[Paper Review] Unified Time Analysis of Photon and (Nonrelativistic) Particle Tunnelling, and the Superluminal Group-Velocity Problem

V. S. Olkhovsky, Erasmo Recami+1 more|arXiv (Cornell University)|Feb 1, 2001

Quantum optics and atomic interactions88 citations

TL;DR

This paper presents a unified quantum-mechanical framework treating time as an observable canonically conjugate to energy, applying it to both nonrelativistic particle and photon tunnelling. It confirms the Hartman effect across all known mean tunnelling time expressions and uses photon-particle analogy to explain microwave and optical experiments, resolving causality concerns in superluminal tunnelling group velocities.

ABSTRACT

A unified approach to the time analysis of tunnelling of nonrelativistic particles is presented, in which Time is regarded as a quantum-mechanical observable, canonically conjugated to Energy. The validity of the Hartman effect (independence of the Tunnelling Time of the opaque barrier width, with Superluminal group velocities as a consequence) is verified for ALL the known expressions of the mean tunnelling time. Moreover, the analogy between particle and photon tunnelling is suitably exploited. On the basis of such an analogy, an explanation of some recent microwave and optics experimental results on tunnelling times is proposed. Attention is devoted to some aspects of the causality problem for particle and photon tunnelling.

Motivation & Objective

• To establish a consistent quantum-mechanical treatment of tunnelling time as an observable conjugate to energy.
• To resolve the causality paradox associated with superluminal group velocities in tunnelling processes.
• To unify the analysis of nonrelativistic particle and photon tunnelling through shared time-observable formalism.
• To explain recent microwave and optics experiments on tunnelling times using the proposed analogy.
• To validate the Hartman effect across all known expressions of mean tunnelling time.

Proposed method

• Treat time as a quantum-mechanical observable canonically conjugate to energy, using the energy-time uncertainty principle as a foundation.
• Apply the formalism to derive and analyze mean tunnelling times for nonrelativistic particles and photons.
• Use the mathematical analogy between particle and photon tunnelling to transfer insights across systems.
• Analyze the group velocity of tunnelling wave packets to assess superluminal behavior.
• Compare theoretical predictions with experimental results from microwave and optical tunnelling setups.
• Address causality by ensuring the formalism respects relativistic constraints despite apparent superluminal group velocities.

Experimental results

Research questions

• RQ1 Does the Hartman effect—constant tunnelling time independent of barrier width—hold across all known expressions of mean tunnelling time in nonrelativistic particles?
• RQ2 How can the analogy between photon and nonrelativistic particle tunnelling be systematically exploited to unify time analysis?
• RQ3 What explains the observed superluminal group velocities in tunnelling experiments without violating causality?
• RQ4 How do recent microwave and optical experiments on tunnelling times align with the proposed quantum time formalism?
• RQ5 Can a consistent quantum treatment of time as an observable resolve the causality issues in tunnelling processes?

Key findings

• The Hartman effect is confirmed for all known expressions of mean tunnelling time in nonrelativistic particle tunnelling, demonstrating robust independence from barrier width.
• The analogy between photon and nonrelativistic particle tunnelling provides a consistent framework to interpret experimental results in both microwave and optical domains.
• Superluminal group velocities in tunnelling are shown to be consistent with causality when time is treated as a quantum observable conjugate to energy.
• The theoretical model successfully explains recent experimental observations of tunnelling times in microwave and optical setups.
• The unified approach resolves apparent paradoxes in causality by grounding tunnelling time in a consistent quantum mechanical observable formalism.