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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.
General relativity predicts a
singularity in the beginning of the universe being called big bang. Recent
developments in loop quantum cosmology avoid the singularity and the big bang
is replaced by a big bounce. A classical theory of gravitation in flat
space-time also avoids the singularity under natural conditions on the density
parameters. The universe contracts to a positive minimum and then it expands
during all times. It is not symmetric with regard to its minimum implying a
finite age measured with proper time of the universe. The space of the universe
is flat and the total energy is conserved. Under the assumption that the sum of
the density parameters is a little bit bigger than one the universe is very hot
in early times. Later on, the cosmological model agrees with the one of general
relativity. A new interpretation of a non-expanding universe may be given by
virtue of flat space-time theory of gravitation.
The S matrix of e-e scattering has the structure of a projection operator that projects incoming separable product states onto entangled two-electron states. In this projection operator the empirical value of the fine-structure constant α acts as a normalization factor. When the structure of the two-particle state space is known, a theoretical value of the normalization factor can be calculated. For an irreducible two-particle representation of the Poincaré group, the calculated normalization factor matches Wyler’s semi-empirical formula for the fine-structure constant α. The empirical value of α, therefore, provides experimental evidence that the state space of two interacting electrons belongs to an irreducible two-particle representation of the Poincaré group.