Abstract
Within the context of Newton’s theory of gravitation, restricted to point-like test particles and central bodies, stable circular orbits in ordinary space are related to stable circular paths on a massless, unmovable, undeformable vortex-like surface, under the action of a tidal gravitational field along the symmetry axis. An interpretation is made in the light of a holographic principle, in the sense that motions in ordinary space are connected with motions on a selected surface and vice versa. Then ordinary space is conceived as a 3-hypersurface bounding a n-hypervolume where gravitation takes origin, within a n-hyperspace. The extension of the holographic principle to extra dimensions implies the existence of a minimum distance where test particles may still be considered as distinct from the central body. Below that threshold, it is inferred test particles lose theirs individuality and “glue” to the central body via unification of the four known interactions and, in addition, 1) particles can no longer be conceived as point-like but e.g., strings or membranes, and 2) quantum effects are dominant and matter turns back to a pre-big bang state. A more detailed formulation including noncircular motions within the context of general relativity, together with further knowledge on neutron stars, quark stars and black holes, would provide further insight on the formulation of quantum gravity.
Highlights
According to current QCDM cosmologies, the universe as a whole is increasingly expanding e.g., [1] which cannot be true for subsystems
The concept of space curvature may be introduced considering a vortex-like surface under the action of a tidal gravitational field along the symmetry axis, where the distance of a surface point from the symmetry axis relates to the distance of a test particle from a central body
Could the above mentioned holographic principle be extended to ordinary space, conceived as a 3-hypersurface, where test particles are subjected to a constant gravitational force from extra dimensions? If yes, could quantum effects and unification of the four known interactions be interpreted in this context?
Summary
According to current QCDM cosmologies, the universe as a whole is increasingly expanding e.g., [1] which cannot be true for subsystems. In the light of general relativity, the final configuration is point-like but the occurrence of quantum effects could yield strings or membranes, leaving the gravitational field outside the instability region (where test particles cannot remain in stable equilibrium) spherical-symmetric. The concept of space curvature may be introduced considering a vortex-like surface under the action of a tidal gravitational field along the symmetry axis, where the distance of a surface point from the symmetry axis relates to the distance of a test particle from a central body. Could the above mentioned holographic principle be extended to ordinary space, conceived as a 3-hypersurface, where test particles are subjected to a constant gravitational force from extra dimensions? A special vortex-like surface and an analogy for the invariance of light velocity are presented in the Appendix A1 and Appendix A2, respectively
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