Bohm, david special theory of relativity (routledge, 2009)

The Special Theory of Relativity The Special Theory of Relativity David Bohm London and New York First published 1965 by W.A.Benjamin, Inc This edition published in the Taylor & Francis e-Library, 2009 To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk This edition published 1996 by Routledge Park Square, Milton Park, Abingon, Oxon, OX14 4RN Simultaneously published in the USA and Canada by Routledge 270 Madison Ave, New York NY 10016 © 1965, 1996 Sarah Bohm Foreword © 1996 B.J.Hiley All rights reserved No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication Data A catalogue record for this book has been requested ISBN 0-203-20386-0 Master e-book ISBN ISBN 0-203-26638-2 (Adobe ebook Reader Format) ISBN 0-415-14808-1 (hbk) ISBN 0-415-14809-X (pbk) Foreword The final year undergraduate lectures on theoretical physics given by David Bohm at Birkbeck College were unique and inspiring As they were attended by experimentalists and theoreticians, the lectures were not aimed at turning out students with a high level of manipulative skill in mathematics, but at exploring the conceptual structure and physical ideas that lay behind our theories His lectures on special relativity form the content of this book This is not just another text on the subject It goes deeply into the conceptual changes needed to make the transition from the classical world to the world of relativity In order to appreciate the full nature of these radical changes, Bohm provides a unique appendix entitled “Physics and Perception” in which he shows how many of our “self-evident” notions of space and of time are, in fact, far from obvious and are actually learnt from experience In this appendix he discusses how we develop our notions of space and of time in childhood, freely using the work of Jean Piaget, whose experiments pioneered our understanding of how children develop concepts in the first place Bohm also shows how, through perception and our activity in space, we become aware of the importance of the notion of relationship and the order in these relationships Through the synthesis of these relationships, we abstract the notion of an object as an invariant feature within this activity which ultimately we assume to be permanent It is through the relationship between objects that we arrive at our classical notion of space Initially, these relations are essentially topological but eventually we begin to understand the importance of measure and the need to map the relationships of these objects on to a co-ordinate grid with time playing a unique role His lucid account of how we arrive at our classical notions of space and absolute time is fascinating and forms the platform for the subsequent development of Einstein’s relativity After presenting the difficulties with Newtonian mechanics and Maxwell’s electrodynamics, he shows how the Michelson-Morley experiment can be understood in terms of a substantive view of the ether provided by Lorentz and Fitzgerald The difficulties in this approach, which assumes actual contraction of material rods as they move through the ether, are discussed before a masterful account of Einstein’s conception of space-time is presented Bohm’s clarity on this topic was no doubt helped by the many discussions he had with Einstein in his days at Princeton The principle of relativity is presented in terms of the notion of relationship and the order of relationship that were developed in the appendix and he argues that a general law of physics is merely a statement that certain relationships are invariant to the way we observe them The application of this idea to observers in relative uniform motion immediately produces the Lorentz transformation and the laws of special relativity Interlaced with the chapters on the application of the Lorentz transformation, is a chapter on the general notion of the falsification of theories Here he argues against the Popperian tradition that all that matters is mere experimental falsification Although a preliminary explanation might fit the empirical data, it may ultimately lead to confusion and ambiguity and it is this that could also lead to its downfall and eventual abandonment in favour of another theory even though it contradicts no experiment His final chapters on time and the twin paradox exhibit the clarity that runs throughout the book and makes this a unique presentation of special relativity B.J.HILEY Preface The general aim of this book is to present the theory of relativity as a unified whole, making clear the reasons which led to its adoption, explaining its basic meaning as far as possible in non-mathematical terms, and revealing the limited truth of some of the tacit “common sense” assumptions which make it difficult for us to appreciate its full implications By thus showing that the concepts of this theory are interrelated to form a unified totality, which is very different from those of the older Newtonian theory, and by making clear the motivation for adopting such a different theory, we hope in some measure to supplement the view obtained in the many specialized courses included in the typical program of study, which tend to give the student a rather fragmentary impression of the logical and conceptual structure of physics as a whole The book begins with a brief review of prerelativistic physics and some of the main experimental facts which led physicists to question the older ideas of space and time that had held sway since Newton and before Considerable emphasis is placed on some of the efforts to retain Newtonian concepts, especially those developed by Lorentz in terms of the ether theory This procedure has the advantage, not only of helping the student to understand the history of this crucial phase of the development of physics better, but even more, of exhibiting very clearly the nature of the problems to which the older concepts gave rise It is only against the background of these problems that one can fully appreciate the fact that Einstein’s basic contribution was less in the proposal of new formulas than in the introduction of fundamental changes in our basic notions of space, time, matter, and movement To present such new ideas without relating them properly to previously held ideas gives the wrong impression that the theory of relativity is merely at a culminating point of earlier developments and does not properly bring out the fact that this theory is on a radically new line that contradicts Newtonian concepts in the very same step in which it extends physical law in new directions and into hitherto unexpected new domains Therefore, in spite of the fact that the study of the basic concepts behind the ether theory occupies valuable time for which the student may be hard pressed by the demands of a broad range of subjects, the author feels that it is worthwhile to include in these lectures a brief summary of these notions Einstein’s basically new step was in the adoption of a relational approach to physics Instead of supposing that the task of physics is the study of an absolute underlying substance of the universe (such as the ether) he suggested that it is only in the study of relationships between various aspects of this universe, relationships that are in principle observable It is important to realize in this connection that the earlier Newtonian concepts involve a mixture of these two approaches, such that while space and time were regarded as absolute, nevertheless they had been found to have a great many “relativistic” properties In these lectures, a considerable effort is made to analyze the older concepts of space and time, along with those of “common sense” on which they are based, in order to reveal this mixture of relational and absolute points of view After bringing out some of the usually “hidden” assumptions behind common sense and Newtonian notions of space and time, assumptions which must be dropped if we are to understand the theory of relativity, we go on to Einstein’s analysis of the concept of viii  Preface simultaneity, in which he regards time as a kind of “coordinate” expressing the relationship of an event to a concrete physical proc ess in which this coordinate is measured On the basis of the observed fact of the constancy of the actually measured velocity of light for all observers, one sees that observers moving at different speeds cannot agree on the time coordinate to be ascribed to distant events From this conclusion, it also follows that they cannot agree on the lengths of objects or the rates of clocks Thus, the essential implications of the theory of relativity are seen qualitatively, without the need for any formulas The transformations of Lorentz are then shown to be the only ones that can express in precise quantita tive form the same conclusions that were initially obtained without mathematics In this way, it is hoped that the student will first see in general terms the significance of Einstein’s notion of space and time, as well as the problems and facts that led him to adopt these notions, after which he can then go on to the finer-grained view that is supplied by the mathematics Some of the principal implications of the Lorentz transformation are then explained,not only with a view of exploring the meaning of this transformation, but also of leading in a natural way to a statement of the principle of relativity—that is, that the basic physical laws are the invariant relationships, the same for all observers The principle of relativity is illustrated in a number of examples It is then shown that this principle leads to Einstein’s relativistic formulas, expressing the mass and momentum of a body in terms of its velocity By means of an analysis of these formulas, one comes to Einstein’s famous relationship, E=mc2, between the energy of a body and its mass The meaning of this relationship is developed in considerable detail, with special attention being given to the problem of “rest energy,” and its explanation in terms of to-and-fro movements in the internal structure of the body, taking place at lower levels In this connection, the author has found by experience that the relationship between mass and energy gives rise to many puzzles in the minds of students, largely because this relationship contradicts certain “hidden” assumptions concerning the general structure of the world, which are based on “common sense,” and its development in Newtonian mechanics It is therefore helpful to go into our implicit common sense assumptions about mass to show that they are not inevitable and to show in what way Einstein’s notion of mass is different from these, so that it can be seen that there is no paradox involved in the equivalence of mass and energy Throughout the book, a great deal of attention is paid quite generally to the habitual tendency to regard older modes of thought as inevitable, a tendency that has greatly impeded the develop ment of new ideas on science This tendency is seen to be based on the tacit assumption that scientific laws constitute absolute truths The notion of absolute truth is analyzed in some detail in this book, and it is shown to be in poor correspondence with the actual de velopment of science Instead, it is shown that scientific truths are better regarded as relationships holding in some limited domain, the extent of which can be delineated only with the aid of future experimental and theoretical discoveries While a given science may have long periods in which a certain set of basic concepts is developed and articulated, it also tends to come, from time to time, into a critical phase, in which older concepts reveal ambiguity and confusion The resolution of such crises involves a radical change of basic concepts, which contradicts older ideas, while in some sense containing their correct features as special cases, limits, or approximations Thus, scientific research is not a process of steady accumulation of absolute truths, which has Preface  ix culminated in present theories, but rather a much more dynamic kind of process in which there are no final theoretical concepts valid in unlimited domains The appreciation of this fact should be helpful not only in physics but in other sciences where similar problems are involved The lectures on relativity end with a discussion of the Minkowski diagram This is done in considerable detail, with a view to illustrating the meaning of the principle of relativity in a graphical way In the course of this illustration, we introduce the K calculus, which further brings out the meaning of Einstein’s ideas on space and time, as well as providing a comparison between the implications of these ideas and those of Newton In this discussion, we stress the role of the event and process as basic in relativistic physics, instead of that of the object and its motion, which are basic in Newtonian theory This leads us on to the (hyperbolic) geometry of Minkowski space-time, with its invariant distinction of the events inside of the past and future light cones from those outside On the basis of this distinction, it is made clear that the relativistic failure of different observers to agree on simultaneity in no way confuses the order of cause and effect, provided that no signals can be transmitted faster than light We include in these lectures a thorough discussion of the two differently aging twins, one of whom remains on Earth while the other takes a trip on a rocket ship at a speed near to that of light This discussion serves to illustrate the meaning of “proper-time” and brings out in some detail just how Einstein’s notions of space and time leave room for two observers who separate to have experienced different intervals of “proper-time” when they meet again Finally, there is a concluding discussion of the relationship between the world and our various alternative conceptual maps of it, such as those afforded respectively by Newtonian physics and Einsteinian physics This discussion is aimed at removing the confusion that results when one identifies a conceptual map with reality itself—a kind of confusion that is responsible for much of the difficulty that a student tends to meet when he is first confronted by the theory of relativity In addition, this notion of re lationship in terms of mapping is one that is basic in modern mathematics, so that an understanding of the Minkowski diagram as a map should help prepare the student for a broader kind of appreciation of the connection between physics and a great deal of mathematics The lectures proper are followed by an appendix, in which Einstein’s notions of space, time, and matter are related to certain properties of ordinary perception It is commonly believed that Newtonian concepts are in complete agreement with everyday perceptual experience However, recent experimental and theoretical developments in the study of the actual process of perception make it clear that many of our “common sense” ideas are as inadequate and confused when applied to the field of our perceptions as they are in that of relativistic physics Indeed, there seems to be a remarkable analogy between the relativistic notion of the universe as a structure of events and processes with its laws constituted by invariant relationships and the way in which we actually perceive the world through the abstraction of invariant relationships in the events and processes involved in our immediate contacts with this world This analogy is developed in considerable detail in the appendix, in which we are finally led to suggest that science is mainly a way of extending our perceptual contact with the world, rather than of accumulating knowledge about it In this way, one can understand the fact that scientific research does not lead to absolute truth, but rather (as happens in ordinary perception) an awareness and understanding of an ever-growing segment of the world with which we are in contact 166  Appendix: Physics and Perception When we use the words “to abstract” we not wish to suggest that there is merely a process of induction, or of taking out some kind of summation of what has been experienced earlier Rather, each abstraction constitutes, as it were, a kind of “hypothesis,” put forth to explain what has been found to be invariant in such earlier experiences Only the abstractions which stand up to further tests and probings will be retained Eventually, however, these become habitual, and we cease to be aware of their basically hypothetical and tentative character, regarding them instead as inherent and necessary features of all that exists, in every possible domain and field of experiencing and investigation Piaget then goes on to describe how with the development of language and logical thinking the child goes on to make still higher level abstractions, in which there are formed structures of words, ideas, concepts, etc., which express the invariant features of the world that he abstractly considers in his perceptions Evidently there is in principle no limit to this process of abstraction Thus science and mathematics may be said to form still higher level abstractions (formulated in words, diagrams, and mathematical symbols), expressing the invariant features of what has been found in experiments and observations (which latter are carried out in terms of the ordinary abstractions of everyday language and common sense) Thus all knowledge is a structure of abstractions, the ultimate test of the validity of which is, however, in the process of coming into contact with the world that takes place in immediate perception It can be seen that a crucial state in this over-all process of abstraction is the setting aside of certain parts of what appears in the “inner show” as not directly representing immediate perception These are what we imagine, conceive, symbolize, think about, etc These parts are then seen to be related to immediate perception as abstractions, representing the general structural features of this perception, much as a map represents the terrain of which it is a map.1 However, as has been pointed out in Section A-2, a young child does not readily distinguish between what has been imagined and what is seen in response to immediate perception In this way, there arises the habit of confusing our abstract conceptual “maps” with reality itself, and of not noticing that they are only maps When the child grows older he is able to avoid this confusion in superficial problems, but when it comes to fundamental concepts, such as space, time, causality, etc., it is much more difficult to so As a result, the adult continues the habit of looking, as it were, at his comparatively abstract conceptual maps, and seeing them as if they were inherent in the nature of things, rather than understanding that they are higher-level abstractions, having only a kind of structural similarity to what has been found to be invariant in lower levels It is this confusion, based on habits of very long standing, which makes a clear discussion of such fundamental problems so difficult We can perhaps best illustrate these notions with the aid of a simple example Suppose that we are looking at a circular disk Now its immediate appearance to our eyes will be that of an ellipse, corresponding to its projection on the retina of the eyes (as would, for example, be portrayed by an artist, who was trying to draw it in perspective) Nevertheless, we know that it is really a circle What is the basis of this knowledge? See also Chapter 29, where a similar role has been suggested for the Minkowski diagram in physics Appendix: Physics and Perception 167 What actually happens is, as we have indicated earlier, that the eye, the head, the body, etc., are always moving In these movements the appearance of the disk is always changing, undergoing in fact a series of projective transformations that are related in a definite way to the movements in question By various means (some of which are discussed in Section A-3) the brain is able to abstract what is invariant in all this movement, change of perspective, etc This abstraction, expressed in terms of the notion that a circular object accounts for all the changing views of it, is the basis of the “construction” of it that we perceive in the “inner show.” The “hypothesis” that this object is really a circle is then further probed and tested in subsequent ways of coming in contact with it perceptually, and it is retained as long as it stands up to such probing and testing But the realization that the perceived object is a circle depends also on knowledge going beyond the level of immediate perception Thus from early childhood a person has learned to imagine looking straight at the object in a perpendicular direction, and seeing its circular shape (as well as feeling it to be circular when his hands grasp it) He may also have learned further to imagine himself represented as a point on a diagram, and to follow the course of the light rays from the circle to his point of perspective, thus being able to see how the circular shape is transformed into an elliptical appearance If he has been further educated, he can go to a still higher level of abstraction, by mathematically calculating the correct shape of the disk, from a knowledge of its appearance in several views and from a knowledge of the relationship of the observer to the disk in all of these views (distance, etc.) In carrying out this calculation he will consciously on a higher level of abstraction what his brain does spontaneously on a lower level, i.e., to find a single structure that accounts for what is invariant in our changing relationships with the object under discussion We see then that there is no sharp break between the abstractions of immediate perception and those which constitute our knowledge, even if we carry this knowledge to the highest levels reached by science and mathematics From the very first, our immediate perceptions express a “construction” in an “inner show,” based on a preconscious abstraction of what is invariant in, or active process of coming into contact with, our environment Each higher level of abstraction repeats a similar process of discovery of what is invariant in lower levels, which is then represented in the form of a picture, an image, a symbolic structure of words and formulas, etc These higher-level abstractions then contribute to shaping the general structure of those at lower levels, even coming down to that of immediate perception So between all the levels of abstraction there is a continual two-way interaction Consider, for example, the experience of looking out at the night sky Ancient man abstracted from the stars the patterns of animals, men, and gods, and thereafter was unable to look at the sky without seeing such entities in it Modern man knows that what is really behind this view is an immeasurable universe of stars, galaxies, galaxies of galaxies, etc., and that each person, having a particular place in this universe, obtains a certain perspective on it, which is what is seen in the night sky Such a man does not see animals, gods, etc., in the sky, but he sees an immense universe there But even the view of modern science is probably true only in a certain domain So future man may form a very different notion of the invariant totality that is behind our view of the night sky, in which present notions will perhaps be seen as a simplification, approximation, and limiting case, but actually very far from being completely true Can we not say then that 168  Appendix: Physics and Perception at every stage man was extending his perception of the night sky, going from one level of abstraction to another, and in each stage thus being led to hypotheses on what is invariant, which are able to stand up better to further tests, probings, etc.? But if this is the case, then the most abstract and general scientific investigations are natural extensions of the very same process by which the young child learns to come into perceptual contact with his environment As we have pointed out on several occasions (e.g., in the discussion of Piaget’s work in Section A-2 and of the perception of movement in Section A-3) one of the basic problems that has to be solved in every act of perception is that of taking into account the special point of view and perspective of the observer The solution of this problem depends essentially on the use of a number of levels of abstraction, all properly related to each other Thus a person not only perceives the immediate elliptical appearance of the disk in front of him He can also perceive the changes in appearance of the disk, which result from certain movements which he himself actively undertakes From these changes his brain is able to abstract information about his relationship to the disk (e.g., how far away it is) The essential point here is that through many levels of abstraction, all going on simultaneously in the mind, it is possible to perceive not only a projection of the object of interest but also the relationship of the observer to the object in question From this it is always possible in principle to obtain an invariant notion as to what is actually going on This is represented in a higher level of abstraction, for example, by imagining space containing the disk and the observer himself, in which both are represented in their proper relationships When a person says that the object is really circular, he is then evidently not referring to an immediate sensation of the shape of the object but to this extended process of abstraction, the essential results of which are represented in this imagined space, containing both the object and himself A very similar problem arises in science Here, the hands, body, and sense organs of the observer are generally, in effect, extended by means of suitable instruments, which are in certain ways more sensitive, more powerful, more accurate, as well as capable of new modes of making contact with the world But in the essential point that the observer is actively probing and testing his environment, the situation is very similartowhat it is in immediate perception, unaided by such instruments In such tests there is always some observable response to this probing and testing; and it is the relationship of variations in this response to known variations in the state of the instruments that constitutes the relevant information in what is observed (just as happens directly with the sense organs themselves) As in the case of immediate perception, however, such an observation has very little significance until one knows the relationship of the instrument to the field that is under observation It is possible to know this relationship with the aid of a series of abstractions Thus in any experiment one not only knows the observed result; one knows the structure of the instrument, its mode of functioning, etc., all of which has been found out with the aid of earlier observations and actions of many kinds In other words, in each process of observation there is always implicit an observation of the observing instrument itself, carried out in terms of different levels of conceptual abstractions But to understand the observation one always needs certain modes of thinking about the problem, in which the instrument and what is observed are represented together, so that one can see “a total picture” in which an invariant field of what is being studied stands in a certain relationship to the instrument, this relationship determining, as it were, how what is in the field “projects” into some observable response of the instrument Appendix: Physics and Perception 169 In Chapter 29 we have already called attention to a special case of the problem discussed above Thus, in the theory of relativity one uses the Minkowski diagram, in which one can in principle represent all the events that happen in the whole of space-time However, each example of such a diagram must contain a line corresponding to the world line of the observer whose results are under discussion This is usually represented by the axis of the diagram Then, if we wish to discuss the results of another observer, we must include in the diagram a representation of his world line In a similar way we must choose a point to represent the place and time which determine the perspective of a given observation By taking all of this into account we are able, from the response of the observing instruments (which is relative to their speed, time and place of functioning, etc.), to calculate the invariant properties of what is observed, in such a way that the different results of different observers are explained by their differing relationships to the process under investigation It can be seen then that relativity theory approaches the universe in a way very similar to that in which a person approaches his environment in immediate perception In both these fields all that is observed is based on the abstraction of what is invariant as seen in various movements, from various points of view, perspectives, frames of reference, etc And in both the invariant is finally understood with the aid of various hypotheses, expressed in terms of higher levels of abstraction, which serve as a kind of “map,” having an order, pattern, and structure similar to that of what is being observed The tendency for the use of such maps to become habitual is also common to scientific investigation and to immediate perception When this happens a person’s thinking is limited to what can fit into such maps, because he thinks that they contain all that can possibly happen, in every condition and domain of experience For example, the common-sense notion of simultaneity of all that is co-present in our immediate perceptions is abstracted into the Newtonian concept of absolute time, with the result that it seems incomprehensible that two twins who are accelerated in different ways and then meet may experience different amounts of time (see Chapter 28) But in Section A-3, we saw that the notion of a single unique time order does not seem to apply without confusion in the field of our immediate perceptions either The main reason that this has been so little noticed is probably our habit of taking seriously only what fits into our habitual perception of all that happens, both inwardly and outwardly, as being in such a unique and universal time order It may be remarked in passing that in the quantum theory the point of view described above is carried even further The reason is basically the indivisibility of the quantum of action, which implies that when we observe something very precisely at the atomic level, it is found that there must be an irreducible disturbance of the observed system by the quanta needed for such an observation (the fact behind the derivation of Heisenberg’s famous uncertainty principle) On the large-scale level the effects of these quanta can be neglected Therefore, although the observer must engage in active movements and probings in order to perceive anything whatsoever, he can in principle (at least in largescale optical perception) refrain from significantly disturbing what he is looking at At the quantum level of accuracy, however, the situation is different Here, the light quanta may be compared to a blind man’s fingers, which can give information about an object only if they move and disturb the latter The blind man is nevertheless able to abstract certain invariant properties of the object (e.g., size and shape), but in doing this, 170  Appendix: Physics and Perception his brain spontaneously takes into account the movement which his perceptual operations impart to the object Similarly, the physicist is still able to abstract certain invariant properties of atoms, electrons, protons, etc (e.g., charge, mass, spin, etc.); but in so doing he must consciously take into account the operations involved in his observation process in a similar way (To discuss this point in detail is, of course, beyond the scope of the present work; but these questions will be treated in subsequent publications.) A-5 THE ROLE OF PERCEPTION IN SCIENTIFIC RESEARCH In the previous discussion we have seen the close similarity between our modes of immediate perception of the world and our modes of approach to it in modern scientific investigations We shall now go on to consider directly the centrally perceptual character of scientific research, which we suggested at the beginning of Section A-4 While man’s scientific instruments constitute, as we have seen, an effective extension of his body and his sense organs, there are no comparable external structures that substitute for the inward side of the perceptive process (in which the invariant features of what has been experienced are presented in the “inner show”) Thus, it is up to the scientist himself to be aware of contradictions between his hypotheses and what he observes, to be sensitive to new relationships in what he observes, and to put forth conjectures or hypotheses, which explain the known facts, embodying these new relationships, and have additional implications with regard to what is as yet unknown, so that they can be tested in further experiments and observations So there is always finally a stage where an essentially perceptual process is needed in scientific research—a process taking place within the scientist himself The importance of the perceptual stage tends to be underemphasized, however, because scientists pay attention mostly to the next stage, in which hypotheses that have withstood a number of tests are incorporated into the body of currently accepted scientific knowledge In effect they are thus led to suppose the essential activity of the scientist is as the accumulation of verified knowledge, toward which goal all other activities of the scientist are ultimately directed If such knowledge could constitute a set of absolute truths, then it would make at least some kind of sense to regard its accumulation as the main purpose of science As we have seen, however, it is the fate of all theories eventually to be falsified, so that they are relative truths, adequate in certain domains, including what has already been observed, along with some as yet further unknown region that can be delimited, to some extent at least, in future experiments and observations But if this is the case then the accumulation of knowledge cannot be regarded as the essential purpose of scientific research, simply because the validity of all knowledge is relative to something that is not in the knowledge itself So one will not be able to see what scientific research is really about without taking into account what it is to which even established and well-tested scientific knowledge must continually be further related, if we are to be able to discuss its (necessarily incompletely known) domain of validity There is also a similar relative validity of the knowledge that we gain in immediate perception But in this field the reason for this is fairly evident Indeed, the world is so vast and has so much that is unknown within it that we are not tempted to suppose that Appendix: Physics and Perception 171 what we learn from immediate perception is a set of absolute truths, the implications of which could be expected to be valid in unlimited domains of future experience Rather, we realize that immediate perception is actually a means of remaining in a kind of contact with a certain segment of the world, in such a way that we can be aware of the general structure of that segment, from moment to moment, if we carry out the process of perception properly In this contact we are satisfied if we are able to keep up with what we see and perhaps, in some respects, get a little ahead of it (e.g., in driving an automobile, we can, to a certain extent, anticipate the movements of other automobiles, people, the turns in the road, etc.) Thus, in the process of immediate perception, one obtains a kind of knowledge, the implications of which are valid in the moment of contact and for some unpredictable period beyond this moment The major significance of past knowledge of this kind is then in its implications for present and future perceptions, rather than in the accumulation of a store of truths, considered to be absolute Thus our knowledge of what happened yesterday is in itself of little significance because yesterday is gone and will never return This knowledge will be significant, however, to the extent that its implications and the inferences that can be drawn from it may be valid today or at some later date Of course, scientific theories evidently have much broader domains of validity of their predictive inferences than the “hypotheses” that arise in immediate perception (these broader domains being purchased, however, at the expense of the need to operate only at very high levels of abstraction) Because the domain of validity is so broad, it often takes a long time to demonstrate its limits Nevertheless, what happens in scientific research is, in regard to the problem under discussion, not fundamentally different from what happens in immediate perception For in science too the totality of the universe is too much to be grasped definitively in any form of knowledge, not only because it is so vast and immeasurable, but even more because in its many levels, domains, and aspects it contains an inexhaustible variety of structures, which escape any given conceptual “net” that we may use in trying to express their order and pattern Therefore, as in the field of immediate perception, our knowledge is adequate for an original domain of contact with the world, extending in an unpredictable way into some further domains Since the goal of obtaining absolutely valid knowledge has no relevance in such a situation, we are led to suggest that scientific research is basically to be regarded as a mode of extending man’s perceptual contact with the world, and that the main significance of scientific knowledge is (as happens in immediate perception) that it is an adjunct to this process The basically perceptual character of scientific research shows up most strongly when the time comes to understand new facts, as distinct from merely accumulating further knowledge Everyone has experienced such a process on various occasions in his life Suppose something unfamiliar is being explained (e.g., a theorem in geometry) At first a person is able to take in only various bits of knowledge, the relationship of which is not yet clear But at a certain stage, in a very rapid process often described as “click” or as a “flash,” he understands what is being explained When this happens he says “I see,” indicating the basically perceptual character of such a process (Of course, he does not see with optical vision but rather, as it were, with the “mind’s eye.”) But what is it that he sees? What he perceives is a new total structure in terms of which the older items of knowledge all fall into their proper places, naturally related, while many new and unsuspected relationships suddenly come into view Later, to preserve this understanding, to communicate it to other people, to apply it, or to test its validity, he may translate it 172  Appendix: Physics and Perception into words, formulas, diagrams, etc But initially it seems to be a single act, in whicholder structures are set aside and a new structure comes into being in the mind When the need arises to develop new theories, the basically new step is generally an act or a series of acts of understanding Previous to such understanding, scientists are facing a set of problems, to which the older theories give rise, when applied in new domains This process eventually leads to an awareness of contradictions, confusions, and ambiguities in the older theories, when applied in the new problems Then if the scientist is ready to set aside older notions his mind may become sensitive to new relationships in terms of which facts, both old and new, may be seen Out of this sensitivity develops a new understanding, i.e., the expression of the old facts in terms of a new structure, having further implications going beyond those of the older points of view Of course, we must not suppose that all such acts of understanding lead immediately to correct theories Far from it, many of them are found to be incapable of solving the basic problems under consideration Hence each such understanding must be tested to see what the domain of validity actually is To this, it is necessary logically to work out the implications of the new structure of ideas that has emerged into the mind Nevertheless, as important as these latter steps are, they all depend on the essentially creative acts of understanding, without which science would eventually either stop developing or else stagnate in a bounded domain that never went beyond some limited circle of ideas There seems to be no limit to the possibility of the human mind for developing new structures in the way described above And it is this possibility that seems to be behind our ability to put forth new theories and concepts, which lead to knowledge that goes beyond the facts that are accessible at the time when the theories are first developed It should be recalled that this possibility exists as much in immediate perception as in scientific research, since very often what is constructed in the “inner show” leads, as we have seen earlier, to many correct predictive inferences for future perceptions It is evident that such an ability cannot be due merely to some sort of mechanism that randomly puts forth “hypotheses” until one of them is confirmed Rather, for reasons that are as yet not known, the human mind in its general process of perception, whether on the immediate level or on the highest level involved in understanding, can create structures that have a remarkably good chance of being correct in domains going beyond that on which the evidence for them is founded On the basis of this possibility, the process of “trial and error” can efficiently weed out those structures that are inappropriate At the same time it can help provide material, the criticism of which leads to a fresh act of understanding or perception, in which yet newer structures are put forth which are generally likely to have a broader domain of validity and better correspondence to the facts than the earlier ones had To sum up, the essential point is that through perception we are always in a process of coming into contact with the world, in such a way that we can be aware of the general structure of the segment with which we have been in contact Science may then be regarded as a means of establishing new kinds of contacts with the world, in new domains, in new levels, with the aid of different instruments, etc But these contacts would mean very little without the act of understanding, which corresponds on a very high level to that process by which what has been invariant is presented in terms of structure in the “inner show” of immediate perception It need then no longer be puzzling that science does not lead to knowledge of an absolute truth For the knowledge supplied by science is (like all other knowledge) basically an expression of the structure that has Appendix: Physics and Perception 173 been revealed in our process of coming from moment to moment into contact with aworld the totality of which is beyond our ability to grasp in terms of any given sets of percepts, ideas, concepts, notions, etc Nevertheless, we can obtain a fairly good grasp of that with which we have thus far been in contact, which is also valid in some domain, either large or small, beyond what is based on this contact By remaining alert to contradictions and sensitive to new relationships, thus permitting the growth of a fresh understanding, we can keep up with our contact with the world, and in some ways we can anticipate what is coming later In science this process takes place at a very high level of abstraction, on a scale of time involving years In immediate perception it occurs on a lower level of abstraction, and it is very rapid In science the process depends strongly on collective work, involving contributions of many people, and in immediate perception it is largely individual But fundamentally both can be regarded as limiting cases of one over-all process, of a generalized kind of perception, in which no absolute knowledge is to be encountered INDEX Aberration of light, 18 Absolute time and space, 48–49 (see also Time) Absolute truth (see Truth) Abstraction in perception, 219–223 Addition of velocities, Galilean law, 66 relativistic law, 67 Annihilation and creation of particles, 111 Aristotle, doctrines of, principles of, Atomic constitution of matter and the ether (see Ether) Atomic theory, 111 Causality compatible with relativity, 156 definition of, 155–156 impossible with signals faster than light, 156–166 irrelevant for events in absolute elsewhere, 159 Chronological order, 50 Clock rates, relativity of, 59–60 Clock rates according to Lorentz transformation (see Lorentz) Conception of mass, origin of (see Mass) Concepts as maps expressing relative invariance, 195 Conservation of energy, 82, 92, 100 of mass, 82, 100 of matter, concept of, 195 of momentum, 82 of number of objects, concept of, 193–196 Contraction according to Lorentz transformation (see Lorentz), Coordinates, relational notion of, 48–51 Copernican theory, Decay of mesons as natural clocks, 76–77 (see also Time) Ditchburn, 198–199 Domains of truth of theories (see Theories) Doppler shift of light emitted by a moving body, 77–80 relativistic, 80 Double star observations, 20 Effective mass of radiant energy (see Mass) Einstein basic hypothesis of, 55 point of departure for theories of, 54–55 railway train experiment, 55–57 Index  175 Electrical forces as states of stress and strain in the ether (see Ether) Elementary particles, structure of, 119–120 Energy conservation in a collection of bodies, 92, 100 deduction of relativistic formula, 84–90 equivalence with mass, 91, 93, 108, 110 of inward and outward movement, 116 kinetic, 92 rest, 92 transformations, 115 Equivalence of mass and energy (see Mass and Energy) Ether according to Lorentz theory, 23 and atomic constitution of matter, 24 drag, 18 hypothesis of, 11, 14, 17 and stresses and strains representing electrical forces, 24 Events, geometry of, 146–150 and processes replacing objects in relativity theory 148 (see also Minkowski diagram) Experimental confirmation of relativity theory (see Relativity) Falsifiability of theories (see Theories) Falsification and confirmation of theories (see Theories) Fizeau’s method of measuring the speed of light, 12, 19, 107 Frames of reference for expression of space and time concepts, 42–47 inertial, space, 44–46 space and time, 48 time, 46–47 Galileo, laws of, transformation of, (see also Laws) Gibson, 197, 201, 204, 207 Gravitational mass (see Mass) Hebb, 212 Held, 201 Hubel, 199, 200 Hyperbolic rotations in relativity, 149 Identification of things, 112 Inertia, law of (see Laws) “Inertial frame” of coordinates (see Frames of reference) Inertial mass (see Mass) Invariance of speed of light under Lorentz transformation (see Lorentz) 176  Index Kant, 213–214 K calculus, 133–145 Lorentz transformation in, 141 Laws of addition of velocities in relativity, 67 Copernican, of Galileo, of inertia, of Lorentz, 23–26 of Maxwell, 11 of Newton, relativistic, 100–105 of Newton in terms of momentum, 81 relational conception of, 4–9 Laws of physics failure of in Newton’s equations, 72 invariance of, 71 in relation to light cones, 150–154 relational concept of, 4–9 Length, relativity of, 58–59 Light (see Speed of light) Lodge’s experiment, 18 Lorentz contraction, 25, 64, 106 equations, invariance of, 108 theory of clocks, 26–30, 64 theory of electrons, 23–26 theory of ether, 23 theory of invariance of speed of light, 38, 62 theory of simultaneity, 31 theory of synchronization of clocks, 32 transformation, 36–39, 106 transformation in Einstein’s theory, 61–63 transformation in K calculus, 141 transformation in vector notation, 69 Mapping of percepts in concepts in young children, 192 Mass conservation of, 82, 100 effective, 27 electromagnetic, 29 as energy of inward and outward movement, 116–117 and equivalence with energy, 91, 93, 108, 110 as explained by internal movement, 93, 117 gravitational aspect of, 113–114 inertial aspect of, 112–113 mechanical, 27 observed, 27 origin of conception of, 110–114 of radiation, effective, 95 relativistic formula for, 84–90 Index  177 at rest, as equal to zero at speed of light, 118 rest, invariance of, 98 Maxwell, equations of (see Laws) Measurements in Lorentz theory, 40–1 as relationships of phenomena to instruments, 54 with rulers, 43 of time, 44 Michelson and Morley experiment, 14, 25, 107 Minkowski diagram, 131–133 events in, 131 as a map of events, 180–184 not a kind of arena, 173–175 principle of relativity in terms of K calculus, 133–145 as a reconstruction, 174–180 and the role of the observer, 182–184 world line in, 132 Momentum, conservation of, 82 deduction of relativistic formula, 88 Newton’s laws of motion, 6, relativistic form, 160 (see also Laws) Newton’s laws in terms of the momentum, 81 (see also Laws) Nuclear transformations, 93 Observer as part of universe, 177 Paradox of “twins” in relativity, 165–167 Particles, annihilation of, 93 Perception and abstraction, 219–223 as active process, 197–207 as attunement, 210–212 breakdown of, 212–213 as construction, 203 as construction of hypotheses, 215–217 as extended by science, 223–224, 230 as mapping, 225 optical, 198–207 role of in scientific research, 226–227 and its similarity to scientific research, 218–226 tactile, 197–198 in terms of structure, 207–215 of time, 208–211 and understanding in science, 228–229 Piaget’s observations on intelligence of children, 187–197 Platt, 199 Popper’s thesis (see Falsifiability of theories) 178  Index Principle of relativity (see Relativity) Principle of relativity in Minkowski diagram (see Minkowski diagram) Proper time (see Time) Ptolemaic theory, Recognition, process of, 188–189 Reflexes circular, 188 coordination of, 188–189 functional, 187–188 Relational conception of the laws of physics (see Laws of physics) Relationships of physical phenomena to suitable measuring instruments (see Measurements) Relative invariance domain of 121 instead of permanence of things, 111–112 in physics, 185–186 in perception, 186 of properties of matter, 120–122 Relative truth of theories (see Theories) Relativity of chronological time compared with psychological time, 172 confirmation of theory of, 106–109 and conservation laws, 89 in electrodynamics, 70 general, 55, 166–170 in laws of electrodynamics and optics, 10 in older laws of physics, 70 in pre-Einsteinian laws of physics, 1, 4–10 principle of, 8, 73–74, 106, 133 special, 55 Rest mass explained as inward movement, 117 (see also Mass) Rest mass, invariance of (see Mass) Science, as an essentially perceptual process, 226 as an extension of perception, 223–224, 230 Signal velocity, speed of light as limit on, 57 Simultaneity ambiguity of in relativity, 107 its ambiguity in Lorentz theory, 32, 52 failure of intuitive notions of, 167–169 meaning of, 53 as nonabsolute in Einstein’s theory, 57 nonequivalence with co-presence, 54 Space absolute, 8, 48 in common sense, 49 coordinates as relationships, 61 infants notions of, 190–191 Index  179 in Kant’s view, 214–215 measurements, 43 new concepts of, 44–50 relativity of, 58–59 and time as continuum, 150 unification with time in relativity, 149 Speed of light as effectively infinite, 47 as finite, 47 invariance of, 62 invariance in Lorentz theory, 38 as limit on signal velocity, 57, 68 measured by Fizeau’s method, 12, 19, 107 in running water, 75 Speed of light as maximum possible velocity of motion of objects, 68, 155–162 “System velocity,” general, 83–84 Theories domains of truth of, 126 falsifiability of, 123–125, 218 falsification and confirmation of, 128 (see also Truth) relative truth of, 127 Time absolute, 9, 48, 50 ambiguity in notions of, 54 concept of, 50 coordinates as relationships, 61 differences, 139 frame of reference, 46–47 infants notions of, 190–191 in Kant’s view, 214–215 measured by meson decay, 76–77 measured by moving clock, 107 measurements, 44 perception of, 208–211 proper, 163–164 relativity of, 59–60 unification with space in relativity, 149 Transformation between systems of space coordinates, 45 Galilean, laws for electric and magnetic fields, 104 laws for energy and momentum, 96–99 nuclear, 93 Truth, absolute, 125–130 dynamic apprehension of, 130 180  Index Understanding in science as a form of perception (see Perception) Unification of coordinates in geometry, 148 of space and time in relativity, 149 Velocity of light in running water (see Light) Wiesel, 199, 200 World line in Minkowski diagram (see Minkowskidiagram) Zero rest mass, 118 (see also Mass) ... 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 2  The Special Theory of Relativity. ..The Special Theory of Relativity The Special Theory of Relativity David Bohm London and New York First published 1965 by W.A.Benjamin, Inc This edition published in the Taylor & Francis e-Library,... the period of rotation of the Earth as the half-life of certain radioactive elements 32  The Special Theory of Relativity Of course it is not enough to consider only the results of individual