Jonas Mureika

The Generalized Uncertainty Principle (GUP) and Extended Uncertainty Principle (EUP) are modifications to the Heisenberg Uncertainly Principle (HUP), expected to apply as the energy approaches the Planck scale. Here, we consider a possible combination of these modifications, the Generalized Extended Uncertainty Principle (GEUP), and analyze the implications in various regions of the [ ] plane. We also consider an alternative combination, the Extended Generalized Uncertainty Principle (EGUP), which exhibits duality between [ ] and [ ], showing that this has some unusual features. The parameters which describe these models are usually assumed to be positive but we extend our analysis to include negative values. All these proposals entail a link between black holes and the various types of Uncertainty Principle. In particular, the GEUP predicts a new kind of strong-gravity black hole and this implies an interesting link between black holes and elementary particles.

We consider quantum gravity corrections to the maximum entropic force that arise from several gravitational uncertainty principles. These include the Generalized Uncertainty Principle (GUP), the Extended Uncertainty Principle (EUP), the Generalized Extended Uncertainty Principle (GEUP), and the Linear-Quadratic GUP (LQGUP). We find that the modified entropic force depends on the dimensionless parameters of the uncertainty principles and, thus, on the underlying quantum gravity theory. Furthermore, the entropic force, which is quantum gravity corrected in the framework of the extended uncertainty principles, also depends on the number of Planck areas that made the “EUP area”.

We discuss the Generalized Uncertainty Principle and the Extended Uncertainty Principle in the context of black hole solutions coming from non-local theories of gravity, focusing, specifically, on Infinite Derivative Gravity. We argue that these modifications of the Heisenberg Uncertainty Principle are effective descriptions arising from the non-local features of gravitational interaction. By comparing the predictions of both the modified uncertainty principles and non-local gravity, we find theoretical constraints on otherwise free parameters as well as universal laws for black hole physics beyond General Relativity.

In this paper, we review the experimental constraints on the parameter [ ] associated with the Generalized Uncertainty Principle (GUP) and the parameter [ ] associated with the Generalized Event Horizon (GEH). The Compton–Schwarzschild correspondence implies a relationship between [ ] and [ ], with both parameters being of order 1. This presents a problem for our previous “[ ]” model since the extra gravitational force at sub-Planckian masses contravenes observations. Various resolutions of this problem are discussed.

This paper explores how a reinterpretation of the generalized uncertainty principle as an effective variation of Planck’s constant provides a physical explanation for a number of fundamental quantities and couplings. In this context, a running fine structure constant is naturally emergent and the cosmological constant problem is solved, yielding a novel connection between gravitation and quantum field theories. The model could potentially clarify the recent experimental observations by the DESI Collaboration that could imply a fading of dark energy over time. When applied to quantum systems and their characteristic length scales, a simple geometric relationship between energy and entropy is disclosed. Lastly, a mass–radius relation for both quantum and classical systems reveals a phase transition-like behavior similar to thermodynamical systems, which we speculate to be a consequence of topological defects in the universe.

We use a string T-duality corrected pair of regular black holes to construct an Einstein-Rosen (ER) bridge with the wormhole throat proportional to the zero-point (Planck) length. This may be a geometric realization of quantum entanglement for particle/antiparticle pairs. We point out that for an extreme mass configuration consisting of a black hole pair, one can have an ER bridge with a horizon area that coincides with the Bekenstein minimal area bound along with a wormhole mass proportional to the Planck mass. This could be related to gravitational self-completeness with quantum mechanical mass limits. We also discuss the ER bridge for sub-Planckian mass horizonless wormholes and show this admits a region of negative energy at the throat, which we posit to be related to a particle of negative mass generated by quantum fluctuations or the Casimir effect. We argue that Hawking radiation could be the best way for the geometric realization of quantum entanglement for particle/antiparticle pairs emitted by black holes. This sheds new light on the ER=EPR conjecture.