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The Direction of Time

The Direction of Time

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by Hans Reichenbach

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Ever a source of philosophical conjecture and debate, the concept of time represents the beating heart of physics. This final work by the distinguished physicist Hans Reichenbach represents the culmination and integration of a lifetime's philosophical contributions and inquiries into the analysis of time. The result is an outstanding overview of such qualitative,


Ever a source of philosophical conjecture and debate, the concept of time represents the beating heart of physics. This final work by the distinguished physicist Hans Reichenbach represents the culmination and integration of a lifetime's philosophical contributions and inquiries into the analysis of time. The result is an outstanding overview of such qualitative, or topological, attributes of time as order and direction.
Beginning with a discussion of the emotive significance of time, Reichenbach turns to an examination of the time order of mechanics, the time direction of thermodynamics and microstatistics, the time direction of macrostatistics, and the time of quantum physics. He offers coherent explanations of the analytic methods of scientific philosophy in the investigation of probability, quantum mechanics, the theory of relativity, and causality — methods that he not only applies here but also helped to develop and refine.
Physics Today observed that "For a generation Professor Reichenbach has worked as almost no other man to bring to the interpretation of modern physics the critical and reflective thinking of a trained philosopher. Most physicists who retain an interest in philosophy, and many who wanted simply to understand physics, have read some of the earlier books of Reichenbach. This one is . . . the best by a good deal." Introduction. Appendix. Index.

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Dover Publications
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Dover Books on Physics
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By Reichenbach Hans, Maria Reichenbach

Dover Publications, Inc.

Copyright © 1984 Maria Reichenbach
All rights reserved.
ISBN: 978-0-486-13725-4



1. The Emotive Significance of Time

The problem of time has always baffled the human mind. Not only the events of the external world but even all our subjective experiences occur in time. It appears as though the flow of time, which orders the events of the physical world, passes through human consciousness and compels it to adjust itself to the same order. Our observations of physical things, our feelings and emotions, and our thinking processes extend through time and cannot escape the steady current that flows unhaltingly from the past by way of the present to the future.

What we experience in one moment, glides, in the next moment, into the past. There it remains forever, irretrievable, exempt from further change, inaccessible to further control by anything that the future will bring us—and yet enshrined in our memory as something that once filled our experience as an immediate present. Will it never come back? Why can it not be with us a second time?

Undisturbed by our query, the flow of time goes on. Already our present is filled by other experiences which, at the earlier time, we could not completely anticipate. Though in part predictable, the present experience contains many unexpected and previously unknowable features. What was uncertain is now determined. Possibilities which we feared, or hoped for, have now become realities; others, which we never had thought of, have intervened. And even the familiar daily experiences, though highly predictable, reveal in their actual occurrences some specific characteristics that could not have been foreseen. What else awaits us in the future? Will there be a war, or some other political catastrophe? Shall we get the long-hoped-for salary raise? Will a letter arrive that tells us about the death of a friend whom we believed to be in good health? Or will a letter announce that some distant relative bequeathed a fortune to us? And what will the little things which we expect be like? Will the car start right away? Shall we get through the intersection before the traffic light turns red? What will Fred say when I tell him that Doris is going to marry John?

All these things are in the future. What is it, this future? Does it keep events in stock, so to speak, and distribute them according to a plan? Or do events grow from chance? Growing means becoming. What is Becoming? How can something unreal become real? And as soon as it is real, it slides into the past, only to become unreal again, leaving nothing but a shadow in our memory. The present is the only reality. While it slips away, we enter into a new present, thus always remaining in the eternal Now. What is time, if all we have of it is this Now, this one moment gliding with us through the current of events that flows from the unchangeable past to the unknowable future?

Questions of this kind reveal the highly emotional content associated with the experience of time. They tempt us to look for answers that satisfy emotions rather than clarify meanings. I do not wish to say that such questions are unreasonable. But the answers to them may look very different from what we expect; and we may even be unable to find the answers, unless we first revise the questions and make precise what, at this stage, is mere groping for meanings. Human thought processes do not follow the pattern of calculating machines, which have an answer to any question, provided the question is asked correctly. We cannot answer every correct question—but we can often answer questions which are not correctly asked, by first giving them a form in which they have meaning. Often the process of reformulating the question and giving the answer is the same process. Looking for answers, we discover new meanings and find out what it was that we were asking for.

This is the scientific approach. Do not expect answers before you have found clear meanings. But do not throw away unclear questions. Keep them on file until you have the means at the same time to clarify and to answer them. Often these means result from developments in other fields, which at first sight appear to have nothing to do with the question.

The history of philosophy offers many illustrations of this process of clarification of meanings. Thales of Miletus believed that water is the substance of which all things are made. Heraclitus argued that, instead, this mysterious substance was fire. But neither of them knew precisely what it means to say that a piece of matter is composed of several substances. Modern chemistry has made this meaning precise by its methods of chemical analysis and has shown that neither water nor fire is a chemical element. Another illustration is found in Plato's philosophy. Plato believed that geometrical relations are known through visions of ideas, a reminiscence of experiences which our souls had in a world beyond the heavens long before their terrestrial lives began. Modern mathematics has shown that the act of visualizing geometrical figures can be understood in a this- worldly way: it is a recollection of everyday experiences with objects of our environment. It is the meaning of the term "visualization" that was clarified in this answer to a question. And only with the modern answer did the question assume a distinct meaning. The inquiry into the nature of time has a similar history. It greatly puzzled the ancients, remained unsolved for two thousand years, and found an answer in developments of modern physics which were not directly concerned with the problem of time, but with that of causality. Before turning to these developments, it may be appropriate to examine more closely the conception of time contained within older philosophical systems, since they reveal the emotional reactions and formulate the logical puzzles which every one of us encounters in the experience of time.

Our emotional response to the flow of time is largely determined by the irresistibility of its passing away. The flow of time is not under our control. We cannot stop it; we cannot turn it back; we have the feeling of being carried away by it, helplessly, like a piece of lumber in the current of a river. We can know the past, but we cannot change it. Our activity can be directed toward the future only. But the future is incompletely known, and unexpected events may turn up which make our plans break down. It is true, the future may also have favorable turns in store. Yet we know that they are limited in number and that adjusting ourselves to what the future may bring cannot help us too much—there is only a limited stretch of time ahead of us, and the end of all this striving and responding to new situations is death. The coming of death is the inescapable result of the irreversible flow of time. If we could stop time, we could escape death—the fact that we cannot makes us ultimately impotent, makes us equals of the piece of lumber drifting in the river current. The fear of death is thus transformed into a fear of time, the flow of time appearing as the expression of superhuman forces from which there is no escape. The phrase "passing away", by means of which we evasively speak of death without using its name, reveals our emotional identification of time flow with death.

Dissatisfied emotion has frequently been projected into logic. In theories of the universe it often reappears in the guise of logical queries and pseudo-logical constructions. A philosopher argues that he has discovered a puzzle of Being which logic cannot solve—he might as well say that he has discovered a fact that arouses his emotional resistance. The fear of death has greatly influenced the logical analysis which philosophers have given of the problem of time. The belief that they had discovered paradoxes in the flow of time is called a "projection" in modern psychological terminology. It functions as a defense mechanism; the paradoxes are intended to discredit physical laws that have aroused deeply rooted emotional antagonism.

Religious philosophers have maintained that the happenings in time do not constitute the sum total of reality. They insist that there is another reality, a higher reality, which is exempt from time flow. Only the inferior reality of human experience is bound to time. The assumed superior reality, strangely enough, has been called eternal, which is a term referring to time. But in the language of these philosophers the term no longer pertains to permanent duration, but rather to something existing beyond time, not subject to time flow. Its opposite in the terminology of the church is secular, a term originally referring to the time span of a human life (in an extended meaning, of a century), but having assumed the meaning of something subject to time flow and thus something earthly, displaying the inferior nature of physical reality. The desire to survive death and to live eternally, in the sense of an unlimited time, a desire obviously incompatible with physical facts, has thus led to a conception in which eternal life is not life in time, but in a different reality. In order to escape the "passing away" with time, a timeless reality was invented.

Among the ancients, Parmenides and Plato developed such concepts of reality, though in different forms. Parmenides tells us that the higher reality does not come into being and does not pass out of being. "It is uncreated and indestructible; for it is complete, immovable, and without end. Nor was it ever, nor will it be; for now it is, all at once, a continuous one." And Plato explains that "time is the moving image of eternity". Here "eternity" does not mean "infinite time". It is supposed to denote a reality not controlled by time flow, which, however, is reflected, so to speak, in the river of time. The happenings in time are, at best, an inferior form of reality; for Parmenides, it seems, they are not real at all, but illusions.

Such philosophies are documents of emotional dissatisfaction. They make use of metaphors invented to appease the desire to escape the flow of time and to allay the fear of death. They cannot be brought into a logically consistent form. Yet, strangely enough, they are often presented as the results of logical analysis. The grounds offered for them are the alleged paradoxes of Becoming. Parmenides argues that if there were Becoming, a thing must grow from nothing into something, which he regards as logically impossible. And his successor in the Eleatic school, Zeno, has supplied us with a number of famous paradoxes which, he thought, demonstrate the impossibility of motion and the truth of Parmenides' conception of Being as timeless.

Zeno's paradoxes of motion have often been discussed. He argues that if motion is travel from one point to another, a flying arrow cannot move as long as it is at exactly one point. But how then can it get to the next point? Does it jump through a timeless interval? Obviously not. Therefore motion is impossible. Or consider a race between Achilles and a tortoise, in which the tortoise is given a head start. First Achilles has to reach the point where the tortoise started; but by then, the tortoise has moved to a farther point. Then Achilles has to reach that other point, by which time the tortoise again has reached a farther point; and so on, ad infinitum. Achilles would have to traverse an infinite number of nonzero distances before he could catch up with the tortoise; this he cannot do, and therefore he cannot overtake the tortoise.

Concerning the arrow paradox, we answer today that rest at one point and motion at one point can be distinguished. "Motion" is defined, more precisely speaking, as "travel from one point to another in a finite and nonvanishing stretch of time"; likewise, "rest" is defined as "absence of travel from one point to another in a finite and non-vanishing stretch of time". The term "rest at one point at one moment" is not defined by the preceding definitions. In order to define it, we define "velocity" by a limiting process of the kind used for a differential quotient; then "rest at one point" is defined as the value zero of the velocity. This logical procedure leads to the conclusion that the flying arrow, at each point, possesses a velocity greater than zero and therefore is not at rest. Furthermore, it is not permissible to ask how the arrow can get to the next point, because in a continuum there is no next point. Whereas for every integer there exists a next integer, it is different with a continuum of points: between any two points there is another point. Concerning the other paradox, we argue that Achilles can catch up with the tortoise because an infinite number of nonvanishing distances converging to zero can have a finite sum and can be traversed in a finite time.

These answers, in order to be given in all detail, require a theory of infinity and of limiting processes which was not elaborated until the nineteenth century. In the history of logic and mathematics, therefore, Zeno's paradoxes occupy an important place; they have drawn attention to the fact that the logical theory of the ordered totality of points on a line—the continuum—cannot be given unless the assumption of certain simple regularities displayed by the series of integers is abandoned. In the course of such investigations, mathematicians have discovered that the concept of infinity is capable of a logically consistent treatment, that the infinity of points on a line differs from that of the integers, and that Zeno's paradoxes are not restricted to temporal flow, since they can likewise be formulated and solved for a purely spatial continuum.

What makes Zeno's paradoxes psychologically interesting, however, is the fact that they were discovered, not as part of the pursuit of a mathematical theory of the continuum, but through a process of rationalization; that they were found because the Eleatic school wanted to prove the unreality of time. Had Zeno not constructed his paradoxes under the spell of this preoccupation with a "metaphysical" aim, he would have come to a different solution. He would have argued that, since arrows do fly and a fast runner does overtake a tortoise, there must be something wrong with his conception of logic, but not with physical reality. But he did not want to come to this conclusion. He wanted to show that change and Becoming are illusory, and he wanted to show that Reality has a timeless existence exempt from the shortcomings of time-controlled human experience—from passing away and from death.

The time theory of Parmenides has become the historical symbol of a negative emotional attitude toward the flow of time. But the actual structure of time is compatible with different emotive reactions; and there has always existed a positive attitude toward time flow, an affirmative emotional response to change and Becoming, for which the future is an inexhaustible source of new experiences and a challenge to our abilities to make the best of emerging opportunities. The historical symbol of this positive emotional attitude toward time flow was created in the philosophy of Parmenides' contemporary and opponent Heraclitus.

"All things are in flux" is the formula in which Heraclitus' philosophy has been summed up. Becoming is for him the very essence of life. "The sun is new every day"—this means, for him, that it is good that every day produces something new. We need not cling to what has been; we can get along very well in a world of continuous change. "You cannot step twice into the same river, for fresh waters are ever flowing in upon you." This seeming paradox is not as profound as Heraclitus believed, for we can very well call the river the same even though its waters change. But Heraclitus' aphorism draws our attention to the logical nature of the physical thing as a series of different states in time; it is not necessary for physical identity that these states be exactly alike. A human being is the same, identical person all the time, although the body grows and changes its chemical building blocks. A physics of things does not require a denial of time flow. Common sense, as well as science, agrees with this conception of Heraclitus.


Excerpted from THE DIRECTION OF TIME by Reichenbach Hans, Maria Reichenbach. Copyright © 1984 Maria Reichenbach. Excerpted by permission of Dover Publications, Inc..
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Meet the Author

Hans Reichenbach was professor of philosophy at UCLA and one of the leading thinkers in the logical empiricist school of philosophy. Maria Reichenbach translated and edited many of her husband's works first written in German. Hilary Putnam, Professor of Philosophy at Harvard University, is author of Meaning and Moral Sciences (1978), and, most recently, Realism with a Human Face (1990).

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The Direction of Time 4 out of 5 based on 0 ratings. 1 reviews.
Guest More than 1 year ago
It is a beautiful but exteremely difficult book. It covers the concept of time and its direction concept from the beginning up to current thinking. Author, being one of the founding fathers of the Philosophical Quantum Physics first introduces a good understanding of Thermodynamics and Statistical Physics and continues to define the order of events to lead into statistical definition of Arrow of Time. A lot of difficult concepts from Classical physics, Probability theory, relativity theory and Mathematical Logic as well as a good understanding of quantum physics is assumed to be in the bag of the reader. After all this book is not a Popular science book. Although the author claims that knowledge of derivations of the formulas used are not critical to understand this study yet time and time the language and logic becames exteremely difficult to follow. This is a must read book in this subject, may be many times over after increasing the understanding of other subjects that are only a tool in this book.