The Principle of Relativity with Applications to Physical Science

Alfred North Whitehead

• Publisher: Dover Publications
• Year: 2012
• ISBN:
  9780486174198
• Topic: Physical Sciences
• Subtopic: Relativity in Physics

An exposition of an alternative rendering of the theory of relativity, this volume is the work of the distinguished English mathematician and philosopher, Alfred North Whitehead. Suitable for upper-level undergraduates and graduate students, its three-part treatment begins with an overview of general principles that may be described as mainly philosophical in character. Part II is devoted to physical applications and chiefly concerns the particular results deducible from the formulas assumed for the gravitation and electromagnetic fields. The final part consists of an exposition of the elementary theory of tensors.
The author notes that the text's order proceeds naturally from general principles to particular applications, concluding with a general exposition of the mathematical theory, special examples of which have occurred in the discussion of the applications. Physicists,
Whitehead suggests, may prefer to start with Part II, referring back to a few formulas mentioned at the end of Part I, and mathematicians may start with Part III. The whole evidence, he adds, requires a consideration of all three parts.

PART I

GENERAL PRINCIPLES

CHAPTER I

PREFATORY EXPLANATIONS

THE doctrine of relativity affects every branch of natural science, not excluding the biological sciences. In general, however, this impact of the new doctrine on the older sciences lies in the future and will disclose itself in ways not yet apparent. Relativity, in the form of novel formulae relating time and space, first developed in connection with electromagnetism, including light phenomena. Einstein then proceeded to show its bearing on the formulae for gravitation. It so happens therefore that owing to the circumstances of its origin a very general doctrine is linked with two special applications.

In this procedure science is evolving according to its usual mode. In that atmosphere of thought doctrines are valued for their utility as instruments of research. Only one question is asked: Has the doctrine a precise application to a variety of particular circumstances so as to determine the exact phenomena which should be then observed? In the comparative absence of these applications beauty, generality, or even truth, will not save a doctrine from neglect in scientific thought. With them, it will be absorbed.

Accordingly a new scientific outlook clings to those fields where its first applications are to be found. They are its title deeds for consideration. But in testing its truth, if the theory have the width and depth which marks a fundamental reorganisation, we cannot wisely confine ourselves solely to the consideration of a few happy applications. The history of science is strewn with the happy applications of discarded theories. There are two gauges through which every theory must pass. There is the broad gauge which tests its consonance with the general character of our direct experience, and there is the narrow gauge which is that mentioned above as being the habitual working gauge of science. These reflections have been suggested by the advice received from two distinguished persons to whom at different times I had explained the scheme of this book. The philosopher advised me to omit the mathematics, and the mathematician urged the cutting out of the philosophy. At the moment I was persuaded: it certainly is a nuisance for philosophers to be worried with applied mathematics, and for mathematicians to be saddled with philosophy. But further reflection has made me retain my original plan. The difficulty is inherent in the subject matter.

To expect to reorganise our ideas of Time, Space, and Measurement without some discussion which must be ranked as philosophical is to neglect the teaching of history and the inherent probabilities of the subject. On the other hand no reorganisation of these ideas can command confidence unless it supplies science with added power in the analysis of phenomena. The evidence is two-fold, and is fatally weakened if the two parts are disjoined.

At the same time it is well to understand the limitations to the meaning of ‘philosophy’ in this connection. It has nothing to do with ethics or theology or the theory of aesthetics. It is solely engaged in determining the most general conceptions which apply to things observed by the senses. Accordingly it is not even metaphysics: it should be called pan-physics. Its task is to formulate those principles of science which are employed equally in every branch of natural science. Sir J. J. Thomson, reviewing in Nature⁴ Poynting’s Collected Papers, has quoted a statement taken from one of Poynting’s addresses:

‘I have no doubt whatever that our ultimate aim must be to describe the sensible in terms of the sensible.’

Adherence to this aphorism, sanctioned by the authority of two great English physicists, is the keynote of everything in the following chapters. The philosophy of science is the endeavour to formulate the most general characters of things observed. These sought-for characters are to be no fancy characters of a fairy tale enacted behind the scenes. They must be observed characters of things observed. Nature is what is observed, and the ether is an observed character of things observed. Thus the philosophy of science only differs from any of the special natural sciences by the fact that it is natural science at the stage before it is convenient to split it up into its various branches. This philosophy exists because there is something to be said before we commence the process of differentiation. It is true that in human thought the particular precedes the general. Accordingly the philosophy will not advance until the branches of science have made independent progress. Philosophy then appears as a criticism and a corrective, and—what is now to the purpose—as an additional source of evidence in times of fundamental reorganisation.

This assignment of the role of philosophy is borne out by history. It is not true that science has advanced in disregard of any general discussion of the character of the universe. The scientists of the Renaissance and their immediate successors of the seventeenth century, to whom we owe our traditional concepts, inherited from Plato, Aristotle and the medieval scholastics. It is true that the New Learning reacted violently against the schoolmen who were their immediate predecessors; but, like the Israelites when they fled from Egypt, they borrowed their valuables—and in this case the valuables were certain root-presuppositions respecting space, time, matter, predicate and subject, and logic in general. It is legitimate (as a practical counsel in the management of a short life) to abstain from the criticism of scientific foundations so long as the superstructure ‘works.’ But to neglect philosophy when engaged in the re-formation of ideas is to assume the absolute correctness of the chance philosophic prejudices imbibed from a nurse or a schoolmaster or current modes of expression. It is to enact the part of those who thank Providence that they have been saved from the perplexities of religious enquiry by the happiness of birth in the true faith. The truth is that your available concepts depend upon your philosophy. An examination of the writings of John Stuart Mill and his immediate successors on the procedure of science—writings of the highest excellence within their limitations—will show that they are exclusively considering the procedure of science in the framing of laws with the employment of given concepts. If this limitation be admitted, the conclusion at once follows that philosophy is useless in the progress of science. But when once you tamper with your basic concepts, philosophy is merely the marshalling of one main source of evidence, and cannot be neglected.

But when all has been said respecting the importance of philosophy for the discovery of scientific truth, the narrow-gauged pragmatic test will remain the final arbiter. Accordingly I now proceed to a summary account of the general doctrine either implicit or explicit in the following pages or in my two previous books⁵ on this subject, and to detail the facts of experience which receive their explanation from it or should be observed if it be true.

A relativistic view of time is adopted so that an instantaneous moment of time is nothing else than an instantaneous and simultaneous spread of the events of the universe. But in the concept of instantaneousness the concept of the passage of time has been lost. Events essentially involve this passage. Accordingly the self-contradictory idea of an instantaneous event has to be replaced by that of an instantaneous configuration of the universe. But what is directly observed is an event. Thus a duration, which is a slab of time with temporal thickness, is the final fact of observation from which moments and configurations are deduced as a limit which is a logical ideal of the exact precision inherent in nature. This process of deducing limits is considered in detail in my two previous books under the title Extensive Abstraction. But it is an essential assumption that a concrete fact of nature always includes temporal passage.

A moment expresses the spread of nature as a configuration in an instantaneous three dimensional space. The flow of time means the succession of moments, and this succession includes the whole of nature. Rest and motion are direct facts of observation concerning the relation of objects to the durations whose limits are the moments of this flow of time. By means of rest a permanent point is defined which is merely a track of event-particles with one event-particle in every moment.

Refined observation (in the form of the Michelson-Morley experiment and allied experiments) shows that there are alternative flows of time—or time-systems, as they will be called,—and that the time-system actually observed is that one for which (roughly speaking) our body is at rest. Accordingly in different circumstances of motion, space and time mean different things, the moments of one time-system are different from the moments of another time-system, the permanent points of one time-system are different from those of another time-system, so that the permanent space of one time-system is distinct from the permanent space of another time-system.

The properties of time and space express the basis of uniformity in nature which is essential for our knowledge of nature as a cohere...