From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this frame of reference is shown to be rather unconventional. In particular, we discuss several subtleties emerging in the relative formulation of central notions, such as vector states, the classical limit, entanglement, uncertainty relations and the complementary principle. A Hamiltonian formulation is also derived which correctly encapsulates effects of fictitious forces associated with the accelerated motion of the frame. Our approach shows, therefore, how to formulate nonrelativistic quantum mechanics within noninertial reference frames which can be consistently described by the theory, with no appeal to classical elements.From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this frame of reference is shown to be rather unconventional. In particular, we discuss several subtleties emerging in the relative formulation of central notions, such as vector states, the classical limit, entanglement, uncertainty relations and the complementary principle. A Hamiltonian formulation is also derived which correctly encapsulates effects of fictitious forces associated with the accelerated motion of the frame. Our approach shows, therefore, how to formulate nonrelativistic quantum mechanics within noninertial reference frames which can be consistently described by the theory, with no appeal to classical elements.

arXiv:1204.5627Journal of Physics A Mathematical and TheoreticalOct 31, 201238 citations

Quantum Mechanics in Non-inertial Frames of Reference

E. Schmutzer, Jerzy F Plebanski

De Gruyter eBooksDec 31, 197710 citations

Fictitious Forces and Simulated Magnetic Fields in Rotating Reference Frames

W. H. Klink, S. Wickramasekara

We show that the Wigner-Bargmann program of grounding nonrelativistic quantum mechanics in the unitary projective representations of the Galilei group can be extended to include all noninertial reference frames. The key concept is the Galilean line group, the group of transformations that ties together all accelerating reference frames, and its representations. These representations are constructed under the natural constraint that they reduce to the well-known unitary, projective representations of the Galilei group when the transformations are restricted to inertial reference frames. This constraint can be accommodated only for a class of representations with a sufficiently rich cocycle structure. Unlike the projective representations of the Galilei group, these cocycle representations of the Galilean line group do not correspond to central extensions of the group. Rather, they correspond to a class of nonassociative extensions, known as loop prolongations, that are determined by three-cocycles. As an application, we show that the phase shifts due to the rotation of Earth that have been observed in neutron interferometry experiments and the rotational effects that lead to simulated magnetic fields in optical lattices can be rigorously derived from the representations of the loop prolongations of the Galilean line group.We show that the Wigner-Bargmann program of grounding nonrelativistic quantum mechanics in the unitary projective representations of the Galilei group can be extended to include all noninertial reference frames. The key concept is the Galilean line group, the group of transformations that ties together all accelerating reference frames, and its representations. These representations are constructed under the natural constraint that they reduce to the well-known unitary, projective representations of the Galilei group when the transformations are restricted to inertial reference frames. This constraint can be accommodated only for a class of representations with a sufficiently rich cocycle structure. Unlike the projective representations of the Galilei group, these cocycle representations of the Galilean line group do not correspond to central extensions of the group. Rather, they correspond to a class of nonassociative extensions, known as loop prolongations, that are determined by three-cocycles. As an application, we show that the phase shifts due to the rotation of Earth that have been observed in neutron interferometry experiments and the rotational effects that lead to simulated magnetic fields in optical lattices can be rigorously derived from the representations of the loop prolongations of the Galilean line group.

Physical Review LettersOct 17, 20136 citations

Mesoscopic mechanical resonators as quantum noninertial reference frames

B. Katz, M. P. Blencowe, Keith Schwab

An atom attached to a micrometer-scale wire that is vibrating at a frequency $\ensuremath{\sim}100\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$ and with displacement amplitude $\ensuremath{\sim}1\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$ experiences an acceleration magnitude $\ensuremath{\sim}{10}^{9}\phantom{\rule{0.28em}{0ex}}{\mathrm{m}\phantom{\rule{0.28em}{0ex}}\mathrm{s}}^{\ensuremath{-}2}$, approaching the surface gravity of a neutron star. As one application of such extreme noninertial forces in a mesoscopic setting, we consider a model two-path atom interferometer with one path consisting of the $100\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$ vibrating wire atom guide. The vibrating wire guide serves as a noninertial reference frame and induces an in principle measurable phase shift in the wave function of an atom traversing the wire frame. We furthermore consider the effect on the two-path atom wave interference when the vibrating wire is modeled as a quantum object, hence functioning as a quantum noninertial reference frame. We outline a possible realization of the vibrating wire, atom interferometer using a superfluid helium quantum interference setup.An atom attached to a micrometer-scale wire that is vibrating at a frequency $\ensuremath{\sim}100\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$ and with displacement amplitude $\ensuremath{\sim}1\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$ experiences an acceleration magnitude $\ensuremath{\sim}{10}^{9}\phantom{\rule{0.28em}{0ex}}{\mathrm{m}\phantom{\rule{0.28em}{0ex}}\mathrm{s}}^{\ensuremath{-}2}$, approaching the surface gravity of a neutron star. As one application of such extreme noninertial forces in a mesoscopic setting, we consider a model two-path atom interferometer with one path consisting of the $100\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$ vibrating wire atom guide. The vibrating wire guide serves as a noninertial reference frame and induces an in principle measurable phase shift in the wave function of an atom traversing the wire frame. We furthermore consider the effect on the two-path atom wave interference when the vibrating wire is modeled as a quantum object, hence functioning as a quantum noninertial reference frame. We outline a possible realization of the vibrating wire, atom interferometer using a superfluid helium quantum interference setup.

arXiv:1409.2137Physical Review AOct 8, 201512 citations

100\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}

vibrating wire atom guide. The vibrating wire guide serves as a noninertial reference frame and induces an in principle measurable phase shift in the wave function of an atom traversing the wire frame. We furthermore consider the effect on the two-path atom wave interference when the vibrating wire is modeled as a quantum object, hence functioning as a quantum noninertial reference frame. We outline a possible realization of the vibrating wire, atom interferometer using a superfluid helium quantum interference setup.