A Local Resolution of the Problem of Time. IV. Quantum outline and piecemeal Conclusion

Abstract

In this final piecemeal treatment of local Problem of Time facets, and underlying Background Independence aspects, we first reconsider the ten local facets and aspects considered so far at the quantum level. This is essential both to appreciate past conceptualization and naming for these aspects and facets, and because the quantum Problem of Time is a more advanced goal than its classical counterpart. The case is made that each piecemeal aspect of Background Independence can be incorporated, i.e. each piecemeal facet of the Problem of Time is resolvable, in a local classical sense, using just Lie's Mathematics. This case is then extended in Articles V to XIII to a joint resolution, i.e. successfully handling the lion's share of the Problem of Time that resides in facet interferences. Relationalism, Closure, Observables and Constructions are argued to be super-aspects ordered to form a claw alias 3-star digraph with Closure as nexus. This is realized twice: faithfully for spacetime and with some modification in the split-Relationalism canonical case. There is finally a Wheelerian 2-way route between the two realizations, with Spacetime Construction from Space in one direction and Refoliation Invariance in the other.

21 pages including 2 figures. v3 has brief but conceptually significant updates

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Cited by in corpus (13)

• A Local Resolution of the Problem of Time. III. The other classical facets piecemeal
• A Local Resolution of the Problem of Time. I. Introduction and Temporal Relationalism
• A Local Resolution of the Problem of Time. V. Combining Temporal and Configurational Relationalism for Finite Theories
• A Local Resolution of the Problem of Time. IX. Spacetime Constructability
• A Local Resolution of the Problem of Time. VII. Constraint Closure
• Geometry from Brackets Consistency
• A Local Resolution of the Problem of Time. XIV. Grounding on Lie's Mathematics
• Problem of Time and Background Independence: classical version's higher Lie Theory
• Nijenhuis-type variants of Local Theory of Background Independence
• Nambu variant of Local Resolution of Problem of Time and Background Independence
• Lie Theory suffices to understand, and Locally Resolve, the Problem of Time
• A Local Resolution of the Problem of Time. VIII. Assignment of Observables
• Comparative Theory of Background Independence