[Paper Review] Radiation reaction in quantum mechanics

Atsushi Higuchi|ArXiv.org|Dec 15, 1998

Quantum Mechanics and Applications4 references3 citations

TL;DR

This paper challenges the classical Lorentz-Dirac radiation reaction formula in quantum mechanics by showing it yields an incorrect classical limit when a charged particle accelerates under a time-independent potential. Using semi-classical analysis, the authors demonstrate that the correct classical limit for position shift arises not from the Lorentz-Dirac formula but from energy loss via the Larmor formula, implying a fundamental inconsistency in the classical limit of radiation reaction in quantum theory.

ABSTRACT

The Lorentz-Dirac radiation reaction formula predicts that the position shift of a charged particle due to the radiation reaction is of first order in acceleration if it undergoes a small acceleration. A semi-classical calculation shows that this is impossible at least if the acceleration is due to a time-independent potential. Thus, the Lorentz-Dirac formula gives an incorrect classical limit in this situation. The correct classical limit of the position shift at the lowest order in acceleration is obtained by assuming that the energy loss at each time is given by the Larmor formula.

Motivation & Objective

• To assess the validity of the Lorentz-Dirac radiation reaction formula in the classical limit of quantum mechanics.
• To identify inconsistencies between the classical radiation reaction formula and quantum mechanical predictions under time-independent potentials.
• To determine the correct classical limit for position shift due to radiation reaction in quantum systems.
• To resolve the discrepancy between semi-classical calculations and the Lorentz-Dirac formula in low-acceleration regimes.

Proposed method

• Performing a semi-classical calculation of position shift for a charged particle under a time-independent potential.
• Comparing the classical limit of quantum mechanical results with the Lorentz-Dirac radiation reaction formula.
• Assessing energy loss per unit time using the Larmor formula as a candidate for the correct classical limit.
• Analyzing the order of magnitude of position shift in acceleration to identify inconsistencies in the Lorentz-Dirac prediction.
• Deriving the classical limit of position shift under the assumption of energy loss via the Larmor formula.
• Confronting the Lorentz-Dirac formula with quantum mechanical expectations to expose its failure in the classical regime.

Experimental results

Research questions

• RQ1 Does the Lorentz-Dirac radiation reaction formula correctly describe the classical limit of position shift in quantum mechanics?
• RQ2 Why does the Lorentz-Dirac formula predict a first-order position shift in acceleration, contradicting quantum mechanical semi-classical calculations?
• RQ3 What is the correct classical limit for radiation reaction position shift when acceleration arises from a time-independent potential?
• RQ4 Can the Larmor formula for energy loss provide a consistent classical limit for radiation reaction in quantum systems?
• RQ5 How does the semi-classical behavior of a charged particle under a time-independent potential challenge the validity of the Lorentz-Dirac equation?

Key findings

• The Lorentz-Dirac formula predicts a first-order position shift in acceleration, which contradicts semi-classical quantum mechanical calculations.
• Semi-classical analysis shows that such a first-order shift is impossible when acceleration arises from a time-independent potential.
• The correct classical limit for position shift is obtained by assuming energy loss at each time follows the Larmor formula.
• The Lorentz-Dirac formula fails to reproduce the correct classical limit in this scenario, indicating an inconsistency in its quantum-to-classical correspondence.
• The discrepancy arises because the Lorentz-Dirac formula does not align with the energy loss mechanism implied by quantum mechanical semi-classical dynamics.
• The study concludes that the Larmor formula provides the physically correct classical limit for radiation reaction in this context.