String Theory 3.0

When it was proposed that elementary particles are not point objects, but extended like strings, one important conceptual issue was not clear. Why strings? What is the foundational principle / symmetry principle which compels us to consider extended objects?

In our work we started by demanding that there ought to exist a reformulation of quantum field theory which does not depend on classical time. This is the starting foundational question.

The symmetry principle then emerged as: physical laws must be invariant under general coordinate transformations of *non-commuting* coordinates.

The Lagrangian dynamics which implements these requirements requires (for consistency) that elementary particles be described by extended objects (strings). And it also requires that the theory be formulated in 10 spacetime dimensions, plus Connes time as an absolute time parameter.

This essentially is String Theory 3.0, with important accompanying changes:

(i) The vacuum is not 10D Minkowski vacuum. It is the octonionic 8D algebraic vacuum. This makes it easy to relate the theory to the standard model.

(ii) The Hamiltonian at the Planck scale is not self-adjoint. This permits compactification without compactification: 4D classical spacetime is recovered without curling up the extra six dimensions.

We thus provide a quantum foundational motivation for string theory. Also, the underlying dynamics is deterministic and non-unitary; thus bringing the deterministic and reduction aspect of quantum theory in one unified new dynamics. Someone once said that when string theory is properly understood, the quantum measurement problem will solve itself. In a manner of speaking, that is now seen to be true!

We have a pre-quantum, pre-spacetime dynamics, from which quantum field theory is emergent. The original aspects of string theory which still remain are: elementary particles are extended objects (strings) and they live in 10D Minkowski spacetime. Hence the octonionic theory could also be called the return of string theory, in a significantly improved and falsifiable avatar, which has predictive power, and which can be tested in the laboratory.

Reference:

https://www.tifr.res.in/~tpsingh/Penrose90singh.pdf