Abstract
Recent developments in quantum set theory are used to formulate a program for quantum topological physics. The world is represented in a Hilbert space whose psi vectors represent abstract complexes generated from the null set by one bracket operator and the usual Grassmann (or Clifford) product. Such a theory may be more basic than field theory, in that it may generate its own natural topology, time, kinematics and dynamics, without benefit of an absolute timespace dimension, topology, or Hamiltonian. For example there is a natural expression for the quantum gravitational field in terms of quantum topological operators. In such a theory the usual spectrum of possible dimensions describes only one of an indefinite hierarchy of levels, each with a similar spectrum, describing nonspatial infrastructure. While c simplices have no continuous symmetry, the q simplex has an orthogonal group 0(m, n). Because quantum theory cannot take the universe as physical system, we propose a “third relativity:”The division between observer and observed is arbitrary. Then it is wrong to ask for “the” topology and dynamics of a system, in the same sense that it is wrong to ask for the “the” psi vectors of a system; topology and dynamics, like psi vectors, are not absolute but relative to the observer.
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Finkelstein, D., Rodriguez, E. Relativity of topology and dynamics. Int J Theor Phys 23, 1065–1098 (1984). https://doi.org/10.1007/BF02213417
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DOI: https://doi.org/10.1007/BF02213417