Quantization of the partial differential equations of motion obtained from an application of the Einstein, Infeld and Hoffmann method to a 4+1 space leads to the concept ofspaceons. The vacuum expectation value of the Hamiltonian for two particles involves a potentialenergy contribution\(V(r) = - (A/r)\int\limits_0^{r/\sigma } {\exp [ - t^2 /2] dt} \) whereA and σ are parameters depending on charge, mass and two additional ones with dimension of length and mass. The use of observations from electron-proton scattering, which suggest a Gaussian distribution, when applied here implies a periodicity length of 3050 m in the additional dimension and that the lowest nonzero energy for a spaceon associated with the electron is ∼ 103 GeV. For the proton, however, the energy of the associated spaceon is ∼ 0.5 GeV.