Abstract
In theories, whose Lorentz invariance is violated by involvement of an external any-rank tensor, we show that the standard relativistic rule still holds true for summing the signal speed, understood as the group velocity of a wave, with the speed of the reference frame. Provided a superluminal signal is available, this observation enables one to arrange a closed time cycle and hence causality violation, notwithstanding the Lorentz noninvariance. Also an optical anisotropy of a moving medium, isotropic at rest, is revealed.
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