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The aim of this paper is to demonstrate an effect of time nonholonomity which appears in accelerated reference systems. We suppose that an accelerated reference system is closely related to a physical field which changes the space-time geometry. On the space-time M = M × R we take a metric g of general form which is invariant under time shifts t → t + t0, only. The physical field is described by a 1-form θ and a function φ given on a spatial manifold M. These considerations are motivated by the model suggested in [1, 2] which interprets the Sagnac effect [4, 5] as an effect caused by a deformation of space-time geometry generated by the disk rotation. We demonstrate that this effect occurs for our general space-time metric. To this end, we consider the space-time M as a principal bundle M → M with group R, and use the fact that the distribution H orthogonal to the fibres gives an infinitesimal connection in this bundle. We note that there arises the same effect, called a generalized Sagnac effect, and prove that this one is determined by the holonomy of connection H, i.e. it occurs because H is not integrable. |
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