We canonically quantize a spin-less non-relativistic point particle in a rigidly rotating cylinder symmetric reference system. The resulting quantum mechanics is investigated in the case of both a two-dimensional cylindrical shell and in the case of the full rotating cylinder; in both cases energy eigenstates exist which exhibit rotation induced negative energies. Based on a reanalysis of the classical Sagnac effect a novel way to compute the quantum Sagnac phase shift is deduced. It is pointed out that certain states on both the cylindrical shell and in the bulk give rise to a novel anomalous quantum Sagnac effect.We canonically quantize a spin-less non-relativistic point particle in a rigidly rotating cylinder symmetric reference system. The resulting quantum mechanics is investigated in the case of both a two-dimensional cylindrical shell and in the case of the full rotating cylinder; in both cases energy eigenstates exist which exhibit rotation induced negative energies. Based on a reanalysis of the classical Sagnac effect a novel way to compute the quantum Sagnac phase shift is deduced. It is pointed out that certain states on both the cylindrical shell and in the bulk give rise to a novel anomalous quantum Sagnac effect.

arXiv:1806.02710Jun 7, 20180 citations

The physics of the Sagnac-Mashhoon effects

Ivano Damião Soares, J. Tiomno

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 $O(\frac{{v}^{2}}{{c}^{2}})$ , 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.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 $O(\frac{{v}^{2}}{{c}^{2}})$, 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.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsAug 15, 199646 citations

Joint Wigner distribution for spin-1/2 particles

Leon W. Cohen, Marlan O. Scully

Foundations of PhysicsApr 1, 198674 citations

Inertial effects of a Dirac particle

Friedrich W. Hehl, Wei-Tou Ni

Stationary laboratories on Earth accelerate and rotate relative to the local inertial frames. Any experiment precise enough would detect and/or need to take into account the effects due to acceleration and rotation. We derive these inertial effects for a Dirac particle in a straightforward and unified way within the framework of special relativity. The effects found include the Bonse-Wroblewski phase shift due to acceleration, the Sagnac-type effect, the rotation-spin effect, and the redshift of the kinetic energy.Stationary laboratories on Earth accelerate and rotate relative to the local inertial frames. Any experiment precise enough would detect and/or need to take into account the effects due to acceleration and rotation. We derive these inertial effects for a Dirac particle in a straightforward and unified way within the framework of special relativity. The effects found include the Bonse-Wroblewski phase shift due to acceleration, the Sagnac-type effect, the rotation-spin effect, and the redshift of the kinetic energy.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsSep 15, 1990441 citations

The Relativistic Sagnac Effect: Two Derivations

Guido Rizzi, Matteo Luca Ruggiero

arXiv:gr-qc/0305084Springer eBooksJan 1, 200429 citations

O(\frac{{v}^{2}}{{c}^{2}})

, 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.