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Binary encoded recursive generation of quantum space-times. (English) Zbl 1507.51035

Summary: Real geometric algebras distinguish between space and time; complex ones do not. Space-times can be classified in terms of number \(n\) of dimensions and metric signature \(s\) (number of spatial dimensions minus number of temporal dimensions). Real geometric algebras are periodic in \(s\), but recursive in \(n\). Recursion starts from the basis vectors of either the Euclidean plane or the Minkowskian plane. Although the two planes have different geometries, they have the same real geometric algebra. The direct product of the two planes yields Hestenes’ space-time algebra. Dimensions can be either open (for space-time) or closed (for the electroweak force). Their product yields the eight-fold way of the strong force. After eight dimensions, the pattern of real geometric algebras repeats. This yields a spontaneously expanding space-time lattice with the physics of the Standard Model at each node. Physics being the same at each node implies conservation laws by Noether’s theorem. Conservation laws are not pre-existent; rather, they are consequences of the uniformity of space-time, whose uniformity is a consequence of its recursive generation.

MSC:

51P05 Classical or axiomatic geometry and physics
15A67 Applications of Clifford algebras to physics, etc.
70S10 Symmetries and conservation laws in mechanics of particles and systems
83F05 Relativistic cosmology
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