Intrinsic Nonlocality of Spin- and Polarization-Resolved Probabilities in Strong-Field Quantum Electrodynamics

Spin and polarization are central to precision tests of fundamental physics and for interpreting radiation from astrophysical sources and ultraintense laser-matter experiments. Here, focusing on the fundamental process of nonlinear Compton scattering, we demonstrate that a key assumption underlying current strong-field quantum electrodynamics (SFQED) models, i.e., that emission can be treated as an instantaneous random event sampled from a local differential rate, is inconsistent once emission angles, electron spin, and/or photon polarization are resolved. Namely, \emph{even in strictly constant and uniform fields}, the resulting fully differential distribution is sign-indefinite, yielding negative inferred probabilities. The physical reason is that the photon emission probability builds up over a finite length of the electron trajectory, the formation region, during which the electron direction changes by roughly the same small angle that defines the radiation cone. Therefore, we put forward a new method where we integrate over this formation region analytically to obtain a physically consistent electron spin and photon polarization model. Simulations of a GeV-class electron-laser collision accessible at current petawatt facilities and of emission in a pulsar-like magnetic field are shown to reveal spin and polarization patterns that differ even qualitatively from state-of-the-art local models. In particular, our new model predicts substantial angle-dependent circular photon polarization where the well-known collinear-emission approach yields none, and a pronounced helicity bias in the recoiling electrons absent from current predictions. These findings have direct implications for upcoming strong-field QED experiments and for interpreting polarized radiation from extreme astrophysical environments.