Note 158 — Chapter XXXIX · THE CO-ORDINATION OF PHYSICAL FACTS ACCOMPLISHED BY RELATIVITY

From the standpoint of scientific method, it is most instructive to contrast with Einstein’s theory one which fails to satisfy the demands of science. We refer to Dr. Whitehead’s attempt to interpret the phenomenon of gravitation in terms of Minkowski’s flat space-time. In the last chapter we noted that prior to Einstein’s sweeping generalisation a solution of gravitation on the basis of flat space-time had been worked out by Poincaré, Nordström and others. Dr. Whitehead wishes to revert to this type of solution. One of its advantages, he claims, is that it obviates the idea that matter influences the structure of space-time. Whether this is an advantage or not is a mere question of feeling, but in science it is a highly dangerous procedure to reject a simple co-ordination of the facts of experience in favour of some a priori preference which offers no means of being put to a test. Dr. Whitehead would probably claim that in his case this criticism does not hold, for he has given definite arguments in support of his contentions. But what are these arguments? The first consists in his writing: “The only possible structure is that of planes and straight lines.” Yet, as no mathematician would agree with this contention, it would appear that Whitehead was merely restating his a priori belief in the inevitable homogeneity of the space-time structure without justifying his views in any way. Elsewhere he writes: “Are these material bodies really the ultimate data of perception, incapable of further analysis? If they are, I at once surrender.” Now, in point of fact, it is scarcely probable that any scientist would agree with Whitehead’s hypothetical opponent in maintaining that material objects do constitute the ultimate data of perception. But what conceivable connection is there between this problem and the totally different one pertaining to a possible action of matter on the structure of space-time? Obviously, Whitehead is implicitly assuming that we know enough of space-time a priori to assert that it can never be affected by whatever is not an ultimate datum of perception. Hence his second argument, just like the first, reduces to a mere restatement of his a priori convictions. Let us proceed.

Having satisfied himself that material bodies are not what his hypothetical opponent claims them to be, he considers his point proved. Material bodies are henceforth referred to as “a certain coherence of sense-objects such as colours, sounds and touches.” And these sense-objects “at once proclaim themselves to be adjectives of events.” This, according to Dr. Whitehead, precludes matter from exerting any effect on space-time, so that Einstein’s general theory must be discarded.

It is hard to see how a solution of the problems of nature will ever be advanced by such loose arguments. At any rate, having assumed space-time to be flat, or at least homogeneous, everywhere and everywhen, Dr. Whitehead is compelled to account in terms of forces generated by matter for the gravitational effects predicted by Einstein. He explains the occurrence of the shift-effect by tracing it “to the combination of two causes, one being the change in the apparent mass due to the gravitational potential and the other being the change in the electric cohesive forces of the molecule due to the gravitational field.” We shall assume on his authority that the first of the two causes he mentions can be deduced from his gravitational equations, and shall concern ourselves solely with the second cause. Now, unless we get our information from text-books of physics, written more than thirty years ago, we shall never labour under the impression that the spectral lines have anything to do with the constitution of the molecule. Molecular vibrations may cause a broadening of the lines owing to a Doppler effect, and are recognised as giving rise to the diffuse band spectra, but modern experiment has traced the visible line spectra to occurrences within the atom. It follows that these molecular adjustments which Dr. Whitehead is seeking to introduce would appear to have no effect one way or another on the shift he proposes to account for. However, it is not from the standpoint of scientific accuracy that we wish to criticise Dr. Whitehead’s statements, but solely from that of method.

By his own admission, nothing can be predicted of the shift until we know more about the molecule (we presume he means atom). Thus, he tells us, “Accordingly, it requires some knowledge of the structure of the molecule to be certain what the shift (if any) of the spectral lines should be.” Dr. Whitehead wrote his book before the shift was observed on the companion of Sirius, and presumably thought it safer to include the parenthetical words “if any.”

The quotation just cited illustrates the weak point of this type of theory. For inasmuch as we know practically nothing about the intra-atomic occurrences responsible for radiation, we may postulate anything we please with impunity, and as a result make the theory predict any shift we wish, be it vanishing or great. But the purpose of a scientific theory is to give us the power to predict phenomena as yet unknown, and not merely to account for what we already know. It was for this reason that Newton’s law of gravitation was so great an advance over Kepler’s laws of planetary motion or Ptolemy’s crystal spheres. For Newton’s law enabled us to predict how a stray comet would move, whereas Kepler’s laws could tell us nothing.

A theory such as Dr. Whitehead’s allows us to predict anything—hence nothing. No experimental test is possible, since whatever experiment discloses can immediately be accounted for by varying our hypotheses ad hoc. Besides, one cannot help but feel that had not Einstein previously predicted the existence of the shift, Dr. Whitehead would never have deduced it from his theory. Similar conclusions would apply to the double bending of a ray of starlight.

One of the reasons why Einstein’s theory commands such respect among scientists is precisely because, by predicting definite occurrences and no others, it allows itself to be submitted to a test. As Einstein wrote in 1918, several years before the shift was finally observed on the companion of Sirius: “If the displacement of spectral fines towards the red by the gravitational potential does not exist, then the general theory of relativity will be untenable.” It is theories permitting such categorical statements that scientists demand. The theories of Newton, of Maxwell and of Einstein are of this sort.