Reply to "Holographic principle in spacetimes with extra spatial dimensions" and "About quantum fluctuations and holographic principle in (4+n)-dimensional spacetime"

TL;DR

This paper responds to critiques of previous work, arguing that the Generalized Uncertainty Principle can be compatible with the Holographic Principle in higher-dimensional spacetimes under specific, unrealistic conditions.

Contribution

It clarifies the conditions under which the Generalized Uncertainty Principle aligns with the Holographic Principle in extra-dimensional spacetimes, addressing previous misconceptions.

Findings

Compatibility depends on specific size-mass relations of the clock.

The proposed compatibility is only valid under unrealistic assumptions.

Rebuttal of previous claims about the general incompatibility.

Abstract

We reply to the comments by P.Midodashvili about our previous paper [1]. We argue that, contrary to the conclusions in Refs. [2,3], the Generalized Uncertainty Principle proposed by Ng and van Dam in Ref. [4] is compatible with the Holographic Principle in spacetimes with extra dimensions only for a very special (and somehow unrealistic) choice of the relation between the size and mass of the clock.