Tunnelling times, Larmor clock, and the elephant in the room

Area of Science:

• Quantum mechanics
• Quantum tunneling
• Atomic and molecular physics

Background:

• The quantum tunnelling time problem highlights challenges in defining the time a particle spends in a region.
• Operational approaches, like using a Larmor clock, attempt to measure this duration by mimicking classical experiments.

Purpose of the Study:

• To investigate the application of a non-perturbing Larmor clock for measuring quantum tunnelling time.
• To analyze the limitations imposed by quantum mechanics, specifically the Uncertainty Principle, on such measurements.

Main Methods:

• Theoretical analysis of Larmor clock behavior in quantum systems.
• Application of quantum mechanical principles, including the Uncertainty Principle, to tunnelling phenomena.

Main Results:

• The Uncertainty Principle fundamentally hinders the use of Larmor clocks for non-perturbing time measurements in classically forbidden transitions.
• Larmor time, regardless of its specific value, cannot be interpreted as a physical time interval due to quantum effects.

Conclusions:

• The inherent quantum nature, particularly the Uncertainty Principle, prevents a direct operational definition of tunnelling time using Larmor clocks.
• A theoretical framework is provided to describe the quantities actually measured by a Larmor clock in this context.