Zero energy ontology
Zero energy ontology states that physical states have vanishing net conserved quantum numbers and states decompose to positive and negative energy state and that the latter one can be said to be located in the geometric future with of the positive energy state at the time-like boundary of the space-time sheet representing the system. It is possible to speak about energy of the system if one identifies it as the average positive energy for the positive energy part of the system.
The matrix ("M-matrix") representing time-like entanglement coefficients between positive and negative energy states unifies the notions of S-matrix and density matrix since it can be regarded as a complex square root of density matrix expressible as a product of real squared of density matrix and unitary S-matrix. The system can be also in thermal equilibrium so that thermodynamics becomes a genuine part of quantum theory and thermodynamical ensembles cease to be practical fictions of the theorist. In this case M-matrix represents a superposition of zero energy states for which positive energy state has thermal density matrix.
- If the positive energy parts of zero energy states appearing in the superposition have only single value of energy, the notion of remote metabolism is certainly well-defined. Even in the case that the system is thermalized remote metabolism makes sense since average energy can be increased by remote metabolism. One can even imagine a statistical variant of the process in which the temperature increases.
- The critical question is whether crossing symmetry prevails in the sense that the positive energy signal propagating to the geometric future is equivalent to a negative energy signal propagating to geometric past. The eigen modes of the modified Dirac operator appearing in the first principle formulation of quantum TGD are characterized by the eigenvalues λ, which are complex. |λ|2 has interpretation as a conformal weight mathematically analogous to a vacuum expectation value of Higgs field. There are reasons to believe that the eigenvalues relate closely to the zeros of Riemann zeta and/or its generalizations. If the eigenvalue and its complex conjugate correspond to a state and its phase conjugate, crossing symmetry fails and would mean also breaking of time reversal symmetry.
Is zero energy ontology consistent with time mirror mechanism
Energy conservation and geometric arrow of time poses strong conditions on the mechanism. If positive energy part of state sends negative energy signal, then negative energy part of state must send a compensating positive energy signal. Furthermore, positive (negative) energy signals propagate towards geometric future (past).
- If only single space-time sheet is involved, either negative energy signal S-: X4-→ Y4- or positive energy signal S+: X4+→ Y4- is possible. The energy of both states is reduced in magnitude. For instance, this process tends to reduce destroy long term memories represented as bit sequences with bit represented by population inverted laser system.
- Second possibility is that X4 are Y4 are disjoint and X4 is in the geometric future of Y4.
The first possibility is S+: X4+ → Y4- and negative energy signal S-: X4-→ Y4-: the energy of both X4 and Y4 is reduced in this case.
Second possibility is S-: X4+→ Y4+ and S+: Y4-→ X4-. X4 would suck energy from Y4 in the geometric past. This option could correspond to both remote metabolism, memory recall, and intentional action. The presence of topological light ray connecting two systems would be also a correlate for time-like quantum entanglement making possible sharing and fusion of mental images and creating a sensation about flow of time just like it creates sensation of depth in stereo vision by fusion of right and left visual fields. Depending on the sign of the energy of the signal one would have memory or precognition. Precognition would require use of metabolic energy and this might be one reason for why it is rather rare.
- Suppose next that the zero energy space-time sheet, call it X4, is inside larger space-time sheet, call it Y4: X4subset Y4. In this case one can have S-: X4+→ Y4+ accompanied by S+: X4-→ Y4-. X4subset Y4 would suck energy from a larger system Y4. It is of course possible to replace signals with signals of opposite energy in opposite time direction.
A possible interpretation is as a metabolic charging of smaller space-time sheets by sucking energy from longer scales or by active pumping of energy to shorter scales. The transformation of long wavelength photons with large Planck constant to short wavelength photons with smaller Planck constant is an analogous process and might realize metabolic charging in biology. For instance, Sun-Earth system could correspond to Y4 and biosphere to X4.
It is not at all obvious whether the proposed picture is consistent with the standard thermodynamics. The transfer of energy from long to shorter length scales making possible to gain metabolic energy and realize the mechanism of long term memory indeed seems a genuinely new element. This process resembles dissipation in the sense that energy is transferred from long to short length scales. In an approach to thermal equilibrium temperature gradients are however reduced whereas remote metabolism favors the active generation of "hot spots".
These considerations relate closely to the notions of entropy and syntropy by Italian mathematician Luigi Fantappie [Fantappie] assigned with the two arrows of time. I learned from the work of Fantappie in SSE conference held in Röros from Antonella Vannini [Vannini] and Ulisse Di Corpo [Corpo].The discovery of Fantappie was that in living systems entropic processes seem to be accompanied by syntropic processes which seem to be finalistic. He assigned these processes to the advanced solutions of wave equations.
It would seem that entropy and syntropy do not relate directly to the notion of remote metabolism.
- Syntropy growth would indeed be the mirror image of entropy growth associated with negative energy mirror image of positive energy dynamics. This dynamics could be seen as sequences of downwards scalings leading from long time scale to short time scale. This sequence would define time sequences proceeding in opposite directions of time for positive and negative energy parts of states. Thus entropy growth would be accompanied by syntropy growth.
- Syntropy growth could be also seen as a consequence of generalized second law applying with respect to subjective time and growth of syntropy would be growth of entropy but manifesting itself at space-time level in reversed direction of geometric time. For instance, the spontaneous assembly of bio-molecules from their parts could be seen as a decay process in the reverse direction of geometric time controlled by phase conjugate control signals.
- Remote metabolism as generation of "hot spots" does not seem to reduce to these notions and might represent a genuine breaking of standard thermodynamical view about the world.
- N is defined as the maximum of the p-adic entanglement negentropy N(p) as a function of the p-adic prime p and thus assigns to an entangled system a unique prime pmax. N(p) is obtained by replacing in the definition of the Shannon entropy the argument of logarithm with its p-adic norm. N is in general positive and thus defines a genuine measure of information.
- The non-negative negentropy defined in this manner characterizes entanglement as a carrier of information rather than the state of either of systems and has nothing to do with the ordinary (non-positive) entropy characterizing the lack of knowledge about the state of either subsystem. Negentropy Maximization Principle [NMP] favors the increase of the number theoretic negentropy and thus formation of entanglement quantum systems and generation of quantum coherence. Depending on the character of entanglement negentropic entanglement might be interpreted as a correlate for some conscious experience with positive content: say experience of understanding (time-like entanglement implying causal structure), of love (space-like entanglement), etc...
- It is not obvious to me whether the remote metabolism as a manner to build hot spots and diversity could be reduced to NMP or whether it should be regarded as something completely independent.
[NMP] The chapter Negentropy Maximization Principle of "TGD Inspired Theory of Consciousness".
[Fantappie] L. Fantappie (1942), Teoria Unitaria del Mondo Fisico e Biologico, Di Renzo Editore, Roma, 1991.
[Vannini] A. Vannini(2007), Advanced Waves, Retrocausality, and Consciousness in The 7th European SSE Meeting August 17-19, 2007, Röros, Norway. Proceedings.
[Corpo] U. Di Corpo (2007), The conflict between entropy and syntropy: the vital needs model in The 7th European SSE Meeting August 17-19, 2007, Röros, Norway. Proceedings.
For details see the chapter Quantum Model of Memory.