Minimal length in quantum gravity, equivalence principle and holographic entropy bound

Abstract

A possible discrepancy has been found between the results of a neutron\ninterferometry experiment and Quantum Mechanics. This experiment suggests that\nthe weak equivalence principle is violated at small length scales, which\nquantum mechanics cannot explain. In this paper, we investigated whether the\nGeneralized Uncertainty Principle (GUP), proposed by some approaches to quantum\ngravity such as String Theory and Doubly Special Relativity Theories (DSR), can\nexplain the violation of the weak equivalence principle at small length scales.\nWe also investigated the consequences of the GUP on the Liouville theorem in\nstatistical mechanics. We have found a new form of invariant phase space in the\npresence of GUP. This result should modify the density states and affect the\ncalculation of the entropy bound of local quantum field theory, the\ncosmological constant, black body radiation, etc. Furthermore, such\nmodification may have observable consequences at length scales much larger than\nthe Planck scale. This modification leads to a \\sqrt{A}-type correction to the\nbound of the maximal entropy of a bosonic field which would definitely shed\nsome light on the holographic theory.\n