Application of the modified Duguay method for measuring the Lorentz contraction of a moving body length

Abstract

According to Lorentz transformations, for a stationary observer, time in a moving inertial reference frame slows down, while the linear dimensions are reduced. While the first effect was observed more than 80 years ago, the second one has not been directly observed so far. The modified Duguay method is proposed in this paper for measuring the Lorentz contraction of a moving body length using the propagation of light pulses in an optical liquid medium. Three variants of the measurement scheme are considered: with a ‘light square’ in an optical medium, with a ‘light ruler’ in two optical media with different refractive indices, and with two relativistic electron bunches in a vacuum. It is shown that the classical effect of compression of spatial intervals between light pulses in an optical medium, which was not considered earlier, considerably reduces the measurement accuracy. It is also shown that the distortion of the sides of a light square oriented orthogonal to the movement direction caused by the different delays of light from different parts of a moving body also reduces the measurement accuracy of the light square method.