Carroll is not completely wrong
Basically I agree with the criticism of Lubos. Carroll fails to realize that second law applies in all length scale and cosmology is only about largest scales. On the other hand, in the fractal Universe of TGD and in good mood;-) one can find in Carrol's idea something which cannot be said to be completely wrong. What I mean is follows.
In TGD framework one is forced to assign to incoming/outgoing elementary particles appearing in the generalized Feynman diagrams future/past directed lightcones analogous to mini-mini versions of big bang/crunch. These lightcones define geometric correlates for irreversibility and for the arrow of subjective time implied by the identification of the subjective time flow as sequence of quantum jumps. Therefore also second law can be said to have representation at space-time level.
The failure of complete classical determinism characterizing the basic variational principle of TGD is crucial for quantum classical correspondence also at level of quantum jumps. The representations of quantum jump sequences at space-time level make also possible symbolic representations for the contents of consciousness at space-time level and explain the "aboutness" character of consciousness: it is possible to become conscious about what one was conscious of (seeing red during this quantum jump and in next quantum jump becoming conscious that one was seeing red). These representations make possible a continual evolution of new reflective levels of consciousness via the feedback analogous to formulas written by a mathematician and inducing further ideas.
The basic fallacies
It is useful to list the fallacies of in the thinking of Lubos and Carroll since these fallacies allow to understand the recent dead end situation in theoretical physics.
- Both Lubos and Carroll and the entire string communitity stubbornly continue to miss the fractality of the Universe reflected as hierarchies of p-adic length scales and Planck constants in TGD framework. The p-adic hierarchy make itself especially visible in the widely different mass scales for elementary particles. Recall that the ratio of mass scales for top quark mass and neutrino is around 1011: despite this the proponents of strings→ GUT at low energies vision try to force these particles inside the same multiplet of unifying gauge group!
- A lot of muddy thinking results from the refusal to reconsider quantum measurement theory. Just the introduction of finite quantum measurement resolution to the theory would help considerably and would give connection with quantum groups and hyper-finite factors.
- I mentioned in the beginning that quantum classical correspondence provides space-time correlates for the sequences of quantum jumps in TGD Universe. One could also ask what are the classical space-time correlates for the choice of quantization axes and end up with the hierarchy of Planck constants. M-theorists are ready to consider incredibly weird brane world scenarios but refuse to consider this kind of idea inspired by need to go forward from the position where the fathers of quantum theory left us.
- Lubos with his ultraconservative hbar=1 vision about Universe refuses to seriously consider the connection between consciousness and quantum theory. I believe that quantum is absolutely crucial for consciousness as is also the understanding of consciousness for quantum physics. Of course, I do not believe that simple wave mechanics could resolve the riddle of consciousness: something much more general is needed.
- A vision about the origin of second law (most naturally quantum jumps) is missing. The erratic identification of the geometric time and experienced time irrespective of the fact that these times are quite different (reversibility/irreversibility, etc.) relates closely to this. Some amount of quantum consciousness theorizing accepting Boolean logic as a starting point would help to get rid of obvious logical paradoxes but what one can do if someone has decided that the idea about connection between quantum and consciousness is dull - as Lubos states it.
- Penrose's conjecture about the special role of gravitation concerning consciousness corresponds in TGD Universe immense values of gravitational Planck constant implying macroscopic quantum coherence in astro length scales. Gravitational interaction becomes fundamental for consciousness and life in TGD Universe.
From above it should be clear that basic problems are conceptual and the development of mathematical methods instead of humble return to the roots is not the manner to make progress.
Second law in standard Big Bang cosmology and TGD inspired cosmology
The considerations of Carrol have roots in the problem of understanding second law in Big Bang cosmology. The necessity of low entropy during primordial times does not quite fit with the standard big bang picture. In TGD long string like objects represent primordial state and this phase has low entropy. Entropy is produced when these objects decay to elementary particles. Dominance of string like objects also means that gravitational mass per comoving volume vanishes linearly as a function of cosmic time (call it t) rather than diverging as 1/t as in radiation dominated cosmology. Big Bang is transformed to a silent whispher gradually amplified to a big roar.