1. Black hole entropy and dark black holes
Lubos made in his posting explicit the 1/hbar proportionality of formulas for black hole entropy. This proportionality reflects the basic thermodynamical implication of quantization: the phase space of N-dimensional system decomposes into cells of volume hbarN and entropy is proportional to the phase space volume using this volume as unit. If hbar becomes large and gigantic as it would in the case of dark gravitation (hbar= GM1M2/v0, v0/c∼ 2-11 for inner planetary Bohr orbits) this means that blackhole entropy is extremely small. Black is dark;-) as I realized for few years ago, and it would be interesting to consider the consequences.
2. Hierarchy of Planck lengths
It deserves to be noticed that the rough order of magnitude estimate for the gravitational Planck constant of Sun can be written as hbargr=x4GM2. This gives for the Planck length the expression
LP= (Ghbar)1/2 = x1/2 2GM .
For x=1 one Planck length would be just Schwartshild radius. This makes sense since these two lengths play rather similar role. Quite generally, one would have a hierarchy of Planck lengths.
3. Dark flow
Second comment is related to the earlier posting of Lubos about the observed dark flow in length scales larger than horizon size towards an attractor outside horizon. The presence of the attractor outside the visible universe conforms with the notion of manysheeted space-time predicting also a manysheeted cosmology.
Many-sheeted cosmology means a hierarchy of space-time sheets obeying their own Robertson-Walker type cosmologies: those with varying p-adic length scale and those labelled by various values of Planck constants at pages of book like structure obtained by gluing together singular coverings and factor spaces of 8-D imbedding space (roughly). Particles at different pages are dark relative to each other in the sense that there are no local interaction vertices: classical interactions and those by exchanges of say photons are possible. Each sheet in many-sheeted cosmology has different horizon size.
The attractor would correspond to a different value of Planck constant and have larger horizon size than our sheet. Dark energy would be dark matter and the phase transitions increasing Planck constant would induce phases of accelerated expansion. In average sense these periods would give ordinary cosmology without accelerated expansion.
4. How to avoid heat death?
Third comment relates to the dark flow and implications of the hierarchy of Planck constants to future prospects of intelligent life. Heat death is believed by standard physicists to be waiting for all forms of life. We would live in the silliest possible Universe. I cannot believe this. I am ready to admit that some of our theories about the Universe are really silly, but entire Universe?--No!
The hierarchy of Planck constants would allow to avoid heat death. For instance, if the rate for the reduction of temperature is proportional to 1/hbar -as looks natural- then there is always an infinite number of hierarchy levels for which temperature is above a given temperature since the temperature at these pages is reduced so slowly.
Life can escape to the pages of the Big Book labelled by larger values of Planck constant without breaking second law since the scaling of the size of the system by hbar increases phase space volume and keeps entropy constant. Evolution by quantum leaps increasing hbar increasing the time scale of planned action and long term memory is another manner to say this.
The observed dark flow might be seen as a direct support for this more optimistic view about Life and the Universe and Everything;-).