Abstract
Using a non-standard model of a collective set theory, this paper proposes a description of a singlet state of quantum particles in terms of quaternions. The basic relation of this theory is the division relation, which is pre-ordering; antisymmetry is rejected. It turns out that the rejection of antisymmetry opens a new perspective for description of singlet states. We obtain two pairs of quaternions describing such states; they are the only quaternions generating these states because they are generators of the same finite group. Moreover, quaternions that form a pair have the same angles of rotation, but the rotations are in opposite directions, and both quaternions designate the same straight line in R3. Finally, we can determine a SU(2) group for the obtained composite state and prove that the investigated state is inseparable; therefore, it is entangled.
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