Alfred North Whitehead (essay date 1920)
SOURCE: "Einstein's Theory," in Essays in Science and Philosophy, Philosophical Library, 1947, pp. 332-42.
[A distinguished English mathematician, philosopher, and educator, Whitehead collaborated with Bertrand Russell on the latter's Principia Mathematica (1910-13), a three-volume treatise on the relationship of logic to mathematics that would eventually inspire the Austrian philosopher Ludwig Wittgenstein in his ground-breaking studies. In the following essay, originally published in the Times Educational Supplement in 1920, Whitehead seeks to explain the major principles of Einstein's work.]
Einstein's work may be analysed into three factors—a principle, a procedure, and an explanation. This discovery of the principle and the procedure constitute an epoch in science. I venture, however, to think that the explanation is faulty, even although it formed the clue by which Einstein guided himself along the path from his principle to his procedure. It is no novelty to the history of science that factors of thought which guided genius to its goal should be subsequently discarded. The names of Kepler and Maupertuis at once occur in illustration.
What I call Einstein's principle is the connexion between time and space which emerges from his way of envisaging the general fact of relativity. This connexion is entirely new to scientific thought, and is in some respects very paradoxical. A slight sketch of the history of ideas of relative motion will be the shortest way of introducing the new principle. Newton thought that there was one definite space within which the material world adventured, and that the sequence of its adventures could be recorded in terms of one definite time. There would be, therefore, a meaning in asking whether the sun is at rest or is fixed in this space, even although the questioner might be ignorant of the existence of other bodies such as the planets and the stars. Furthermore, there was for Newton an absolute unique meaning to simultaneity, so that there can be no ambiguity in asking, without further specification of conditions, which of two events preceded the other or whether they were simultaneous. In other words, Newton held a theory of absolute space and of absolute time. He explained relative motion of one body with respect to another as being the difference of the absolute motions of the two bodies. The greatest enemy to his absolute theory of space was his own set of laws of motion. For it is a well-known result from these laws that it is impossible to detect absolute uniform motion. Accordingly, since we fail to observe variations in the velocities of the sun and stars, it follows that any one of them may with equal right be assumed to be either at rest or moving in any direction with any velocity which we like to suggest. Now, a character which never appears in the play does not require a living actor for its impersonation. Science is concerned with the relations between things perceived. If absolute motion is imperceptible, absolute position is a fairy tale, and absolute space cannot survive the surrender of absolute position.
So far our course is plain: we give up absolute space, and conceive all statements about space as being merely expositions of the internal relations of the physical universe. But we have to take account of two very remarkable difficulties which mar the simplicity of this theoretical position. In the first place there seems to be a certain absoluteness about rotation. The fact of this absoluteness is inherent in Newton's laws of motion, and the deducted consequences from these premises have received ample confirmation. For example, the effect of the rotation of the earth is manifested in phenomena which appear to have no connexion with extraneous astronomical bodies. There is the bulge of the earth at its equator, the invariable directions of rotation for cyclones and anti-cyclones, the rotation of the plane of oscillation of Foucault's pendulum, and the north-seeking property of the gyrocompass. The mass of evidence is decisive, and no theory which burkes it can stand as an adequate explanation of observed facts. It is not so obvious how to combine these facts of rotation with any principle of relativity.
Secondly, the ether contributes another perplexity just where it might have helped us. We might have regained the right quasi-absoluteness of motion by measuring velocity relatively to the ether. The facts of rotation could have thus received an explanation. But all attempts to measure velocity relatively to the ether have failed to detect it in circumstances when, granting the ordinary hypotheses, its effects should have been visible. Einstein showed that the whole series of perplexing facts concerning the ether could be explained by adopting new formulae connecting the spatial and temporal measurements made by observers in relative motion to each other. These formulae had been elaborated by Larmor and Lorentz, but it was Einstein who made them the foundation of a novel theory of time and space. He also discovered the remarkable fact that, according to these formulae, the velocity of light in vacuous space would be identical in magnitude for all these alternative assumptions as to rest or motion. This property of light became the clue by which his researches were guided. His theory of simultaneity is based on the transmission of light signals, and accordingly the whole structure of our concept of nature is essentially bound up with our perceptions of radiant energy.
In view of the magnificent results which Einstein has achieved it may seem rash to doubt the validity of a premiss so essential to his own line of thought. I do, however, disbelieve in this invariant property of the velocity of light, for reasons which have been partly furnished by Einstein's own later researches. The velocity of light appears in this connexion owing to the fact that it occurs in Maxwell's famous equations, which express the laws governing electromagnetic phenomena. But it is an outcome of Einstein's work that the electro-magnetic equations require modification to express the association of the gravitational and electro-magnetic fields. This is one of his greatest discoveries. The most natural deduction to make from these modified equations is that the velocity of light is modified by the gravitational properties of the field through which it passes, and that the absolute maximum velocity which occurs in the Maxwellian form of the equations has in fact a different origin which is independent of any special relation to light or electricity. I will return to this question later.
Before passing on to Einstein's later work a tribute should be paid to the genius of Minkowski. It was he who stated in its full generality the conception of a four-dimensional world embracing space and time, in which the ultimate elements, or points, are the infinitesimal occurrences in the life of each particle. He built on Einstein's foundations, and his work forms an essential factor in the evolution of relativistic theory.
Einstein's later work is comprised in what he calls the theory of general relativity. I will summarize what appear to me as the essential components of his thought, at the same time warning my readers of the danger of misrepresentation which lies in such summaries of novel ideas. It is safer to put it as my own way of envisaging the theory. What are time and space? They are the names for ways of conducting certain measurements. The four dimensions of nature as conceived by Minkowski express the fact that four measurements with a certain peculiar type of mutual independence are required to formulate the relations of any infinitesimal occurrence to the rest of the physical universe. These ways of measurement can be indefinitely varied by change of character, so that four independent measurements of one character will specify an occurrence just as well as four other measurements of some other character. A set of four measurements of a definite character which assigns a special type to each of the four measurements will be called a measure-system. Thus there are alternative measure-systems, and each measure-system embraces, for the specification of each infinitesimal occurrence, four assigned measurements of separate types, called the coordinates of that occurrence. The change from one measure-system to another appears in mathematics as the change from one set of variables (pl, p2, p3, p4) to another set of variables (q1, q2, q3, q4), the variables of the p-system being functions of the q-system, and vice versa. In this way all the quantitative laws of the physical universe can be expressed either in terms of the p-variables or in terms of the q-variables. If a suitable measure-system has been adopted, one of the measurements, say p4, will appear to us as a measurement of time, and the remaining measurements (p1, p2, p3) will be measurements of space, which are adequate to determine a point. But different measure-systems have this property of subdivision into spatial and temporal measurements according to the different circumstances of the observers. It follows that what one observer means by space and time is not necessarily the same as what another observer may mean. It is to be observed that not every change of measure-system involves a change in the meanings of space...
(The entire section is 3832 words.)