Wednesday, October 18, 2006

Some thoughts inspired by certain blog posting

Lubos represented quite an interesting series of arguments (Googolplex of e-foldings relating to the arrow of time, second law, initial values in cosmology, anthropic principle, etc... Even God was mentioned and I thought to bring in also Angels;-).

1. Why we need a proper theory of consciousness?

I agree full-heartedly with Lubos that our arguments (we, the physicists;-)) should be independent of our personal idiosyncracies, the details of our particular species, our culture, etc... It seems however that to achieve this freedom, "we" should have some kind of abstract overview about all possible species and all possible cultures. The only hope to achieve this kind of rough overview is by extending physics to a theory of consciousness allowing to say something very universal about life and intelligence. I am a little bit surprised how few theoreticians are taking this challenge seriously although the quantum consciousness movement began already at eighties (Esalem, Finkelstein). Perhaps super string models caught the attention of the most imaginative brains at that time.

2. Geometric time and experienced time

A proper theory of consciousness could remove a lot of mist floating around the concept of time. Experienced time and geometric time are very different things but for some odd reason most physicists stubbornly continue to identify them. The paradoxes are unavoidable. For instance, Lubos mentions the paradox implied by "Now as the maximum of entropy" assumption made by some cosmologists.

I think that the lack of understanding about the relation between experienced time (or "de-coherence arrow of time") and geometric time is the main source of confusion and a treasure trove of misleading arguments. If one accepts that these two times are different notions, one must among other things ask whether both of these times have an arrow. I would guess "Yes": by quantum classical correspondence space-time geometry should provide a representation for the sequence of quantum jumps and therefore for the contents of consciousness (in my own theory world). Note that this requires the failure of strict classical determinism for the dynamics of space-time surfaces and can serve as a valuable guideline. The directions of these arrows of time could in principle be independent. Indeed, for phase conjugate laser beams the arrow of geometric time and de-coherence time seem to be opposite. Self-assembly in living systems would be a decay in a reverse direction of geometric time and consistent with the second law a deeper level.

3. The issue of initial conditions

Lubos talked also about the issue of initial conditions and the new view about time allows a fresh approach to the problem. First of all, I would talk about boundary conditions in the geometric past since geometric time is in the same role as spatial dimensions in any relativistic theory. Secondly, the idea about the initial/boundary conditions as something fixed by God at the moment of creation carries a flavor of medieval theology. If theorist must fix initial conditions by some educated guess of what medieval God willed, most of the predictive power of theory is lost, and in principle the theory becomes intestable since one cannot compare the time evolutions of different classical worlds. It is somewhat surprising that theoreticians still use this medieval conceptualization. Perhaps an introductory course to philosophical problems of physics without professional jargon and in science fictive spirit would help.

The notion of boundary conditions at big bang has different interpretation if one accepts some amount of consciousness theory. Suppose that you believe that conscious existence is a sequence of quantum jumps replacing the quantum superposition of classical four-worlds (analogous to Bohr orbits) with a new one (what these quantum jumps are, is of course a non-trivial question). The key observation is that the average boundary/initial conditions defined by the quantum superposition change in every quantum jump. Quantum jump re-creates also the geometric past. Quantum jump sequences are expected to lead to asymptotic self organization patterns and they could correspond to rather specific boundary conditions in the geometric past (somewhat misleadingly, "moment of big bang"). The basin of attractor leading asymptotically to a particular effective cosmological history becomes a more natural notion.

In this framework the victories of anthropic principle could be interpreted differently. Asymptotic self organization patterns resulting in quantum jump sequences correspond to very specific values of coupling constant parameters of the theory. If one also accepts that quantum jump sequence gives rise to as genuine evolution then these values would favor intelligent life in some form. Genuine evolution would however require a new kind of variational principle. There is room for this kind of principle since there must be some law telling what it is possible to tell about dynamics of quantum jumps defining the dynamics of conscious existence. The first guess for the principle would be that the amount of conscious information in quantum jump is maximized (Negentropy Maximization Principle). The task would be to show that this principle is not conflict with the second law.

4. Universe or Universes?

Lubos talks about Universe as the only one of its kind and having age of about 13.7 billion years. I would talk in plural. This particular universe of ours would be a self-organization pattern extending 13.7 billion years to the geometric past. My motivation is that if one accepts space-time as a 4-D surface, one cannot avoid a profound generalization of space-time concept to what I call many-sheeted space-time. As the first step you end up with what you might call Russian doll cosmology. This idea can be probably expressed also in branish although I personally would prefer plain english.

5. What is space-time correlate for mind stuff?

Many-sheeted space-time is not all that is needed. Number theoretical vision about physics as something which is number theoretically universal leads to the introduction of infinite number p-adic variants of real number based physics requiring the fusion of real and p-adic variants of imbedding space together along algebraic points. This allows the identification of space-time correlates of cognition and intentions, the mind stuff of Descartes. But even this is not enough.

6. Dark matter and quantized Planck constant

Lubos did not mention dark matter at all. Perhaps he believes that dark matter is just some exotic particle. I do not believe this. Here I must introduce some more TGD related stuff. The basic dogma of quantum physics is still that Planck constant is a universal constant, just a conversion factor which can be taken to be hbar=1 in suitable units and nothing else. History has not respected the constancy of fundamental constants so that one has right to ask whether Planck constant is really a universal constant, could it be quantized, and if so, how.

Associating Planck constant with dark matter (there are also empirical motivations to do so) one could ask where there could exist a hierarchy of dark matters with levels labelled by different values of Planck constant. I believe that this is possible. At more technical level I propose that the hierarchy of dark matters corresponds to the hierarchy of Jones inclusions for hyper-finite factors of type II1 labelled by ADE groups appearing in McKay correspondence. The motivation comes from the observation that the infinite-dimensional Clifford algebra of the world of classical worlds is hyper-finite factor of type II1, and from the vision that entire TGD emerges in some sense from this kind of structure.

Topologically/geometrically the hierarchy of Planck constants requires a considerable generalization of the notion of 8-D imbedding space (counterpart of 10-D target space in super string models) since one cannot allow quantized Planck constant in quantum theory based on the standard view about space-time. Very loosely, different Planck constants correspond to different branches of imbedding space replaced with a tree like structure obtained by gluing various copies of imbedding space together along common M4 or CP2 factor. In this framework dark matter at a given level of hierarchy can quantum control the lower levels. This control hierarchy would make the matter living. Even phase transition changing Planck constants and identified as leakage between different branches becomes a well defined notion.

7. Angels and Gods and physicist

The predicted infinite hierarchy of conscious entities identified as levels of dark matter would be the physicists counterpart for the angels and spirits of religious world views. The core of religious world view is that there exists something better than this cruel everyday world and that we can directly experience this something now and then. Dark matter hierarchy could give a justification for this belief. The Universe itself would take the role of a dynamical God re-creating itself again and again ("moment of mercy" instead "updating" is perhaps a more proper word here;-)). Our recent physics would be only a humble beginning. A new period of voyages of discovery to the higher, more spriritual, levels of hierarchy using the methods of empirical science would be waiting for us whereas anthropic principle would define a foolproof recipe for the end of physics.


Mahndisa S. Rigmaiden said...

10 19 06

Hello Matti:
Good read. I have really been thinking about this topic for a while now. And although I was raised as a Christian, I think that the real "truth" about the universe etc is far broader than anything our human minds have concocted.

I too am worried that so many theoretical physicists are stuck with stringiness and haven't evolved to another level. I think some of the formalism in stringiness is beautiful and somewhat plausible, however, the faith that many folk have put in it has impeded research in other areas-particularly consciousness.

From what I gather, almost all the PAdic physics papers I have read have a sort of mystical quality to them, as though this PAdic number theory provides us with new ways of viewing the world. I thought of you when I read a paper by Varadajan called: "Did God make the Quantum World P-Adic?"I am quite certain that you are on the right track in the development of your theories. It always seems that those on the cutting edge are often not appreciated in their lifetimes.

Bit without rambling too much more, thanks. By visiting this site, I have learned quite a bit and been inspired to pursue this knowledge.

Latest topic of interest? Fractional calculus. I figured you would like that:)

Matti Pitkänen said...

We need visions. It is good to see that the situation in theoretical physics is forcing us to question the basic dogmatics. I have myself tried to get rid of the reactive attitude to religion and see religious experience as something trying to tell something very profound about consciousness.

Conformal field theories, that part of mathematics of string theories that I understand a little bit about, are something which certainly remains from string theories.

Probably there exist many fractional calculi: I have been too lazy to follow all this inventiveness. q-Laquerre and q-hydrogen atom forced me however to take one particular fractional calculus seriously. My own version was a little bit different since q is root of unity in my case rather than in the range (0,1]. There is a whole industry about q-special functions. It would be interesting to find q-variants of harmonic oscillator, and other simple systems for roots of unity.

Thank you for the link to Varadarjan's paper. I will read it.

Mahndisa S. Rigmaiden said...

10 19 06

Cool Matti:
I am curious as to what you think of that paper. And as to fractional calculus, well interestingly enough I learnt about the topic from YOU! I had read and reread your Fractional Q Laguerre post for a while and began to research the tie in with derivatives taken to arbitrary rational powers, and looking at quantization relationships considering non integer powers for n.
Thanks for the hints about the Q special functions.

BTW I have not found any of Mr. Motl's responses to your posts rewarding in any way. Although he bothers me a bit, I still think he is quite bright. What bothers me is the orthodoxy with which he limits the theories of others.

Once again, you are onto something.

I must leave now, but wish you well:)

Matti Pitkänen said...

Dear Mahndisa,

Lubos Motl's comments are certainly not rewarding! What I see significant is that he bothers to comment at all from those Harwardian heights. This perhaps sounds strange but I have lived in an academic community which has made not a single comment about my work or my existence during these 28 years except the response to my docent application for more that decade ago which claimed that I am a crackpot. Brings in my mind the funny game of my childhood: the winner is the one who is able to resist laugh for longest. Each player does best to make another player to giggle. I think this kind of stony silence is possible only in the academic circles of Finland. But finnish scientists are well-known from their exceptional seriousness;-)!

Lubos Motl remains a mystery to me. I would expect that a person with his brain would see the failure of super strings as a personal opportunity rather than loss. Could it be that his contribution to matrix models has made him kind of a stock owner;-).

Matti Pitkänen said...

Dear Mahndisa,

I am happy to hear that my blog has inspired you to work with fractional calculus (as a matter fact, I learned from you posting that I had been doing fractional calculus;-)!). This probably makes sense also for algebraic extensions of p-adics containing
quantum phase q (root of unity since polynomial ansatz for differential equations gives algebraic equations.

I skimmed through the papers. The starting point of papers is humble, I would say too humble;). Accept quantum mechanics and QFT as such and try to formulate the p-adic variants of it.

The first question is obvious. At what level you should introduce p-adic numbers. Do you p-adicize space-time but not Hilbert space or do you p-adicize both of them? If Schrodinger amplitudes are kept ordinary complex numbers you have no problems with integration. When you make Schrodinger amplitude p-adic you have problems with inner product (the troublesome integration). In special cases, such as harmonic oscillator, you can overcome these problems but not generally and you lose completely the numerical touch to the situation. I have spent a lot of time by considering possible manners of defining physically acceptable definite integral in the p-adic context. There exists certainly a lot of high-browed mathematical literature about this. "Physically acceptable" is however the key word.

My own approach is different and based on trust on my admittedly irrational gut feeling that the best thing for a physicist is to proceed as a physicist rather than go to math library and return back as totally beaten by the horrible amount of something that physicist cannot even dream of understanding during this life time.

As a physicist I must be able fuse all the p-adic physics and real physics to a single coherent whole. Even S-matrix elements between states belonging between different number fields must make sense since as a just born cognitive physicist I dream that the students of my students write S-matrix elements for intention-to-action processes.

Adelic physics mentioned in the articles is what comes in mind first but does not conform with the idea that p-adic physics is something genuinely new since decomposition of real amplitudes to a product of p-adic one generalizing adelic formula in some sense could be in question at best.

I am not able to see any other alternative than algebraic universality. This would be achieved by algebraic continuation. There is huge amount of wisdom which could help in this and known as algebraic geometry and about which I know virtually nothing.

Essentially same *algebraic* formulas (very important!) would represent both real and p-adic space-time surfaces, quantum fields, etc... and you just reinterpret everything in terms of real or p-adic numbers.

The basic objection is that the classical field equations need not allow this. This objection does not bite in the recent almost topological QFT formulation of TGD and one could actually say that expressibility of lightlike partonic 3-surfaces using algebraic equations (rational functions with algebraic coefficients) to some replaces the conditions from ordinary dynamics.

Whether this true for 4-D space-time sheets satisfying field equestion defined by Kahler action is far from clear. It might be that only real 4-D space-time sheets are necessary for the formulation of S-matrix which involves only partonic 3-surfaces.

As I mentioned, I see integration as the basic problem. The idea is simple and inspired by the fact that real and p-adic 3-surface satisfy the same algebraic equations. Why ot define conserved quantities in the p-adic realm by calculating the real conserved quantities as ordinary integrals and re-interpret them as p-adic numbers: this is possible if the result belongs to the algebraic extension of p-adics used. Analogous recipe would hold quite generally.

In particular, algebraic points existing in p-adic imbedding space (algebraic extensions of p-adics are allowed) are interpreted as common points of p-adic and imbedding spaces. These points form a discrete set which suggests that the ultimate formulation could be discrete even for real-to-real S-matrix. At least in some phases of the theory (quantum phase q non-trivial). In the case of partonic 2-surfaces discrete points would define strands of braid and you would have a nice connection with braiding S-matrices and topological QFTs, anyonic physics, and quantum groups.

The nice thing is that this kind of discretization would be completely number theoretical, it would involve no ad hoc elements, and would be consistent with the symmetries unlike lattice formulations.

This approach naturally inspires some number theoretical conjectures such as number theoretical universality of Riemann Zeta stating highly non-trivial things about zeros of Zeta. The truth or non-truth of these conjectures is however not crucial for TGD proper.