The Special Theory of Relativity

David Bohm

• Publisher: Routledge
• Year: 2015
• ISBN:
  9781136747601
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

In these inspiring lectures David Bohm explores Albert Einstein's celebrated Theory of Relativity that transformed forever the way we think about time and space. Yet for Bohm the implications of the theory were far more revolutionary both in scope and impact even than this. Stepping back from dense theoretical and scientific detail in this eye

1

Introduction

The theory of relativity is not merely a scientific development of great importance in its own right. It is even more significant as the first stage of a radical change in our basic concepts, which began in physics, and which is spreading into other fields of science, and indeed, even into a great deal of thinking outside of science. For as is well known, the modern trend is away from the notion of sure “absolute” truth (i.e., one which holds independently of all conditions, contexts, degrees, and types of approximation, etc.) and toward the idea that a given concept has significance only in relation to suitable broader forms of reference, within which that concept can be given its full meaning.

Just because of the very breadth of its implications, however, the theory of relativity has tended to lead to a certain kind of confusion in which truth is identified with nothing more than that which is convenient and useful. Thus it may be felt by some that since “everything is relative,” it is entirely up to each person’s choice to decide what he will say or think about any problem whatsoever. Such a tendency reflecting back into physics has often brought about something close to a skeptical and even cynical attitude to new developments. For the student is first trained to regard the older laws of Newton, Galileo, etc., as “eternal verities,” and then suddenly, in the theory of relativity (and even more, in the quantum theory) he is told that this is all out of date and it is implied that he is now receiving a new set of “eternal verities” to replace the older ones. It is hardly surprising, then, that students may feel that a somewhat arbitrary game is being played by the physicists whose only goal is to obtain some convenient set of formulas that will predict the results of a number of experiments. The comparatively greater importance of mathematics in these new developments helps add to the impression, since the older conceptual understanding of the meaning of the laws of physics is now largely given up, and little is offered to take its place.

In these notes an effort will be made to provide a more easily understood account of the theory of relativity. To this end, we shall go in some detail into the background of problems out of which the theory of relativity emerged, not so much in the historical order of the problems as in an order that is designed to bring out the factors which induced scientists to change their concepts in so radical a way. As far as possible, we shall stress the understanding of the concepts of relativity in non-mathematical terms, similar to those used in elementary presentations of earlier Newtonian concepts. Nevertheless, we shall give the minimum of mathematics needed, without which the subject would be presented too vaguely to be appreciated properly. (For a more detailed mathematical treatment, it is suggested that the student refer to some of the many texts on the subject which are now available.)

To clarify the general problem of changing concepts in science we shall discuss fairly extensively several of the basic philosophical problems that are, as it were, interwoven into the very structure of the theory of relativity. These problems arise, in part, in the criticism of the older Lorentz theory of the ether and, in part, in Einstein’s discovery of the equivalence of mass and energy. In addition, by replacing Newtonian mechanics after several centuries in which it had an undisputed reign, the theory of relativity raised important issues, to which we have already referred, of the kind of truth that scientific theories can have, if they are subject to fundamental revolutions from time to time. This question we shall discuss extensively in several chapters of the book.

In the Appendix we give an account of the role of perception in the development of our scientific thinking, which, it is hoped, will further clarify the general implication of a relational (or relativistic) point of view. In this account, the mode of development of our concepts of space and time as abstractions from everyday perception will be discussed; and in this discussion it will become evident that our notions of space and time have in fact been built up from common experience in a certain way. It therefore follows that such ideas are likely to be valid only in limited domains which are not too far from those in which they arise. When we come to new domains of experience, it is not surprising that new concepts are needed. But what is really interesting is that when the facts of the process of ordinary perception are studied scientifically, it is discovered that our customary way of looking at everyday experience (which with certain refinements is carried into Newtonian mechanics) is rather superficial and in many ways, very misleading. A more careful account of the process of perception then shows that the concepts needed to understand the actual facts of perception are closer to those of relativity than they are to those of Newtonian mechanics. In this way it may be possible to give relativity a certain kind of immediate intuitive significance, which tends to be lacking in a purely mathematical presentation. Since effective thinking in physics generally requires the integration of the intuitive with the mathematical sides, it is hoped that along these lines a deeper and more effective way of understanding relativity (and perhaps the quantum theory) may emerge.

2

Pre-Einsteinian Notions of Relativity

It is not commonly realized that the general trend to a relational (or relativistic) conception of the laws of physics began very early in the development of modern science. This trend arose in opposition to a still older Aristotelian tradition that dominated European thinking in the Middle Ages and continues to exert a strong but indirect influence even in modern times. Perhaps this tradition should not be ascribed so much to Aristotle as to the Medieval Scholastics, who rigidified and fixed certain notions that Aristotle himself probably proposed in a somewhat tentative way as a solution to various physical, cosmological, and philosophical problems that occupied Ancient Greek thinkers.

Aristotle’s doctrines covered a very broad field, but, as far as our present discussion is concerned, it is his cosmological notion of the Earth as the center of the universe that interests us. He suggested that the whole universe is built in seven spheres with the Earth as the middle. In this theory, the place of an object in the universe plays a key role. Thus, each object was assumed to have a natural place, toward which it was striving, and which it approached, in so far as it was not impeded by obstacles. Movement was regarded as determined by such “final causes,” set into activity by “efficient causes.” For example, an object was supposed to fall because of a tendency to try to reach its “natural place” at the center of the Earth, but some external “efficient” cause was needed to release the object, so that its internal striving “principle” could come into operation.

In many ways Aristotle’s ideas gave a plausible explanation to the domain of phenomena known to the Ancient Greeks, although of course, as we know, they are not adequate in broader domains revealed in more modern scientific investigations. In particular, what has proved to be inadequate is the notion of an absolute hierarchial order of being, with each thing tending toward its appropriate place in this order. Thus, as we have seen, the whole of space was regarded as being organized into a kind of fixed hierarchy, in the form of the “seven crystal spheres,” while time was later given an analogous organization by the Medieval Scholastics in the sense that a certain moment was taken as that of creation of the universe, which later was regarded as moving toward some goal as end. The development of such notions led to the idea that in the expressions of the laws of physics, certain places and times played a special or favored role, such that the properties of other places and times had to be referred to these special ones, in a unique way, if the laws of nature were to be properly understood. Similar ideas were carried into all fields of human endeavor, with the introduction of fixed categories, properties, etc., all organized into suitable hierarchies. In the total cosmological system, man was regarded as having a key role. For, in some sense, he was considered to be the central figure in the whole drama of existence, for whom all had been created, and on whose moral choices the fate of the universe turned.

A part of Aristotle’s doctrine was that bodies in the Heavens (such as planets) being more perfect than Earthly matter, should move in an orbit which expresses the perfection of their natures. Since the circle was considered to be the most perfect geometrical figure, it was concluded that a planet must move in a circle around the Earth. When observations failed to disclose perfect circularity, this discrepancy was accommodated by the introduction of “epicycles,” or of “circles within circles.” In this way, the Ptolemaic theory was developed, which was able to “adjust” to any orbit whatsoever, by bringing in many epicycles in a very complicated way. Thus, Aristotelian principles were retained, and the appearances of the actual orbits were “saved.”

The first big break in this scheme was due to Copernicus, who showed that the complicated and arbitrary system of epicycles could be avoided, if one assumed that the planets moved around the Sun and not around the Earth. This was really the beginning of a major change in the whole of human thought. For it showed that the Earth need not be at the center of things. Although Copernicus put the Sun at the center, it was not a very big step to see later that even the Sun might be only one star among many, so that there was no observable center at all. A similar idea about time developed very naturally, in which one regarded the universe as infinite and eternal, with no particular moment of creation, and no particular “end” to which it was moving.

The Copernican theory initiated a new revolution in human thought. For it eventually led to the notion that man is no longer to be regarded as a central figure in the cosmos. The somewhat shocking deflation of the role of man had enormous consequences in every phase of human life. But here we are concerned more with the scientific and philosophical implications of Copernican notions. These could be summed up by saying that they started an evolution of concepts leading eventually to the breakdown of the older notions of absolute space and time and the development of the notion that the significance of space and time is in relationship.

We shall explain this change at some length, because it brings us to the core of what is meant by the theory of relativity. Briefly, the main point is that since there are no favored places in space or moments of time, the laws of physics can equally well be referred to any point, taken as the center, and will give rise to the same relationships. In this regard, the situation is very different from that of the Aristotelian theory, which, for example, gave the center of the Earth a special role as the place toward which all matter was striving.

The trend toward relativity described above was carried further in the laws of Galileo and Newton. Galileo made a careful study of the laws of falling objects, in which he showed that while the velocity varies with time, the acceleration is constant. Before Galileo, a clear notion of acceleration had not been developed. This was perhaps one of the principal obstacles to the study of the movements of falling objects, because, without such a notion, it was not possible clearly to formulate the essential characteristics of their movements. What Galileo realized was, basically, that just as a uniform velocity is a constant rate of change of position, so one can conceive a uniform acceleration as a constant rate of change of velocity—i.e.,

where t is the time and ∆t is a small increment of time. [v(t) is, of course, the velocity at the time t, and v(t + ∆t) is the velocity of the time, t + ∆t.] This means that a falling body is characterized by a certain relationship in its changing velocities, a relationship that does not refer to a special external fixed point but rather to the properties of the motion of the object itself.

Newton went still further, along these lines, in formulating his law of motion:

pre-einsteinian notions of relativity 9

where

is the acceleration of the body and F is the force on it. In these laws Newton comprehended Galileo’s results through the fact that the force of gravity is constant near the surface of the Earth. At the same time he generalized the law to a relationship holding for any force, constant or variable. Implicit in Newton’s equations of motion is also the law of inertia—that an object under no forces will move with constant velocity (or zero acceleration) and will continue to do so until some external force leads to a change in its velocity.

An important question raised by Newton’s laws is that of the so-called “inertial frame” of coordinates, in which they apply. Indeed, it is clear that if these laws are valid in a given system S, they will not apply in an accelerated system S′ without modification. For example, if one adopts a rotating frame, then one must add the centrifugal and Coriolis forces. As a first approximation, the surface of the Earth is taken as an inertial frame; but because it is rotating such an assumption is not exactly valid. Newton proposed that the distant “fixed stars” could be regarded as the basis of an exact frame, and this indeed proved to be feasible, since under this assumption the orbits of the planets were ultimately correctly calculated from Newton’s laws.

Although the assumption of the “fixed stars” as an inertial frame worked well enough from a practical point of view, it suffered from a certain theoretical arbitrariness, which was contrary to the trend implicit in the development of mechanics, i.e., to express the laws of physics solely as internal relationships in the movement itself. For a “favored role” had, in effect, been transferred from the center of the Earth to the fixed stars.

Nevertheless, a significant gain had been made in “relativizing” the laws of physics, so as to make them cease to refer to special favored objects, places, times, etc. Not only was there no longer a special center in space and time but, also, there was no favored velocity of the coordi...