Quantum mechanical rotation of a photon polarization by Earth’s gravitational field

We describe the quantum mechanical rotation of a photon state, the Wigner rotation—a quantum effect that couples a transformation of a reference frame to a particle’s spin, to investigate geometric phases induced by Earth’s gravitational field for observers in various orbits. We find a potentially measurable quantum phase of the Wigner rotation angle in addition to the rotation of standard fame, the latter of which is computed and agrees well with the geodetic rotation. When an observer is in either a circular or a spiraling orbit containing non-zero angular momentum, the additional quantum phase contributes 10−6 degree to 10−4 degree respectively, depending on the altitude of the Earth orbit. In the former case, the additional quantum phase is dominant over the near-zero classical geodetic rotation. Our results show that the Wigner rotation represents a non-trivial semi-classical effect of quantum field theory on a background classical gravitational field.

Generalization of the Thomas-Wigner Rotation to Uniformly Accelerating Boosts

In the current paper we present a generalization of the transforms from the frame co-moving with an accelerated particle for uniformly accelerated motion into an inertial frame of reference. The motivation is that the real life applications include accelerating and rotating frames with arbitrary orientations more often than the idealized case of inertial frames; our daily experiments happen in Earth-bound laboratories. We use the transforms in order to generalize the Thomas-Wigner rotation to the case of uniformly accelerated boosts.

Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

Helicity rotation induced by Lorentz boosts

In this paper, we calculate the helicity rotation angle induced by Lorentz boosts. This is relevant for the study of Lorentz boost effects on quantum entanglement encoded in pairs of massive fermions, which are described in terms of positive energy solutions of the Dirac equation with definite helicity. A Lorentz boost describing the change to an inertial frame moving at uniform speed will in general rotate the particle’s helicity. We obtain the coefficients of the helicity superposition in the boosted frame and specialize our results for a perpendicular boost geometry. We verify that the helicity rotation angle can be obtained in terms of the Wigner rotation angle for spin [Formula: see text] states, bridging the framework considered in our previous works to the one of the Wigner rotations. Finally, we calculate the boost-induced spin-parity entanglement for a single particle.

Visualization of Thomas-Wigner Rotations

It is well known that a sequence of two non-collinear Lorentz boosts (pure Lorentz transformations) does not correspond to a Lorentz boost, but involves a spatial rotation, the Wigner or Thomas-Wigner rotation. We visualize the interrelation between this rotation and the relativity of distant simultaneity by moving a Born-rigid object on a closed trajectory in several steps of uniform proper acceleration. Born-rigidity implies that the stern of the boosted object accelerates faster than its bow. It is shown that at least five boost steps are required to return the object's center to its starting position, if in each step the center is assumed to accelerate uniformly and for the same proper time duration. With these assumptions, the Thomas-Wigner rotation angle depends on a single parameter only. Furthermore, it is illustrated that accelerated motion implies the formation of an event horizon. The event horizons associated with the five boosts constitute a natural boundary to the rotated Born-rigid object and ensure its finite size.