New Physics and Mind

Lubos has commented in his blog article "New Physics and the Mind" the new popular book New Physics and the Mind of Robert Paster (can be found at Amazon) containing also a brief summary of TGD inspired theory of consciousness. Unfortunately, the limitation to the length of comments at Lubos blog is so severe that I have to react through my own blog to the comments of Rae Ann and Nigel Cook.

Glad to hear that Lubos has received the book with such an enthusiasm!;-) Lubos is clearly taking TGD (and TGD inspired theory of consciousness) rather seriously as is clear both from the fact that he has even added a stub to Wikipedia about certain finnish physicist;-), and from private discussions. There are excellent reasons to do this and I recommend the powerpoint representations at my homepage and also my blog site for those interested on what these reasons might be.

Speaking seriously, and to Rae Ann in particular, I am really surprised that someone manages to associate anthropic stuff with the idea that consciousness is something universal and that future physics must be able to say something non-trivial about it, congratulations;-). I cannot of course speak for other approaches to consciousness discussed in this popular book but the spirit of TGD inspired theory of consciousness is just to get rid of antropocentrism. I really believe that on order to make progress in physics we must extend quantum measurement theory to a theory of consciousness by bringing observer from an outsider a key concept of physical theory. Only in this manner we can avoid antropocentrism.

Just a random example about what this approach has produced is quantum measurement theory with finite measurement resolution based on von Neumann algebras known as hyper-finite factors of type II_1 (see my blog for a brief summary) and leading to an interpretation of non-commutative quantum theory in terms of characterization of measurement resolution in terms of Jones inclusions. This justifies also the notion of quantum entanglement modulo resolution playing a key role in TGD inspired theory of consciousness and making a highly non-trivial prediction that consciousness is not something completely private: we have a shared pool of mental images making possible social structures and moral rules.

Hyper-finite factors of type II_1, implied by the assumption that quantum states corresponds to classical spinor fields in the infinite-D "world of classical worlds" consisting of lightlike 3-surfaces in certain 8-D imbedding space, predicts also that finite quantum measurement sequence cannot reduce completely entanglement so that universe indeed forms a single coherent whole. At the pure physics side this theory has profound implications for the structure of S-matrix (determined also modulo measurement resolution). What is especially interesting is that coupling constant evolution reduces to the level of "free" theory. Mention also a huge extension of super-conformal symmetries of super-string models implied by partons as light-like 3-D surfaces: this should stimulate some interest also inside stringy camp.

Nigel Cook in turn manages to confuse TGD inspired theory of consciousness with theology, congratulations again:-)! Any theory of consciousness must be able to say something about the general structure of consciousness. The boring theory, as Nigel expresses his impressions, of the last chapter represents a particular theory of consciousness unavoidably predicting a hierarchy of conscious entities from very general assumptions. Amusingly, our own mental images correspond also to consciousness entities, only at the level next below us. The prediction of this hierarchy unavoidably means that something is said also about the origins of religion too. If this prediction makes TGD a branch of theology, let us call it quantitative theology.

This boring theory indeed makes a lot of testable quantitative predictions such as a hierarchy of EEGs relying heavily on a model of high Tc superconductivity as quantum critical phenomenon with precise predictions for biorhythms as scaled versions of EEG resonances, which in turn are predicted correctly. The hierarchy of EEGs can be seen as a direct signature for the hierarchy of conscious entities correlating directly with predicted dark matter hierarchy characterized by the scaled up values of scaled up Planck constant making possible macroscopic quantum phases. Therefore we can indeed speak about quantitative theology although I would personally prefer quantum theory of consciousness made quantitative.

With Best Regards,

Matti Pitkanen

Still a little correction to the quantization of Planck constants

The Jones inclusions for the sub-algebras of infinite-dimensional Clifford algebras for world of classical worlds, or more technically configuration space of 3-surfaces, should by quantum classical correspondence have classical space-time correlates. Indeed Jones inclusions N into M based on groups G_a× G_b acting as invariance group of elements of N have precise classical correlate at space-time level. The bundle projections H→ H/G_a× G_b for singular G_a× G_b bundle represent geometric duals for Jones inclusions. The gauge fixing assigning to each point of H/G_a× G_b point of H would correspond to Jones inclusion.

The generalized imbedding space is obtained by gluing all these copies of H with singular bundle structure together. If G_a is common group then gluing occurs isometrically along M⁴_+/- factor and if G_b is common group then same occurs isometrically along common CP₂ factors. More precisely, the Cartesian product of these factors with with fixed points in the second factors is shared by the two copies of H. The common points of M⁴_+/- (CP₂) factors correspond to the singular orbifold points of bundle remaining invariant under the two groups G_a (G_b). For G_a:s acting as plane rotations and reflections the set of singular points is time-like plane corresponding to the choice of rest system and a unique quantization axis for angular momentum so that Jones hierarchy has interpretation in terms of quantum measurement theory. If G_a corresponds to the symmetries of tedrahedron or icosahedron (exceptional group E₆ or E₈ by McKay correspondence) then the set of singular points reduces to a time-like line and the choice of quantization axes is not unique since maximal cyclic subgroup can perform rotations around any 3- (5-) symmetry axis of tedrahedron (icosahedron).

The quantization of Planck constants h(M⁴_+/-)=n_ah₀ and h(CP₂)=n_bh₀ and its geometric counterpart at imbedding space level is now also reasonably well understood. The original naive argument led to the guess that M⁴ and CP₂ covariant metrics are scaled by n_b² and n_a² respectively. In the case of CP₂ metric this scaling however implies a gigantic size of CP₂ for dark matter in astrophysical length scales: effectively imbedding space would look like 8-D Minkowski space. This looks weird. Also a mathematical problem emerges in the attempt to glue imbedding spaces with same group G_b isometrically along the common CP₂ factors since the sizes of CP₂:s are not same and gluing can be only partial and would be discontinuous. For M⁴_+/- factors with different scaling factors of metric non-compactness allows to circumvent the problem.

The resolution of the problem was trivial. Kähler action is invariant under over-all scaling of the metric of H so that one can perform the 1/n_a² scaling for H metric besides the naive scalings and this implies that M⁴_+/- metric is scaled by (n_b/n_a)² and CP₂ metric remains invariant (as is natural since projective space is in question). Ordinary Planck constant has a purely geometric interpretation. The quantitative predictions of the existing scenario are not affected by the more precise view about situation since quantum dynamics does not depend on the overall scaling of H metric.

For more details see the chapter Does TGD Predict the Spectrum of Planck Constants? or the chapter TGD and Astrophysics.

About physical interpretation of non-commutative geometry and discreteness

Characteristic for the recent day strongly methodology based approach to theoretical physics is that many people are working with refined mathematical notions but very few of them seems to be asking whether these notions could have some clear physical content.

The ideas about non-commutativity and discreteness of the space-time geometry at Planck length scale are good examples in this respect. Archives are filled with quantum deformations of all imaginable algebras and discrete theories of quantum gravity. The fact that both non-commutativity of space-time coordinates and discreteness are inconsistent with general coordinate invariance does not seem to bother these pragmatists. I have nothing against methological virtuosity but a more profound view about what the the use of the notion of Planck length actually implies might help to gain a more balanced view.

In TGD framework non-commutativity and discreteness have much less mysterious origin. The progress in quantum physics and mathematics has been to high degree based on an explicit articulation of our limitations (Heisenberg and Gödel) and I believe that an approach based on systematic attempt to identify the inherent limitations of perception and thought could be a useful strategy.

Indeed, non-commutativity emerges naturally when one constructs quantum measurement theory based on finite measurement resolution in terms of Jones inclusions N subset M of von Neumann algebras. Quantum non-commutativity in this sense occurs only at the level of operator algebras and quantum spinors, that is for inherently linear structures, rather than at level of space-time so that there are no problems with general coordinate invariance.

Discreteness in turn could reflect the limitations of our ability in representing our cognitions in the real world (consider only numerical computations contra analytic work), and leads naturally to an expression of S-matrix elements involving a discrete set of points defining a number theoretic braid. Space-time itself remains boringly continuous and only the "infinite-dimensional world of classical worlds" brings in some sexy elements but is probably something too abstract for an average shopper in the free market of ideas.

1. Non-commutativity and quantum measurement theory with resolution

Von Neumann algebras known as hyper-finite factors of type II₁ (HFFs shortly) play a key role in TGD Universe since the Clifford algebra of the world of classical worlds is direct sum of these factors. Recall that this infinite-dimensional space is a union of subworlds consisting of lightlike 3-surfaces of H=M⁴_+/-×CP₂. Subworlds of .... in the union are labelled by positions of tips of lightcones in Minkowski space.

Jones inclusions N subset M for HFF:s provide a very natural algebraization of quantum measurement theory with a finite measurement resolution (this is something new!). The space of resolvable degrees of freedom is quantum space N/M and corresponds in the simplest case to quantum version of 2×2 matrices and thus to quantum group SU(2)_q having fractal dimension M:N= 4cos²(π/n) from the quantization of the Jones index. That dimension M:N is below 4 reflects the non-commutativity of matrix elements implying that they are not completely independent. Corresponding quantum spinors have fractal dimension d=(M/N)^1/2: the interpretation of non-commutativity as reducer of effective dimension is completely analogous.

M/N is N-module and this means that N takes the role of complex numbers in "quantum quantum theory". One must generalize the notions of unitarity, hermiticity, eigenvalue, etc.. so that N replaces complex numbers. For instance, hermitian operators have as eigenvalues hermitian operators in N. Unitary operator is unitary matrix with N valued elements (exponent of N-hermitian operator).

The measurement resolution defined by N means following things.

1. In ordinary quantum measurement ideal state function reduction occurs to a 1-dimensional complex ray of state space. Now the reduction occurs to a 1-dimensional N-ray equivalent with N. Therefore a sequence of quantum measurements defines a sequence M contains M₁ contains M₂ contains... of Jones inclusions rather than leading to a fixed point in the first step. This in the case that it is possible to improve the resolution and quantum jumps do not interfere with the process.

2. Quantum measurement never fully reduces the entanglement. The reader is encouraged to consider a quantum version of Zeno's paradox from this point of view. In quantum theory of consciousness this implies that we share a pool of fused mental images correspond to entanglement below the resolution. Stereo vision is example of shared and fused mental images which now correspond to right and left visual fields. At collective level of consciousness our selves could fuse during sleep to a huge stereo view about human condition. TGD Universe would be infinitely sized conscious organism (sincere apologies for skeptics and the additional message that I am only bringing the message;-)).

3. The measurement of S-matrix (or reaction rates) corresponds to a measurement of unitary time like entanglement (Tr(SS⁺)=Tr(Id)=1!) for positive and negative energy components of zero energy states (all states of the Universe are creatable from vacuum in zero energy ontology natural in TGD Universe). A hierarchy of S-matrices identified as characterizers of time like entanglement results corresponding to a hierarchy of Jones inclusions with improving measurement resolution. S-matrix must be consistent with the N-module structure which is guaranteed by crossing symmetry with respect to the transfer of elements of N between initial and final states combined with hermitian conjugation. This follows from a more general crossing symmetry. Hermitian conjugation modifies sligtly the basic property of entanglement defined by Connes tensor product. Together with huge super-conformal symmetries extending those of super string models (S-matrix as super-conformal invariant) this could imply uniqueness of S-matrix with a given measurement resolution.

4. The measurement of spin J₃ for quantum spinor means that a physical state results for which either component of quantum spinor annihilates the state. This leads to a contradiction if one requires that the physical state is annihilated by second spinor component and is ordinary eigen state of second spinor component. The problem disappears if second component acts like an element of N and thus does not leave the quantum state invariant (C is indeed replaced with N!). The non-commutativity of different N-valued eigenvalues implies that non-commutativity of elements of J₃ does not lead to contradiction.

5. The moduli squared for quantum spinor commute and their eigenvalue spectrum is universal depending only on integer characterizing quantum phase. Eigen values for moduli are rational numbers. For M:N<4 fuzzy logic and fuzzy beliefs result.

To me this picture about quantum measurement with finite resolution replacing the usual horribly ugly cutoff description looks very beautiful and elegant. Non-commutativity would not be a fundamental property of space-time but would characterize finite measurement resolution and would apply at the level of quantum spinors rather than space-time coordinates (sorry for my spontaneous "auch!" which I cannot hide when I even imagine "[x^μ,x^ν]=...";-)). Quantum classical correspondence however encourages to think that this picture has also space-time correlate.

2. New view about discretization

The second misty idea of Planck length mystics is that space-time somehow becomes discrete in Planck scales and that continuum is an approximation emerging at long length scales. For some reason (not difficult to guess!) the alternative view that space-time is continuous and that discreteness might reflect the limitations of our cognition, has not gained popularity. In non-materialistic TGD Universe, where thinking is allowed, the latter view emerges naturally when one looks at space-time correlates of quantum measurement.

1. The generalized eigenvalue spectrum of the modified Dirac operator contains the scaling factor log(p), p prime, as an overall scaling factor, which means that one can assign to a given lightlike partonic 3-surface a unique p-adic prime. One implication is that coupling constant evolution in TGD framework can be identified as a discrete p-adic coupling constant evolution induced by this log(p)-proportionality of the generalized eigenvalue spectrum of the modified Dirac operator (recall that p-adic length scale is proportional to p^1/2). It is now possible to write renormalization group equations explicitly at the level of eigenspinors of modified Dirac operator so that coupling constant evolution emerges at the level of free field theory rather than from calculation of radiative corrections.

2. If partonic 3-surface is represented by algebraic equations then its p-adic counterpart is also well-defined and has a discrete set of common points with its real counterpart. Algebraic equations are possible since light-likeness is the only condition on partonic 3-surfaces and extremality property in the case of Chern-Simons action for induced Kähler gauge potential means only to at most 2-D CP₂ projection.

3. Number theoretic universality requires that S-matrix elements are algebraic numbers. This can be achieved if only a finite subset of points in the algebraic intersection of p-adic and real space-time sheet contributes to the definition of S-matrix elements. The definition of S-matrix assigns a number theoretic braid to each incoming particle with strands carrying sub-partonic quantum numbers, essentially operators of the super-conformal algebras involved. The emergence of number theoretic braids is very natural for hyper-finite factors of type II₁ whose inclusion sequences define inclusion sequences of Temperley-Lieb algebras associated with braids.

4. Discretization by number theoretic braids has nothing to do with the discreteness of space-time at fundamental level but reflects basically the limitations of cognition if p-adic space-time sheets are identified as representations of cognition and intentionality. p-Adic bosonic partons would correspond to intentions transforming in quantum jump to actions represented by real partons. Pair of real and p-adic fermionic parton would define state together with its cognitive representation analogous to hole and negative energy fermion kicked out of Dirac sea.

To me all this looks nice, elegant, and rational but probably I am correct in guessing that colleagues will stubbornly continue their exercises in Planck length mystics. In the so called free market of ideas "Planck length scale" and "black hole" are much sexier buzz words than "quantum measurement theory" and "measurement resolution". "Cognition" and "intention" are of course mere crack-talk for those fascinated by reductionism extended down to Planck length.