No. 43, October 16, 2001

Book Review by Soshichi Uchii: The Discovery of Dynamics by Julian Barbour

Editor: Soshichi Uchii

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The Discovery of Dynamics: A study from a Machian point of view of the discovery and the structure of dynamical theories by Julian Barbour, Oxford University Press, 2001

This book is essentially a paperback reprint of Barbour's first book, Absolute or Relative Motion? Vol. 1, published from Cambridge University Press, 1989. A new preface is added, where the author responds to the major reviews of the preceding book, and explains why the Volume 2 (which has been long awaited by many, including this reviewer) has not appeared yet. In the meantime, Barbour has published a number of important technical results (reconstruction of classical and relativistic dynamics in terms of relational ideas), edited an important book on Mach's Principle, and published another book, The End of Time, which was reviewed in the last issue of this Newsletter. Since The Discovery of Dynamics is valuable for any students of the philosophy of space and time, I should like to remind the reader of its merits, on this occasion.

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1. This book is not a mere history of dynamics

Since the author, Julian Barbour, is primarily a theoretical physicist, many historians of science may question the manner of Barbour's treatment of historical materials, ranging from Aristotle to Mach and Einstein. In fact, Barbour quotes (in the new preface) Eric Aiton's severe criticism: "Everything is judged in relation to what the author regards as the correct theory: that is, the explanation accepted today ... The idea of a linear progression towards the modern world view ... has long been abandoned by historians of science" (viii). This may be true to some extent, but I think the word "everything" is clearly an exaggeration, based on Aiton's prejudice or "conceit" as a historian. Historians often denounce "Whig history", but they often use a "double-standard" or ambiguous standard, something like "mine is non-Whiggish but so-and-so's is Whiggish or ideological", the other party saying exactly the same!

Such quibbles aside, I agree with Barbour's judgment that "There are criteria of good science" (ix), and we are interested in "how such good science emerged". If some say that taking this perspective is "Whiggish", I would say it's no sin. Consider the discipline of history itself. Many say "Whig history is a bad history"; so this implies they have the distinction between good history and bad history. And if they want to write "the history of good history", they have to commit themselves to the criteria of good history. Isn't the situation exactly similar to the history of science?

Be that as it may, we have to notice the subtitle of Barbour's book: it clearly announces that this book is written from a Machian point of view, and, as I see it, that's what makes this book valuable. Of course, some historians may complain that such a philosophically-oriented history is "uninteresting"; but to us, philosophers of science and philosophically minded historians, their unphilosophical works are uninteresting, and so let them live and let us live also! Although Barbour relies on many secondary sources as well as on primary sources, it is quite amazing that he covered such a wide span of history, ranging from Aristotle, Ptolemy, through the founders of modern astronomy and physics, to the 19th century figures such as Carl Neumann, Lutwig Lange, and Mach. And all chapters (there are 12) are united by the common perspective, i.e., the Machian point of view. So it is important to grasp the significance of this perspective. Barbour has a strong philosophical motivation from the beginning, and he has made it clear at the start.

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2. Newton, Mach, and Einstein

Since Barbour is one of the leading Machians of our day, and since one of the highlights of absolute-relative debates is in Mach's criticism of Newton, Barbour's Introduction naturally begins with this story:

Confronted with a restless, shifting universe that stretched seemingly to infinity but also with the undoubted existence of inertial motion, Newton identified absolute space and time as the ultimate framework of all motion. ... In the decades immediately following the publication of the Principia in 1687, Newton's concepts of absolute space and time were severely criticized, above all by Huygens, Leibniz, and Berkeley. ...

But Huygens died soon and neither Leibniz nor Berkeley could produce any sort of theory to rival Newton, and their objections were gradually forgotten, until they were rediscovered in the second half of the nineteenth century by Ernst Mach. ... He suggested that inertial motion here on the earth and in the solar system is causally determined in accordance with some quite definite but as yet unknown law by the totality of the matter in the universe. (1-2)

This last idea is usually called "Mach's Principle"; the word itself was coined by Einstein, and many physicists follow Einstein's formulation (ambiguous and unstable, however; see Barbour and Pfister 1995, Hoefer's article). But Barbour argues that Einstein misunderstood Mach, and hence he thinks that we have to examine the historical roots of dynamics, the notion of inertia in view, in particular. Thus he writes:

...careful reading of Mach's book and Einstein's papers written while he was working on the creation of general relativity led me to a surprising conclusion: that although Einstein professed great admiration for Mach and claimed to be intent on solving the problem of inertia as laid bare by Mach, he did in fact have a significantly different understanding---one could go so far as to call it a misunderstanding---of the problem. Above all, Einstein appeared to confuse two quite distinct uses of the word inertia. (5)

What are these two distinct uses? When Mach raised the question of inertia, he was exclusively concerned with Newton's First Law, the Law of Inertia. This is the first sense of inertia. But Newton had another use of inertia, in his Second Law, i.e. the concept of inertial mass, or inertial force or resistance. And Mach proposed an operational definition of inertial mass, in order to replace Newton's, but Mach regarded the notion of inertial mass entirely unproblematic, in sharp contrast to the Law of Inertia.

This discovery led Barbour to his own approach: to go back to first principles in the Machian problem of inertia, and to reconstruct dynamics in terms of relative distances and relative velocities (and eventually, even dispensing with distances! This work is still developing and going on; see the last section of the new preface). We have to provide a dynamical explanation for the law of inertia, or its equivalents in a newer theory, such as general relativity. As regards "the Machian problem" in general (according to Barbour), the reader is referred to this.

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3. The origins of the two senses of inertia

But the reader may feel this question: then why does he need a historical study for such a theoretical or philosophical research? Instead of answering this question in general terms, it is more illuminating to illustrate the point in terms of specific examples. So let us consider the two senses of inertia just mentioned; where do they come from? Of course we have to examine Newton's Principia; but is that enough? No, we have to go back further, since the law of inertia comes from Galileo, and also from Descartes. But who invented the word "inertia" in the first place? Historians say it's Kepler; but in what sense did Kepler use "inertia"? Answers to these questions can be found in chapters 6-8. In a word, Einstein's confusion or misunderstanding has a deeper root than you may imagine at first sight. Thus you may begin to understand Barbour's point. He is not a conventional (or standard) physicist, hired by some academic institution; he does not make his own living out of physical research but out of other means (translating Russian journals, living in a farm); because he wants to do what he wants, to his own satisfaction, he can spend enough time for historical research as well as for theoretical research.

Getting back to inertia, Barbour's description goes as follows:

Of much more relevance for the development of the fundamental concepts of dynamics was Kepler's introduction of the concept of inertia as the quantitative measure of a body's tendency to remain at rest. Out of it, following a very significant transmutation by Newton, the modern concept of the inertial mass of a body arose. (325-6)

Kepler intended something like "resistance to motion"; but when Newton adopted the same word, "inertia means resistance to acceleration, not resistance to motion itself" (329). Later, in chapter 12, Barbour comes back to inertia and says as follows:

This is the point at which to make an important remark. It relates to the two different uses made of the word inertia. There has in fact been a subtle and potentially confusing shift in the commonly accepted meaning of this word. Both Kepler and Newton used the word for the capacity of matter to resist changes in its state. With Kepler this is quite explicit: he merely took over the Latin word for laziness. For Kepler it was quite clearly what we now call a scalar quantity, a number characterizing an intrinsic property of matter. When Newton first introduced the word into his own vocabulary, in De gravitatione, he followed Kepler very closely. He said: 'Inertia is force within a body, lest its state should be easily changed by an external exciting force.' Note that inertia is a resistance to change of state. What state is not specified, though it is obvious Newton is thinking in terms of change from one state of motion to another rather than the simple Keplerian idea of the transition from rest to motion. The point which needs to be made is that the concept of resistance to change of state is by no means the same thing as the state. Indeed the transition from Kepler to Newton illustrates this point perfectly: the concept of laziness survived but the state (or rather states) changed. A priori, there is absolutely no reason why the states between which a resistance barrier must be overcome are states of uniform rectilinear motion. (678-9)

In a word, Newton's notion of inertia as a power of resistance comes from Kepler, but Newton related it to his Second Law (force is proportional to mass and acceleration, i.e. change of velocity). However, as such, there is no connection between inertia and the state of motion such as uniform rectilinear motion. "There is no suggestion at all in the Principia that the word inertia should be used to describe the state" (679). However,

Long after Newton was dead, the connotation of the word inertia was to a considerable degree transferred from the resistance to the state. What Newton called Lex Prima, the First Law, and stated in the form

Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it

became known as the Law of Inertia. (679)

Thus the ambiguity of inertia became prevalent. This is Barbour's diagnosis. However, I think Newton himself was responsible for this to some extent, at least, because his third definition (definition of vis insita or vis inertiae) explicitly refers to Lex Prima.

The vis insita, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, continues in its present state, whether it be of rest, or of moving uniformly forwards in a right line.

Barbour himself says that "its content does not differ much from the statement of his First Law" (568). Having read this definition first, the reader will naturally associate "inertia" with the First Law, even though the latter does not contain the word inertia. But this point does not detract anything from Barbour's analysis; it merely suggests that association of ideas could become so strong that even specialists may become a victim of this sort of ambiguity. I myself have been very uncomfortable with Einstein's use of such words as "relativity of inertia" (see, e.g., Jammer 2000, 147-150), which seems to have magnified the confusion.

As regards the origin of the First Law, Barbour's description and analysis are detailed and illuminating. Any students of physics who take this law as "a matter of course" should realize how important a role this law played in the history of dynamics (read chapters 7-10; and for a glimpse of this, see Inertia).

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4. The Significance of Mach

Due to the limited space, I have to skip almost all other subjects in Barbour's thick book (746 pages!). But we cannot skip the final chapter 12, where the significant conceptual clarification of Newtonian dynamics in the 19th century is treated, and where Barbour comes back to Mach again.

The difficulties of absolute space and time were not the only difficulties of the Newtonian dynamics. Since Barbour has completed his graduate studies in Munich, he is well acquainted with the German literature on dynamics, now obsolete and disregarded in the English-speaking world (but on the other hand, this reviewer was somehow puzzled by the absence of any reference to Karl Pearson's work on the foundations of dynamics, which is similar to Mach's view). Thus he mentions "the significant clarification achieved in the second half of the nineteenth century", by Carl Neumann, Lutwig Lange, and Ernst Mach. Why are their works valuable?

First, in its own right, in that it provided a coherent and intellectually satisfying account of how all the essential features of dynamics can be identified empirically in phenomena. ... Second, by identifying very clearly the basic elements from which empirical dynamics can be constructed, it simultaneously showed that there is nothing a priori or sacrosanct about these elements. It showed that these elements depend on nature and not metaphysical necessity, as Newton in part believed, and that their selection is suggested ultimately by observation and could therefore be modified in the light of further observation. ... Third, the empirical definitions of inertial system by Lange, of equality of time intervals by Neumann, and of mass by Mach provided paradigms of the operational definition of the basic concepts of dynamics in terms of observable objects and processes. (645-6)

Among the contemporary philosophers of science, it seems that operationism and its siblings are now out of fashion, and various sort of "realism" (belief in the existence of theoretical entities, theoretical laws, etc.; and in the spacetime philosophy, it takes the form of "substanvalism" or "absolutism" of spacetime) is more popular; and the Machian view as they understand is often denounced on account of its affinity to the "sense-datum theory", of "instrumentalism", and of "phenomenalism". But do they really try to understand what Mach was after? Do we pay enough attention to the context of their inquiry? We've got to listen to what Barbour says, as a practicing physicist.

Thus, it is quite instructive to know the point of Neumann's introduction of the strange concept of Body Alpha. Neumann says "there must be a special body in the universe which serves us as the basis of our judgment, with respect to which all motions are to be referred" (648), and this body is Body Alpha. This statement is not an "April Fool"; Neumann tried to draw our attention to an important problem, in terms of Body Alpha. His point was, according to Barbour, this:

It is worth spelling out what exactly happens in the Neumann process. It is what astronomers call materialization of the frame of reference. The Newtonian concept of absolute space is of no value whatsoever unless the absolute frame of reference can be explicitly linked to observable matter; this linking is what is meant by materialization. (652)

Next, Lange coined the word inertial system, now familiar to any student of physics (I will omit the explanation of the manner Lange came to this notion; see 654-8). But what was the point of introducing this word? Many figures before Newton recognized what we now call inertial motion. Galileo first recognized this, in his argument of a ball falling from the top of the mast of a moving ship, in his treatment of a projectile, etc., on the earth; Huygens, accepting Descarte's version of the law of inertia, extended it to motion outside of the earth, and hence Barbour called it a "cosmic drift" (477).

Newton made a valiant effort to define and explain this cosmic drift in terms of transcendental, or metaphysical, concepts (absolute space and time). Neumann and Lange rejected this approach as being conceptually unsatisfying and experimentally valueless. Instead of attempting to put a foundation under the cosmic drift, they made it the foundation. For the important point is that the reference system, both in its spatial and its temporal part, is, in principle at least, constructed explicitly from material particles that are allowed to follow the cosmic drift. ... In our intuition we conceive that space and time exist, providing the framework within which motion takes place. Space and time define motion. But the truth is the other way round. For in the Neumann-Lange scheme the space and time coordinates are explicitly constructed from the motions. It is on them that the universal scaffolding of space and time are erected. (659)

Finally, comes Mach. He is known for his criticism of Newton's definition of mass, as well as for his criticism of absolute space and time. Newton's Principia begins with this definition:

The quantity of matter is the measure of the same, arising from its density and bulk conjointly.

Dissatisfied by this definition, which may well become circular depending on the meaning of "density", Mach tried to replace it by his own.

More clearly than any of his contemporaries, Mach realized that any successfully functioning scientific theory or discipline must in the last resort rest on experimentally observable phenomena. For otherwise it could not make meaningful and nontrivial statements about observed phenomena. In particular, most of the key concepts in science are those which permit scientists to associate definite numbers with the concepts. Examination of ways in which these numbers are actually determined would then give one a clue to the phenomena which provide the ultimate justification for the concepts themselves. ... Mach developed this technique into a systematic art---the art of the operational definition of the fundamental concepts of physics. (684-5)

Mach did not have any ambition to begin from the foundations of geometry.

Instead, he accepted distance measurement as given and also, for purposes of the clarification of the concepts of mass and force, that clocks exist and that the distant stars define a frame of reference with respect to which all motions are to be defined. Then the first observational fact on which dynamics rests is the law of inertia: In the frame of reference defined for practical purposes by the stars, bodies are usually observed to travel in straight lines with uniform speed. (658)

On this basis, we can obtain the velocity of each particle, and then can go to accelerations. Unlike Newton, Mach insists that the observable accelerations should come first, since otherwise force cannot be known. Thus, in a nutshell, by observing the change of velocity of each particle (interacting with others), we can obtain the ratio of the change of one particle to that of another. Mach's idea is that given the set of such ratios for the particles in question, we can introduce the mass concept; and if we make the mass of a chosen particle the unit mass by definition, we can obtain definite values (see Mach's Principle). Mach obtained more: the Third Law of Motion (action and reaction) is obtained at the same time by the preceding operational definition of mass; for, "Bodies normally travel on straight lines relative to the stars but, under suitable conditions, two or more bodies can mutually accelerate each other" (685), and this action-reaction is what makes possible the definition of mass.

In this manner, we can go on to define force; but what is the point of all this?

What is then the essence of dynamics? It is in the recognition of universal correlations in the observed behaviour of bodies. The basis of it all, the ground on which the correlations are observed, is the possibility of measuring distances and times and the existence of bodies that can be recognized at different times ... (687)

Thus emerges the essential Machian vision: everything in the universe is interacting with each other, and the basis of any dynamical law must be sought in such interactions; the law of inertia is no exception, hence Mach's Principle, adapted to Mach's own idea. As Barbour pointed out at the beginning, Mach's idea is not obsolete; Barbour's message is that it is an essential part of good science. That's why Barbour spent so much time for completing this thick book. I recommend this book very warmly to any student of the philosophy of physics, and of space and time.

References

Barbour, Julian (1989) Absolute or Relative Motion? Vol. 1, Cambridge University Press.

Barbour, Julian (2000) The End of Time, Phoenix.

Barbour, J. and Pfister, H., eds. (1995) Mach's Principle (Einstein Studies 6), Birkhaeuser.

Jammer, Max (2000) Concepts of Mass in Contemporary Physics and Philosophy, Princeton University Press.

Pearson, Karl (1892) The Grammar of Science, Adam and Charles Black (1st ed., 1892; 2nd ed., 1900; 3rd ed., 1911).

October 16, 2001; corrected October 18. (c) Soshichi Uchii

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