Problems with Modified Commutators

• URL: http://arxiv.org/abs/2302.08122v1
• Date: Thu, 16 Feb 2023 07:09:32 GMT
• Title: Problems with Modified Commutators
• Authors: Matthew J. Lake and A. Watcharapasorn
• Abstract summary: We show how an apparently simple assumption can generate generalised uncertainty relations without modifying the basic form of the canonical Heisenberg algebra. This assumption has huge implications for the quantisation of space-time and, therefore, gravity. We argue that these proposals should be taken seriously, as a potential solution to the pathologies that plague minimum length models based on modified commutators.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The purpose of this paper is to challenge the existing paradigm on which contemporary models of generalised uncertainty relations (GURs) are based, that is, the assumption of modified commutation relations. We review an array of theoretical problems that arise in modified commutator models, including those that have been discussed in depth and others that have received comparatively little attention, or have not been considered at all in the existing literature, with the aim of stimulating discussion on these topics. We then show how an apparently simple assumption can solve, or, more precisely, evade these issues, by generating GURs without modifying the basic form of the canonical Heisenberg algebra. This simplicity is deceptive, however, as the necessary assumption is found to have huge implications for the quantisation of space-time and, therefore, gravity. These include the view that quantum space-time should be considered as a quantum reference frame (QRF) and, crucially, that the action scale characterising the quantum effects of gravity, $\beta$, must be many orders of magnitude smaller than Planck's constant, $\beta \sim 10^{-61} \times \hbar$, in order to recover the present day dark energy density. We argue that these proposals should be taken seriously, as a potential solution to the pathologies that plague minimum length models based on modified commutators, and that their implications should be explored as thoroughly as those of the existing paradigm, which has dominated research in this area for almost three decades.

Related papers

• Quantifying fault tolerant simulation of strongly correlated systems using the Fermi-Hubbard model [31.805673346157665]
  Building a holistic understanding of strongly correlated materials is critical. Fault-tolerant quantum computers have been proposed as a path forward to overcome these difficulties. We estimate the resource costs needed to use fault-tolerant quantum computers for obtaining experimentally relevant quantities.
  arXiv  Detail & Related papers  (2024-06-10T17:50:56Z)
• Table-top nanodiamond interferometer enabling quantum gravity tests [34.82692226532414]
  We present a feasibility study for a table-top nanodiamond-based interferometer. By relying on quantum superpositions of steady massive objects our interferometer may allow exploiting just small-range electromagnetic fields.
  arXiv  Detail & Related papers  (2024-05-31T17:20:59Z)
• Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation [39.20075231137991]
  We address the computation of the cumulative distribution function (CDF) of the spectral measure of the Hamiltonian. We introduce a signal processing technique for identifying the inflection point of the CDF. We conduct numerical experiments on a 26-qubit fully-connected Heisenberg model using a truncated density-matrix renormalization group (DMRG) initial state of low bond dimension.
  arXiv  Detail & Related papers  (2024-05-06T18:00:03Z)
• Conceptual Problems in Quantum Squeezing [0.0]
  We show that external fields might induce squeezing of canonical observables $q$ and $p$ in charged particles. We present some exactly solvable instances of this problem, observed in symmetric evolution intervals. Our findings are linked with a straightforward application of Toeplitz matrices, offering a more accessible description of the problem.
  arXiv  Detail & Related papers  (2024-04-06T13:30:34Z)
• Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity [72.27323884094953]
  We make a conceptual overview of an approach to the initial-value problem in canonical gauge theories. We stress how the first-class phase-space constraints may be relaxed if we interpret them as fixing the values of new degrees of freedom.
  arXiv  Detail & Related papers  (2024-02-19T19:00:02Z)
• Quantum reference frames, revisited [0.0]
  We point out potential inconsistencies in the mainstream approach to this subject. We reject the notion that transformations between QRFs can be represented by unitary operators. An experimental protocol, capable of empirically distinguishing between competing definitions of the term, is also proposed.
  arXiv  Detail & Related papers  (2023-12-06T18:15:52Z)
• Time and Quantum Clocks: a review of recent developments [0.0]
  We present the problem of time in quantum physics, including a short history of the problem and the known objections about considering time a quantum observable. The lack of a consistent theory of time is currently hindering the formulation of a full-fledged theory of quantum gravity.
  arXiv  Detail & Related papers  (2022-03-23T17:25:48Z)
• Generalised Uncertainty Relations and the Problem of Dark Energy [0.0]
  We outline a new model in which generalised uncertainty relations, that govern the behaviour of microscopic world, and dark energy, are intrinsically linked via the quantum properties of space-time. In this approach the background is treated as a genuinely quantum object, with an associated state vector, and additional fluctuations of the geometry naturally give rise to the extended generalised uncertainty principle (EGUP) An effective dark energy density then emerges from the field that minimises the modified uncertainty relations.
  arXiv  Detail & Related papers  (2021-12-27T23:36:16Z)
• WKB approach to the gravity-matter dynamics: a cosmological implementation [0.0]
  We propose a different model for the quantization of the gravity-matter system. The time parameter is defined via an additional term, i.e. the kinematical action, which acts as a clock for quantum matter. It is shown with a WKB expansion that quantum gravity corrections to the matter dynamics arise at the next order of expansion, and such contributions are unitary.
  arXiv  Detail & Related papers  (2021-10-09T17:32:39Z)
• Quantum Causal Inference in the Presence of Hidden Common Causes: an Entropic Approach [34.77250498401055]
  We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links. This approach can lay the foundations of identifying originators of malicious activity on future multi-node quantum networks.
  arXiv  Detail & Related papers  (2021-04-24T22:45:50Z)
• Theoretical methods for ultrastrong light-matter interactions [91.3755431537592]
  This article reviews theoretical methods developed to understand cavity quantum electrodynamics in the ultrastrong-coupling regime. The article gives a broad overview of the recent progress, ranging from analytical estimate of ground-state properties to proper computation of master equations. Most of the article is devoted to effective models, relevant for the various experimental platforms in which the ultrastrong coupling has been reached.
  arXiv  Detail & Related papers  (2020-01-23T18:09:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.