An Uncertainty Relation of Space-Time.

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  • Sasakura Naoki
    Department of Physics, Kyoto University, Kyoto 606–8502, Japan

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  • An Uncertainly Relation of Space-Time

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Abstract

We propose an uncertainty relation of space-time. This relation is characterized by G (h/2π) T <~ δ V, where T and δ V denote a characteristic time scale and a spatial volume, respectively. Using this uncertainty relation, we give qualitative estimations for the entropies of a black hole and our universe. We obtain qualitative agreements with the known results. The holographic principle of 't Hooft and Susskind is reproduced. We also discuss cosmology and give a relation to the cosmic holographic principle of Fischler and Susskind. However, as for the maximal entropy of a system with an energy E, we obtain the formula √{EV/G(h/2π)2, with V denoting the volume of the system, which is distinct from the Bekenstein entropy formula ER / (h/2π) with R denoting the length scale of the system.

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