We present a novel generalization of the Heisenberg uncertainty principle which introduces the existence of a maximal observable momentum and at the same time does not entail a minimal indeterminacy in position. The above result is an exact generalized uncertainty principle (GUP), valid at all energy scales. For small values of the deformation parameter β, our ansatz is consistent with the usual expression for GUP borrowed from string theory, doubly special relativity and other quantum gravity candidates that provide β with a negative sign. As a preliminary analysis, we study the implications of this new model on some quantum mechanical applications and on the black hole thermodynamics.

我们提出了海森堡不确定性原理的新概括，它引入了最大可观察动量的存在，同时不包含位置的最小不确定性。上述结果是一个精确的广义不确定性原理 (GUP)，在所有能量尺度上都有效。对于变形参数β 的小值，我们的 ansatz 与从弦论、双狭义相对论和其他为β提供负号的量子引力候选中借用的 GUP 的通常表达式一致。作为初步分析，我们研究了这种新模型对某些量子力学应用和黑洞热力学的影响。