Uncertainty principle in larmor clock

Chuan Qiao, Zhongzhou Ren

It is well known that the spin operators of a quantum particle must obey uncertainty relations. We use the uncertainty principle to study the Larmor clock. To avoid breaking the uncertainty principle, Larmor time can be defined as the ratio of the phase difference between a spin-up particle and a spin-down particle to the corresponding Larmor frequency. The connection between the dwell time and the Larmor time has also been confirmed. Moreover, the results show that the behavior of the Larmor time depends on the height and width of the barrier.

C. G. DARWIN

D. Sokolovski, Elena V. Akhmatskaya

A controversy surrounding the "tunnelling time problem" stems from the seeming inability of quantum mechanics to provide, in the usual way, a definition of the duration a particle is supposed to spend in a given region of space. For this reason, the problem is often approached from an "operational" angle. Typically, one tries to mimic, in a quantum case, an experiment which yields the desired result for a classical particle. One such approach is based on the use of a Larmor clock. We show that the difficulty with applying a non-perturbing Larmor clock in order to "time" a classically forbidden transition arises from the quantum Uncertainty Principle. We also demonstrate that for this reason a Larmor time (in fact, any Larmor time) cannot be interpreted as a physical time interval. We provide a theoretical description of the quantities measured by the clock.

Jan Hilgevoord, Jos Uffink

D. Sokolovski, J. N. L. Connor

The tunneling-time problem is shown to be analogous to the interpretation of the two-slit interference experiment. A measurement assuming an arbitrarily small interaction between a particle and a clock is shown to contradict the uncertainty principle and leads to complex times. A real non-negative traversal time is obtained in a measurement which selects Feynman paths that spend in the barrier a known amount of time; this, however, strongly perturbs the tunneling. The Larmor clock demonstrates both types of behavior.

B. Kivel