Dec 1945
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1945natur.156..747m&link_type=abstract
Nature, Volume 156, Issue 3973, pp. 747-748 (1945).
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Scientific paper
MY attention has been directed to Prof. H. Dingle's recent letter in Nature1. His supposed refutation of kinematical relativity is on a par with Dr. Samuel Johnson's refutation of metaphysics; my failure to reply to him directly is due to my reluctance to engage in such trivialities. I have already given him all the answer he needs by referring him to my mathematical papers, where the case of the collision of equivalent particle-observers is fully dealt with. You cannot wantonly re-graduate any casual clock and expect to secure a consistent physics. Kinematical relativity does not do so. In kinematical relativity it is shown that for consistent time-keeping to be possible, the various particle-observers whose temporal experiences constitute clocks must be members of equivalences. Regraduation is applied only to such equivalences; and it was shown by Whitrow and myself2 that if two members of an equivalence ever coincide, then all members coincide at the same event. This technical point is well known to all who have studied time-keeping in relation to equivalences; it is fundamental, for example, in some recent unpublished work by A. G. Walker. In its application, it means that in a contracting universe of time-keepers, there would be a singularity which would be the counterpart of `creation' in an expanding universe. Prof. Dingle is concerned with the timing of `subsequent events' there would be no subsequent events-Prof. Dingle would not survive the catastrophe-just as in an expanding universe there are no events anterior to `creation'. There are other objections to a contracting universe, but the `absurdity' which preoccupies Prof. Dingle is a monster of his own construction which simply adds point to the absurdity of a contracting universe. As the universe is observed to be expanding, Prof. Dingle's difficulties never arise.
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