TITLE:
On the Spacetime Statistical Equivalence Principle and Its Applications within the Framework of a Non-Expanding Steady-State Cosmological Model
AUTHORS:
Chenxi Guo, Mingli Wu
KEYWORDS:
Spacetime Statistical Equivalence, Ergodicity, Spatial Ergodicity, Statistical Steady-State Universe, Einstein Static Universe
JOURNAL NAME:
Journal of Modern Physics,
Vol.17 No.10,
October
20,
2026
ABSTRACT: This paper proposes and rigorously defines a “Spacetime Statistical Equivalence Principle”: in a statistical system satisfying stationarity, spatial homogeneity, weak correlation, and ergodicity, the statistical distribution obtained by long time-series sampling of the same event and the statistical distribution obtained by single sampling of a large number of spatially independent events both converge to the same ensemble average in the mean-square sense, with the same order of convergence. Specifically, under the stated assumptions, the variance (and hence the mean-square error) of both the time average and the spatial average decays as O(1/N), equivalently the standard deviation decays as O(N−1/2). This principle is a natural generalization of the traditional ergodic theorem in the spatial dimension, and its essence is the statistical equivalence of the “time average” and the “spatial average”, rather than a symmetry transformation between spacetime coordinates. On this basis, the equivalence relation is applied to a non-expanding steady-state cosmological model: under the premise that the stationarity assumption holds, it is demonstrated that its large-scale statistical state possesses time-translation invariance, and a logical-level compatibility comparison is made with Einstein’s static universe solution. This paper does not introduce a cosmological constant or dark energy, nor does it rely on any expansion dynamics, aiming to provide a statistical-mechanical foundation for the steady-state view of the universe.