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The Sagnac Effect Explained Using the Special Relativity Theory

Jan Olof Jonson
Year: 2009 Pages: 8
Keywords: Sagnc Effect, Special Relativity
The discovery by Sagnac in the 1910s that a light beam that is forced to travel in a circular path along an orbiting circular disk needs different time to make a revolution, dependent on the direction, along or against. the direction of revolution. Kelly in a paper discusses efforts being made by different scientists in order to explain the Sagnac effect. Kelly himself succeeds in deriving a model able to explain the numerical results, thereby claiming that the Special relativity theory is not needed; a classical approach suffices.

Another author, Post, analyses the Sagnac experiment thoroughly and uses the relativistic concept of time dilatation when evaluating an expression for the different propagation time along the two directions of the rays. He thereby uses a model developed by Langevin, which results in an expression for the times for the two rays as if they had a relative velocity approximately equal to c-v and c-v with respect to the sender. He claims this to be in line with the SRT He is speaking of a ?recasting' of the Lorentz transformation into polar coordinates.

Einstein on his part basically pretends that the relative velocity of light is c, but is also hesitating, when the question of non-liner movement arises. In one connection for example he claims that the time loss for a clock being moved between two points is independent of which way the journey is being performed; it might even be ?along any polygonal line', he claims, which is problematic when regarding the results of the Sagnac experiment.

However, in this paper it is being shown that the Special Relativity Theory (SRT), too, is able to explain the Sagnac effect, thereby giving just the same results as Kelly. This is a pure matter of coincidence and if velocities increase, the similarity begins to disappear. There are problems in connections with the Kelly theory, as his model implies observers' seeing velocities higher than that of light, whereas the usage of SRT presumes the velocity of light to be the highest one can ever observe. The SRT succeeds through the usage of the concept of time dilatation, extended in a differential sense when applied to a circular orbit.