Discreteness of Space from the Generalized Uncertainty Principle

Understand

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).