Abstract
The von Neumann quantum logic lacks two basic symmetries of classical logic, that between sets and classes, and that between lower and higher order predicates. Similarly, the structural parallel between the set algebra and linear algebra of Grassmann and Peano was left incomplete by them in two respects. In this work a linear algebra is constructed that completes this correspondence and is interpreted as a new quantum logic that restores these invariances, and as a quantum set theory. It applies to experiments with coherent quantum phase relations between the quantum and the apparatus. The quantum set theory is applied to model a Lorentz-invariant quantum time-space complex.
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References
Barnabei, M., Brini, A., and Rota, G.-C. (1985). On the exterior calculus of invariant theory,Journal of Algebra,96, 120–160.
Bergmann, P. G. (1957), Two-component spinors in general relativity,Physical Review,107, 624–629.
Deruelle, N., and Madore, J. (1986). Kaluza-Klein cosmology with the Lovelock Lagrangians, preprint.
Feynman, R., and Hibbs, A. R. (1965).Quantum Mechanics Via Path Integrals, Wiley, New York.
Finkelstein, D. (1967). Space-time code,Physical Review, (1969).
Finkelstein, D. (1986). Hyperspin and hyperspace,Physical Review Letters,56, 1532–1533.
Finkelstein, D. (1987). The universal quantum, Paper presented at the conference on The World View ov Contemporary Physics, Colorado State University, Fort Collins, September 25, 1986, to be published.
Finkelstein, D., and Rodriguez, E. (1986). Quantum time space and gravity, inQuantum Concepts in Time and Space, R. Penrose and C. Isham, eds., Oxford.
Holm, C. (1986). Christoffel formula and geodesic motion in hyperspin manifolds,International Journal of Theoretical Physics, in press.
Lovelock, D. (1971). The Einstein tensor and its generalizations,Journal of Mathematical Physics,12, 498.
Misner, C. W., Thorne, K., and Wheeler, J. A. (1973).Gravitation, Freeman, San Francisco.
Peano, G. (1888).Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann, proceduto dalle operazioni della logica deduttiva, Bocca, Turin [Partial translation in H. C. Kennedy,Selected Works of Giusseppe Peano, University of Toronto (1973)].
Schrödinger E. (1948).Statistical Thermodynamics, Cambridge.
Zumino, B. (1986). Gravity theories in more than four dimensions,Physics Reports,137, 109.
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Finkelstein, D. Coherent quantum logic. Int J Theor Phys 26, 109–129 (1987). https://doi.org/10.1007/BF00669595
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DOI: https://doi.org/10.1007/BF00669595