Is it possible to integrate quantum loops into helical quantum loops which might be related to twistor string theory?(adsbygoogle = window.adsbygoogle || []).push({});

Wilson lines / loops are common to both quantum loop gravity [QLG] and the various string theories [ST].

As I attempt to understand QLG and ST, I developed some speculative analogies.

Since various mental models can be constructed, this speculation may rise to a conjecture.

Probably a Smolin or Witten will be needed for proof if this is possible.

It may be that this is contained within the proof of the ‘Moonshine’ Monster simple group by Borcherds.

Model 1 - Substitute helicoids [springs or slinky-toys] for all loops in the Rovelli home page 3D-image for LQG.

http://www.cpt.univ-mrs.fr/%7Erovell...um_gravity.jpg [Broken]

At first, such a substitution appears to yield a fourth dimension representing time. But since the helical angle can also vary, this may be a fifth dimension resulting in helical quantum loops that are not necessarily identical.

Model 2 - This image from SOLARIA BINARIA by Alfred de Grazia and Earl R. Milt might represent planetary orbital loops when time-independent of the sun. When the sun is in motion, then these relatively simple loops are transformed into helical planetary orbital loops which are time-dependent on the sun.

http://www.grazian-archive.com/quantavolution/QuantaHTML/vol_05/figs/sb_f14.jpg

Model 3 - Quantum loops might be represented by planar modulo arithmetic [or clock arithmetic]. Helical modulo arithmetic might then represent helical quantum loops.

Another example may be in noting that an end-on view of the 3D helices in AC electricity phasor equations [Grassman Algebra] and QM Schroedinger wave equations [Clifford Algebra] are in a loop configuration.

Ian Balitsky in ‘High-Energy QCD and Wilson Lines’ discusses straight lines in his abstract:

“At high energies the particles move very fast so their trajectories can be approximated by straight lines collinear to their velocities. The proper degrees of freedom for the fast gluons moving along the straight lines are the Wilson lines -- infinite gauge factors ordered along the straight line. I discuss the small-x evolution and the high-energy effective action in terms of Wilson-line degrees of freedom.”

Straight lines in the usual anthropic perspective of cartesian coordinates may become curves in log-polar [spherical or elliptical] coordinates.

Straight lines on a flat map of sea lanes or air flights become great circles on a globe.

Conversely, the derivative of a helical quantum loop may be quantum loop.

This might be demonstrated by cross sections of a rifled gun barrel.

Consider the discussion of a ‘twistor machine' by Lilja Precision Rifle Barrels, Inc.

"We feel very fortunate to have recently obtained a twist deviation inspection machine ... This device checks the twist rate of a rifle barrel and determines if there is any deviation to the actual rate."

“Here is a view of thehelicalrifling guide that controls thetwist rateon the "pull" end of the button/rod."

http://www.riflebarrels.com/articles/barrel_making/twist_machine.htm

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# Does integration of quantum loops become a string theory?

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