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.
[159] The difference is, however, exceedingly minute, as we can judge by reverting to the expression for the invariant space-time distance
. If
is expressed in metres and
