Contrasting Classical and Quantum Vacuum States in Non-Inertial Frames

Abstract

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each non-inertial coordinate frame has its own vacuum state. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. Based upon the classical analysis, it is suggested that the claimed heating effects of acceleration through the vacuum may not exist in nature.

29 pages

References in corpus (6)

• The Unruh effect and its applications
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• The Blackbody Radiation Spectrum Follows from Zero-Point Radiation and the Structure of Relativistic Spacetime in Classical Physics
• Derivation of the Planck Spectrum for Relativistic Classical Scalar Radiation from Thermal Equilibrium in an Accelerating Frame
• Classical Physics of Thermal Scalar Radiation in Two Spacetime Dimensions
• Classical and Quantum Interpretations Regarding Thermal Behavior in a Coordinate Frame Accelerating Through Zero-Point Radiation

Cited by in corpus (4)

• Understanding Zero-Point Energy in the Context of Classical Electromagnetism
• Quantum field theory in the Weyl-Wigner representation
• Conflict Between Classical Mechanics and Electromagnetism: The Harmonic Oscillator in Equilibrium with a Bath
• Classical Zero-Point Radiation and Relativity: The Problem of Blackbody Radiation Revisited