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In black hole physics, inflationary cosmology, and quantum field theories, itis conjectured that the physical laws are subject to radical changes below thePlanck length. Such changes are due to effects of quantum gravity believed tobecome significant at the Planck length. However, a complete and consistentquantum theory of gravity is still missing, and candidate models of quantumgravity have not yet overcome major formal and conceptual difficulties. Anotherproblem is how to determine a geometry of physical space that features aminimal length scale such as the Planck length. In the present paper it isdemonstrated that the said geometry can be any geometric system omittingcontinuity, i.e., a geometry that possesses only a finite number of points.

Resolving the trans-Planckian problem along the lines of a finite geometry