Physical states are zero energy states: an ontology consistent with the existing world view?
The factorizing S-matrices seem unavoidably as basic building blocks of S-matrix in TGD framework and it might be that the S-matrix, which depends on von Neumann inclusion characterizing the limitations of quantum measurer, could quite generally reduce to a tensor product of these S-matrices in partonic degrees of freedom. The basic problem has been the fact that these S-matrices are essentially trivial as far as scattering in momentum degrees of freedom is considered. After many wrong guesses an incredibly simple solution to the puzzle emerged and the almost triviality of factorizing S-matrices transformed from a curse to blessing.
1. Zero energy states as the ultimate building block of matter
The idea is to modify the original vision about particle reactions somewhat and in complete consistency with the prediction that in TGD Universe all quantum states have vanishing total quantum numbers. Instead of thinking scattering of positive energy particles as creation of zero energy state from vacuum, the original vision, one considers scattering of zero energy states. I have proposed already earlier that this scattering and also higher level scatterings occur but that this process corresponds to higher level process in the cognitive hierarchy than the scattering that we detect in laboratory. What is nice is that one can deduce scattering rates for the illusory scattering of positive energy particles from this higher level S-matrix as thermal expectation values in a sense von Neumann would have defined them. One could of course assume that also positive energy states are there but scattering for them would be rather trivial and they would not correspond to observed particles.
In the new rather Buddhistic ontology zero energy states are identified as experienced events and objective reality in the conventional sense becomes only an illusion. Before the new view can be taken seriously one must demonstrate how the illusion about positive energy reality is created and why it is so stable.
- The very fact that the factorizing S-matrices are trivial apart from the changes in the internal degrees of freedom means that the event pairs are extremely stable once they are generated (how they are generated is an unavoidable question to be addressed below). Infinite sequences of transition between states with same positive energies and same initial energies occur. What is nice that this makes it possible to test the predictions of the theory by experiencing the transition again and again.
- Statistical physics becomes statistical physics for an an ensemble consisting of zero energy states |m+n-> including also their time reversals |n+,m->. In the usual kinetics one deduces equilibrium values for various particle densities as ratios for the rates for transitions m+→ n+ and their reversals n+→ m+ so that the densities are given by n(n+)/n(m+)= ∑n+Γ(m+→ n+)/∑n+Γ/(n+→ m+). In the recent situation the same formula can be used to define the particle number densities in kinetic equilibrium using the proposed identification of the transition probabilities.
- Because of the stability of the zero energy states, one can construct many particle systems consisting of zero energy states and can speak about the density of zero energy states per volume. Also the densities n+,i (n-,i) of initial (final) states of given type can be defined and densitites of positive energy states can be identified as densities assignable to the ordinary matter. Also densities of particles contained by these states can be defined. It would seem that the new ontology can reproduce the standard ontology as something which is not necessary but to which we are accustomed and which does not produce too much harm.
- The sequence of quantum jumps between negative energy states defines also a sequence between initial (final) states of quantum jumps and, as far as momentum and color degrees of freedom are considered, this sequence represents rather immutable reality if S-matrix is factorizing.
2. How does the quantum measurement theory generalize?
There are also important questions related to the quantum measurement theory. The zero modes associated with the interior degrees of freedom of space-time surface represent classical observables entangled with partonic observables and this entanglement is reduced in quantum jump. Negentropy Maximization Principle is the TGD based proposal for the variational principle governing the statistical dynamics of quantum jumps. NMP states that entanglement negentropy tends to be maximized in the reduction of entanglement. Number theoretic variants of Shannon entropy making sense for rationally or even algebraically entangled states can be positive so that NMP can also lead to generation of this kind of entanglement and gives rise to a highly stable bound state entanglement.
Does this picture generalize to the new framework in which zero energy states become physical states? Factorizing S-matrices describe partonic dynamics and should be responsible for generating entanglement in the partonic degrees of freedom. One should understand also the S-matrix generating entanglement between zero modes and partonic degrees of freedom and quantum classical correspondence is the only guideline in the recent situation.
3. Understanding quantum computation in the new ontology?
The understanding of what really happens in quantum computation, in particular topological quantum computation, is a challenge for the recent framework since the theory of quantum computation relies heavily on the Hamiltonian time evolution which cannot be an exact description in the new ontology. The basic element is entanglement between positive and negative energy states. It is generated by time evolution in standard framework whereas in the recent framework the creation of the quantum computer program and its realization reduces to the creation of a zero energy state realizing this entanglement. Note that also entanglement between positive energy states can be used for quantum computational purposes.
The problem is obvious: the creation of quantum computer program requires a creation of a zero energy state realizing the program. Can one allow quantum jumps creating zero energy states representing the desired program? The extreme stability of the zero energy states against evolution defined by a factorizing S-matrix does not allow the popping up of zero energy states from vacuum since four-momenta are in this case vanishing. Must be accept that we are passive spectators who just observe the already existing zero energy states representing quantum computer programs as we drift towards geometric future along larger space-time sheet?
It seems that this is not necessary. p-Adic physics as a physics of intentionality and cognition however suggests how the obstacle could be overcome at the level of principle. For zero energy states, p-adic-to-real transitions and vice versa are in principle possible and I have in fact proposed a general quantum model for how intentions might be transformed to actions in this manner. In the second direction the process corresponds to formation of cognitive representation of a zero energy physical state.
In the degrees of freedom corresponding to configuration space spinors situation is very much like for reals. Rational, and more generally algebraic number based physics applies in both cases. p-Adic space-time sheets however differ dramatically from their real counterparts since they have only rational (algebraic) points in common with real space-time sheets and p-adic transcendentals are infinite as real numbers. The S-matrix elements for p-adic-to-real transitions can be formulated using n-point functions restricted to these rational points common to matter and mind stuff. If this picture is not terribly wrong, it would be possible to generate zero energy states from vacuum and the construction of quantum computer programs would be basically a long and tedious process involving very many intentional acts.
One can of course, make a further question. What about the generation of intentions: can p-adic space-time sheets and quantum numbers pop up spontaneously from vacuum? What kind of p-adic space-time sheets and quantum numbers assignable to their partonic 2-surfaces can do so spontaneously?
Here an interesting aspect of the p-adic conservation laws passes a helping hand. p-Adic integration constants are pseudo constants in the sense that a quantity having vanishing (say) time derivative can depend on a finite number of pinary digits tn of the time coordinate t=∑ntnp-n. Could one think that quantum jumps can generate from vacuum exact vacuum states as vacuum tensor factors of the configuration space spinor, and that in subsequent quantum jumps factorizing p-adic S-matrix conserving quantum numbers only in p-adic sense transforms this state into a non-trivial zero energy state which then transforms to real state in intentional action? Note that if conserved quantum numbers are integers they are automatically pseudo constants. p-Adic conservation laws could allow also the p-adic zero energy states to pop up directly from vacuum.
Real-to-p-adic transitions would represent transformation of reality to cognition and would be also possible and mean destruction of zero energy states universe. The characteristic and perhaps the defining feature of living matter would be its highly developed ability to reconstruct reality by performing p-adic-to-real transitions and their reversals.
The chapter Construction of Quantum Theory of "Towards S-matrix" represents the detailed construction as it is now (it could change!).