But what if the eigenvalues and thus also eigenvectors of the density matrix, which are algebraic numbers, do not belong to the algebraic extensions involved. Can state function reduction reduction occur at all so that this kind of NE would be stable?
The following argument suggests that also more general algebraic entanglement could be reasonably stable against NMP, namely the entanglement for which the eigenvalues of the density matrix and eigenvectors are outside the algebraic extension associated with the parameters characterizing string world sheets and partonic 2-surfaces as space-time genes.
The restriction to a particular extension of rationals - a central piece of the number theoretical vision about quantum TGD - implies that density matrix need not allow diagonalization. In eigen state basis one would have has algebraic extension defined by the characteristic polynomial of the density matrix and its roots define the needed extension which could be quite well larger than the original extension. This would make state stable against state function reduction.
If this entanglement is algebraic, one can assign to it a negative number theoretic entropy. This negentropic entanglement is stable against NMP unless the algebraic extension associated with the parameters characterizing the parameters of string world sheets and partonic surfaces defining space-time genes is allowed to become larger in a state function reduction to the opposite boundary of CD generating re-incarnated self and producing eigenstates involving algebraic numbers in a larger algebraic extension of rationals. Could this kind of extension be an eureka experience meaning a step forwards in cognitive evolution?
If this picture makes sense, one would have both the unitary NE with a density matrix, which is projector and the algebraic NE with eigen values and NE for which the eigenstates of density matrix outside the algebraic extension associated with the space-time genes. Note that the unitary entanglement is "meditative" in the sense that any state basis is possible and therefore in this state of consciousness it is not possible to make distinctions. This strongly brings in mind koans of Zen buddhism and enlightment experience. The more general irreducible algebraic entanglement could represent abstractions as rules in which the state pairs in the superposition represent the various instances of the rule.
For details see the chapter Negentropy Maximization Principle of "TGD Inspired Theory of Consciousness" or the article Impressions created by TSC2015 conference.
For a summary of earlier postings see Links to the latest progress in TGD.
7 comments:
Negentropy is formed from a decrease in energy, and as energy is a graded scale, formed of 'bits' also its counterpart, or negentropy, should express the same, but opposite to entropy.
Hence negentropy is describing a degraded energetic state, what is a quantum state, also it is fractal, so a comparision to FQHE is in order.
Entanglement can also be a result of superposition, added energy, and also this state can be graded, fractal, but upwards to higher energy level.
The electron story of this (excitation - jump) is maybe just that - a story, a fancy tale? What is the real electron?
In the case of thermodynamics one can express differential of energy in terms of differentials of entropy, pressure etc.. Entropy flow involves flow of energy typically. In case of entanglement entropy which becomes negative for negentropic entanglement (number theoretic definition is essential) situation is not so clear. One can certainly image generalisation of thermodynamics formulas.
Entanglement entropy and thermodynamical entropy are closely related but no identical in TGD. There has been rumours that gravity has killed Schrodinger cat (decoherence would happen in isolated system and be due to gravity). Bee defended in her last posting gravity and clearly stated that gravity is innocent;-).
In her defines she discussed how she sees the generation of decoherence .http://backreaction.blogspot.fi/2015/06/no-gravity-hasnt-killed-schrodingers-cat.html. Bee identified decoherence as increase of entanglement entropy reflecting the generation of entanglement.
I would in turn identify decoherence as increase of thermodynamical entropy for ensemble and it would be a result of state function reduction. I tend to forget that TGD view about state function reduction is much more refined than ordinary one. For instance, quantum measurement as measurement of density matrix is assumed to be completely universal process and occurs for that subsystem-complement pair of isolated system for which maximal negentropy gain is largest (if can of course happen that nothing occurs as during the sequence of repeated state function reductions defining self ). This is definitely new as compared to standard quantum measurement theory. Also the contribution of zero energy ontology is totally new element.
The question about real electron looks to me unnecessary. If one accepts identification of quantum state- such as electron- with its mathematical description, the question disappears. This makes sense if conscious experiences are assign with state function reductions and are thus in the replacement of mathematical object representing quantum state with a new one. Between two worlds rather than in world. I have found that this view about ontology of consciousness is practically non-communicable;-).
(if can of course happen that nothing occurs as during the sequence of repeated state function reductions defining self )
This must in my opinion be a part of a protected state, having very few state function reductions. This means that the symmetry breakings are not happening at random, but are purely directed and also in a way hierarchial.
Regarding the electron, say the Tesla magnetic induction, how does that electron form? It is not that the electron is a stable particle?
I know magnetic and electric flow interact, forming 'magnetic' and 'electric' prticles, temporal ones. Is this interaction basement for the time-scale? This interaction basically comes from state function reduction too.
In ZEO state function reductions by definition leave the state at second "passive" boundary invariant. This is TGD counterpart of Zeno effect. The original hypothesis was that during its lifetime self manages to avoid entanglement with environment but I could not justify it in positive energy ontology. This is also the basic problem of quantum computers scientists who work in positive energy ontology. Quantum computer program running is in TGD framework the life cycle of conscious entity.
Electron is stable particle in ZEO but observationally in the sense that we *do not observe decays of electrons*! This is true also in ZEO. CD represents the space-time region about which self has experiences and electron cannot say anything about what happens outside its CD. Does the space-time surface representing electron continue outside CD or not. By the way, to electron one can assign CD with minimum size of order Earth size - .1 light seconds.
Self with bigger CD having electron CD would experience electron sub-CD as sub-self mental image representing observation of electron. The bigger self cannot say whether the electron's space-time surface continues beyond the boundaries if its CD.
The basic question still not answered conclusively is whether CD represents the 4-D "perceptive field" of self -say electron- or whether it represents entire 4-D existence for which boundaries CD mean the beginning and end of the world. Or saying the same differently: do only the events defined by CDs exist or are interiors of CDs parts of bigger structure so that space-time surfaces continue above/below upper/lower boundaries of CDs. The latter option would conform with western view, the first option with eastern view. I must admit that I have not been able to decide;-).
Read here about protected states, one among many, many papers. http://arxiv.org/pdf/1110.4469.pdf
this is much more rational?
I am talking here about theory of quantum measurement generalised to a theory of consciousness, not about some
specific model suggesting a mechanism of high temperature super conductivity. Negentropic entanglement is completely general notion and key to the understanding
of basic aspects of consciousness.
The only association to TGD is via the word "room-temperature super-conductivity". For this TGD provides a general new physics mechanism applying in living matter and also explaining high T_c superconductivity. This will be taken seriously only after the notion of magnetic flux tube is accepted: the empirical evidence for it is emerging all the time but it takes few years before physicists are mature to realize how elegantly they explain high T_c superconductivity for which anti ferromagnetism is essential ingredient.
The so called protected states discussed in the article relate to an attempt to obtain room-temperature superconductivity without introducing new physics. Quite generally, these attempts have failed (and very probably continue to fail) and high T_c superconductivity still remains a mystery. Protected states assigned with a very specific condensed matter system. Also pseudo Majora fermions are introduced: in Nature there are no Majorana fermions although media hypists make different claims;-)..
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