The Salecker-Wigner-Peres Quantum Clock, Feynman Paths, and a Tunnelling Time that Should NOT Exist

The Salecker-Wigner-Peres Quantum Clock, Feynman Paths, and a Tunnelling Time that Should NOT Exist The Salecker-Wigner-Peres (SWP) clock is often used to determine the duration a quantum particle
is supposed to spend is a specified region of space Ω. By construction, the result is a real positive
number, and the method seems to avoid the difficulty of introducing complex time parameters, which
arises in the Feynman paths approach. However, it tells very little about what is being learnt about
the particle’s motion. We investigate this matter further, and show that the SWP clock, like any
other Larmor clock, correlates the rotation of its angular momentum with the durations τ Feynman
paths spend in Ω, therefore destroying interference between different durations. An inaccurate
weakly coupled clock leaves the interference almost intact, and the need to resolve resulting ”which
way?” problem is the main difficulty at the centre of the ”tunnelling time” controversy. In the
absence of a probability distribution for the values of τ , the SWP results are expressed in terms
of moduli of the ”complex times”, given by the weighted sums of the corresponding probability
amplitudes. It is shown that over-interpretation of these results, by treating the SWP times as
physical time intervals, leads to paradoxes and should be avoided. We analyse various settings of
the SWP clock, different calibration procedures, and the relation between the SWP results and the
quantum dwell time. Our general analysis is applied to the cases of stationary tunnelling and tunnel
ionisation.