Operational measurement of relativistic equilibrium from stochastic fields alone

Ira Wolfson

Operational measurement of relativistic equilibrium from stochastic fields alone

Ira Wolfson

Abstract

Relativistic equilibrium is described by the inverse-temperature four-vector $β^μ= u^μ/(k_B T_0)$ rather than by a frame-dependent scalar temperature. We show that $β^μ$ 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 $β^μ$ 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 $β^μ$ 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.

Operational measurement of relativistic equilibrium from stochastic fields alone

Abstract

Relativistic equilibrium is described by the inverse-temperature four-vector

rather than by a frame-dependent scalar temperature. We show that

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

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

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.

Paper Structure (8 equations, 3 figures)

This paper contains 8 equations, 3 figures.

Figures (3)

Figure 1: Angle-resolved electromagnetic noise spectra and reconstruction of the effective temperature factor governed by Eq. (7). (a) Angular PSD at fixed laboratory frequency for a drifting Drude medium, compared with a Doppler-only reference assuming isotropic temperature. (b) Ratio of the two predictions, isolating the thermodynamic factor $1/(1-\beta\cos\theta)$. (c) Effective temperature factor extracted from noisy PSD data using the known response $\sigma(\omega)$. (d) Forward-backward asymmetry versus laboratory frequency for several boost velocities; dotted lines indicate the constant-$\sigma$ limit.
Figure 2: Monte Carlo reconstruction of $(\beta, T_0)$ from synthetic angle-resolved PSD data. Percent-level precision is achieved at SNR $\gtrsim 20$.
Figure 3: Feasibility for laboratory plasmas. Predicted asymmetry versus frequency and required integration times from Dicke radiometer scaling.