Classical Disappearance of the Ultraviolet Catastrophe via Stochastic Boundary Conditions

The Ultraviolet Catastrophe is not an inevitable prediction of classical statistical physics applied to a continuum field. Instead, it is the result of a mathematical modeling mistake in which homogeneous boundary conditions are employed in a context with stochastic boundary conditions. By explicitly modeling the stochastic boundary conditions, the thermal equilibrium energy in a one-dimensional linear scalar field is shown to be finite when coupled to thermal oscillators at its boundary points, without quantum assumptions. This analysis does not claim to reproduce the blackbody radiation spectrum nor claim to replace Planck's quantum hypothesis with some classical mechanism. It has only been shown that the standard ultraviolet divergence of the energy in a continuum field is consequence of a mathematical modeling mistake where the incorrect boundary conditions are used.