We carry out a complete examination of the effects of rotation on the physics of spin-\textonehalf{} particles. The origin of these effects is connected to the fact that the frame of the rotating experiment is Fermi-Walker transported, and is related to the inertia rest frame (with respect to which the apparatus rotates with angular velocity $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}$) by an instantaneous Lorentz boost plus a time-dependent spatial rotation, in that order. Two distinct sets of effects are obtained. The first depends on the spin-rotation interaction, and consists of the Mashhoon effect and a mass split effect due to the Lorentz boost mentioned above. In a neutron interferometer the latter effect produces a phase shift smaller than the Mashhoon phase shift by a factor of order
O(c2v2), where
v is the velocity of the particles in the beams of the interferometer. The detection of the Mashhoon effect is crucial to decide if free spin-\textonehalf{} particles actually behave as gyroscopes. The second set appears already in the eikonal approximation and is due to the active boost of the particles by the rotating apparatus; it results in the Sagnac effect. We also discuss a criterion to fix the frame of the experiment among all mathematically admissible frames in the Brill-Wheeler formulation, and show that frames used in the literature to derive the Sagnac-Mashhoon effect cannot be physically realized.
Abstract The fundamental dual nature of neutrons –sometimes a particle (when detected) and sometimes a wave (when traversing the interferometer) – is wonderfully mani-fested by the non-local nature of the neutron interferometry experiments discussed in this chapter. We begin with a discussion of the series of experiments, called gravitationally induced quantum interference, in Section 7.1. Then in Section 7.2, the effect of the Earth’s rotation on the phase of a neutron de Broglie wave is described. This is the quantum mechanical analogue of the Michelson et al. (1925) experiment with light. An experiment in which this Sagnac phase shift was observed due to rotation of the interferometer on a turntable phase within the laboratory frame is also discussed (Atwood et al. 1984). An experiment related to the small effective mass of the neutron propagating in a crystal under Bragg reflecting conditions and its deflection due to the Coriolis force is discussed in Section 7.2.3 (Raum et al. 1997). Acceleration-induced interference, which is related to the gravity experiments by the principle of equivalence, is discussed in Section 7.3 (Bonse and Wroblewski 1983). Phase shifts caused by the motion of matter within the interferometer are related to the optical Fizeau effect. Several neutron Fizeau-type experiments are discussed in Section 7.4.
Einstein's theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle's intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin's coupling with the angular velocity of a rotating magnetic field. This coupling is a purely quantum mechanical extension of the Sagnac effect. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree with the predictions derived from the Pauli-Schrodinger equation.
Abstract Einstein’s theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle’s intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin’s coupling with the angular velocity of a rotating magnetic field. This coupling is a purely quantum mechanical extension of the Sagnac effect. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree with the predictions derived from the Pauli–Schrödinger equation.
Abstract Non-inertial physics is seldom considered in quantum mechanics and this contrasts with the ubiquity of non-inertial reference frames. Here, we show an application to the Dirac oscillator which provides a fundamental model of relativistic quantum mechanics. The model emerges from a term linearly dependent on spatial coordinates added to the momentum of the free-particle Dirac Hamiltonian. The definition generates peculiar features (mutating vacuum energy, non-Hermitian momentum, accidental degeneracies of the spectrum, etc). We interpret these anomalies in terms of inertial effects. The demonstration is based on the decoupling of the Dirac equation from the stereographic projection that maps the 3D geometry of the dynamical problem to the complex plane. The decoupling shows that the fundamental mechanical model underpinning the Dirac oscillator reduces to the representation of the oscillator in the rotating reference frame attached to the orbital angular momentum. The resulting Coriolis-like contribution to the Hamiltonian accounts for the peculiarities of the model (mutating vacuum energy, form of the non-minimal correction to the momentum, classical intrinsic spin and gain of its quantum value, accidental degeneracies of the energy spectrum, supersymmetric potential). The suggested interpretation has an interdisciplinary character where stereographic geometry, classical physics of the Coriolis effect and quantum physics of Dirac particles contribute to the definition of one of the few exactly soluble models of relativistic quantum mechanics.
Although the final conclusion of a preceding paper was incorrect, as we shall explain, the main point remains, and should entail the existence of sui generis recoil effects associated with nonzero values of curl $\ensuremath{\sigma}$ ($\ensuremath{\sigma}$ is the spin density). These should be observed by testing, not with solids as was previously proposed, but with the probability fluids associated with moving particles; this more refined type of experiment should be able to select, among the set of integrally equivalent energy-momentum tensors, the one describing locally the true or physical energy-momentum flux. In this paper it is shown, by an explicit calculation, that cylindrical type solutions of the extreme relativistic Dirac equation exist with no
z dependence of the wave function (and thus no
kz component of the momentum) but still with a
z component of the Dirac probability current; as this conclusion is reached with a
t dependence of the wave function of strictly the form $\mathrm{exp}(\ensuremath{-}\frac{\mathrm{iWt}}{\ensuremath{\hbar}})$, there is no question of having to perform a Foldy-Wouthuysen transformation to extract the positive energy contribution (or equivalently, to use the Newton-Wigner position operator). The "transverse inertial spin effect" we predict is locally described by the flux of the Dirac current per time
dt and surface
ds, and corresponds to the local transition probabilities between the dynamical state of the beam and a pointlike localization of the incident particles.