The non-gravitational interactions of microscopic particles are governed by the laws of quantum mechanics and so obey Heisenberg’s uncertainty principle. This may be derived rigorously from the canonical quantum formalism or introduced, heuristically, via the Heisenberg microscope thought experiment. Extending the thought experiment argument to include the effects of gravitational attraction between particles and/or a background dark energy density leads to generalized uncertainty relations, which contain additional non-Heisenberg terms, but how to embed these within an extended quantum formalism remains an open problem in fundamental physics.

Two of the most widely studied relations, proposed in the phenomenological quantum gravity literature, are the generalized uncertainty principle (GUP) and extended uncertainty principle (EUP). The GUP incorporates the effects of attractive gravity and implies a minimum length scale of the order of the Planck length, whereas the EUP accounts for the effects of repulsive vacuum energy and implies a minimum momentum of the order of the de Sitter momentum. This is the momentum a canonical quantum particle would have if its de Broglie wavelength were of the order of the de Sitter radius, which is comparable to the present day radius of the Universe. Expanding the Heisenberg microscope argument to include the effects of canonical gravity and dark energy implies the extended generalized uncertainty principle (EGUP) which predicts the existence of both a minimum length and a minimum momentum scale in nature.

For almost three decades the most common method used to construct generalizations of the Heisenberg uncertainty principle has been to introduce modiﬁed commutation relations. These then lead, directly, to modiﬁed uncertainty relations, via the standard Schrodinger-Robertson relation. Unfortunately, despite its widespread use, this approach remains fraught with difﬁculties and modiﬁed commutator models lead to several well known pathologies, including:

(a) violation of the equivalence principle,

(b) reference-frame dependence of the ‘minimum’ length,

(c) violation of Lorentz invariance in the relativistic limit,

(d) the inability to construct sensible multi-particle states, known as the soccer ball problem.

This strongly motivates new approaches to the ﬁeld, as well as critical analyses of traditional models, or their possible reﬁnements, which aim to address these vital issues head-on.

In this Research Topic, we seek papers exploring all approaches to generalized uncertainty relations and their phenomenological implications. We aim to provide a broad overview the subject including summaries of the major approaches presented, to date, in this important ﬁeld, as well as summaries of non-standard approaches based on new models.

Though many studies focus on the familiar GUP, EUP and EGUP formulae, which include position and linear momentum, we especially welcome explorations of generalized uncertainty relations for time, energy, angular momentum, quantum mechanical spin, and entropy, motivated by quantum gravitational phenomenology. Proposals for new relations, which have not yet been explored in the existing literature, are also warmly welcomed, and will be considered without prejudice.

We acknowledge the funding of the manuscripts published in this Research Topic by National Astronomical Research Institute of Thailand (NARIT). We hereby state publicly that NARIT has had no editorial input in articles included in this Research Topic, thus ensuring that all aspects of this Research Topic are evaluated objectively, unbiased by any specific policy or opinion of NARIT.

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