A Theory We're Incapable to Understand?

[member 11137]

If this was addressed to me I'm just going to supply my highly personal view. not the standard ST view.

Usually the string tension is assumed to be constant, and longitutal oscillations imply non-uniform string tension, and generally also oscillating tension. Then somehow the strings would not be as "fundamental" anymore. I THINK this would be the "standard answer", even though it is not much of an answer.

In the way I see it, where the string index, could be viewed as a the continuum limit of the value space of reconstructed probabiltiy [0,1], the question of asking about longitutadal oscillations is to ask why the [0,1] state space doesn't "stretch". It doesn't as it's one somehow what sets the scale, what can happen however, is that the density of states oscillates - this would correspond to pure tension oscillations with the string size kept fixed. The interpretations of this in the view I have, there tension changes correspond of changes in the equiprobability measure.

This is why in my view, the fundamental thing isn't "strings" - it's what I call sysstems of microstructures (which are always having a finite total complexity), in which a "string" can be almost special case, in a special limit. This is my only route to connect to strings - the simplest possible continuum-like measure complex, is something like a string. This can be further "provocated" or "excited" but sufficient excitation will transform it into more general things (in my view that is).

/Fredrik

If the purpose of ST is to find an analogy between one given particle and a string, then -in a first approach- one is not obliged to think about the wave representation of that particle but one can adopt the very classical point of view of the 3D microscopic sphere moving along the time and ask in which way its behavior can be compared with those of a string. The answer migh be the following: (a) in absence of gravitation (or of any other force; in extenso: the particle moves with constant speed) the trajectory is a line; (b) in presence of gravitation: the trajectory will be deformed and thus -perhaps what you call the external view of the situation- give the sensation of a curved string. Since any particle is supposed to travel at a speed smaller than c (speed of ligth in vacuum) the extremity of the string (the trajectory) is always moving at a speed between [0, 1] in an ad hoc frame. In general relativity, of course spacetime is stretching... Could it not be the starting point for a simple and clear representation?
Thanks for the answers about longitudinal oscillations. I think I did not give a precize enougth description of what I meant; that's now done. This was also a personal view -sorry.

 

[Fra]

Could it not be the starting point for a simple and clear
representation?

Assuming we're discussing possible motivation or "possible" first principles of ST, I'm sorry but I don't understand your proposal.

Do you think of instead of replacing points with strings, replace it with probability distributions in 3D space? (like a fuzzed out point) If I'm not mistaken sometime along the history of ST some people considered that (like oscillating blobs), but for me that doesn't adress all questions of the microstructure of an inference system which is my focus.

My only proposal into possible make sense of "strings" appear in the process of describing inference starting from sets of flucutating bits, and histories of the same, as a close resemblance to a continuum index (probability distribution). This is long before notion of space and time is defined.

So in a sense, to understand my first proposal it might help to note that it's not physics. I'm trying to just abstract the mathematical properties that you need to ascribed to an inference system. It has things that are naturally associated to inertia. Inference as per entropic evolution also contains a natural notion of action, and defines a flow. This in the abstracted sense does not yet connect to physics.

My conjecture is that there is one though, and it's what fascinates and drives me in this.

/Fredrik

 

[member 11137]

Assuming we're discussing possible motivation or "possible" first principles of ST, I'm sorry but I don't understand your proposal.

Do you think of instead of replacing points with strings, replace it with probability distributions in 3D space? (like a fuzzed out point) If I'm not mistaken sometime along the history of ST some people considered that (like oscillating blobs), but for me that doesn't adress all questions of the microstructure of an inference system which is my focus.

My only proposal into possible make sense of "strings" appear in the process of describing inference starting from sets of flucutating bits, and histories of the same, as a close resemblance to a continuum index (probability distribution). This is long before notion of space and time is defined.

So in a sense, to understand my first proposal it might help to note that it's not physics. I'm trying to just abstract the mathematical properties that you need to ascribed to an inference system. It has things that are naturally associated to inertia. Inference as per entropic evolution also contains a natural notion of action, and defines a flow. This in the abstracted sense does not yet connect to physics.

My conjecture is that there is one though, and it's what fascinates and drives me in this.

/Fredrik

Not exactly. Any classical particle has a birthday and a death. The trajectory in between is the string of its history. The elasticity of such string is represented by the many possible pathes it could have taken (Feynman's pathes). As long as the particle exists, it is situated at the living extremity of its string. It is possible to think that local circonstances are determinating the "longitudinal" tension and so are explaining the soon coming future of this string.

 

[member 11137]

Not exactly. Any classical particle has a birthday and a death. The trajectory in between is the string of its history. The elasticity of such string is represented by the many possible pathes it could have taken (Feynman's pathes). As long as the particle exists, it is situated at the living extremity of its string. It is possible to think that local circonstances are determinating the "longitudinal" tension and so are explaining the soon coming future of this string.

As I said at the begining: this is only the very classical view. You can now inverse the glove and consider a very thin cylinder (a piece of string with a very small cross section) placed in vacuum and connecting the two extremities of universe. Since the latter is expanding and since the tube is certainly "feeling" some gravity we can consider that each infinitesimal part of this tube is in someway behaving like a classical string. if we do so and make some ad hoc caculations, you find the wellknown equation "pressure + density of energy = 0". This was my idea and proposal. (Blackforest)

 

[member 11137]

As I said at the begining: this is only the very classical view. You can now inverse the glove and consider a very thin cylinder (a piece of string with a very small cross section) placed in vacuum and connecting the two extremities of universe. Since the latter is expanding and since the tube is certainly "feeling" some gravity we can consider that each infinitesimal part of this tube is in someway behaving like a classical string. if we do so and make some ad hoc caculations, you find the wellknown equation "pressure + density of energy = 0". This was my idea and proposal. (Blackforest)

The proof.

 

[ensabah6]

LQG as of now is no candidate for a ToE by construction. The LQG approach is restricted to quantum gravity. It is compatible with matter interaction, the mathamtical formulation (gauge theory) is rather close in a certain sense. But there are no direct attempts to unify gravity with matter.

There are some ideas how particles could emergy from "braided" or "twisted" spin networks, but that seems to be highly speculative. If you like I can give you some references.

There is the idea to harmonize non-commutative geometry with the LQG approach which could lead to standad model matter emerging in the LQG framework; again this is an idea, not a fully developed research program. You can get references if you like.
.

Could particles in LQG be both braiding (a la Sundance) AND noncommutative geometry?

 

[tom.stoer]

I would say no. Or to be more precise: yes, could be, but I see no good reason for it. Either braiding itself is powerful enough to let SM particles emergy from spin networks (I think you need a quantum deformation on a boundary Hilbert space according to Chern-Simons, Smolin's ideas etc. in order to define braids). Or NC is the way to go. Doing both for me means doing too much. One concept should be sufficient.

Braiding is fascinating as it - if it works - requires nothing else but "quantum geometry".

To be honest: in the modern physics literature there is a trend towards mathematically involved constructions w/o physical results. Noncommutative geometry with topological aspects of supergravity AdS/CFT quantum deformations in compactified extra-dimensions derived from M-theory motivated 3-algebras ... This is not how physics works (in my opinion) A theory must be simple enough in order to be true.

As a reference look at these papers:

http://arxiv.org/abs/1005.1057
Spin Foams and Noncommutative Geometry
Domenic Denicola (Caltech), Matilde Marcolli (Caltech), Ahmad Zainy al-Yasry (ICTP)
48 pages, 30 figures
(Submitted on 6 May 2010)
We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the encoding of the gravitational field via holonomies. We then describe convolution algebras of spin networks and spin foams, based on the different ways in which the same topology can be realized as a branched covering via covering moves, and on possible composition operations on spin foams. We illustrate the case of the groupoid algebra of the equivalence relation determined by covering moves and a 2-semigroupoid algebra arising from a 2-category of spin foams with composition operations corresponding to a fibered product of the branched coverings and the gluing of cobordisms. The spin foam amplitudes then give rise to dynamical flows on these algebras, and the existence of low temperature equilibrium states of Gibbs form is related to questions on the existence of topological invariants of embedded graphs and embedded two-complexes with given properties. We end by sketching a possible approach to combining the spin network and spin foam formalism with matter within the framework of spectral triples in noncommutative geometry.

http://arxiv.org/abs/0907.5510
On Semi-Classical States of Quantum Gravity and Noncommutative Geometry
Authors: Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke, Ryszard Nest
(Submitted on 31 Jul 2009)
We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated as a spectral triple over holonomy loops. The semi-classical limit of the spectral triple gives the Dirac Hamiltonian in 3+1 dimensions. Also, time-independent lapse and shift fields emerge from the semi-classical states. Our analysis shows that the model might contain fermionic matter degrees of freedom.
The semi-classical analysis presented in this paper does away with most of the ambiguities found in the initial semi-finite spectral triple construction. The cubic lattices play the role of a coordinate system and a divergent sequence of free parameters found in the Dirac type operator is identified as a certain inverse infinitesimal volume element.

 

[member 11137]

The proof.

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[ZapperZ]

Closed pending moderation.

Zz.