Monday, August 31, 2009

A resolution of cosmological entropy paradox

Anonymous made an interesting question about how TGD solves the cosmological entropy paradox. The initial state of cosmology seems to be maximum entropy state. The recent state should have even larger entropy if second law holds. One can however argue that this is not the case.

The TGD inspired proposal is that the resolution of cosmological entropy paradox relates to the relationship between subjective and geometric time.

  1. It is subjective time with respect to which second law holds true. It corresponds to the geometric time of observer only locally.

  2. One can apply second law only for to what happens inside 4-D causal diamond (CD) corresponding to the time scale of observations: in positive energy ontology second law is applied at fixed value of geometric time and this leads to problems. In cosmology the relevant CD extends from the moment of big bang and to the recent time or even farther to geometric future. The idea that entropy grows as a function of cosmic time is simply wrong if you accept zero energy ontology.

More concretely.

  1. In each quantum jump re-creating entire 4-D Universe the entire geometric future and past changes.

  2. Initial state of big bang in geometric sense(!)- the zero energy states associated with small CDs near the light-cone boundary corresponding to Big Bang- are replaced by a new one at every moment of subjective time. Hence the "subjectively recent" initial state of Big Bang can be assumed to have maximum entropy as also states after that when the time scale of observations (size of CD) is the age of the universe. Gradually the entire geometric past ends up to a maximum entropy state in time scales below the time scale characterizing the time scale of observations. Thermal equilibrium in 4-D sense rather than 3-D sense results and the paradox disappears.

Note: The breaking of strict classical determinism of Kahler action allowing CDs within CDs picture is essential mathematical prerequisite: otherwise this picture does not make sense. It makes possible also space-time correlates for quantum jump sequence rather than only for quantum states.

Note: One proposal for the resolution of entropy paradox could relate to generation of black holes with large entropy. In TGD framework this does not work since for gravitational Planck constant the value of black hole entropy is ridiculously small.

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