Noncommutative spectral geometry, algebra doubling and the seeds of quantization

Understand

A physical interpretation of the two-sheeted space, the most fundamental ingredient of noncommutative spectral geometry proposed by Connes as an approach to unification, is presented.

• It is shown that the doubling of the algebra is related to dissipation and to the gauge structure of the theory, the gauge field acting as a reservoir for the matter field.
• In a regime of completely deterministic dynamics, dissipation appears to play a key role in the quantization of the theory, according to 't Hooft's conjecture.
• It is thus argued that the noncommutative spectral geometry classical construction carries implicit in its feature of the doubling of the algebra the seeds of quantization.