Sir, - We would like to respond however belatedly to Dr Kelly's comments (April 2nd) on the subject of Einstein's Theory of Relativity. Dr Kelly holds the view that the Sagnac effect, which involves the reflection of light by a series of mirrors on a rotating platform, cannot be explained by Einstein's theory. We remain unconvinced by Dr Kelly's comments, and we have no difficulty in explaining this effect within Einstein's theory.
In support of his view, Dr Kelly refers to a 1993 paper by Hasselbach & Nicklaus which references 21 theoretical explanations for the Sagnac effect. What is not clear from Dr Kelly's comments, however, is that all these explanations are completely successful in predicting the experimental results achieved by many different researchers using light, neutron, electron and even atomic beams. The multiplicity of explanations partly reflects the fact that the Sagnac effect has now been observed in many different experimental situations each of which required a slightly different analysis. Partly, however, it reflects the depth, the richness and the complete interdependence of the scientific ideas involved in the effect. If we tamper with Einstein's theory in the manner suggested by Dr Kelly, then the interdependent structure collapses and the different analyses become logically inconsistent. "Things fall apart; the centre cannot hold; mere anarchy is loosed upon the world".
Dr Kelly suggested in his comments that we produce the subtle analysis we claimed was necessary to explain the Sagnac effect, and send it to the Institute of Engineers of Ireland for publication. There is no need for us to do so since the analysis is well known and standard, and is available in the literature. A particularly clear account, for example, is that given by Anandan (Physical Review D, Vol 24, 1981).
Let us explain why the analysis needed is a subtle one. Einstein's Special Theory deals directly with systems which move with constant linear velocity with respect to each other. Since the Sagnac effect involves rotational motion, Einstein's Special Theory does not directly apply. If however, the rotation is built out of a sequence of small linear velocity changes, then each of these small changes can be analysed using the Special Theory and at each step, the velocity of light remains constant. When the analysis is carried out in this way, the explanation for the Sagnac effect is seen to be a consequence of the slowing down of moving clocks required by Einstein's Special Theory. This explains Pauli's comment (which we quoted in our previous letter) that the Sagnac effect provides a particularly nice confirmation of Special Relativity.
Before we consider replacing Einstein's theory, we must produce sound evidence of its failure. No incontrovertible evidence of failure presently exists in the literature. Perhaps Dr Kelly can explain what is incorrect with Anandan's analysis. Perhaps he will point out where the statement is made in the 1993 article of Hasselbach & Nicklaus (to which he refers) that the Sagnac Effect contradicts Einstein's theory. - Yours, etc.,
Trinity College,
Dublin 2.