5. The Redshift Experiment and Whitehead's Theory
In the previous section we have summarized chronologically the various opinions of physicists concerning the experimental tests of Whitehead's theory as compared with Einstein's. Taking these accounts into considerations, I will try to make clear the meanings of new experimental situations available today so that Whitehead's theory may be reexamined and modified within this context.
First, we should bear in mind the fact that Whitehead's theory contains two levels of arguments. One is propounded as a physical hypothesis, open to the future refutation, and the other is his philosophy of nature which is the guiding principle of his physical theories. For example, his basic equation of gravitation such as
is a refutable hypothesis which Whitehead was able to abandon without altering his background philosophy. In a similar way we can consider it as a hypothesis, and not an inescapable result of his philosophy, to state that "the gravitational forces are propagated along straight lines in Mincowski's space, whereas electromagnetic waves are deflected by the contingencies of the universe," though it is a natural interpretation of Whitehead's formulae. So in one sense it was understandable that Fowler would conclude his remark on Will's alleged refutation by stressing the paradigm-difference.
The present author, however, believes that it is not productive, and is even sterile, to insist too much on the paradigm-priority over observed data. Even today it is logically possible that we believe in the Ptolemaic theory by postulating peripheral hypotheses in order to explain the planetary motion. But physics needs more than logical consistency. We had better consider the refutability of a physical theory on its merit. We always learn something at the time of refutation of our pet-theories.
Take, for example, the thesis that space-time must be "fiat". This thesis was the guiding principle of Whitehead's formulae for gravitation. He admitted openly that he was very willingly to believe that each permanent space is either uniformly elliptic or uniformly hyperbolic, "if any observations are more simply explained by such a hypothesis." But the postulate that the curvature of space-time must be constant was thought by Whitehead to be essential to any satisfactory theory of space-time. It was not a hypothesis, but one of the fundamental principles of Whitehead's theory. I will try to show that the very postulate that the metric structure of space-time must be uniform should be abandoned if we want to learn seriously from experiments which are available today, but were unknown to Whitehead.
We will confine the discussion to the effects of redshift experiments on Whitehead's theory. This does not mean that the problem situations raised by Clark and Will may well be ignored. On the contrary, they should be considered as very important contributions even if there remain some ambiguities concerning their results. Lengthy discussions and mathematical technicalities are involved, if we are to grapple with the problern of earth tides or of conservation laws. Moreover if we abolish the thesis of a uniform metric, we need not insist, as Whitehead did, on the global inertial system, which was responsible for the earth tides in Will's criticism. So it is justifiable first to discuss the problem of the metric structure of space-time.
Einstein, as was pointed out in the first section of this paper, stressed the importance of the gravitational redshifts so much that he dared to say that he would abandon the general theory of relativity if it was not observed. The result, however, of astronomical observations by Freundlich (1930) and others were not satisfactory because of an inaccuracy of measurement. This was one of the reasons why many physicists thought the experimental evidence for the general theory of relativity was not convincing. The situation, however, has changed since 1965, because the aforementioned experiment by the use of the Moesbauer effect gave strong support to Einstein's prediction Since this result is interpreted as verifying the principle of equivalence, some kind of reformulation of Whitehead's theory is necessitated because Whitehead did not accept the principle of equivalence in his original formulations.
Whitehead's theory in its original version (1922), using a simplified model of a radiating atom obtained a gravitational redshift slightly different from that of Einstein's theory by the factor of 7/6. Whitehead also predicted that the values of redshift would depend on the directions of emitted light (Limb Effect), which, at least qualitatively, corresponded to the data of astronomical observation. So it seemed as if the predictive power of Whitehead's theory were equivalent to Einstein's concerning the redshift phenomena, but in fact such an equivalence does not hold. First we must notice the difference of physical interpretations when both theories derive the gravitational redshift. Whereas Whitehead's theory needs additional hypotheses concerning the structure of atomic clock and the nature of interaction between a gravitational field and other force fields, Einstein's theory does not need such auxiliary hypotheses, because the latter postulated that the gravitational fields should directly influence the metric of space-time. One of the most important results of this difference is that whereas Einstein's theory should predict the uniformity of gravitational redshift independently of physical conditions, Whitehead's theory can not expect such a uniformity. This mean that Einstein's theory has a stronger structure than Whitehead's because it runs the risk of being refuted by possible varieties of gravitational redshift. But since Einstein's prediction of redshift has been corroborated by empirical tests since 1965, it gains the advantage of Whitehead's theory because of its completeness.
