The Special Theory of Relativity

David Bohm

• Publisher: Routledge
• Year: 2003
• Print ISBN: 9780415148092
• eBook ISBN: 9781134753864
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

Based on his famous final year undergraduate lectures on theoretical physics at Birkbeck College, Bohm presents the theory of relativity as a unified whole, making clear the reasons which led to its adoption and explaining its basic meaning. With clarity and grace, he also reveals the limited truth of some of the "common sense" assumptions which make it difficult for us to appreciate its full implications.
With a new foreword by Basil Hiley, a close colleague of David Bohm's, The Special Theory of Relativity is an indispensable addition to the work of one of greatest physicists and thinkers of the twentieth century.

APPENDIX
Physics and Perception

A-l. INTRODUCTION

Throughout this book we have seen that in Einstein’s theory of relativity, the notions of space, time, mass, etc., are no longer regarded as representing absolutes, existing in themselves as permanent substances or entities. Rather, the whole of physics is conceived as dealing with the discovery of what is relatively invariant in the everchanging movements that are to be observed in the world, as well as in the changes of points of view, frames of reference, different perspectives, etc., that can be adopted in such observations. Of course, the laws of Newton and Galileo had already incorporated a number of relativistic notions of this kind (e.g., relativity of the centre of coordinates, of the orientation, and speed of the frame of reference). But in them the basic concepts of space, time, mass, etc., were still treated as absolutes. Einstein’s contribution was to extend these relativistic notions to encompass the laws, not only of mechanics, but also those of electrodynamics and optics, in the special theory, and of gravitation in the general theory. In doing this he was led to make the revolutionary step to which we have referred, i.e., of ceasing to regard the properties of space, time, mass, etc., as absolutes, instead treating these as invariant features of the relationships of observed sets of objects and events to frames of reference. In different frames of reference the space co-ordinates, time, mass, energy, etc., to be associated to specified objects and events will be different.
Yet there are various sets of transformations (e.g., rotations, space displacements, Lorentz transformations) relating the many aspects of the world, as observed in any one frame to those as observed in another. And in these transformations, certain functions (such as the interval and the rest mass) represent invariant properties, the same for all frames of reference, within the set in question. Of course, such invariance will in general hold only in some domain, so that as the domain under investigation is broadened, we may expect to come to new invariant relationships, containing the older ones as approximations and limiting cases. The lawfulness of nature is thus seen to correspond just to the possibility of finding what is invariant. But because each kind of invariance is only relative to a suitable domain, science may be expected to go on to the discovery of ever new kinds of invariant relationships, each of which contributes to the understanding of some new domain of phenomena.

At first sight the point of view described above may seem to be very different to that of “common sense” (as well as of the older Newtonian physics). For are we not in the habit of regarding the world as constituted of more or less permanent objects, satisfying certain permanent laws? That is to say, in everyday life we never talk about “invariant relationships,” but rather we refer to tables, chairs, trees, buildings, people, etc., each of which is more or less unconsciously conceived as being a certain kind of object or entity, which, added to others, makes up the world as we know it. We do not regard these objects or entities as relative invariants which along with their properties, and the laws that they satisfy, have been abstracted from the total flux of change and movement. There appears then to be a striking difference between the way we conceive the world as observed in immediate experience (as well as in the domain of classical nonrelativistic physics) and the way it is conceived in relativity theory.

In this Appendix we shall show that the difference between the notions of common experience and those of relativity theory arise mainly because of certain habitual ideas concerning this experience, and that there is now a great deal of new, but fairly well confirmed, scientific evidence suggesting that our actual mode of perception of the world (seeing it, hearing it, touching it, etc.) is much closer in character and general structure to what is suggested by relativistic physics than it is to what is suggested by prerelativistic physics. In the light of this evidence it would seem that nonrelativistic notions appear more natural to us than relativistic notions, mainly because of our limited and inadequate understanding of the domain of common experience, rather than because of any inherent inevitability of our habitual mode of apprehending this domain.

A-2. THE DEVELOPMENT OF OUR COMMON NOTIONS IN INFANTS AND YOUNG CHILDREN

The evidence in favor of the suggestion at the end of Chapter 1 comes from many different fields. We shall begin with the fascinating studies of the development of intelligence in infants and young children carried out by Piaget.¹ On the basis of long and careful observations of children of all ages from birth up to 10 or more years, he was actually able to see the development of our customary ideas of space, time, the permanent objects, the permanent substance with the conserved total quantity, etc., and thus to trace the process in which such notions are built up until they seem natural and inevitable.

The very young infant does not behave as if he had the adult’s concept of a world separate from himself, containing various more or less permanent objects in it. Rather, Piaget gives good evidence suggesting that the infant begins by experiencing an almost undifferentiated totality. That is to say he has not yet learned to distinguish between what arises inside of him and outside of him, nor to distinguish between the various aspects of either the “outer” or the “inner” worlds. Instead there is experienced only one world, in a state of continual flux of sensations, perceptions, feelings, etc., with nothing recognizable as permanent in it. However, the infant is endowed with certain inborn reflexes, connected with food, movements, etc. These reflexes can develop so as to selectively accommodate different aspects of the environment; and in this way the environment begins effectively to be differentiated to the extent of taking on certain “recognizable”
features. But at this stage recognition is largely functional (e.g., some objects are “for eating,” some “for drinking,” some “for pulling” etc.), and there seems to be little or no development of the adult’s ability to recognize an object by the shape, form, structure, or other perceived characteristics.

At first these reflexes and functions are carried out largely in the satisfaction of primary needs, indicated by sensations, such as hunger, etc. In the next stage, however, there develops the so-called “circular reflex,” which is crucial to the development of intelligence. In such a reflex there is an outgoing impulse (e.g., leading to the movement of the hand) followed, not mainly by the satisfaction of need, but rather by some incoming sensory impulse (e.g., in the eye, ear, etc.). This may be said to be a beginning of real perception. For the most elementary way of coming into contact with something that is not just the immediate satisfaction of a bodily need is by incorporating it into a process in which a certain impulse toward action is accompanied by a certain sensation.

This principle of the circular reflex is carried along in all further developments. Thus, at a certain stage, the infant begins to take pleasure in operating such reflexes, in order, as Piaget puts it, “to produce interesting spectacles.” He finds, for example, that pulling a certain cord will produce an interesting sensation of movement in front of him (e.g., if the cord is attached to a colored object). It must not be supposed that he understands the causal connection between the cord and the movement, or even that he foresees the sensation of movement in his imagination and then tries to realize it by some operation.
Rather, he discovers that by doing such an operation he gets a pleasant sensation that is recognizable. In other words, recognition that a past event has been repeated comes first; the ability to call up this event in the memory comes only much later. Thus, at this stage, he only knows that a certain operation will lead to some recognizable experience that is pleasurable.

The ability to recognize something as similar to what was experienced before is certainly a necessary prerequisite for beginning to see something relatively permanent in the flux of process that is very probably the major element in the infant’s early experiences. Another important prerequisite for this is the coordination of many different kinds of reflexes that are associated to a given object. Thus, at first the infant seems to have little or no realization that the object he sees is the same as the object he hears.
Rather, there seem to be fairly separate reflexes, such as listening, looking with the eyes, etc. Later, however, these reflexes begin to be coordinated, so that he is finally able to understand that he sees what he hears, grasps what he sees, etc. This is an important step in the growth of intelligence, for in it is already implicit the notion that will finally develop—of a single object that is responsible for all of our different kinds of experience with it.

The infant is, however, as yet far from the notion of a permanent object, or of permanent causal relationships between such objects. Rather, his behavior at this stage suggests that when presented with something familiar he now abstracts certain vaguely recognizable totalities of sensation and response, involving the coordination of hand, eye, ear, etc. Thus there is a kind of a germ of the notion of the invariant here; for in the total flux of experience he can now recognize certain invariant combinations of features of the pattern. These combinations are themselves experienced as totalities, so that the object is not recognized outside of its customary context.

Later the infant begins to follow a moving object with his eyes, being able to recognize the invariance of its form, etc., despite its movement. He is thus beginning to build up the reflexes needed for perceiving the continuity of existence of certain objects, apart from their customary contexts. However, he still has no notion of anything permanent. Rather, he behaves as if he believed that an object comes into existence where he first sees it and passes out of existence where he last sees it. Thus, if an object passes in front of him and disappears later from his field of view, he looks for it, not in the direction where he has last seen it, but rather toward the place where he first saw it, as if this were regarded asthe natural source of such objects. Thus, if an object goes behind an obstacle, he does not seem to have any notion of looking for it there. The realization that this can be done comes only later, after the child has begun to work with what Piaget calls “groups of operations.” The most elementary of these is the “group of two.” That is, there are operations such as turning something round and round, hiding it behind an obstacle and bringing it back to view, shaking something back and forth, etc., which have in common that there is an operation, the result of which can be “undone” by a second operation, so that the two operations following each other lead back to the original state of affairs. It is only after he understands this possibility that the infant begins to look for an object behind the obstacle where it vanished from view. But his behavior suggests that he still does not have the idea of a permanent object, existing even when he doesn’t see it.
Rather, he probably feels that he can “undo” the vanishing of an object, by means of the “operation” of putting his hand behind the obstacle and bringing forth the object in question.

In this connection we must recall that the infant still sees no clear and permanent demarcation between himself and the world, or between the various objects in it. However, he is building up the reflexes and operations needed to conceive this demarcation later. Thus, he is beginning to develop the notion of causality, and the distinction of cause and effect. At first he seems to regard causality as if it were a kind of “sympathetic” magic. He may discover that certain movements applied to a string or other object near him will produce corresponding movements elsewhere. He does not immediately realize the need for a connection, but often acts as if he expected the results to follow directly as a kind of magical response to his movements. This is, of course, not really unexpected, if one considers that the child does not yet clearly distinguish what is inside him from what is outside. Thus, in many cases, movements will in fact produce perceptible internal effects without a visible intermediary connection. Therefore, as long as the child views all aspects of his experience as a single totality, with no clear distinction of “within” and “without,” there is nothing in his experience to deny the expectation of such sympathetic magical causality. Later, however, he begins to see the need for intermediate connections in causal relationships, and still later he is able to recognize other people, animals, and even objects as the causes of things that are happening in his field of experiencing.

Meanwhile, the notions of space and time are being built up. Thus as the child handles objects and moves his body he learns to coordinate his changing visual experiences with the tactile perceptions and bodily movements. At this stage, his notion of groups of movements is being extended from the “group of two” to more general groups. Thus, he is learning that he can go from one place A to another B by many different paths, and that all these paths lead him to the same place (or alternatively that if he goes from A to B by any one path, he can “undo” this and return to A by a large number of alternative paths).
This may seem to be self-evident to us, but for an infant living on a flux of process it is probably a gigantic discovery to find out that in all of this movement there are certain things that he can always return to in a wide variety of ways. The notion of the reversible group of movements or operations thus provides a foundation on which he will later erect that of permanent places to which one can return, and permanent objects, which can always be brought back to something familiar and recognizable by means of suitable operations (e.g., rotations, displacements, etc.).

Meanwhile the child is gradually learning to call up images of the past, in some approximation to the sequence in which it occurred, and not merely to recognize something as familiar only after he sees it. Thus begins true memory, and with it the basis for the notion of the distinction of past time and present time (and later future time, when the child begins to form mental images of what he expects).

A really crucial step occurs when the child is able to form an image of an absent object, as existing even when he is not actually perceiving it. Just before he can do this he seems to deal with this problem as if he regarded the absent object as something that he (or other people) can produce or create with the aid of certain operations. But now he begins to form a mental image of the world, containing both perceived and unperceived things, each in its place. These objects, along with their places, are now conceived as permanently existing, and in a set of relationships corresponding perfectly to the groups of movements and operations already known to him (e.g., the picture of a space in which each point is connected to every other by many paths faithfully represents the invariant feature of his experience with groups of operations, in which he was able to go from one point to another by many routes).

At this stage it seems that the child begins to see clearly the distinction between himself and the rest of the world. Until now he could not make such a distinction, because there was only one field of experiencing what was actually present to his total set of perceptions. However, with his ability to create a mental image of the world, i.e., to imagine it, he now conceives a set of places which are permanent, these places being occupied by various permanent objects. But one of these objects is himself. In his new mental “map” of the world he can maintain a permanent distinction between himself and other objects. Everything on this map falls into two categories—what is “inside his skin”
and what is not. He learns to associate various feelings, pleasures, pains, desires, etc.,
with what is “inside his skin,” and thus he forms the concept of a “self,” distinct from the rest of the world, and yet having its place in this world. He similarly attributes “selves” to the insides of other people’s skins, as well as to animals. Each “self” is conceived as both initiating causal actions in the world and suffering the effects of causal actions originating outside of it. Eventually he learns to attribute to inanimate objects a lower and more mechanical kind of “selfhood” without feelings, aims, and desires, but still having a certain ability to initiate causal actions, and to suffer the effects of causes originating outside of it. In this way the general picture of a world in space (and time), constituted of separate and permanent entities which can act on each other causally, is formed.

The notions of an objective world and of a subject corresponding to one of the objects in the world are, as we have seen, thus formed together, in the same step. And this is evidently necessary, since the mental image of the world that serves as a kind of conceptual “map” requires the singling out of one of the objects on this “map” to represent the place of the observer, in order that his special perspective on the world at each moment can be taken into account. That is to say, just as the relativistic “map,” in the form of the Minkowski diagram (as discussed at the end of Chapter 29), must contain something in it to represent the place, time, orientation, velocity, etc., of the observer, so the mental map that is created by each person must have a corresponding representation of that person’s relationship to the environment.

It must not be supposed, of course, that the child knows that he is making a mental image or map of the world. Rather, as Piaget brings out very well, young children often find it difficult to distinguish between what is imagined or remembered in thought and what is actually perceived through their senses (e.g., they may think that other people are able to see the objects that they are thinking about). Thus the child will take this mental map as equivalent to reality. And this habit is intensified with each new experience, because once the map is formed it enters into and shapes all immediate perceptions, thus interpenetrating the whole of experience and becoming inseparable from it. Indeed, it is well known that how we see something depends on what we know about it. (E.g., an extreme case is that of an ambiguou...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Foreword
• Preface
• I. Introduction
• II. Pre-Einsteinian Notions of Relativity
• III. The Problem of the Relativity of the Laws of Electrodynamics
• IV. The Michelson-Morley Experiment
• V. Efforts to Save the Ether Hypothesis
• VI. The Lorentz Theory of the Electron
• VII. Further Development of the Lorentz Theory
• VIII. The Problem of Measuring Simultaneity In the Lorentz Theory
• IX. The Lorentz Transformation
• X. The Inherent Ambiguity In the Meanings of Space-Time Measurements, According to the Lorentz Theory
• XI. Analysis of Space and Time Concepts In Terms of Frames of Reference
• XII. “Common-Sense” Notions of Space and Time
• XIII. Introduction to Einstein’s Conceptions of Space and Time
• XIV. The Lorentz Transformation In Einstein’s Point of view
• XV. Addition of Velocities
• XVI. The Principle of Relativity
• XVII. Some Applications of Relativity
• XVIII. Momentum and Mass In Relativity
• XIX. The Equivalence of Mass and Energy
• XX. The Relativistic Transformation Law for Energy and Momentum
• XXI. Charged Particles In an Electromagnetic Field
• XXII. Experimental Evidence for Special Relativity
• XXIII. More About the Equivalence of Mass and Energy
• XXIV. Toward a New Theory of Elementary Particles
• XXV. The Falsification of Theories
• XXVI. The Minkowski Diagram and the K Calculus
• XXVII. The Geometry of Events and the Space-Time Continuum
• XXVIII. The Question of Causality and the Maximum Speed of Propagation of Signals In Relativity Theory
• XXIX. Proper Time
• XXX. The “Paradox” of the Twins
• XXXI. The Significance of the Minkowski Diagram As a Reconstruction of the Past
• Appendix: Physics and Perception