A novel interpretation of the Klein-Gordon equation

The relativistically-correct Klein-Gordon equation requires twice the boundary conditions of the non-relativistic Schrodinger equation and does not have an accepted configuration-space interpretation. Instead of interpreting its solution as a probability wave determined by an initial boundary condition, this paper considers the possibility that the solutions are determined by both an initial and a final boundary condition. By constructing a relativistically invariant probability weight from the size of the solution space, it is shown that the usual probability distributions can nearly be recovered in the non-relativistic limit. The non-exact results imply small but potentially measurable deviations from standard quantum mechanics.