scholarly journals Generalised Uncertainty Relations for Angular Momentum and Spin in Quantum Geometry

Universe ◽  
2020 ◽  
Vol 6 (4) ◽  
pp. 56 ◽  
Author(s):  
Matthew J. Lake ◽  
Marek Miller ◽  
Shi-Dong Liang

We derive generalised uncertainty relations (GURs) for orbital angular momentum and spin in the recently proposed smeared-space model of quantum geometry. The model implements a minimum length and a minimum linear momentum and recovers both the generalised uncertainty principle (GUP) and extended uncertainty principle (EUP), previously proposed in the quantum gravity literature, within a single formalism. In this paper, we investigate the consequences of these results for particles with extrinsic and intrinsic angular momentum and obtain generalisations of the canonical so ( 3 ) and su ( 2 ) algebras. We find that, although SO ( 3 ) symmetry is preserved on three-dimensional slices of an enlarged phase space, corresponding to a superposition of background geometries, individual subcomponents of the generalised generators obey nontrivial subalgebras. These give rise to GURs for orbital angular momentum while leaving the canonical commutation relations intact except for a simple rescaling, ħ → ħ + β . The value of the new parameter, β ≃ ħ × 10 − 61 , is determined by the ratio of the dark energy density to the Planck density, and its existence is required by the presence of both minimum length and momentum uncertainties. Here, we assume the former to be of the order of the Planck length and the latter to be of the order of the de Sitter momentum ∼ ħ Λ , where Λ is the cosmological constant, which is consistent with the existence of a finite cosmological horizon. In the smeared-space model, ħ and β are interpreted as the quantisation scales for matter and geometry, respectively, and a quantum state vector is associated with the spatial background. We show that this also gives rise to a rescaled Lie algebra for generalised spin operators, together with associated subalgebras that are analogous to those for orbital angular momentum. Remarkably, consistency of the algebraic structure requires the quantum state associated with a flat background to be fermionic, with spin eigenvalues ± β / 2 . Finally, the modified spin algebra leads to GURs for spin measurements. The potential implications of these results for cosmology and high-energy physics, and for the description of spin and angular momentum in relativistic theories of quantum gravity, including dark energy, are briefly discussed.

2021 ◽  
Vol 75 (8) ◽  
Author(s):  
Wei Li ◽  
Shengmei Zhao

Abstract The inseparability of quantum correlation requires that the particles in the composite system be treated as a whole rather than treated separately, a typical example is the Einstein–Podolsky–Rosen (EPR) paradox. In this paper, we provide a theoretical study on the uncertainty relations of two kinds of bipartite observables in two-photon orbital angular momentum (OAM) entanglement, that is, the relative distance and centroid of the two photons at azimuth. We find that the uncertainty relations of the bipartite observables holds in any two-photon state, and they are separable in two-photon OAM entanglement. In addition, the entangled state behaves as a single particle in the bipartite representation. Finally, we find that the uncertainty relations of the bipartite observables can be used to manipulate the degree of the entanglement of an EPR state. Graphic abstract


Author(s):  
Mehul Malik ◽  
Mohammad Mirhosseini ◽  
Martin P. J. Lavery ◽  
Jonathan Leach ◽  
Miles J. Padgett ◽  
...  

2015 ◽  
Vol 17 (3) ◽  
pp. 033037 ◽  
Author(s):  
Adrien Nicolas ◽  
Lucile Veissier ◽  
Elisabeth Giacobino ◽  
Dominik Maxein ◽  
Julien Laurat

Galaxies ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 11 ◽  
Author(s):  
Matthew J. Lake

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 , ℏ , Λ , e . Evaluated numerically, the charged particle limit corresponds to the order of magnitude value of the electron mass ( m e ), while the neutral particle limit is consistent with current experimental bounds on the mass of the electron neutrino ( m ν 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.


2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohammed M. Khalil

Various theories of quantum gravity predict the existence of a minimum length scale, which leads to the modification of the standard uncertainty principle to the Generalized Uncertainty Principle (GUP). In this paper, we study two forms of the GUP and calculate their implications on the energy of the harmonic oscillator and the hydrogen atom more accurately than previous studies. In addition, we show how the GUP modifies the Lorentz force law and the time-energy uncertainty principle.


Author(s):  
Ryohei Yamagishi ◽  
Hiroto Otsuka ◽  
Ryo Ishikawa ◽  
Akira Saitou ◽  
Hiroshi Suzuki ◽  
...  

2014 ◽  
Vol 3 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Piero Chiarelli

This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle is fully compatible with the postulate of finite transmission speed of light and information. The theory shows that the measurement process performed in the large scale classical limit in presence of background noise, cannot have a duration smaller than the time need to the light to travel the distance up to which the quantum non-local interaction extend itself. The product of the minimum measuring time multiplied by the variance of energy fluctuation due to presence of stochastic noise shows to lead to the minimum uncertainty principle. The paper also shows that the uncertainty relations can be also derived if applied to the indetermination of position and momentum of a particle of mass m in a quantum fluctuating environment.


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