Abstract
Although highly predictive in their respective macroscopic and microscopic domains of applicability, General Relativity and quantum mechanics are mathematically incompatible, perhaps most markedly in assumptions in their formalisms concerning the nature of space and time. In <em>perspective</em> we already have a conceptual structure that links the local, macroscopic frame and the remote, apparently microscopic frame. A mathematical principle is invoked as a natural limit on D(n), so that effects which are clearly perspectival at D=3 become ‘more real’ (<em>effectively</em> observer-independent) with each D(n) increment. For instance, the apparently microscopic becomes the effectively microscopic and <em>scale extremes are juxtaposed</em>, so that black holes are local, macroscopic vanishing-points, in a similar way to that in which in projective geometry the point at infinity is incorporated into the foreground. (In other words, <em>a black hole is a blown-up ‘Planck-scale’ singularity</em>.) Characteristics of the earthbound frame are applied to D&gt;3, suggesting a physical basis for entanglement, and perspectival interpretations of quantum gravity, dimensional reduction and the information paradox. We claim that the familiar processes whereby multiple physical states become describable by a single state in which composition information appears to be lost (e.g., ‘falling into a black hole’, the state of quantum linearity, and the state of freefall) are all examples of effective convergence of a space or <em>n</em>-surface to a single point of perspective.
Highlights
1.1 BackgroundWhilst General Relativity (GR) and quantum mechanics (QM) are rigorously proven and highly predictive, their mathematical formalisms and respective macroscopic and microscopic domains of applicability have remained conceptually disparate
11) Observer-dependency of the horizon can be expressed as the fact that 2-distance to the horizon is a constant in every frame
We note that at D2|D3, observer-dependency of the planetary horizon is just the fact that 2-distance to the horizon is a constant in every frame
Summary
Whilst General Relativity (GR) and quantum mechanics (QM) are rigorously proven and highly predictive, their mathematical formalisms and respective macroscopic and microscopic domains of applicability have remained conceptually disparate. The field equations are highly nonlinear, and unconstrained geodesic convergence leads to the formation of a black hole, with a central singularity at which GR breaks down. The information and firewall paradoxes point to profound conceptual issues in our understanding of black holes. The linearity of H is such that any linear combination ( , ) = ( , ) + ( , ) of ≥ 2 solutions, where ( , ) and ( , ) are complex weighted, linearly superposed alternatives, is a solution. The Copenhagen Interpretation (CIQM) comprises two, conceptually conflicting dynamics; (i) the U-process, which describes the linear, unitary, continuous, deterministic, and reversible development of complex-weighted, superposed alternatives, and (ii) the R-process, which describes the nonlinear, nonunitary, discontinuous, nondeterministic and irreversible projection (in von Neumann’s scheme) of | 〉 onto an eigenbasis of mutually apr.ccsenet.org
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