There is No Einstein-Podolsky-Rosen Paradox in Clifford-Spaces

It is shown how one can attain the desired locally causal property of QM in Clifford-spaces despite the spacelike separation of two massive spin-12 particles involved in the Einstein-Podolksy-Rosen (EPR) experiment. This is achieved by proving why the addition laws of the particles poly-vector-valued momentum in Clifford-space is null-like. This is the key reason why it is possible to implement a locally causal QM theory in Clifford-spaces despite that QM has a non-local character in ordinary spacetime. The two particles can exchange signals in Clifford-space encoding their respective spin measurement values. Consequently, there is no EPR paradox in the Clifford space associated with the Clifford algebra Cl(3, 1) of the underlying 4D spacetime. PACS numbers: 03.65.Ud, 03.67.-a, 02.10.Ud Not so long ago Borchsenius [1] argued that when the quantum measurement principle is adapted to the generating space of Clifford algebras the transition probabilities for two-fold degenerate paths in space-time equals the transition amplitudes for the underlying paths in Clifford space. This property was used to show that the apparent non-locality of quantum mechanics in a double slit experiment and in an EPR type of measurement is resolved when analyzed in terms of the full paths in the underlying Clifford space. Most recently, Christian [2] has shown that Bell’s theorem fails for Cliffordalgebra-valued local realistic variables. This was shown by exactly reproducing the Quantum Mechanical expectation values for the EPR-Bohm type spin correlations observables by means of local, deterministic, Clifford algebra valued variables, and without necessitating either remote contextuality or backward causation. Since the Clifford product of poly-vector (multivector) variables is non-commutative in general, the spin correlations values derived within such