Operational measurement of relativistic equilibrium from stochastic fields alone

arXiv:2602.16765v1 Announce Type: new
Abstract: Relativistic equilibrium is described by the inverse-temperature four-vector $beta^mu = u^mu/(k_B T_0)$ rather than by a frame-dependent scalar temperature. We show that $beta^mu$ can be reconstructed directly from electromagnetic fluctuations emitted by a drifting medium, without external probes, spectral lines, or absolute intensity calibration. A Lorentz boost converts isotropic rest-frame noise into correlated electric and magnetic fields, producing a gain-independent fluctuation observable that yields the drift velocity purely from stochastic data. Combined with angle-resolved noise spectra governed by the covariant fluctuation–dissipation theorem, this enables full reconstruction of $beta^mu$ using electromagnetic measurements alone. Monte Carlo analysis demonstrates percent-level accuracy at realistic signal-to-noise ratios, and feasibility estimates indicate sub-microsecond integration times for laboratory plasmas. To our knowledge, this constitutes the first method that reconstructs the covariant thermal state $beta^mu$ of a relativistic medium from passive stochastic fields alone, without absolute calibration, spectral lines, or external probes. These results establish vacuum electromagnetic fluctuations as a direct operational probe of relativistic equilibrium.