Measurable maximal energy and minimal time interval

Dahab, Eiman Abou El; Tawfik, A.

doi:10.1139/cjp-2013-0661

Cited by 7 publications

(5 citation statements)

References 46 publications

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“…valid, for any l, instead of the traditional HUR. Note that due to (28), this new form of UR is sharper than the HUR. For instance, if we want (30) to be equal to the GUP, we need to set…”

Section: Generalized Exact Uncertainty Principlementioning

confidence: 94%

“…valid, for any l, instead of the traditional HUR. Note that due to (28), this new form of UR is sharper than the HUR.…”

Section: Generalized Eupmentioning

confidence: 94%

“…The second condition states that for infinitesimal values of ∆N l the formula (25) does not differ from the original EUP scaling. The last requirement (28) is the crucial ingredient of the EUP modification which simply aims to build up the fluctuations whenever κ > 1. As an easy example, if w (z) = z 1/s , with s > 1, the modified scaling law would give ∆N l → κ s ∆N l .…”

Section: Generalized Exact Uncertainty Principlementioning

confidence: 99%

“…I find it sufficient to expect, that due to various possible physical reasons such as potential existence of maximal proper acceleration [25] (note that this preserves Lorentz invariance [26]), the equation (1) or a similar one replaces the HUR [27]. Let me only observe that the mathematical structure of (1) and its counterparts, lead by a straightforward optimization to the minimal measurable length [23], or in other cases to existence of minimal measurable momentum, minimal time interval or maximal measurable energy [28]. Such constrains, when considered, influence various domains of physics such as description of black holes [29] or Newton's laws of gravity [30].…”

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confidence: 99%

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Nonlinear Schrödinger equation from generalized exact uncertainty principle

Rudnicki

2016

J. Phys. A: Math. Theor.

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Inspired by the generalized uncertainty principle (GUP), which adds gravitational effects to the standard description of quantum uncertainty, we extend the exact uncertainty principle (EUP) approach by Hall and Reginatto [J. Phys. A: Math. Gen. (2002) 35 3289], and obtain a (quasi)nonlinear Schrödinger equation. This quantum evolution equation of unusual form, enjoys several desired properties like separation of non-interacting subsystems or planewave solutions for free particles. Starting with the harmonic oscillator example, we show that every solution of this equation respects the gravitationally-induced minimal position uncertainty proportional to the Planck length.Quite surprisingly, our result successfully merges the core of classical physics with non-relativistic quantum mechanics in its extremal form. We predict that the commonly accepted phenomenon, namely a modification of a free-particle dispersion relation due to quantum gravity might not occur in reality. arXiv:1602.05004v2 [quant-ph]

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“…valid, for any l, instead of the traditional HUR. Note that due to (28), this new form of UR is sharper than the HUR. For instance, if we want (30) to be equal to the GUP, we need to set…”

Section: Generalized Exact Uncertainty Principlementioning

confidence: 94%

“…valid, for any l, instead of the traditional HUR. Note that due to (28), this new form of UR is sharper than the HUR.…”

Section: Generalized Eupmentioning

confidence: 94%

Section: Generalized Exact Uncertainty Principlementioning

confidence: 99%

mentioning

confidence: 99%

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Nonlinear Schrödinger equation from generalized exact uncertainty principle

Rudnicki

2016

J. Phys. A: Math. Theor.

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“…There are several observations supporting the concept of GUP approaches and offering a possibility of studying the influence of the minimal length on the properties of a wide range of physical systems, especially at quantum scale [25,26,34]. The effects of linear GUP approach have been studied on compact stars [46], Newtonian law of gravity [45], inflationary parameters and thermodynamics of the early Universe [47], Lorentz invariance violation [48] and measurable maximum energy and minimum time interval [73]. Furthermore, the effects of QG on the quark-gluon plasma (QGP) are studied [49].…”

Section: Applicability Of Gup To the Cosmic Inflationmentioning

confidence: 99%

Generalized Uncertainty Principle and Recent Cosmic Inflation Observations

Tawfik,

Diab

2014

Preprint

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The recent background imaging of cosmic extragalactic polarization (BICEP2) observations are believed as an evidence for the cosmic inflation. BICEP2 provided a first direct evidence for the inflation, determined its energy scale and debriefed witnesses for the quantum gravitational processes.The ratio of scalar-to-tensor fluctuations r which is the canonical measurement of the gravitational waves, was estimated as r = 0.2 +0.07 −0.05 . Apparently, this value agrees well with the upper bound value corresponding to PLANCK r ≤ 0.012 and to WMAP9 experiment r = 0.2. It is believed that the existence of a minimal length is one of the greatest predictions leading to modifications in the Heisenberg uncertainty principle or a generalization of the uncertainty principle (GUP) at the Planck scale. In the present work, we investigate the possibility of interpreting recent BICEP2 observations through quantum gravity or GUP. We estimate the slow-roll parameters, the tensorial and the scalar density fluctuations which are characterized by the scalar field φ. Taking into account the background (matter and radiation) energy density, φ is assumed to interact with the gravity and with itself. We first review the Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe and then suggest modification in the Friedmann equation due to GUP. By using a single potential for a chaotic inflation model, various inflationary parameters are estimated and compared with the PLANCK and BICEP2 observations. While GUP is conjectured to break down the expansion of the early Universe (Hubble parameter and scale factor), two inflation potentials based on certain minimal supersymmetric extension of the standard model result in r and spectral index matching well with the observations. Corresponding to BICEP2 observations, our estimation for r depends on the inflation potential and the scalar field. A power-law inflation potential does not.

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A minimal length uncertainty approach to cosmological constant problem

Diab

Tawfik

2021

Astron Nachr

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Based on quantum mechanical framework for the minimal length uncertainty, we demonstrate that the generalized uncertainty principle (GUP) parameter could be best constrained by recent gravitational waves observations on one hand. On the other hand, this suggests modified dispersion relations (MDRs) enabling an estimation for the difference between the group velocity of gravitons and that of photons. Utilizing features of the UV/IR correspondence and the obvious similarities between GUP (including non-gravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant (apparently manifesting gravitational influences on the vacuum energy density), we suggest a possible solution for the cosmological constant problem.

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Measurable maximal energy and minimal time interval

Cited by 7 publications

References 46 publications

Nonlinear Schrödinger equation from generalized exact uncertainty principle

Nonlinear Schrödinger equation from generalized exact uncertainty principle

Generalized Uncertainty Principle and Recent Cosmic Inflation Observations

A minimal length uncertainty approach to cosmological constant problem

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