Principle of Relativity (Barnes & Noble Library of Essential Reading)

By Alfred North Whitehead and Amit Hagar

Interweaving science and metaphysics, The Principle of Relativity presents what is commonly acknowledged as the most interesting alternative to Einsteins general theory of relativity. The great mathematician and philosopher Alfred North Whitehead furthermore spells out his view of geometry, space-time, and Nature in this intriguing book. Originally published in 1922, the book offers a different paradigm from Einsteins, elegant and simple in its mathematical formulation with its own philosophical background and agenda. Few other books exemplify as it does the intricate inter-relations between physics and philosophy. Scholars from both domains shall find here much to chew on, as well as the layman who is interested in the history of ideas of the twentieth century.

• Language: English
• Publisher: Barnes & Noble
• Release date: Sep 1, 2009
• ISBN: 9781411431072

Book preview

INTRODUCTION

INTERWEAVING science and metaphysics, The Principle of Relativity presents what is commonly acknowledged as the most interesting alternative to Einstein’s general theory of relativity (GTR). The great mathematician and philosopher Alfred North Whitehead furthermore spells out his view of geometry, spacetime, and Nature in this intriguing book. Originally published in 1922, the book offers a different paradigm from Einstein’s, elegant and simple in its mathematical formulation with its own philosophical background and agenda. Few other books exemplify as it does the intricate inter-relations between physics and philosophy. Scholars from both domains shall find here much to chew on, as well as the layman who is interested in the history of ideas of the twentieth century.

The youngest of four children of an Anglican vicar, Whitehead (1861-1947)—one of the most interesting and imaginative scholars of our era—showed no sign of the genius that he was later in life. As a scholar, his academic interests spanned mathematics, science, and metaphysics, all of which were thoroughly and carefully treated by him with a unique style. Guided by the intellectual honesty and the personal touch that is so characteristic of his writings, only few follow Whitehead in the rarely taken path that combines physics and philosophy. His ingenuity and creativity shall remain an inspiration to generations of scholars.

After winning two scholarships for studying mathematics in Trinity College, Cambridge, Whitehead was offered a fellowship as an assistant lecturer there. Despite a poor publication record he was soon promoted and became a lecturer. The shift of emphasis in his career, from teaching to publishing, came with his marriage in late 1890. It was also marked by his decision to renounce Christianity. He himself stated that the biggest factor in his becoming an agnostic was the rapid developments in science; particularly his view that Newton’s physics was false. It may seem surprising to many that the correctness of Newton’s physics could be a major factor in deciding anyone’s religious views. However, one has to understand the complex person that Whitehead was and, in particular, the interest which he was developing in philosophy and metaphysics.

Whitehead left Cambridge in 1910 and went to London, and then to Harvard, where he was the chair of the philosophy department until his retirement. Apart from his metaphysics, he is perhaps best known for his collaboration with Bertrand Russell, who came to Cambridge in 1890 as an undergraduate and was immediately spotted by the talented lecturer. A decade later, the student and the master began collaborating on one of the most ambitious projects in the philosophy of mathematics, Principia Mathematica, which was an attempt to supply mathematics with rigorous logical foundations. When the first volume of this monumental work was finished, Whitehead and Russell began to go their separate ways. Perhaps inevitably, Russell’s anti-war activities during World War I, in which Whitehead lost his youngest son, also led to something of a split between the two men. Nevertheless, they remained on relatively good terms for the rest of their lives. It was then that Whitehead turned his attention to the philosophy of science. This interest arose out of the attempt to explain the relation of formal mathematical theories in physics to their basis in experience and was sparked by the revolution brought on by Einstein’s GTR, to which he had developed an alternative.

Whitehead’s theory of gravity has been called a thorn in Einstein’s side. Since it agrees with GTR in its prediction for all the classical tests, the real issues between Whitehead and Einstein are not physical but philosophical. The theory is closely connected with Whitehead’s philosophy of nature and with his metaphysics, which are spelled out in his The Concept of Nature (1920), Science and the Modern World (1925), and Process and Reality (1928). Its popular debut was in The London Times Educational Supplement in January 1920, shortly after Arthur Eddington, the famous British astrophysicist, verified GTR’s predictions about the bending of light in the vicinity of the sun during the 1919 eclipse. Eddington himself proved a few years later that Whitehead’s alternative has the same solution as Einstein’s in the special case of the stationary gravitational field due to a single mass point. This meant that it was indeed empirically equivalent to GTR, at least with respect to the standard tests that GTR has passed so far, e.g., the perihelion precession of Mercury and the bending of light rays.

Later on in the 1920s, the comparison between the two rival theories was conducted mainly on the level of conceptual analysis. With the shift of interest among physicists to the realms of quantum mechanics and nuclear physics during the 1930s and the 1940s, Whitehead, by then regarded as a metaphysician, was ignored. The re-evaluation of Whitehead’s ideas began in the 1950s due to an Irish physicist, Synge, who esteemed Whitehead’s theory for its elegance and originality. Setting aside Whitehead’s philosophical agenda, Synge reconstructed Whitehead’s mathematical formulae in Einstein’s terminology to make them accessible to contemporary physicists. In the 1960s, there was a revival of empirical tests for gravitational theories, especially due to the rapid progress in technology and astronomy. In 1965, a series of experiments were conducted measuring the galactic red shift (an effect similar to the Doppler effect due to the expansion of the universe). The accuracy of this experiment was about twenty times higher than previous astronomical observations and was proven to be a strong support to Einstein’s GTR. Whitehead’s theory in its original form predicted a gravitational red shift slightly different than that of Einstein, but qualitatively the two rival theories were still empirically equivalent.

It was only in the early 1970s when the American astrophysicist Clifford M. Will claimed to have shown that Whitehead’s theory should be in conflict with experimental data with respect to certain geophysical effects. Yet also here it was pointed out that the alleged refutation of Whitehead’s theory on geophysical grounds relied on a certain astronomical assumption that was probably false. This loophole did not necessarily resurrect Whitehead’s theory, but it did imply that there is interesting work yet to be done.

Einstein presented his special theory of relativity as stemming from two phenomenological principles: the principle of relativity and the principle of the constancy of the velocity of light in vacuum. Based on these two principles one can, as Minkowski did, construct spacetime as a four-dimensional manifold equipped with a Minkowskian (flat) metric and extract the Lorentz transformations between different inertial reference frames. To these principles Einstein added the equivalence principle between gravitation and inertia and generalized his special theory to the case of non-inertial frames. The consequences of Einstein’s GTR were far-reaching: Physical objects such as electromagnetic and matter fields were now treated as geometrical objects, and the geometry of spacetime was fixed by the distribution of matter in it. With the absence of matter one should expect spacetime to be flat, or Euclidean; with its presence—curved, or non-Euclidean.

Whitehead’s theory differs from Einstein’s in its physical content as well as in its philosophical background. Whitehead rejected Einstein’s equivalence principle and proposed a different reconstruction of the Minkowskian four-dimensional manifold based on weaker principles than Einstein’s. His main objection was to the idea that spacetime can change its geometry contingent upon the presence of matter. To Whitehead, who believed in the uniformity of Nature, the idea of variable curvature implied the precedence of matter over spacetime, and as such had no room in the metaphysics he was developing. As he stresses in the preface to The Principle of Relativity, it is the uniformity which is crucial to his outlook, and not the specific geometry of spacetime. The former is a necessary condition—a guiding principle for doing physics, indeed for conducting science in general —while the latter is open to empirical revisions: Spacetime could possess either flat or curved geometry, according to Whitehead, as long as it is uniform.

Whitehead’s metaphysics, also known as Process Philosophy, is as original as his physics. In its core are the ideas of the priority of events over objects and the precedence of becoming over being. Material objects, in this view, are not subjects of predicates or bearers of properties, but adjectives of events; they do not affect spacetime structure, rather they are affected by it and merely represent it. Relying on this priority, and combining it with an epistemological argument, Whitehead deduced the idea that Nature must be uniform, and that all events are interconnected through a relation of relatedness.

This metaphysics resulted in an alternative theory of gravitation that describes gravity as a retarded action-at-a-distance force and in a spacetime metric that describes the uniform dynamic relatedness of events in process. Whitehead’s metric, as Jonathan Bain, a contemporary American philosopher, nicely puts it in a recent article, . . .is absolute insofar as this dynamic relatedness is uniform and exists in causal independence of matter fields in order for knowledge and induction to be possible. . . , and . . .is dynamic insofar as it describes not a fixed eternally existing set of substantival spacetime points, but rather an ever-changing flux of interrelated events. The title of the book is thus a misnomer: It should have been The Principle of Relatedness.

Thought-provoking and genuine, Whitehead’s The Principle of Relativity stands as one of the classics in the philosophy of spacetime physics, and the ideas it propounds continue to attract and inflame physicists and philosophers even today. Referring as he was to Einstein, Whitehead himself said in the book that the worst homage we can pay to genius is to accept uncritically formulations of truths which we owe to it. This kind of spirit applies in the case of Whitehead as well.

Amit Hagar is a philosopher of physics with a Ph.D. from the University of British Columbia, Vancouver. His area of specialization is the conceptual foundations of modern physics, especially in the domains of statistical and quantum mechanics.

PREFACE

THE present work is an exposition of an alternative rendering of the theory of relativity. It takes its rise from that ‘awakening from dogmatic slumber’—to use Kant’s phrase—which we owe to Einstein and Minkowski. But it is not an attempt to expound either Einstein’s earlier or his later theory. The metrical formulae finally arrived at are those of the earlier theory, but the meanings ascribed to the algebraic symbols are entirely different. As the result of a consideration of the character of our knowledge in general, and of our knowledge of nature in particular, undertaken in Part I of this book and in my two previous works¹ on this subject, I deduce that our experience requires and exhibits a basis of uniformity, and that in the case of nature this basis exhibits itself as the uniformity of spatio-temporal relations. This conclusion entirely cuts away the casual heterogeneity of these relations which is the essential of Einstein’s later theory. It is this uniformity which is essential to my outlook, and not the Euclidean geometry which I adopt as lending itself to the simplest exposition of the facts of nature. I should be very willing to believe that each permanent space is either uniformly elliptic or uniformly hyperbolic, if any observations are more simply explained by such a hypothesis.

It is inherent in my theory to maintain the old division between physics and geometry. Physics is the science of the contingent relations of nature and geometry expresses its uniform relatedness.

The book is divided into three parts. Part I is concerned with general principles and may roughly be described as mainly philosophical in character. Part II is devoted to the physical applications and deals with the particular results deducible from the formulae assumed for the gravitational and electromagnetic fields. In relation to the spectral