, this would mean that, for example, the world could not have existed before there were people present to observe it. As a matter of fact, it could not have existed before I was present, since I can only know my own sensations, and cannot therefore be sure that any other consciousness exists.

The important thing is that Einstein himself was initially impressed by these arguments, which left their mark on his early writings on relativity. This has, beyond doubt, exercised the most harmful influence upon modern science. Whereas Einstein was capable of realising his mistake, and attempted to correct it, those who have slavishly followed the master, have been incapable of sorting out the chaff from the grain. As often happens, over-eager disciples become dogmatic. They are more Papist than the Pope! In his autobiography, Karl Popper shows clearly that in his later years Einstein regretted his earlier subjective idealism, or "operationalism," which demanded the presence of an observer to determine natural processes:

"It is an interesting fact that Einstein himself was for years a dogmatic positivist and operationalist. He later rejected this interpretation: he told me in 1950 that he regretted no mistake he ever made as much as this mistake. The mistake assumed a really serious form in his popular book, Relativity: The Special and the General Theory. There he says ‘I would ask the reader not to proceed farther until he is fully convinced on this point.’ The point is, briefly, that ‘simultaneity’ must be defined— and defined in an operational way—since otherwise ‘I allow myself to be deceived…when I imagine that I am able to attach a meaning to the statement of simultaneity.’ Or in other words, a term has to be operationally defined or else it is meaningless. (Here in a nutshell is the positivism later developed by the Vienna Circle under the influence of Wittgenstein’s Tractatus, and in a very dogmatic form)."

This is important, because it shows that Einstein in the end rejected the subjectivist interpretation of relativity theory. All the nonsense about "the observer" as a determining factor was not an essential part of the theory, but merely the reflection of a philosophical mistake, as Einstein frankly confirmed. That, unfortunately, did not prevent the followers of Einstein from taking over the mistake, and blowing it up to the point where it appeared to be a fundamental cornerstone of relativity. It is here that we find the real origin of Heisenberg’s subjective idealism:

"But many excellent physicists," Popper continues, "were greatly impressed by Einstein’s operationalism, which they regarded (as did Einstein himself for a long time) as an integral part of relativity. And so it happened that operationalism became the inspiration of Heisenberg’s paper of 1925, and of his widely accepted suggestion that the concept of the track of an electron, or of its classical position-cum-momentum, was meaningless." (44)

The fact that time is an objective phenomenon, reflecting real processes in nature was first demonstrated by the laws of thermodynamics, which were worked out in the 19th century and which still play a central role in modern physics. These laws, particularly as developed by Boltzmann, firmly establish the idea not only that time exists objectively, but that it flows in only one direction, from past to future. Time cannot be reversed, nor is it dependent upon any "observer."

Boltzmann and Time

The fundamental question which has to be addressed is: Is time an objective feature of the physical universe? Or is it something purely subjective, an illusion of the mind, or merely a convenient way of describing things to which it has no real relationship? The latter position has been held, in one or other degree, by a number of different schools of thought, all of them closely related to the philosophy of subjective idealism. Mach, as we have seen, introduced this subjectivism into science. It was decisively answered towards the end of the 19th century by the pioneer of the science of thermodynamics, Ludwig Boltzmann.

Einstein, under the influence of Ernst Mach, treated time as something subjective, which depended on the observer, at least in the beginning before he realised the harmful consequences of this approach. In 1905, his paper on the special theory of relativity introduced the notion of a "local time" associated with each separate observer. The concept of time here contains an idea carried over from classical physics, namely that time is reversible. This is really quite an extraordinary notion, and one which flies in the face of all experience. Film directors often resort to a trick photography, in which the camera is put into reverse, whereupon the most peculiar events occur: milk flows from the glass back into the bottle, buses and cars run backwards, eggs return to their shells, and so on. Our reaction to all this is to laugh, which is what is intended. We laugh because we know that what we are seeing is not just impossible, but absurdly so. We know that the processes which we are seeing cannot be reversed.

Boltzmann understood this, and the concept of irreversible time lies at the heart of his famous theory of the arrow of time. The laws of thermodynamics represented a major breakthrough in science, but were controversial. These laws could not be reconciled with the existing laws of physics at the end of the 19th century. The second law cannot be derived from the laws of mechanics or quantum mechanics, and, in effect, marks a sharp break with the theories of previous physical science. It says that entropy increases in the direction of the future, not the past. It denotes a change in state over time, which is irreversible. The notion of a tendency towards dissipation clashed with the accepted idea that the essential task of physics was to reduce the complexity of nature to simple laws of motion.

The idea of entropy, which is usually understood as a the tendency of things towards greater disorganisation and decay with the passing of time, entirely bears out what people have always believed: that time exists objectively and that it is a one-way process. The two laws of thermodynamics imply the existence of the phenomenon known as entropy that is conserved in all irreversible processes. Its definition is based on another property known as available energy. The entropy of an isolated system may remain constant or increase, but it cannot decrease. One of the results of this is the impossibility of a "perpetual motion machine."

Einstein considered the idea of irreversible time to be an illusion that had no place in physics. In Max Planck’s words, the second law of thermodynamics expresses the idea that there exists in nature a quantity which changes always in the same sense in all natural processes. This does not depend on the observer, but is an objective process. But Planck’s view was in a small minority. The great majority of scientists, like Einstein, attributed it to subjective factors. Einstein’s position on this question shows up the central weakness of his standpoint in making objective processes depend upon a non-existent "observer." This was undoubtedly the weakest element in his entire outlook, and, for that very reason, is the part which has proved most popular with his successors, who do not seem aware of the fact that Einstein himself changed his mind on this towards the end of his life.

In physics and mathematics the expression of time is reversible. A "time-reversal invariant" implies that the same laws of physics apply equally well in both situations. The second event is indistinguishable from the first and the flow of time does not have any preferred direction in the case of fundamental interactions. For example, a film of two billiard balls colliding can be run forward or backward, without giving any idea of the true time sequence of the event. The same was assumed to be true of interactions at the sub atomic level, but evidence to the contrary was found in 1964 in weak nuclear interactions. For a long time it was believed that the fundamental laws of nature were "charge symmetrical." For example, an antiproton and a positron behave like a proton and an electron. Experiments have now shown that the laws of nature are symmetrical if three basic things are combined—time, charge and parity. This is known as a "CPT mirror."

In dynamics, the direction of a given trajectory was irrelevant. For example, a ball bouncing on the ground would return to its initial position. Any system can thus "go backwards in time," if all the points involved in it are reversed. All the states it previously went through would simply be retraced. In classical dynamics, changes such as time reversal (t —> –t) and velocity reversal (v —> –v) are treated as mathematically equivalent. This kind of calculation works well for simple closed systems, where there are no interactions. In reality, however, every system is subject to many interactions. One of the most important problems in physics is the "three-body" problem, for example, the moon’s motion is influenced by the sun and the earth. In classical dynamics, a system changes according to a trajectory that is given once and for all, the starting point of which is never forgotten. Initial conditions determine the trajectory for all time. The trajectories of classical physics were simple and deterministic. But there are other trajectories that are not so easy to pin down, for example, a rigid pendulum, where an infinitesimal disturbance would be enough to set it rotating or oscillating.

The importance of Boltzmann’s work was that he dealt with the physics of processes rather than the physics of things. His greatest achievement was to show how the properties of atoms (mass, charge, structure) determine the visible properties of matter (viscosity, thermal conductivity, diffusion, etc.). His ideas were viciously attacked during his lifetime, but vindicated by the discoveries of atomic physics shortly before 1900, and the realisation that the random movements of microscopic particles suspended in a fluid ("Brownian motion") could only be explained in terms of the statistical mechanics invented by Boltzmann.

The bell-shaped Gauss curve describes the random motion of molecules in a gas. An increased temperature leads to an increase in the average velocity of the molecules and the energy associated with their motion. Whereas Clausius and Maxwell approached this question from the standpoint of the trajectories of individual molecules, Boltzmann considered the population of molecules. His kinetic equations play an important role in the physics of gases. It was a major advance in the physics of processes. Boltzmann was a great pioneer, who was treated as a madman by the scientific establishment. He was finally driven to suicide in 1906, having previously been compelled to retreat from his attempt to establish the irreversible nature of time as an objective feature of nature.

Whereas in the theory of classical mechanics, the events in the film earlier described are perfectly possible, in practice, they are not. In the theory of dynamics, for example, we have an ideal world in which such things as friction and collision do not exist. In this ideal world, all the invariants involved in a given motion are fixed at the start. Nothing could happen to alter its course. By these means, we arrive at a completely static view of the universe, where everything is reduced to smooth, linear equations. Despite the revolutionary advances made possible by relativity theory, Einstein, at heart, remained wedded to the idea of a static, harmonious universe—just like Newton.

The equations of motion of Newtonian or for that matter quantum mechanics have no built-in irreversibility. It is possible to run a movie film forward or backwards. But this is not true of nature in general. The second law of thermodynamics predicts an irreversible tendency towards disorder. It states that randomness always increases in time. Until recently, it was thought that the fundamental laws of nature are symmetrical in time. Time is asymmetrical and moves only in one direction, from past to future. We see fossils, footprints, photographs and hear recordings of things from the past, but never from the future. It is easy to mix eggs to make an omelette or put milk and sugar into a cup of coffee, but not to reverse these processes. The water in the bath transfers its heat to the surrounding air, but not vice versa.

The second law of thermodynamics is the "arrow of time." The subjectivists objected that irreversible processes like chemical affinity, heat conduction, viscosity, etc., would depend on the "observer." In reality, they are objective processes that take place in nature, and this is clear to everyone in relation to life and death. A pendulum (at least in an ideal state) can swing back to its initial position. But everyone knows that the life of an individual moves in only one direction, from the cradle to the grave. It is an irreversible process. Ilya Prigogine, one of the leading theorists of chaos theory, has devoted a lot of attention to the question of time. When he first began to study physics as a student in Brussels, Prigogine recalls that he was "astonished by the fact that science had so little to say about time, especially since his earlier education had centred mainly around history and archaeology." In relation to the conflict between classical mechanics (dynamics) and thermodynamics, Prigogine and Stengers write:

"To a certain extent, there is an analogy between this conflict and the one that gave rise to dialectical materialism. We have described…a nature that might be called "historical"—that is, capable of development and innovation. The idea of a history of nature as an integral part of materialism was asserted by Marx and, in greater detail, by Engels. Contemporary developments in physics, the discovery of the constructive role played by irreversibility, have thus raised within the natural sciences a question that has long been asked by materialists. For them, understanding nature meant understanding it as being capable of producing man and his societies.

"Moreover, at the time Engels wrote his Dialectics of Nature, the physical sciences seemed to have rejected the mechanistic world view and drawn close to the idea of an historical development of nature. Engels mentions three fundamental discoveries: energy and the laws governing its qualitative transformations, the cell as the basic constituent of life, and Darwin’s discovery of the evolution of species. In view of these great discoveries, Engels came to the conclusion that the mechanistic world view was dead."

Against the subjective interpretation of time, the authors conclude: "Time flows in a single direction, from past to future. We cannot manipulate time, we cannot travel back to the past." (45)

Relativity and Black Holes

In Einstein’s view, unlike that of Newton, gravity affects time because it affects light. If one could imagine a particle of light poised on the edge of a black hole, it would be suspended indefinitely, neither advancing nor retreating, neither losing energy, nor gaining it. In such a state, it is possible to argue that "time stands still." This is the argument of the relativist proponents of the black hole and its properties. What this boils down to is that if all motion were to cease, then there would be no change either of state or position, and therefore no time in any meaningful sense of the word. Such a situation is alleged to exist at the edge of a black hole. This, however, seems a highly speculative and mystical interpretation of a phenomenon, the existence of which is, in itself, unproved.

All matter exists in a constant state of change and motion, and therefore, all that is being said here is that if matter and motion are eliminated, there is no time either, which is a complete tautology. It is like saying—if there is no matter, there is no matter, or if there is no time, there is no time. Because both statements mean just the same thing. Strangely enough, one would seek in vain in the theory of relativity for a definition of what time and space are. Einstein certainly found it difficult to explain. However, he came close to it when he explained the difference between his geometry and the classical geometry of Euclid. He said that one could imagine a universe in which space was not warped, but it would be completely devoid of matter. This points clearly in the right direction. After all the fuss about black holes, you may also be surprised to discover that this subject was not even mentioned by Einstein. He relied upon a rigorous approach, mainly based on very complicated mathematics, and made predictions which could be verified by observation and experiment. The physics of black holes, in the absence of clearly established empirical data, has an extremely speculative character.

Despite its successes, it is still possible that the general theory of relativity may be wrong. Unlike special relativity, the experimental tests which have been carried out on it are not very many. There is no conclusive proof, although up to the present time no conflict has been found between the theory and the observed facts. It is not even ruled out that the assertion of special relativity, that nothing can move faster than the speed of light, may be shown to be incorrect in the future*.

Alternative theories of relativity have been put forward, for example, by Robert Dicke. Dicke’s theory predicted a deflection of the moon’s orbit of several feet towards the sun. Using advanced laser technology, the McDonald observatory in Texas found no trace of this displacement. However, there is no reason to suppose that the last word has been spoken. So far, Einstein’s theories have been borne out by repeated experiment. But the constant probing of extreme conditions must sooner or later reveal a set of circumstances that are not covered by the equations, preparing the way for new epoch-making discoveries. The theory of relativity cannot be the end of the line, any more than Newtonian mechanics, Maxwell’s theory of electromagnetism, or any previous theory.

For two hundred years, the theories of Newton were held to be absolutely valid. His authority could not be challenged. After his death, Laplace and others carried his theories to an extreme where they became absurd. The radical break with the old mechanistic Absolutes was a necessary condition for the further advance of physics in the 20th century. It was the proud boast of the new physics that they had forever killed off the ogre of the Absolute. Suddenly thought was free to move into hitherto unheard of realms. These were heady times! Unfortunately, such happiness cannot last forever. In the words of Robert Burns:

"But pleasures are like poppies spread:
You seize the flow’r, its bloom is shed."

The new physics solved many problems, but only at the cost of creating new contradictions, which remain unresolved even at the present time. For most of the present century, physics has been dominated by two imposing theories: quantum mechanics and relativity. What is not generally realised is that the two theories are at variance. In fact, they are incompatible. The general theory of relativity takes no account whatever of the uncertainty principle. Einstein spent the last years of his life attempting to resolve this contradiction, but failed to do so.

Relativity theory was a great and revolutionary theory. So was Newtonian mechanics in its day. Yet it is the fate of all such theories to become transformed into orthodoxies, to suffer a kind of hardening of the arteries, until they are no longer able to answer the questions posed by the march of science. For a long time, theoretical physicists have been content to rest on the discoveries of Einstein, in the same way that an earlier generation were content to swear by Newton. And in just the same way, they are guilty of bringing general relativity into disrepute by reading into it the most absurd and fantastic notions, which its author never even dreamed of.

Singularities, black holes where time stands still, multiverses, a time before time began, about which no questions must be asked—one can imagine Einstein clutching his head! All this is supposed to flow inevitably from general relativity, and anyone who raised the slightest doubt about it is immediately confronted with the authority of the great Einstein. This is not one whit better than the situation before relativity, when the authority of Newton was similarly wielded in defence of the existing orthodoxy. The only difference is that the fantastic notions of Laplace seem extremely sensible alongside the mystical gobbledygook written by some physicists today. And even less than Newton can Einstein be made responsible for the outlandish flights of fancy of his successors, which represent the reductio ad absurdum of the original theory.

These senseless and arbitrary speculations are the best proof that the theoretical framework of modern physics is in need of a complete overhaul. For the problem here is one of method. It is not just that they provide no answers. The problem is that they do not even know how to ask the right questions. This is not so much a scientific as a philosophical question. If everything is possible, then one arbitrary theory (more correctly, guess) is as good as the next. The whole system has been pushed near to breaking-point. And to cover up the fact, they resort to a mystical kind of language, in which the obscurity of expression does not disguise the complete lack of any real content.

This state of affairs is clearly intolerable, and has led a section of scientists to begin to question the basic assumptions on which science has been operating. David Bohm’s investigations into the theory of quantum mechanics, Ilya Prigogine’s new interpretation of the Second Law of Thermodynamics, Hannes Alfvén’s attempt to work out an alternative to the orthodox cosmology of the big bang, above all, the spectacular rise of chaos and complexity theory—all this indicates the existence of a ferment in science. While it is too early to predict the exact outcome of this, it seems likely that we are entering into one of those exciting periods in the history of science, when an entirely new approach will emerge.

There is every reason to suppose that eventually the theories of Einstein will be surpassed by a new and broader-based theory, which, while preserving all that is viable in relativity, will correct and amplify it. In the process, we shall certainly arrive at a truer and more balanced understanding of the questions relating to the nature of time, space and causality. This does not signify a return to the old mechanical physics, any more than the fact that we can now achieve the transformation of the elements means a return to the ideas of the alchemists. As we have seen, the history of science frequently involves an apparent return to earlier positions, but on a qualitatively higher level.

One thing we can predict with absolute confidence: when the new physics finally emerges from the present chaos there will be no place in it for time-travel, multiverses, or singularities which compress the whole of the universe into a single point, about which no questions are allowed to be asked. This will sadly make it much more difficult to win big cash prizes for providing the Almighty with scientific credentials, a fact which some may regret, but which, in the long term, may not be a bad thing for the progress of science!

* This prediction appears to have been confirmed far sooner than we expected. Before the book was sent to the printers, reports appeared in the press of an experiment conducted by American scientists which appear to indicate that photons can travel faster than the speed of light. The experiment is a complicated one, based on a peculiar phenomenon known as "quantum tunnelling." If it is shown to be correct, this will demand a fundamental rethinking of the whole concept of relativity.