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On the Machian Properties of the Universe

By analogy with the original Brans-Dicke relation GM2R � 1 , several other similar relations can be obtained, relating the angular momentum, absolute temperature T , and the cosmological ”constant”, with R , where R , M stand for the radius (scale-factor) and the mass of the causally related Universe. We show here that these properties, which characterize Machian Universes, can be derived from the conjecture that the total energy of the Universe is null, and imply that the angular momentum runs like R 2 ; T , like R − 1 2 ; so that the total entropy of the Universe increases with R 3 2 , and, then, also as M 3 2 . This also solves the ”loss of information paradox”,