Suppose we accept the identification of dark matter in astrophysical length scales as matter with a gigantic gravitational Planck constant suggested by Bohr orbitology of planetary orbits. For instance, hbar =GM2/v0, v0=1/4, would hold true for an ideal black hole with Planck length (hbarG)1/2 equal to Schwartshild radius 2GM. Since black hole entropy is inversely proportional to hbar, this would predict black hole entropy to be of order single bit. This of course looks totally non-sensible if one believes in standard thermodynamics. For the star with mass equal to 1040 Planck masses discussed in the example of Lubos the entropy associated with the initial state of the star would be roughly the number of atoms in star equal to about 1060. Black hole entropy proportional to GM2/hbar would be of order 1080 provided the standard value of hbar is used as unit.
This stimulates some questions.
- Does second law pose an upper bound on the value of hbar of dark black hole from the requirement that black hole has at least the entropy of the initial state. The maximum value of hbar would be given by the ratio of black hole entropy to the entropy of the initial state and about 1020 in the example of Lubos to be compared with GM2/v0 ≈1080.
- Or should one generalize thermodynamics in a manner suggested by zero energy ontology by making explicit distinction between subjective time (sequence of quantum jumps) and geometric time? The arrow of geometric time would correlate with that of subjective time. One can argue that the geometric time has opposite direction for the positive and negative energy parts of the zero energy state interpreted in standard ontology as initial and final states of quantum event. If second law would hold true with respect to subjective time, the formation of ideal dark black hole would destroy entropy only from the point of view of observer with standard arrow of geometric time. The behavior of phase conjugate laser light would be a more mundane example. Do self assembly processes serve as example of non-standard arrow of geometric time in biological systems? In fact, zero energy state is geometrically analogous to a big bang followed by big crunch. One can however criticize the basic assumption as ad hoc guess. One should really understand the the arrow of geometric time. This is discussed in detail in the article About the Nature of Time.