Abstract

I propose a scheme for observing the Wigner angle using an optical parametric amplifier. The Wigner angle is a curious interesting concept from special relativity that most of us have encountered in another guise as Thomas precession in atomic physics.The Wigner angle arises because the subset of pure Lorentz transformations (“boosts”) does not constitute a group. Put more explicitly, the product of two boosts along different directions is not a boost but a boost multiplied by a rotation. The angle of rotation is known as Wigner's angle. Let us confine ourselves to 2 space and 1 time dimension(s), denoting by L(ξ, ϑ) a boost of velocity v = c tanhξ at an angle ϑ to the x-axis and by R(ϑ) a rotation (of the coordinate system) in the x-y plane by the angle ϑ.

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