*Post by R***@Lycos.com*Could a theory like Loop Quantum Gravity (Except more simplified, so

that it's all geometry, no property on the nodes and such.) give rise

to string theory if we assumed that energy was a geometric property of

space?

Let me rephrase your question a little differently: could there be a

natural, but not yet fully seen or exploited, correspondence between

string theory and other more traditional foundations (a' la

Schroedinger-Heisenberg)?

Consider the relativistic particle, and assume it has positive spin.

At the semi-classical level its motion may be described by the

Dirac-Kemmer Hamiltonian

H = alpha.(pc) + beta (mc^2)

where alpha = (alpha^1, alpha^2, alpha^3) and beta belong to the

algebra generated by the Kemmer matrices.

(For spin 1/2, these reduce to the familiar expressions involving the

Dirac matrices; spin 1 Kemmer matrices are 10x10; things get more

complex for spin 3/2 and above).

In the Heisenberg picture, the equations of motion describe a

(quantized) lightlike helical worldline.

A central mystery, if you're only looking from within the particle

frame of mind, is where this bizarre behavior comes from. There's

nothing within the classical theory (the geodesic law) which mandates

anything like this behavior for particle-like singularities.

But when you move up 1 dimension, things change. Though the

1-singularities in classical theory describe nice straight worldlines,

the singularities of dimension 2 or above follow the generalization of

the geodesic law, which identifies the corresponding n-brane as a

harmonic map.

For the 2-brane, in the form of an open string, Thierre was the first

to published a closed solution. This solution is consists of a 2-sheet

which is generated as the locus of the midpoints (in a suitable

coordinate representation) taken from -- a helical worldline.

This suggests the a more general duality between particles of positive

spin and strings; the particles' worldline arising as a suitable

averaging of the strings' coordinates and, a' la Thierre, the string

being generated by a natural geometric construction from the particle

worldline.