European Journal of Physics

On the phase change of a spinor due to a rotation through 2 pi

W Gough

Published Jul 1, 1992• 4 citations

Abstract

Experiments on neutron interference do not prove beyond dispute that the wavefunction of a spinor has periodicity 4 pi with respect to a rotation of the coordinate axes. The observed sign change in the wavefunction after one Larmor revolution could be explained by a changing phase factor due to 'tumble'. The case for and against tumble is briefly considered.

DOI: 10.1088/0143-0807/13/4/003

Related papers

Proposed neutron interferometer observation of the sign change of a spinor due to 2π precession

Michael A. Home

If a spin-½ particle is placed in a constant uniform magnetic field for a time t during which, classically, the Larmor precession angle would be θ, then according to quantum mechanics the components of the spin part of the wave function undergo phase changes of ±θ/2. Hence, corresponding to a classical precession of 2π radians, there is a sign change of the spinor, whatever the initial polarization may be. Bernstein pointed out that this sign change can be observed by coherently splitting a fermion beam, subjecting one part to the magnetic field, and coherently recombining the parts. Evidently, the same interference effect can be achieved by subjecting the two parts of the beam to fields which would classically cause precessions of π radians in opposite senses. He noted advantages in studying neutral rather than charged particles, and outlined a proposal for an interferometry experiment with neutrons. The recent invention and application of a remarkable single-crystal neutron interferometer greatly increases the feasibility of observing the sign change. In the experiment of Ref. 3 a neutron beam is split, and the two parts follow paths of different elevations. The interference of the recombined parts exhibits the effect of gravitational potential difference between the two elevations. In the experiment which we propose, the paths could be kept at the same elevation, but phase differences would be produced by appropriate magnetic fields.

Cambridge University Press eBooksFeb 26, 19930 citations

Observability of the Sign Change of Spinors under 2 π Rotations

Yakir Aharonov, Leonard Susskind

We consider the observability of the sign change of spinors under $2\ensuremath{\pi}$ rotations. We show that in certain circumstances there are observable consequences of such rotations, contrary to the classical case. We suggest experiments which can in principle be done to demonstrate such effects.

Physical ReviewJun 25, 1967199 citations

Observation of 2π Rotations by Fresnel Diffraction of Neutrons

A. G. Klein, G. I. Opat

We report on the first observation of Fresnel diffraction of a beam of unpolarized slow neutrons by individual ferromagnetic domain boundaries. The observed occurrence of destructive interference in the experiment demonstrates that the phase of a spinor wave function changes by a factor of - 1 when the particle described by that wave function is rotated by an odd multiple of $2\ensuremath{\pi}$ radians.

Physical Review LettersAug 2, 1976104 citations

Spinor Symmetry and Spin Superposition

Helmut Rauch, Samuel A. Werner

The observation of the 4π symmetry of spinor wave functions was one of the first and highly debated neutron interference experiments. Polarized neutrons have been used to verify the spin-superposition principle on a macroscopic level when the spin in one beam path is inverted with respect to the other one. This results in a spin polarization perpendicular to both initial spins. When a Rabi flipper is used the final spin polarization rotates in this perpendicular plane with the Larmor frequency of the flipper field. Thus, it produces a “frozen” Larmor spin rotation in free space. In this case the spin-flip is associated with an energy (photon) transfer which causes this effect. A magnetic Josephson effect-like situation exists when spin-flippers with slightly different resonance frequencies are used in both beam paths. When such a spin reversal is done in both beam paths a magnetic Josephson effect analog has been realized which shows a remarkably high energy resolution. Multiphoton exchange can be achieved when off-resonance fields are used.

Oxford University Press eBooksJan 15, 20150 citations

Critical Remark on the Observability of the Sign Change of Spinors under 2π Rotations

Gerhard C. Hegerfeldt, K. Kraus

In a recent paper, Aharonov and Susskind claimed rotations by 2π to have observable effects on spinors. Their reasoning is shown to be inconclusive.Received 21 September 1967DOI:https://doi.org/10.1103/PhysRev.170.1185©1968 American Physical Society

Physical ReviewJun 25, 196817 citations

The curious problem of spinor rotation

Mark P. Silverman

Can the sign change of a spinor wavefunction rotated by 360 degrees be observed? If so, does this violate any basic quantum mechanical principles? The answers are yes and no, respectively. Tests of this fundamental quantum mechanical prediction are discussed, and the close analogy between the experimental methods employed and well-known processes in classical physical optics is pointed out.

European Journal of PhysicsApr 1, 198050 citations