Discreteness of space from the generalized uncertainty principle

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Ali, Ahmed Farag
Das, Saurya
Vagenas, Elias C.
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Various approaches to Quantum Gravity (such as String Theory and Doubly Special Relativity), as well as black hole physics predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called Generalized Uncertainty Principle (GUP). We propose a GUP consistent with String Theory, Doubly Special Relativity and black hole physics, and show that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it implies that the space which confines it must be quantized. This suggests that space itself is discrete, and that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this signals the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale.
Sherpa Romeo green journal. Open access article. Creative Commons Attribution License (CC BY) applies.
Generalized uncertainty principle , String theory , Doubly special relativity , Black hole physics , Quantum gravity , Hamiltonian
Ali, A. F., Das., S., & Vagenas, E. C. (2009). Discreteness of space from the generalized uncertainty principle. Physics Letters B, 678(5), 497-499. doi: 10.1016/j.physletb.2009.06.061