However, if we leave these aesthetic urges aside, we may say that the methodology that has yielded us the theory of relativity is the same methodology that has yielded all the great scientific discoveries. It is the methodology of Galileo, Newton and Maxwell: First, ascertain experimental facts; then, as needs be, frame tentative hypotheses or scaffoldings for the sole purpose of co-ordinating these facts into a consistent whole with a maximum of simplicity. Only when the theory has succeeded in accumulating a sufficient number of facts can its philosophical implications be studied. It follows that any attempt to reverse the normal order and posit the philosophy before the science will result in hampering future discovery by subordinating accuracy of treatment to loose guesswork. The history of human thought is full of discarded philosophic prejudices swept away by the onward march of science. Every new scientific discovery reveals aspects of nature, or even of the mind, as in pure mathematics, which we never suspected before. To-day, both the discoveries of relativity and the quantum hypothesis are case in point. It is precisely because the philosophy of a theory of mathematical physics can only be attained a posteriori, coming as a crowning achievement, that the philosophy which is beginning to disentangle itself from Einstein’s discoveries is still in an embryonic stage. It is not that a scientific philosopher of sufficient scope could not be found; it is because there are many scientific aspects of the subject which are still in doubt. The following passage from Einstein will explain what we mean:
“From the present state of theory it looks as if the electromagnetic field as opposed to the gravitational field rests upon an entirely new formal motif, as though nature might just as well have endowed the gravitational ether [metrical field[155]] with fields of quite another type, for example with fields of a scalar potential instead of fields of the electromagnetic type.
“Since according to our present conceptions the elementary particles of matter are also in their essence nothing else than condensations of the electromagnetic field, our present view of the universe presents two realities which are completely separated from each other conceptually, although connected causally, namely, gravitational ether [metrical field] and electromagnetic field, or—as they might also be called—space and matter.
“Of course it would be a great advance if we could succeed in comprehending the gravitational field and the electromagnetic field together as one unified conformation. Then, for the first time, the epoch of theoretical physics founded by Faraday and Maxwell would reach a satisfactory conclusion. The contrast between ether [metrical field] and matter would fade away and through the general theory of relativity the whole of physics would become a complete system of thought like geometry and the theory of gravitation.”
We have quoted this passage at length, because it appears to us that by reading between the lines it is possible to realise the deeper philosophical problems pertaining to our knowledge of nature, hence to knowledge in general, which still obscure the significance of relativity.
CHAPTER XXXIX
THE CO-ORDINATION OF PHYSICAL FACTS ACCOMPLISHED BY RELATIVITY
IN the preceding chapter, we saw that the Newtonian synthesis had succeeded in co-ordinating terrestrial mechanics with celestial mechanics, or again ordinary mechanics with the laws of planetary motions; and that later Maxwell had brought together optics and electricity. The theory of relativity goes much farther, and obtains a synthesis of practically all the various realms of physical science, including cosmology and the internal mechanisms of the atoms. Just as Newton’s discoveries were made possible thanks to the introduction of the inertial frame of reference attached to the stars, so was Einstein’s synthesis the natural outcome of the principle of the relativity of Galilean motion, and of the postulate of the invariance of the velocity of light in vacuo as referred to any Galilean frame.
We may recall that the physical facts co-ordinated by Einstein were originally altogether of an electromagnetic nature. In the first place, all the negative experiments were accounted for automatically, but there was of course no merit in this, since the entire theory is based on the acceptance of these negative results. Similar arguments, however, no longer hold when we consider Fizeau’s experiment; for there exists no apparent connection between the experiments of Michelson and of Fizeau. Hence the fact that Fizeau’s result is a necessary consequence of Einstein’s theory constitutes a first strong point in favour of relativity. We might also mention that the theory demands a numerical result slightly different from that anticipated by Fresnel and Lorentz, so that more precise observations should permit experimenters to verify the correctness of the theory.
Perhaps the most striking success of the special theory in electromagnetics consists in its allowing us to foretell how electric and magnetic fields will appear to be modified when we pass from one Galilean frame to another. For instance, experiment proves that an electron at rest is surrounded by an electrostatic field; whereas the same electron in relative motion is known to develop an additional magnetic field at right angles to the electrostatic field. Prior to the discovery of the Lorentz-Einstein transformations, these experimental results were noted but no explanation could be given to account for this generation of a magnetic field with motion. Accordingly, an empirical formula was appealed to in order to define its lay and intensity. But as soon as the transformation formulæ were applied the entire problem was cleared up, a theoretical explanation of these mysterious facts was obtained, and the classical empirical formulæ were found to be only approximate. It was then seen that the electric and magnetic fields were no longer separate units, but merely relative aspects of the same entity—the electromagnetic-field tensor.
Considering the theory from a purely mathematical point of view, we found that great beauty and symmetry were introduced into our co-ordination of the equations of electrodynamics; formulæ which had always appeared disconnected now revealed themselves as intimately related. This was especially apparent in the laws expressing the conservation of electromagnetic energy and momentum. From the standpoint of the theoretical investigator, these mathematical simplifications are of great importance, in that they reveal that unity and harmony in nature which, rightly or wrongly, make us believe we are on the right track. Passing to mechanics, we find that the increase of mass with relative velocity becomes a necessary consequence of the theory; and in this way Bucherer’s experiment is accounted for with extreme simplicity. For the same reason, when extending these discoveries to the astronomy of the atom, Sommerfeld was able to prophesy the existence of fine spectral rays since observed by Paschen. A further requirement of the theory was the identification of mass with energy; and this unforeseen relationship enabled scientists to explain the mysterious anomalies in the atomic weights of the successive atoms. It also followed that light, being a form of energy, must manifest mass, and hence momentum; so that Maxwell’s and Bartoli’s previous theoretical anticipations (later verified by experiment) were also found to be in harmony with relativity. In a similar way the electromagnetic energy of the electron would cause it to possess mass. As in the case of the conservation theorems in electricity, the same beautiful symmetry was apparent in mechanics. The special theory entails, as we know, the existence of space-time; and with space-time in place of separate space and time, the difficulties were finally overcome which classical science encountered when seeking to conceive of a structure for space capable of accounting for the differences in the dynamical manifestations accompanying Galilean and accelerated motion. This closes the list of the most important facts co-ordinated by the special theory.