Relativistic deceleration vs acceleration, Unruh effect observation, and the Schott energy

Abstract

This article examines finite-time relativistic deceleration and its energy balance within the Lorentz-Abraham-Dirac equation, with special attention to boundary Schott-energy terms. From experimental and kinematical viewpoints, deceleration differs from acceleration. Proper accelerations or decelerations relevant to Unruh-effect observations may be more naturally realized in deceleration than in comparable acceleration scenarios. Deceleration from finite initial energy to rest can occur only over a finite time interval, unlike idealized acceleration, which can continue indefinitely. Thus, finite acceleration or deceleration must include boundary transitions in the radiation-energy balance. We first obtain expressions for the time and distance required for a relativistic particle with nonzero initial velocity to stop under constant deceleration. Applied to the Lynch-Cohen-Hadad-Kaminer (LCHK) estimate, they show that the quoted extremely large deceleration cannot represent sustained classical uniform proper deceleration over a macroscopic crystal length. The stopping time and distance would be too small, and the upper bound on sustained deceleration is far below that estimate. We next consider a charged particle entering and leaving a uniform acceleration or deceleration interval without a velocity jump. This motion can be described within the LAD equation if the external force includes impulses during the short transitions between inertial and uniformly accelerated or decelerated motion. External work is not locally converted directly into radiation during the uniform segment. The Schott energy acts instead as an intermediate reservoir: it changes during the transitions and supplies the radiated energy during the subsequent uniform interval. This idealized LAD radiation mechanism is absent from the Lorentz-equation description and from LAD descriptions that neglect boundary conditions.