Reconciling a quantum gravity minimal length with lack of photon dispersion

Bishop, Michael; Contreras, Joey; Lee, Jaeyeong; Singleton, Douglas

doi:10.1016/j.physletb.2021.136265

Cited by 19 publications

(16 citation statements)

References 36 publications

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“…Before concluding this section, however, we highlight an essential aspect of the smeared space model, which distinguishes it from nearly all other GUR models proposed in the existing quantum gravity literature (see [21,22] for a notable exception). It is straightforward to show that the GURs ( 17) and ( 21) can be obtained as the standard deviations of generalised position and momentum operators, Xi and Pj , satisfying the commutation relations [12,14,15] […”

Section: Gurs From Quantum Nonlocal Geometrymentioning

confidence: 99%

“…These problems are well known [10,11,18,19], but have remained essentially unsolved for over 25 years, ever since rigorous GUP models based on the modified commutator method were first formulated in the mid-1990's [20]. Recently, alternative GUR models have been proposed in which the canonical position and momentum operators are modified, giving rise to modified uncertainty relations including the EGUP (4), but in which the canonical Heisenberg algebra remains unchanged [21,22], except possibly for a small rescaling of the form → (1 + δ) where δ ≪ 1 [12][13][14][15][16][17]. In this talk, we explore one such model, originally proposed in the series of works [12][13][14][15][16][17] and explain how it gives rise to an effective dark energy density for the Universe.…”

Section: Introductionmentioning

confidence: 99%

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Minimum Length Uncertainty Relations in the Presence of Dark Energy

Lake

2019

Galaxies

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We introduce a dark energy-modified minimum length uncertainty relation (DE-MLUR) or dark energy uncertainty principle (DE-UP) for short. The new relation is structurally similar to the MLUR introduced by Károlyházy (1968), and reproduced by Ng and van Dam (1994) using alternative arguments, but with a number of important differences. These include a dependence on the de Sitter horizon, which may be expressed in terms of the cosmological constant as l dS ∼ 1/ √ Λ. Applying the DE-UP to both charged and neutral particles, we obtain estimates of two limiting mass scales, expressed in terms of the fundamental constants {G, c, , Λ, e}. Evaluated numerically, the charged particle limit corresponds to the order of magnitude value of the electron mass (me), while the neutral particle limit is consistent with current experimental bounds on the mass of the electron neutrino (mν e ). Possible cosmological consequences of the DE-UP are considered and we note that these lead naturally to a holographic relation between the bulk and the boundary of the Universe. Low and high energy regimes in which dark energy effects may dominate canonical quantum behaviour are identified and the possibility of testing the model using near-future experiments is briefly discussed. Acknowledgments 24Appendix: Conceptual issues -is r < (∆x total ) min physical? 24References 25 arXiv:1712.00271v3 [gr-qc]

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Section: Gurs From Quantum Nonlocal Geometrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minimum Length Uncertainty Relations in the Presence of Dark Energy

Lake

2019

Galaxies

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“…Equations ( 34) and (35) show that GURs, including the GUP, EUP and EGUP, may be obtained without non-canonical modifications of the Heisenberg algebra [16,18,19]. (See also [37] for a similar result.) This allows the smeared space model to evade the problems that plague existing modified commutator models, including violation of the equivalence principle, the velocity-dependence of the minimum length, and the soccer ball problem [26,38].…”

Section: A Details Of the Modelmentioning

confidence: 86%

Why space could be quantised on a different scale to matter

Lake

2021

SciPost Phys. Proc.

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The scale of quantum mechanical effects in matter is set by Planck’s constant, \hbarℏ. This represents the quantisation scale for material objects. In this article, we present a simple argument why the quantisation scale for space, and hence for gravity, may not be equal to \hbarℏ. Indeed, assuming a single quantisation scale for both matter and geometry leads to the `worst prediction in physics’, namely, the huge difference between the observed and predicted vacuum energies. Conversely, assuming a different quantum of action for geometry, \beta \ll \hbarβ≪ℏ, allows us to recover the observed density of the Universe. Thus, by measuring its present-day expansion, we may in principle determine, empirically, the scale at which the geometric degrees of freedom should be quantised.

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“…If we do not modify the commutator nor modify the operators, we would obviously end up with ordinary quantum mechanics, which does not have a minimal length. Thus, we want modified position and momentum operators X and P which give rise to the usual commutator [ X, P ] = i , [29,30]. This in turn leads to a standard looking uncertainty relationship but now in terms of the modified operators ∆X∆P ≥ 2 .…”

Section: A Gup With An Unmodified Commutatormentioning

confidence: 99%

“…then leads to the standard looking commutator [ X, P ] = i as can be verified by the substitution of ( 9) and ( 10) into the commutator. Another variant with a capped momentum is given in [29] by…”

Section: A Gup With An Unmodified Commutatormentioning

confidence: 99%

A Subtle Aspect of Minimal Lengths in the Generalized Uncertainty Principle

Bishop,

Contreras,

Singleton

2022

Preprint

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In this work, we point out an overlooked and subtle feature of the generalized uncertainty principle (GUP) approach to quantizing gravity: namely that different pairs of modified operators with the same modified commutator, [ X, P ] = i (1+βp 2 ), may have different physical consequences such as having no minimal length at all. These differences depend on how the position and/or momentum operators are modified rather than only on the resulting modified commutator. This provides guidance when constructing GUP models since it distinguishes those GUPs that have a minimal length scale, as suggested by some broad arguments about quantum gravity, versus GUPs without a minimal length scale.

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Reconciling a quantum gravity minimal length with lack of photon dispersion

Cited by 19 publications

References 36 publications

Minimum Length Uncertainty Relations in the Presence of Dark Energy

Minimum Length Uncertainty Relations in the Presence of Dark Energy

Why space could be quantised on a different scale to matter

A Subtle Aspect of Minimal Lengths in the Generalized Uncertainty Principle

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