Quanta Without Quantization

TL;DR

This paper demonstrates that quantum mechanics and key string theory elements can be derived directly from the geometric tangent tower structure of classical general relativity, without traditional quantization.

Contribution

It introduces a novel geometric approach that derives quantum and string theory structures directly from classical gravity's tangent tower, bypassing quantization procedures.

Findings

Quantum mechanics elements derived from tangent tower structure

String theory components like Virasoro algebra obtained geometrically

No quantization needed to produce quantum and string theory features

Abstract

The dimensional properties of fields in classical general relativity lead to a tangent tower structure which gives rise directly to quantum mechanical and quantum field theory structures without quantization. We derive all of the fundamental elements of quantum mechanics from the tangent tower structure, including fundamental commutation relations, a Hilbert space of pure and mixed states, measurable expectation values, Schroedinger time evolution, collapse of a state and the probability interpretation. The most central elements of string theory also follow, including an operator valued mode expansion like that in string theory as well as the Virasoro algebra with central charges.