Strong-field electrodynamics at eleven parameters: the Schwinger field as the acceleration bound of the electron
Abstract
Special relativity at eleven parameters (SR11) bounds the proper acceleration of a body of mass m by a max = mc 3 /ℏ, the Planck acceleration scaled by the mass in Planck units. The bound arises from a hyperbolic generator of the conformal algebra exactly as v ≤ c arises from the Lorentz boost. Strong-field quantum electrodynamics organises its regimes by the quantum nonlinearity parameter χ = eℏ |F µν p ν |/(m 3 c 4 ), the field in the electron's rest frame in units of the Schwinger field E S = m 2 c 3 /(eℏ). This paper states and exploits an identity: χ is the proper acceleration of the Lorentz force in units of the bound of SR11, χ = a/a max (e), exactly and covariantly, so that the Schwinger field is the field in which the electron reaches its kinematic bound, eE S /m = mc 3 /ℏ = 2.33 × 10 29 m s -2 . The consequences are read off. The photon's parameter χ γ is the acceleration that the field would give an electron of the photon's momentum, in units of the bound, and nonlinear Breit-Wheeler pair creation is the photon's form of the bound. The Unruh temperature of an electron at χ is χ times the maximal temperature of the electron bath, mc 2 /(2πk B ) = 81 keV. The rest-frame energy of the photons an electron emits is ℏa/c = χ mc 2 , so the bound is reached exactly where the emission recoil equals the rest energy, which is the onset of quantum radiation reaction. The classical theory's own limit, the field E S /α at which the Lorentz-Abraham-Dirac equation becomes pathological, lies 137 times beyond the bound, so that a body of SR11 never reaches it. The classical radiated power of a body is bounded by (2α/3)(m/M P ) 2 times the Planck power, 0.31 MW for an electron. Two readings of the bound are distinguished. In the categorical one the one-body description ends at χ = 1 and quantum electrodynamics takes over with the electron no longer a body, which agrees with everything known. In the dynamical one the achieved acceleration saturates as the velocity does, a/a max = χ/ 1 + χ 2 , the analogue of v/c = (p/(mc))/ 1 + (p/(mc)) 2 . That reading reduces the classical radiated power by 1/(1 + χ 2 ) and the constant-field paircreation exponent from π/χ to π 1 + χ 2 /χ, a factor e -1.3 in the rate at χ = 1. The second reading is the one SR11 announced as its signature, and it is falsifiable by the experiments that reach χ ≃ 1 in this decade, LUXE and E-320, whose numbers are given; the first is not, and the paper says which observation would decide between them.
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BibTeX
@misc{reynaud2026strongfield,
title = {{Strong-field electrodynamics at eleven parameters: the Schwinger field as the acceleration bound of the electron}},
author = {Patrick B. Reynaud},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05759281v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Strong-field electrodynamics at eleven parameters: the Schwinger field as the acceleration bound of the electron
AU - Patrick B. Reynaud
PY - 2026
DA - 2026/09/22
PB - HAL
UR - https://hal.science/hal-05759281v2
AB - Special relativity at eleven parameters (SR11) bounds the proper acceleration of a body of mass m by a max = mc 3 /ℏ, the Planck acceleration scaled by the mass in Planck units. The bound arises from a hyperbolic generator of the conformal algebra exactly as v ≤ c arises from the Lorentz boost. Strong-field quantum electrodynamics organises its regimes by the quantum nonlinearity parameter χ = eℏ |F µν p ν |/(m 3 c 4 ), the field in the electron's rest frame in units of the Schwinger field E S = m 2 c 3 /(eℏ). This paper states and exploits an identity: χ is the proper acceleration of the Lorentz force in units of the bound of SR11, χ = a/a max (e), exactly and covariantly, so that the Schwinger field is the field in which the electron reaches its kinematic bound, eE S /m = mc 3 /ℏ = 2.33 × 10 29 m s -2 . The consequences are read off. The photon's parameter χ γ is the acceleration that the field would give an electron of the photon's momentum, in units of the bound, and nonlinear Breit-Wheeler pair creation is the photon's form of the bound. The Unruh temperature of an electron at χ is χ times the maximal temperature of the electron bath, mc 2 /(2πk B ) = 81 keV. The rest-frame energy of the photons an electron emits is ℏa/c = χ mc 2 , so the bound is reached exactly where the emission recoil equals the rest energy, which is the onset of quantum radiation reaction. The classical theory's own limit, the field E S /α at which the Lorentz-Abraham-Dirac equation becomes pathological, lies 137 times beyond the bound, so that a body of SR11 never reaches it. The classical radiated power of a body is bounded by (2α/3)(m/M P ) 2 times the Planck power, 0.31 MW for an electron. Two readings of the bound are distinguished. In the categorical one the one-body description ends at χ = 1 and quantum electrodynamics takes over with the electron no longer a body, which agrees with everything known. In the dynamical one the achieved acceleration saturates as the velocity does, a/a max = χ/ 1 + χ 2 , the analogue of v/c = (p/(mc))/ 1 + (p/(mc)) 2 . That reading reduces the classical radiated power by 1/(1 + χ 2 ) and the constant-field paircreation exponent from π/χ to π 1 + χ 2 /χ, a factor e -1.3 in the rate at χ = 1. The second reading is the one SR11 announced as its signature, and it is falsifiable by the experiments that reach χ ≃ 1 in this decade, LUXE and E-320, whose numbers are given; the first is not, and the paper says which observation would decide between them.
ER -