One of the main problems of
contemporary physics is to find a quantum description of gravity. This present
approach attempts to remedy the problem through the quantization of a finite
but large flat Minkowski space-time by means of Fourier expansion of the displacement
four vector. By applying second
quantization techniques, space-time emerges as a superposition of space-time
eigen states or lattices of quantized space-time vibrations also known as
gravitons. Each lattice element four vector is a graviton and traces out an
elementary four volume (lattice cell). The stress-momentum tensor of each
graviton defines its curvature and also the curvature of the associated lattice
as described by General Relativity. The eigen states of space-time are found to
be separated by a quantum of energy equal to the product of the Hubble constant
and the Planck constant. The highest energy state is at Planck energies. This
paper also shows that gravitons can be absorbed and emitted by the space-time lattice
changing the volume of its primitive cells and that particles of observable
matter are associated with a graviton whose frequency is equal to the
particle’s Compton frequency which the lattice can absorb producing a
perturbation in the lattice.The space-time lattice is found to be unstable
and decays by radiating low energy gravitons of energy equal to the product of
the Hubble constant and the Planck constant. This decay causes the space-time
superstructure to expand. The
graviton is seen a composite spin 2 particle made from a combination of spin
half components of the displacement four vector elements. The spin symmetry of
its constituent elements can breakdown to give rise to other vector or scalar
bosons. Dark Matter is seen as a
consequence of Bose-Einstein statistics of gravitons which results in some
regions of the lattice having more energy than others.
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