The Common Logic of Quantum Universe—Part I: The Case of Non-relativistic Quantum Mechanics

Tessarotto, Massimo; Cremaschini, Claudio

doi:10.1007/s10701-022-00547-z

Found Phys

2022

DOI: 10.1007/s10701-022-00547-z

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The Common Logic of Quantum Universe—Part I: The Case of Non-relativistic Quantum Mechanics

Massimo Tessarotto

Claudio Cremaschini

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Cited by 2 publications

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“…For additional useful features of CQG-theory we refer to the original formulation given in refs. [6,7], the discussion of the Heisenberg uncertainty principle [10,11], and the recent contributions on quantum logic [12,13] where it was shown that CQG-theory admits a quantum logic analogous to that of quantum mechanics.…”

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confidence: 99%

On the Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity

Tessarotto

Cremaschini

2023

Symmetry

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The theoretical prediction of the stochastic property of the quantum cosmological constant and the quantum stochastic nature of event horizons has crucial implications on the physics of space-time and black holes in particular. One of these consequences concerns a new mechanism, which is investigated here, for the stochastic regularization of singular black-hole solutions of classical general relativity. The problem is posed in the context of the theory of covariant quantum gravity (CQG-theory), namely the manifestly covariant, constraint-free and finite graviton-mass quantum Hamiltonian approach developed by Cremaschini and Tessarotto (2015–2022), which permits to cast the theory in a frame-independent setting. It is precisely the trajectory-dependence feature of the theory and the intrinsic stochastic property of quantum gravity which turn out to be crucial properties for reaching quantum regularization of classical singular solutions.

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On the Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity

Tessarotto

Cremaschini

2023

Symmetry

Self Cite

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Planck Length Emerging as the Invariant Quantum Minimum Effective Length Determined by the Heisenberg Uncertainty Principle in Manifestly Covariant Quantum Gravity Theory

Cremaschini,

Tessarotto

2024

Symmetry

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The meaning of the quantum minimum effective length that should distinguish the quantum nature of a gravitational field is investigated in the context of manifestly covariant quantum gravity theory (CQG-theory). In such a framework, the possible occurrence of a non-vanishing minimum length requires one to identify it necessarily with a 4-scalar proper length s.It is shown that the latter must be treated in a statistical way and associated with a lower bound in the error measurement of distance, namely to be identified with a standard deviation. In this reference, the existence of a minimum length is proven based on a canonical form of Heisenberg inequality that is peculiar to CQG-theory in predicting massive quantum gravitons with finite path-length trajectories. As a notable outcome, it is found that, apart from a numerical factor of O1, the invariant minimum length is realized by the Planck length, which, therefore, arises as a constitutive element of quantum gravity phenomenology. This theoretical result permits one to establish the intrinsic minimum-length character of CQG-theory, which emerges consistently with manifest covariance as one of its foundational properties and is rooted both on the mathematical structure of canonical Hamiltonian quantization, as well as on the logic underlying the Heisenberg uncertainty principle.

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The Common Logic of Quantum Universe—Part I: The Case of Non-relativistic Quantum Mechanics

Cited by 2 publications

References 30 publications

On the Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity

On the Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity

Planck Length Emerging as the Invariant Quantum Minimum Effective Length Determined by the Heisenberg Uncertainty Principle in Manifestly Covariant Quantum Gravity Theory

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