## Project Details

### Description

We have been working on a very aggressive grand program with the big final goal of finding the right model for the deep microscopic quantum spacetime and build the theory of its dynamics, and achieved the first set of breakthrough results successfully formulating quantum mechanics as a theory of particle dynamics on a quantum model of the physical space all aspects of which go to the Newtonian limit. Our unique approach is based on a quantum relativity perspective. The spacetime model is a representation of the relativity group. The corresponding representation of the group C*-algebra gives the algebra of observables. Time evolution is obtained naturally as an automorphism flow of the observable algebra as the Heisenberg picture matched to the unitary flow on the Hilbert space generated by the energy observable. The contraction limit exactly retrieves the Newtonian results in all aspects. More importantly, the approach as based on the group C*-algebra is naturally applicable to settings at any deeper or higher up levels of our quantum relativity picture. Our results establish the configuration part and the momentum part of the quantum phase space as like space and time in Minkowski spacetime, parts which can be handled separately only as the Newtonian approximation. And the noncommutativity nature of the physical space manifests itself even without considering gravity. We have also essentially finished the formulation of a Lorentz covariant version of quantum mechanics and its quantum spacetime model along the line, giving as its contraction limits our formulation of the quantum mechanics and quantum physical space as well as the Lorentz covariant and Newtonian classical theories. On the complementary side, we have succeeded in giving a picture of the noncommutative geometry of the quantum observable algebra as exactly the symplectic geometry of the usual quantum phase space. The position and momentum operators serve as a set of six noncommutative coordinates of the otherwise infinite (real) dimensional projective Hilbert space with the coordinate transformation description explicitly presented. Conceptual consistency is established by the successful introduction of the notation of a noncommutative value of an observable with an explicit description of it as a set of infinite number of real numbers. The noncommutative value contains the full information about an observable on a fixed state beyond the full statistical distribution of repeated von Neumann measurements, and is experimentally accessible.The current grant project applied plans on focusing on two aspects. One is to apply our formulations and new perspectives to some experimental setting, including looking into composite system or particle with spin, trying to extract useful new information or even new physics predictions. The latter will be particularly interesting for our Lorentz covariant theory which is somewhat different from the usual ‘relativistic’ quantum mechanics both theoretically and practically.The second aspect is to start pursuing the corresponding formulation towards so-called Planckian physics with more noncommutativity. We will use our group representation framework to work backwards or upwards finding the right representation that has our current results as approximations through the rigorous contraction limits.

Status | Finished |
---|---|

Effective start/end date | 1/08/20 → 28/02/22 |

### Keywords

- Quantum Relativity
- Quantum Spacetime
- Fundamental (Particle) Dynamics
- Symmetry Contraction
- Noncommutative Geometry
- Quantum Geometry
- Observable Algebra
- New Conceptual Picture of Quantum Mechanics
- Lorentz Covariant Quantum Mechanics

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