Wednesday, March 14, 2007

Inverting reductionism upside down

In the recent New Scientists there is an article about string nets. For a more technical description the article Photons and electrons as emergent phenomena of Michael Levin and Xiao-Gang Wen is recommended. I found myself resonating with several ideas appearing in this work but also enjoy of disagreeing.

1. Inverting reductionism upside down

  1. What makes me happy is that the work challenges the basic dogmas of reductionism and locality which have led to the recent blind alley in the official theoretical physics. One might say that the standard reductionistic view is turned upside down: local structures such as gauge bosons and fermions emerge from non-local ones. Condensed matter physics is taken as starting point in attempt to build a model for fundamental physics. It is really enjoyable to see that genuine thinking is still taking occasionally place in theoretical physics.

  2. The basic inspiration comes from topological quantum computation. The crucial element of quantum computation is quantum entanglement which in the case of topological quantum computation is robust against perturbations. This implies now non-locality at fundamental level. Universal (topological) quantum computers are able to mimic any dynamics at the level of discrete approximation. The point of view taken by the authors is that that there is no fundamental level involving elementary gauge bosons and fermions. Particle spectrum and dynamics of gauge theories could result as this kind of mimicry. Hence the breakdown of reductionism in the sense that everything emerges from the dance of quarks and leptons or some even smaller structures.

2. String nets as fundamental structures

Consider now a more concrete view about the model.

  1. One might think that braid like structures would have been introduced as fundamental objects. This was not the case, and probably because they are not enough for the desired inverse reduction. Instead, strings are taken as the basic objects. Strings can form string nets by fusing together along their ends and string network becomes the fundamental notion giving rise to elementary particles as its excitations. There are different type of strings and only those fusion vertices are favored for which the interaction energy is small. Besides this Hamiltonian contains kinetic energy and string tension term. If string tension is very high one obtains large number of small string nets. If it is small, large string nets emerge.

  2. These models predict excitations having interpretation in terms of gauge bosons and fermions. From string model point of view this is perhaps not surprising. For instance, transversal excitations of string would naturally give rise to bosonic excitations and ends of string would behave like fermions.

3. Some criticism

I do not try to pretend of being objective and I confess that my criticism reflects strongly my TGD based belief system also profoundly influenced by the beautiful ideas of topological quantum computation.

  1. In order to pass as a unified theory the model should be able to provide fundamental dynamics based on some simple principle. The string net Hamiltonian can be however tailored to reproduce any gauge theory. This smells first like a reincarnation of string landscape. At the second thought there is nothing wrong with this kind of flexibility but I would take it as a reflection of the fact that universal topological quantum computer is able to mimic any system when discretization is allowed. To me the correct question would be "What is the fundamental dynamics allowing topological quantum computation as a fundamental process?".

    Perhaps it is un-necessary to tell the reader that the belief that standard model based physics really allows universal topological quantum computation is only a belief. Personally I regard this belief as wrong. The point is that much more than a mere construction of a discrete Hamiltonian characterizing the quantum computation is needed. Fundamental physics must allow the entire process culminating to a conscious experience about the result of the computation. The basic challenge is the identification of the principles of the fundamental dynamics allowing any topological computation. One cannot circumvent the fact before there can be a topological computer there must also be intention to build it and theory must describe also this.

  2. Could string nets (or something more general) then be fundamental non-local structures? My answer based on my personal belief system is a qubit somewhere between yes and no.

    Most of the qubit consists of "No". I do not believe that strings of any kind are really the fundamental objects. In TGD framework strings are replaced by 3-dimensional light-like 3-surfaces as basic objects and they define generalized Feynman diagrams. The interpretation is as orbits of 2-dimensional partons (in honor of Feynman's deep intuition) which can have arbitrarily large size. Classical space-time dynamics emerges in a well-defined sense as a classical correlate for the quantum physics of these light-like 3-surfaces. Quantum physics is not anymore local at space-time level since 3-surface behaves as a single coherent whole (very important for the proper understanding of living systems). Interestingly, quantum physics however remains local and formally completely classical (apart from quantum jump) at the level of the "world of classical worlds".

    Qubit contains also some "Yes".

    • The dynamics of TGD involves definitely stringy aspects, in particular generalized super-conformal symmetries and the stringy character of fermionic anti-commutation relations.

    • Also TGD Universe predicts the existence of string like objects and of fractal string networks consisting of magnetic flux quanta. This network plays a key role in cosmology: for instance, dark energy corresponds to magnetic energy. In TGD inspired nuclear physics nuclei are identified as highly tangled nuclear strings.

  3. I would have been happy to see braids, which served as starting point, as fundamental objects because they represent really deep mathematics.

  4. Braid statistics is an essentially 2-dimensional phenomenon. Hence I would have expected that 2-dimensional surfaces would have been introduced explicitly as fundamental objects.

  5. In the model of Levin and Wen one could see bosons (strings) and fermions (string ends) as dual manners to describe dynamics and this kind of eliminative reductionism makes me very skeptic. In TGD framework the counterpart of string is interior dynamics of space-time and corresponds to classical physics as exact part of quantum theory necessary for quantum measurement theory whereas bosons and fermions as counterparts of string ends correspond to quantum states of light-like partonic 3-surfaces.

  6. Effective 2-dimensionality is absolutely essential for the braid statistics and is of course only an assumption subject to criticism. Standard model skeptic might argue that standard model quantum physics does not allow to achieve effective 2-dimensionality in such a good an approximation as to guarantee the effective topologization of the dynamics. Standard model skeptic might be right. It is of course experimental fact that anyons are there but their existence might only demonstrate that the belief system of standard model skeptic is in need of updating.

  7. The idea of giving up fermions as fundamental dynamical objects looks to me questionable. For instance, for Jones inclusions for which braid statistics emerges naturally only q=exp(iπ/n), n≥3 is allowed as quantum phase and one does allow fermionic braid statistics. The second reason for my skepticism is more personal. In TGD framework the Clifford algebra of the world of classical worlds has interpretation in terms of fermionic oscillator operators so that a beautiful geometrization of fermion number results. This algebra is identifiable as fundamental hyper-finite factor of type II1 responsible for the beauty of TGD and also lurking behind the magic of braids. I am ready to describe bosons as fermion-antifermion bound states but refuse to continue further.

4. What if one requires that Universe is topological quantum computer?

Topological quantum computation has strongly inspired also the development of quantum TGD. This inspires me to pose the key question differently. Suppose that Universe is topological quantum computer. What can one conclude about the fundamental dynamics? You can of course guess the outcome and for me this is still one exercise to deduce TGD Universe from some simple basic assumptions in the hope (I am really incurable optimist!) that the message could finally permeate through the magnificently effective cognitive immune (or its it insulation-?) system of main stream theoretical physicist.

  1. The first requirement is that, as far as fermionic quantum dynamics is considered, the fundamental objects are effectively 2-dimensional and carry braids as fundamental objects. This makes braid statistics a genuine statistics and allow topological quantum computation at the fundamental level. In particular, topological braid dynamics would be genuinely topological and not only approximately so.

    Conformal symmetries are natural in 2-dimensional context and lead naturally to braid statistics. Requiring the generalization of super-conformal invariance as a fundamental symmetry leads to the identification of fundamental dynamical objects as light-like 3-surfaces identifiable as orbits of partonic 2-surfaces containing braids. Chern-Simons type action emerges as the only possible action principle and gives rise to almost (light-likeness!) topological QFT.

    A generalization of topological quantum computation emerges since parton replication accompanied by braid replication is involved and has interpretation in terms of copying of information. Particle exchanges in generalized Feynman diagrams have interpretation in terms of communication whereas incoming and outgoing lines could be interpreted as involving topological quantum computations.

  2. The condition that braids emerge as fundamental structures is very strong and it is very difficult to imagine how they could emerge naturally in the standard mathematical framework of physics. In the physics based on the fusion of real physics and various p-adic physics interpreted in terms of cognition and intentionality, the fundamental braids emerge naturally as subsets of the rational (more generally algebraic) intersection of real parton and its p-adic counterpart obeying same algebraic equations. It seems that we have got a lot of TGD already. Bringing in the condition that standard model quantum numbers appear at fundamental level or accepting the vision about physics as a generalized number theory gives the rest of TGD (or all of it).

  3. The quantum dynamics of TQC Universe need not rely on standard quantum theory. Indeed, new quantum physics based on hyper-finite factors of type II1 with brand new quantum measurement theory with measurement resolution as a basic concept implying automatically non-commutative physics is involved. This physics emerges from both the Clifford algebra of the world of classical worlds and from the braid models of topological quantum computation. TGD suggests also strongly the quantization of Planck constant so that quantum entanglement in arbitrarily long length scales becomes possible and one can understand dark matter as macroscopic quantum phases responsible also for the very special properties of living matter.


At 12:13 AM, Blogger Mahndisa S. Rigmaiden said...

03 15 07

Hello Matti:
Nice post. The notion of the universe as a big computer is quite clever and coincides nicely with world of classical worlds thoughts. At smaller scale, DNA is computer too and this makes a lot of sense to me.

Now, I don't think it is too hard to see braids arise in a standard mathematical framework of physics. HOWEVER, this depends upon what frame of mind one is coming from. What if you grow up in a culture where braids are everywhere in hairstyles, clothing, dance, etc? Then a braided object is just as fundamental as a wheel perhaps. Even ancient Incas did not have wheel but had extensive accounting system based upon knots...

As I consider language itself, and the human minds ability to process information and HOW, consider looking at the hand as the fundamental human calculator. I say whatever you can do with your hands can represent a computation.

See my post from a while back about twisted strands. I will develop this further, but braids have broad place in landscape of physics and mathematics but have not been investigated as they should up to this point.

At 12:54 AM, Blogger Matti Pitkanen said...

Dear Mahndisa,

still one aspect about braids. When you make braids timelike (or lightlike as in my case) you get dynamical braids. This is nothing but dancers spinning around and changing partners now and then. Humanity has been always dancing and even birds during their mating rituals! Perhaps dance is at some level information processing;-). In my fractal mood I cannot avoid the feeling that this everyday world (there are people regarding it as boring!) tries to tell me something very important.

At 8:07 PM, Blogger Kea said...

What do you mean, you refuse to continue further? Just for now? OK. Matti, when you dabbled with 2-operads did you think about planar algebras (a la Jones subfactors) in that context?

At 8:53 PM, Blogger Matti Pitkanen said...

Dear Kea,

Yes, I had just tried to understand planar algebras. They are certainly very deep notion (and frustratingly difficult with my meager technical background, I have been used to think quite differently!). They are very natural when one thinks inclusion sequences as analogs of sequences of algebraic extensions of rationals and even more: also representations for them. I am only gradually beginning to understand the inclusions at deeper mathematical level.

Now I have been reading Wenzl's thesis about generalization of inclusions to give inclusions with index having all values for the square of quantum dimension of SU(n) representations. All points to the direction that HFFs based physics kind of universal physics analogous to Turing machine in computer science for which I have proposed concrete realization in terms of generalize imbedding space: this might also be the counterpart for string dualities.

What I meant with my statement is that I regard fermion statistics as fundamental rather than emergent.

First, the canonical representation of hyperfinite-factor of type II_1 is infinite-D Clifford algebra having interpretation in terms of fermionic oscillator operator algebra and spans the gamma matrix algebra at the tangent space of the "world of classical worlds". If one gives for this space spinor structure one obtains second quantized fermions unavoidably.

Secondly, for Jones inclusions only quantum phase q=exp(i2pi/n), n>2 appear so that n=2 giving q=-1 and thus Fermi statistics seems to be fundamental rather than emergent.



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