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Holographic Cosmology and Uncertainty Relation

M. A. Per·A. Segui
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Abstract

It is believed that a primary principle of the theory of quantum gravity is the Holographic Principle according to which a physical system can be described only by degrees of freedom living on its boundary. The generalized covariant formulation of the principle considers the entropy content on truncated light-sheets: light-like hypersurfaces of non-positive expansion orthogonally generated from a boundary. When we construct the truncated light-sheets for cosmological observers we find a general expression for the minimum cosmic time interval from the apparent horizon to verify the holographic prescription; this minimum time is related to quantum effects involved in the entropy computation. Finally, we arrive to the uncertainty relation from the Holographic Principle, which suggests a deep connection between general covariance, entropy bounds and quantum mechanics.

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M. A. Per, A. Segui. 2005-02-07. Holographic Cosmology and Uncertainty Relation. https://arxiv.org/abs/gr-qc/0502025

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