In 1935, Vladimir Fock showed that the quantum mechanical bound Kepler problem is equivalent to the problem of a free particle confined to a three-dimensional unit sphere in four-dimensional space. Specifically, Fock showed that the Schrödinger wavefunction in the momentum space for the Kepler problem was the stereographic projection of the spherical harmonics on the sphere. Rotation of the sphere and re-projection results in a continuous mapping of the elliptical orbits without changing the energy, an SO(4) symmetry sometimes known as Fock symmetry ; quantum mechanically, this corresponds to a mixing of all orbitals of the same energy quantum number n. Valentine Bargmann noted subsequently that the Poisson brackets for the angular momentum vector L and the scaled LRL vector A formed the Lie algebra for SO(4). Simply put, the six quantities A and L correspond to the six conserved angular momenta in four dimensions, associated with the six possible simple rotations in that space (there are six ways of choosing two axes from four). This conclusion does not imply that our universe is a three-dimensional sphere; it merely means that this particular physics problem (the two-body problem for inverse-square central forces) is mathematically equivalent to a free particle on a three-dimensional sphere.