Did Bergson actually reject the now well established phenomenon of time dilation? From his acceptance of reciprocity ie. earth moving away at speed from immobile rocket and v.v.; he had to reject real ontological time change. In fact the single referrent of the earth clock is the critical one in the experiment establishing time dilation, the observer in the plane looking at a slowing clock on the ground drops out of consideration. He writes in an appendix to Duration and Simultaneity :
In short, there is nothing to change in the mathematical expression of the theory of relativity. But physics would render a service to philosophy by giving up certain ways of speaking which lead the philosopher into error, and which risk fooling the physicist himself regarding the metaphysical implications of his views. For example, we are told above that "if two identical, synchronized clocks are at the same spot in the system of reference, if we shift one very rapidly and then bring it back again next to the other at the end of time t (the time of
the system), it will lag behind the other by t- adt." In
reality we should say that the moving clock exhibits this slowing at the precise instant at which it touches, still moving, the motionless system and is about to re-enter it. But, immediately upon re-entering, it points to the same time as the other (it goes without saying that the two instants are practically indistinguishable). For the slowed time of the moving system is only attributed time; this merely attributed time is the time indicated by a clock hand moving before the gaze of a merely imagined physicist; the clock before which this physicist is situated is therefore only a phantasmal clock, substituted for the real clock throughout its journey: from phantasmal it again turns into real the moment it is returned to the motionless system. It would, moreover, have remained real for a real observer during the trip. It would not have undergone any slow ing. And that is precisely why it shows no slowing when it is again found to be a real clock upon arrival.
That was written in 1922 but one must remember that :
Therefore as A. P. French (1968) states in his textbook on relativity, the length contraction is not a real property of matter, it is a measurement effect, “something inherent in the measurement process” (p. 114).(from a paper by Dr. Stephen E. Robbins on Bergson and S.T.R.)
In the textbooks I studied in the 1970s, the explanations of length contraction routinely told this story. The length contraction is not real. It is an effect of measurement only. The length is a space-time invariant, but no single observer has a claim on knowing the “true length.” The student is warned not to fall into “the length contraction is real” trap. In truth, we must remember, there is little choice. To say that it is a real effect is to say that the Michelson-Morley apparatus arm is actually contracting somehow.
The book by French is Special Relativity New York: Norton.
More anon on Robbins and his 'Bergsonianism'. robbins