Abstract
The quantum gravity problem that the notion of a quantum state, representing the structure of space-time at some instant, and the notion of the evolution of the state, does not get traction, since there are no real “instants”, is avoided by having initial Octonionic geometry embedded in a larger, nonlinear “pilot model” (semi classical) embedding structure. The Penrose suggestion of recycled space time avoiding a “big crunch” is picked as the embedding structure, so as to avoid the “instants” of time issue. Getting Octionic gravity as embedded in a larger, Pilot theory embedding structure may restore Quantum Gravity to its rightful place in early cosmology without the complication of then afterwards “Schrodinger equation” states of the universe, and the transformation of Octonionic gravity to existing space-time is explored via its possible linkage to a new version of the HUP involving metric tensors. We conclude with how specific properties of Octonion numbers algebra influence the structure and behavior of the early-cosmology model. This last point is raised in Section 14, and is akin to a phase transition from Pre-Octonionic geometry, in pre-Planckian space-time, to Octonionic geometry in Planckian space-time. A simple phase transition is alluded to; making this clear is as simple as realizing that Pre-Octonionic is for Pre-Planckian Space-time and Octonionic is for Planckian Space-time. We state that the Standard Model of physics occurs during Planckian Space-time. We also argue that the Standard Model does not apply to Pre Planckian Space-time. This is commensurate with the Octonion number system NOT applying in pre-Planckian space-time, but applying in Plankian space-time. And the last line of Equation (54) gives a minimum time step in pre-Planckian space-time when we do NOT have the Standard Model of physics, or Octonionic Geometry.
Highlights
Introduction to the Metric Tensor asContribution to Quantum GravityWhat Is Quantum Gravity? Does Quantum Gravity Have Relevance to Planckian Physics?In general relativity the metric gab(x, t) is a set of numbers associated with each point which gives the distance to neighboring points
We argue that the Standard Model does not apply to Pre Planckian Space-time
Equation (9) is such that even if one is in flat Euclidian space, and i= j, if the phase transition from Pre-Octonionic to Octonionic has occurred
Summary
What Is Quantum Gravity? Does Quantum Gravity Have Relevance to Planckian Physics?. In general relativity the metric gab(x, t) is a set of numbers associated with each point which gives the distance to neighboring points. The paper refers to these regimes of space time where the octonionic commutation relations DO hold. The assertion made, is that before Planck temperature is reached, i.e. there is a natural embedding of space time geometry with the octonionic structure reached as the initial conditions for expansion of the present universe. Our re statement of this idea is to say that one has quantum effects emerging in highly specialized circumstances, with collective variables behaving like squeezed states of space time matter. The octonionic gravity regime, obeying quantum commutation behavior has its analog in simplification of collective variable treatment of a gravitational field, which becomes very quantum commutation like in its behavior in the Planck temperature limit. This paper will endeavor as to describe the emergent collective treatment of the gravitational field appropriately so octonionic gravity is a definite limiting structure emerging in extreme temperatures and state density. Pre-Octonionic δ 0 ph ase chan ge→δ t∆E ≥ Octonionic with δ t ≥ fixed δ gtt ∆E (7b)
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