About "interpretational problems" of QM
If Feynman were somewhere witnessing the recent deep regression in theoretical physics, he would probably deeply regret for ever launching his shut-up-and-calculate interpretation. Fortunately there are also signs of healthy development.
During last weeks there have been a lot of discussion about fundamentals inspired by Lee Smolin's article at http://arxiv.org/abs/hep-th/0507235 addressing among other things to the interpretational problems of quantum theory and to the problem of background dependence plaguing string theories (see Not Even Wrong and Lubos Motl's blog site). Even Witten made in Strings 2005 panel discussion a remark that quantum theory might be in need of modification.
The discussion in Not-Even-Wrong has been censored down to attempts to interpret what Names have possible meant with their casual remarks (this endless appeal to authorities and censoring of any new idea as off-topics astonishes me again and again and I wonder whether it correlates with the recent intellectual regression in USA). Lubos Motl in turn is convinced that there is nothing to be added to QM, discussion of fundamentals is waste of time, and that M-theory is the final answer to all problems which deserve answer. I am however happy to find that colleagues are perhaps finally forced to do what have they have avoided so long: to use their own brains and realize that it is extremely unprobable that a theory plagued by logical paradoxes and invented after 500 hundred years after birth of physics as a science could be final.
"Interpretational problems" of quantum mechanics is a delicately constructed euphemism for much deeper problems, and developing still one new interpretation is a waste of time. Personally I see no other way to make real progress than attacking the real problem which is construction of a quantum theory of consciousness. First of all this includes solving the logical paradox due to non-determinism of Schroedinger equation and non-determinism of quantum jump, and this seems impossible without new view about the relation between experienced time and geometric time of physicist.
Serious consideration of "interpretational problems" requires a lot of wandering at the boundaries of human consciousness which is very slow and painful process as compared to mechanical symbol manipulation requiring only technical skills. On basis of my experience of two decades of consciousness theory I am however happy to tell that this kind of activity is not at all sterile "study of foundations" or copying quotations from classics. Developing consistent interpretations for new mathematical ideas in turn allowing to develop these ideas further is what makes this kind of approach so rewarding. I dare say that in TGD framework this process has led to a rather concrete new vision about physics, consciousness, and biology.
At philosophical side a precise quantitative characterization for the failure of reductionism emerges and I am now developing further the concrete implications in nuclear physics, physics of condensed matter, and biology emerged during last fifteen years. Chiral selection in living matter and fundamental mechanisms of bio-catalysis define one application.
The new view about the relation between experienced time and geometric time of physicist ermges and has as a dual a new view about relationship between gravitational and inertial mass. The new view about energy and time predicts new energy and communication technologies based on the possibility of negative inertial energies and classical communications backwards in geometric time.
At mathematical side the construction of quantum states as classical spinor fields in the infinite-dimensional space of "world of classical worlds" (3-surfaces) generalizing Wheeler's super-space provides a solution to the background independence problem.
It also leads to the identification of hyperfinite type II_1 factors (having spinors of separable Hilbert space as a canonical representation) as the basic building blocks of quantum TGD (factors type I_n and I_infty appear in nonrelativistic quantum mechanics and factors of type III appear in algebraic quantum field theory). This implies direct connection with conformal field theories, braid groups, knot and 3-manifold invariants, and quantum groups. The hierarchy of Jones inclusions has interpretation in terms of sub-system-system inclusions with dynamical quantized value of hbar characterizing this inclusion. The inclusion hierarchies of II_1 factors provide a concrete realization to the hierarchy of conscious entities predicted by TGD inspired theory of consciousness. The hierarchy of dark matters appears as their physical correlate. This hierarchy relates closely to other hierarchies of quantum TGD (fractal hierarchy of space-time sheets, hierarchy of infinite primes identifiable as hierarchy of second quantizations of arithmetic QFT, hierarchy of conscious entities ("selves") in TGD inspired theory of consciousness, hierarchy of average durations of quantum jump with respect to geometric time).
A generalization of braid diagrams to Feynman diagrams suggests strongly itself together with a symmetry principle generalizing string model duality. Diagrams would be classified by the topology of the lowest genus two-surface allowing the imbedding of diagram and all diagrams with homologically trivial loops at this genus are equivalent to a minimal diagram characterized by its homology class for the minimal genus. The absence of homologically non-trivial loops has in TGD framework straightforward interpretation: there is no path integral over all possible 4-surface since configuration space geometry assigns an almost unique space-time surface to a given 3-surface identifiable as a generalized Bohr orbit. Almost uniqueness means the failure of strict classical determinism: this makes it possible to assign space-time correlates not only to quantum states but also quantum jump sequences.
At phenomenological side this leads to a prediction of a hierarchy of dark matters relying on the identification of dark matter as a quantum coherent phase with large value of hbar. A more refined definition of darkness is forced by many-sheeted space-time and p-adic length scale hypothesis (relative darkness, partial darkness). This identification is directly relevant to the understanding of living matter as a system involving interaction of several hierarchy levels of this kind as also predicted by the basic postulates of consciousness theory. The physics of water is full of anomalies, one of them being the finding that neutron diffraction and electron scattering at attosecond time scale give evidence for the formula H_1.5O. The interpretation that one fourth of protons is in dark phase, leads to a model for clustering of water providing considerable insights to the anomalies.
During last months I have been applying the idea about dark matter as a large hbar phase to nuclear physics and condensed matter, where the predicted long ranged classical weak and color fields have been a long standing interpretational head ache. The interpretation of these fields in terms of dark matter hierarchy involving p-adically scaled down copies of electro-weak bosons and gluons gives excellent hopes of solving the problems, explains anomalies like tetra-neutron and cold fusion, and makes testable predictions. The long range weak fields allow to understand chiral selection in living matter as a strong electroweak parity breaking effect for dark matter forming the quintessential part of living matter.
To decide personally whether serious consideration of fundamentals can give something to physics see "What's New" links of various books about TGD at http://tgd.wippiespace.com/public_html/. Matti Pitkanen