A fundamental geometry of quantum physics (original) (raw)
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A general theory of quantum relativity
Physics Letters B, 2004
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical. These postulates remain compatible within a background independent extension of quantum theory with a local intrinsic time implying the relativity of the concept of a quantum event. In this extension the space of quantum events becomes dynamical and only individual quantum events make sense observationally. At the core of such a general theory of quantum relativity is the three-way interplay between the symplectic form, the dynamical metric and non-integrable almost complex structure of the space of quantum events. Such a formulation provides a missing conceptual ingredient in the search for a background independent quantum theory of gravity and matter. The crucial new technical element in our scheme derives from a set of recent mathematical results on certain infinite dimensional almost Kahler manifolds which replace the complex projective spaces of standard quantum mechanics. 1
Proposal for a New Quantum Theory of Gravity
Zeitschrift für Naturforschung A, 2019
We recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu–Goto + Kalb–Ramond string [R. T. Hammond, Rep. Prog. Phys. 65, 599 (2002)]. We explain why this is a significant gravitational theory and in what sense classical general relativity is an approximation to it. We propose that a noncommutative generalisation of this theory (in the sense of Connes’ noncommutative geometry and Adler’s trace dynamics) is a “quantum theory of gravity.” The theory is in fact a classical matrix dynamics with only two fundamental constants – the square of the Planck length and the speed of light, along with the two string tensions as parameters. The guiding symmetry principle is that the theory should be covariant under general coordinate transformations of noncommuting coordinates. The action for this noncommutative torsion gravity can be elegantly expressed as an invariant area integral and represents an atom of space–time–matter. The statistical thermodynamics of ...
On the Integration of General Relativity with Quantum Theory and the Standard Model
2018
We propose (1) that the flat space-time metric that defines the traditional covariant Heisenberg algebra commutation rules of quantum theory between the four-vector position and momentum, be generalized to be the space-time dependent Riemann metric satisfying Einstein’s equations for general relativity (GR), which determine the metric from the energy-momentum tensor. The metric is then a function of the four-vector position operators which are to be expressed in the position representation. This then allows one (2) to recast the Christoffel symbols, and the Riemann and Ricci tensors in Einstein’s GR differential equations for the metric, as an algebra of commutation relations among the four-vector position and momentum operators (a generalized Lie algebra). This then (3) defines the structure constants of the rest of the Poincare algebra with the space-time dependent metric of general relativity tightly integrating it with quantum theory. (4) We propose that the four momentumoperat...
Some reflections on the status of conventional quantum theory when applied to quantum gravity
The Future of Theoretical Physics and Cosmology: …
All current approaches to quantum gravity employ essentially standard quantum theory including, in particular, continuum quantities such as the real or complex numbers. However, I wish to argue that this may be fundamentally wrong in so far as the use of these continuum quantities in standard quantum theory can be traced back to certain a priori assumptions about the nature of space and time: assumptions that may be incompatible with the view of space and time adopted by a quantum gravity theory. My conjecture is that in, some yet to be determined sense, to each type of space-time there is associated a corresponding type of quantum theory in which continuum quantities do not necessarily appear, being replaced with structures that are appropriate to the specific space-time. Topos theory then arises as a possible tool for 'gluing' together these different theories associated with the different space-times. As a concrete example of the use of topos ideas, I summarise recent work applying presheaf theory to the Kochen-Specher theorem and the assignment of values to physical quantities in a quantum theory.
A Specimen of Theory Construction from Quantum Gravity
The Creation of Ideas in Physics, 1995
I describe the history of my attempts to arrive at a discrete substratum underlying the spacetime manifold, culminating in the hypothesis that the basic structure has the form of a partial-order (i.e. that it is a causal set). Like the other speakers in this session, I too am here much more as a working scientist than as a philosopher. Of course it is good to remember Peter Bergmann's description of the physicist as "in many respects a philosopher in workingman's* clothes", but today I'm not going to change into a white shirt and attempt to draw philosophical lessons from the course of past work on quantum gravity. Instead I will merely try to recount a certain part of my own experience with this problem, explaining how I arrived at the idea of what I will call a causal set. This and similar structures have been proposed more than once as discrete replacements for spacetime. My excuse for not telling you also how others arrived at essentially the same idea [1] is naturally that my case is the only one I can hope to reconstruct with even minimal accuracy.
1 A ( geometrical ) Hilbert space based quantum gravity model
2020
In the book „The Mathematical Reality, Why Space and Time are an Illusion“, (UnA1), , the concept of „Vision – Mathematization – Simplification“ is proclaimed. The overall „Vision“ is about a simplification of the incompatible SMEP and the cosmology model, by reducing the number of current „constants of nature“, especially regarding the „constant speed of light“ (→ variable speed of light, (UnA)) and the „Planck constant“.
A Quantum-Physical Theory of Gravitation
A Quantum-Physical Theory of Gravitation, 2024
Of the General Theory of Relativity it has been said that it is one of the most beautiful theories invented by man, in fact personally also at the time it impressed me a lot, which led me to study Tensor Analysis and to try to understand Riemannian Geometry, but the truth is that all that world seemed to me very complicated and therefore not very beautiful, and I understood why, when it was launched, it is said that only 12 people understood it. Enrique Loedel in his excellent book writes... “arriving at the same results obtained from the exact Schwarzchild solution... whose extremely simple structure does not agree with the extreme complication of the field equations, make us think of the possibility of obtaining such a solution in a simpler and more direct way”(7,pg318). It was this that motivated me, among others, to the present solution of the gravitational fields, after having applied the concept of Basic Systemic Unit in the derivation of the Pendulum Formula, of the Schrödinger wave equation and those of Special Relativity.
2009
This work is devoted to the sudy of the vacuum structure, special relativity, electrodynamics of interacting charged point particles and quantum mechanics, and is a continuation of [6, 7]. Based on the vacuum field theory no-geometry approach, the Lagrangian and Hamiltonian reformulation of some alternative classical electrodynamics models is devised. The Dirac type quantization procedure, based on the canonical Hamiltonian formulation, is developed for some alternative electrodynamics models. By means of the developed approach a combined description, both of electrodynamics and gravity, is analyzed. MIRAMARE – TRIESTE September 2008 nikolai bogolubov@hotmail.com pryk.anat@ua.fm, prykanat@cybergal.com
Quantum Geometry and Its Ramifications
Space-Time Structure: Einstein and Beyond, 2005
Loop quantum gravity, Quantum dynamics in loop quantum gravity, quantum cosmology, black hole mechanics, quantum field theory in curved space-times, spin foams, canonical approach.