Friday, October 07, 2011

Does Witten prefer knots over strings?

Peter Woit tells in his blog some the news from Dublin is that Witten will be in town soon to give the Hamilton Lecture, with the Irish Times reporting that

Witten’s Hamilton Lecture will abandon string theory, however, in favour of knots, with a talk entitled: The Quantum Theory of Knots.

Suppose that this statement is true and not only journalistic exaggeration. What if means if taken at face value?

  1. Strings can get knotted (and linked and braided) in 3-D space: Witten's paper which led to a Fields medal was about topological theory based on Chern-Simons action, which he used to classify knots and 3-topologies in terms of invariant known as Jones polynomial.

  2. In 4-D space one has 2-knots and their knotting. Linking is replaced with the intersection of four-surfaces in 4-D case. The so called intersection form is a topological invariant used to classify four-manifolds so that intersection string world sheets could be used to classify four-topologies. Note than linking and knotting are not the same thing in dimensions higher than D=3.

D=4 is the dimension of space-time surface containing string world sheet in TGD framework and I have of course done my best to transform in my own humble physicists's style Witten's horribly technical approach to the description of knots and also knots and also 2-knots in TGD framework (see this).

In TGD Universe knots, links, and braids can be assigned with two kinds of 3-surfaces.

  1. 3-surfaces can be light-like 3-surfaces at which the signature of the induced metric changes: they are identified as basic building bricks of elementary particles. One could speak of light-like braids (somewhat illogically I have talked about time-like braids).
  2. The second kind of 3-surfaces are space-like 3-surfaces at the ends of space-time sheets at boundaries of causal diamonds. These could be called space-like braids.
Also two-knots emerge in D=4. These light-like resp. space-like braids corresponds to the space-like and light-like boundaries of 2-knots in the interior of space-time defining the counterparts of string world sheets. The basic operations (admittedly somewhat violent;-)) that Alexander the Great used to open knots have interpretation in terms of basic reaction vertices for strings.

This suggests that string diagrams can be used to describe the Alexandrian method of opening knots whose generalization is widely used in Finnish academic life to resolve more abstract problems related to funding issues. If so, a careful recording the steps of this rather unpleasant procedure (from the point of view of knot and -in more abstract context - of finnish scientific dissident) would define a knot invariant.

In TGD framework the topology of the imbedding of string world sheet has a deep physical meaning. DNA as topological quantum computer vision provides a more concrete application of these ideas in quantum biology. One beautiful application is a concrete mechanism of memory coding based on braiding of magnetic flux tubes (amusingly, knots have been used as a manner to code memories!).

So: the innocent question is whether Witten is beginning or has has begun to realize that TGD exists (should I add ";-)" or not?)?


At 1:54 AM, Blogger Leo Vuyk said...

perhaps an example for a new stansard model based on knots:

Leo Vuyk.

At 10:20 AM, Blogger ThePeSla said...


Of course it is said that linear knots only exist in three space- not the same thing as you said. Yet why could it not be from some view? In any case, if this is somehow the concept of memory, as if it is a physical thing like the idea of matter as knots in space. In the TGD model is there anything in the idea of memory as unique that can exist outside a specific organism or do these tubes vanish and the memory so vanishes?

Leo, your model does not seem deep enough for me as it seems to be must making linear knots borrowing this same question about strings- after all knots can be classified as having one sided topology and they can fall apart if pulled tightly into their kinks.

Matti thanks for you detailed reply to one of my earlier questions, the links you list do seem to me just to be an outline or record of your discoveries.

The Pe Sla

At 8:45 PM, Anonymous said...

Almost any physical process can be interpreted as a memory. What is needed is however coding of physical processes to memories: carving to stone one might say.

The DNA as topological quantum computer model is based on simple idea.

*Magnetic flux tubes connecting DNA nucleotides to lipids of nuclear or cell membrane define braid strands. They are like threads connecting dancers feet to a wall.

*Dancers moving in the parquette correspond now to lipids flowing like 2-D liquid in the lipid layer (liquid crystal). The threads represented by magnetic flux tubes connected to DNA nucleotides get braided.

*The braiding pattern of the threads after the night is over codes for the memories of the nice evening in the parquette to memory.

*Actual memories are coded in the following manner. For instance, nerve pulse patterns induce 2-D lipid flows in the axonal membranes and all these flows are coded into memories in this manner.

*The dance itself, the temporal braiding at lipid layer codes for topological quantum computation in a robust manner since only the topology of the braiding matters.

This resolves the basic problem related to quantum computations: quantum entanglement /coherence is destroyed by external perturbations. Also the large value of hbar and possibility of negentropic entanglement stable against state function reduction helps to overcome the problem. What is worrying me is that TGD Universe looks too good to be true;-).

At 1:35 PM, Blogger Ulla said...

I have promised to make short post as kind of 'TGD lectures' on FB, of course from my simple biologist view.

Can this be used?

At 12:44 AM, Blogger Ulla said...

Magnetic monopoles

At 12:37 PM, Blogger Ulla said...



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