Thursday, March 22, 2007

Now and Then

Now and then it is not possible to avoid the situation when the head is completely empty of ideas, questions, inspirations, and all that which makes you a happy thinker. This week has been such a period of time. Luckily, blog discussions have helped to live through this period and the best manner to get a new idea is to explain old idea. Thank you for Kea and Mahndisa (Resources in Category Theory, Braid Theory, Coxeter Dynkin Diagrams and Spider Diagrams with Tesselations for good measure) and Carl Brannen for patience.

This morning there was a nice piece of text by Connes about universal time evolution for factors of type III and the idea about emergent time in Noncommutative Geometry. There was already discussion in Kea's blog about this.

Personally I am not sure about the emergence of time. But on the other hand, I have proposed that imbedding space and the "world of classical worlds" could indeed emerge from von Neumann algebra framework... I should be able to decide. Be as it may, I find the idea about the universality of time evolution really fascinating. Some questions.

  1. Universal time evolution is fixed apart from inner automorphisms. How to achieve completely unique dynamics? Could inner automorphisms be identified as universal local gauge symmetries? In the case of HFFs of type II1 one can also ask whether outer automorphisms could be seen as analogs of global gauge transformations.

  2. Could the unique time evolution of HFF of type III operator algebra induce such an evolution in HFF of type II1 as one restricts the consideration to physical states and to quantized values of time parameter? From "Noncommutative Geometry" I remember the representation of HFF of type III as a crossed product of Z and HFF of type II1 with Z represented as shifts in tensor factor (I hope I understood correctly!). Could the reduction of Z to N, analogous to restriction of oscillator operators to creation operators, imply reduction to a HFF of type II1?

  3. The idea about emergence of time is fascinating but leaves a lot of room for models. A weaker form of this idea would be a universal dynamics at single particle level but assuming that quantum dynamics has space-time correlates. My own proposal identifies light-like 3-surfaces as basic dynamical objects and non-commutative dynamics would result at the level state space from the finite measurement resolution characterized by inclusion. Also quantum geometry could be a manner to describe finite measurement resolution.

    Universal geometric time could correspond to the light-like coordinate and the universal time evolution would be that associated with the light-like orbits of partons appearing as lines in the generalized Feynman diagrams defined by light-like 3-surfaces and would give rise to universal propagators as one integrates over the end points of internal lines. This would be single particle time evolution and would not give vertices: they would correspond to isomorphisms between tensor products of incoming and outgoing HFFs of type II1. If the above ideas make sense, the dynamics provided by the generalized eigen modes of what I call modified Dirac operator should boil down to a universal dynamics.


At 3:33 AM, Blogger CarlBrannen said...

"This would be single particle time evolution and would not give vertices: they would correspond to isomorphisms between tensor products of incoming and outgoing HFFs of type II1."

I think that I like this idea. The real mystery in elementary particle is the mass interaction. If it is Higgsless, then a particle comes in left handed and leaves right handed. The vertex has only two legs.

At 4:27 AM, Blogger Matti Pitkanen said...

There are vertices but they would not be described in terms of the universal time evolution. At vertices incoming partonic 3-surface meet at their 2-dimensional end. This is nothing but a replacement of the vertices of ordinary Feynman diagram with 2-D partonic surfaces and lines with lightlike 3-surfaces.

Higgs corresponds in TGD framework to a tiny "wormhole contact" connecting two space-time sheets with Minkowski signature of metric. The contact itself having size of order 10^4 Planck lengths has Euclidian signature of metric.

At throats the induced metric is degenerate and throats correspond to a special case of lightlike 3-surfaces that I have been talking about. The throats would carry quantum numbers of left and right handed fermion which makes alltogether a Higgs like particle.

Higgs differs from standard model Higgs in that it contributes only little to fermion mass and can have much weaker couplings to fermions than standard model and MSSM Higgs since p-adic thermodynamics gives the dominating contribution to fermion mass. This could explain why even light Higgs could have remained undetected.

At 2:30 PM, Blogger Kea said...

Matti, if the structure of the tensor product was different (for categorical reasons, say) could you do without the Higgs tubes? It would be nice to have good agreement on the existence/non-existence of the Higgs.

At 10:43 PM, Blogger Matti Pitkanen said...

Dear Kea,

I am unable to imagine how tensor product structure could give rise to Higgs.

In TGD framework p-Adic thermodynamics gives the dominating contribution to fermion masses and predicts them succesfully so that in fermionic sector Higgs is not absolutely necessary.

In bosonic sector W-Z mass ratio is group theoretically determined (Weinberg angle) and it is very difficult to understand it if p-adic thermodynamics contribution dominates. Higgs contribution as a dominating one allows to understand this. For p-adic thermodynamics thermal contribution to mass squared depends on p-adic temperature T=1/n, n=1,2,... For n>1 thermal contribution is small and Higgs can dominate. For fermions one has maximal temperature T=1 and for bosons T=1/n<1.

The identification of Higgs as wormhole contact fits very nicely with the general view about Higgs type massivation as being due to "topological condensation". Also the relationship between gravitational and inertial masses can be understood. Therefore I dare to hope that the question about Higgs is settled.

There is very loose analogy with the model of Connes in which one has two copies of Minkowski space and Higgs emerges in some mysterious-to-me manner from this. Now one has two space-time sheets connected by wormhole contacts having identification as Higgs.


At 11:53 PM, Blogger Mahndisa S. Rigmaiden said...

03 25 07

Hello Matti:
In the conventional view, I thought that the Higgs arises due to field excitation of Higgs field and that via interaction with Higgs field, particles derive their mass.

I have always wondered about this view because I don't know how photons interact with the Higgs field but I haven't taken QCD yet either...In any event, the TGD view is so radically different than standard model that it is hard to wrap my head around it sometimes.

HOWEVER, the padic with extension to irrationals seems like a VERY reasonable foundation for an emergent theory. As I pondered the definition of prime numbers a few posts ago, I realized that restriction to set of Counting Numbers is irrational! heheheheh Meaning that we MUST extend to irrationals to make the picture complete. If we wanna talk about prime numbers, at least round out the lesson by including their roots:)

Now, I need to study more about padic thermodynamics thanks!

At 12:05 AM, Blogger Mahndisa S. Rigmaiden said...

03 25 07

Oh and Universal time? I have never understood that motion, especially from the standpoint that there is no 'preferred' reference frame.


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