Naturalness, fine-tuning, second law, and love

In previous posting we have had a very nice discussion with Hamed about various aspects of "world of classical worlds" realized as a space of space-time surfaces (very rough statement). I thought that the following comment - intended to be a further response relating to the uniqueness of "world of classical worlds" (WCW) - deserves the status of a separate blog posting.

So called naturalness is the physicist's manner to say "of course" as Bee very neatly expresses the gist of this notion. After the results from LHC we know that standard model is not natural and SUSY in standard form cannot help. What one should think about theories whose predictions change dramatically when some parameter is varied only slightly? Certainly these kind of theories are not very useful. Many people are however ready to accept that theory could be of this kind. I see this as giving up. If theory in unstable under small allowed variations of its parameters it is definitely wrong and this is extremely valuable guideline.

The essential attribute appearing in this claim is " allowed". In some situations one cannot allow any variations. Indeed, classical number fields, groups, etc. are extremely rigid mathematical structures, which do not allow any variations of their structure. In the same manner, in TGD WCW is really something God given (or mathematics given). There are no parameters to be varied and fine-tune.

This is of course the great idea of TGD: physics follows from the mere existence of an infinite-dimensional geometry of WCW - more precisely from the existence of Riemann connection, which forces WCW to be a union of infinite-D symmetric spaces with maximal isometries having interpretation as conformal symmetries or analogs of them (symplectic symmetries of boundary of causal diamond). Among other things, this condition fixes imbedding space uniquely to M⁴ × CP₂ (also the condition that the twistor spaces associated with the Cartesian factors exist and are Kähler manifolds forces the same conclusion) allows to avoid the landscape difficulty of super string models, which is actually much more general problem.

Anthropic principle is second aspect related to fine-tuning. Fine-tuning of certain parameters essential for life seems to be present in physics. The idea behind the anthropic principle is that our own existence allows to deduce the values of fine-tuned parameters. This hypothesis involves however many implicit assumptions. For instance, one assumes that life as we know it recently is the only possible form of life and that there cannot be any other kinds of life forms realized for the other values of the key parameters.

The TDG based explanation for the fine-tuning relies on Negentropy Maximization Principle. NMP implies evolution accompanied by increasing negentropy resources realized in terms of negentropic entanglement. It also means finite-tuning: slowly varying parameters approach quantum jump by quantum jump values, which make possible maximal negentropy resources. The evolutionary self-organization process implied by NMP would lead to highly unique final states. Since NMP is more or less the mirror image of second law, the self-organization process could be mathematically analogous to the approach to thermodynamical equilibrium or thermodynamical non-equilibrium state (in presence of energy feed) polishing out all unessential details and leaving only the gem.

It is often said that life generates huge amounts of entropy. Looks at first just the opposite for what NMP predicts! Of course, the entropy in question is ensemble entropy and has as such nothing do with number theoretic entropy characterizing negentropic entanglement having interpretation as a quantum correlate for rule realized as superposition of its instances. NMP implies second law for ordinary entanglement and this might be enough (NMP however also predicts varying arrow of thermodynamical time, something highly non-trivial although considerable support for this exists in living matter!).

I have also considered the pessimistic conjecture that second law holds true in the following sense. If negentropy associated with negentropic entanglement is generated, it is somehow accompanied by a generation of entropy at least compensating for it. I do not believe this conjecture: the two notions do not simply apply in the same context and I do not have any mechanism for how the entropy would be generated. One can however consider the following natural correlation. Systems with a large number of degenerate states (same energy) in thermodynamical equilibrium have large entropy. The same highly degenerate systems can however entangle negentropically and this gives rise to a large entanglement negentropy. Entropy can transforms to negentropy! Love - for which I have suggested negentropic entanglement to serve as a quantum correlate - makes jewels from dirt!