In relativistic quantum mechanics, elementary particles are
described by irreducible unitary representations of the Poincaré group. The
same applies to the center-of-mass kinematics of a multi-particle system that
is not subject to external forces. As shown in a previous article, for spin-1/2
particles, irreducibility leads to a correlation between the particles that has
the structure of the electromagnetic interaction, as described by the
perturbation algorithm of quantum electrodynamics. The present article examines
the consequences of irreducibility for a multi-particle system of spinless
particles. In this case, irreducibility causes a gravitational force, which in
the classical limit is described by the field equations of conformal gravity.
The strength of this force has the same order of magnitude as the strength of
the empirical gravitational force.
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