Abstract
We make the hypothesis that our universe is threedimensional and curved, hence our universe may be embedded in a fourdimensional Euclidean space where the four dimensions are (x, y, z, t). The fourth dimension is time t which is treated like a spatial dimension. Straightforwardly, this Euclidean space has an underlying hypersquare array for which the edges have a width of one Planck length. The eigenfunctions of each edge of this array are √ 2exp(ix i) where x_i = x, y, z or t. As previously published, the quarks are threedimensional in real space. The quark up has a mass of 2^ 21 eV/c 2 and the quark down 2^22 eV/c 2 (the quark down is an excited state of the quark up). Because the quark up is threedimensional (like the apex of a tetrahedron), each edge of the quark has an eigenvalue of 2 ^7 eV/c 2. Let us consider that the color charge of the gluons are in fact the coordinates in real space (x: red; y:blue; z: green). The gluons have no mass so they have no temporal dimension. Each pair of quarks, share one gluon (the gluons interfere with the quarks edges).Gluons are bosons and quarks are fermions so for each edge of the underlying array (except the temporal edges) we calculate the ground states. In one proton or in one neutron, there are 3 gluons and 3 quarks; as only the temporal edges of the 3 quarks are not in the ground states and because the protons and neutrons obey the Schrödinger equation, the masses of the proton or neutron are equal to 2^ 30 / ln(π)eV/c 2 = 937MeV/c 2. The difference between the masses of the proton and neutron comes from the difference between the experimental masses and the theoretical masses of quarks up and down. Straightforwardly, we found theoretical values of the masses of protons and neutrons within 2% of the experimental values of the masses of protons and neutrons.