Quanta without quantization

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, Schrödinger 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. Introduction The detailed structure of quantum systems follows by fully developing the scaling structure of spacetime. Thus quantum systems despite their Hilbert space of states, operator-valued observables, interfering complex quantities, and probabilities are rendered in terms of classical spacetime variables which simultaneously form a Lie algebra of operators on the space of conformal weights. This remarkable result follows from the tangent tower structure implicit in general relativity. We develop this structure, cite a central theorem, then examine some properties of tensors over the tangent tower. Finally, we apply these ideas to quantum mechanics and string theory, showing how the core elements of both arise classically.