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Nonlocal generalized uncertainty principle and its implications in gravity and entropic Verlinde holographic approach

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Abstract

Recently, a nonlocal generalized uncertainty principle was derived based on the new notion of quantum acceleratum operator within the framework of nonlocal-maximal quantum mechanics. In this study, we discuss some of its properties and some of its implications in Newtonian gravity theory and Verlinde’s entropic holographic approach. A number of features were revealed; in particular, the emergence of a logarithmic correction to the gravitational Newtonian potential, a minimum energy and a minimum mass which depend on the gravitational coupling constant. Based on the concept of holographic principle, Verlinde’s conjecture and equipartition rule, a quantized Newton’s force law of gravity for a particle of mass m gravitating around a Planck mass is derived.

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Acknowledgements

The author is indebted to the anonymous referees for their useful comments and valuable suggestions.

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  1. Mathematics and Physics Divisions, Athens Institute for Education and Research, 8 Valaoritou Street, Kolonaki, 10671, Athens, Greece

    Rami Ahmad El-Nabulsi

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  1. Rami Ahmad El-Nabulsi
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Correspondence to Rami Ahmad El-Nabulsi.

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El-Nabulsi, R.A. Nonlocal generalized uncertainty principle and its implications in gravity and entropic Verlinde holographic approach. Quantum Stud.: Math. Found. 6, 235–240 (2019). https://doi.org/10.1007/s40509-019-00181-x

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