Introduction to the Quantum Theory of Elementary Cycles: The Emergence
of Space, Time and Quantum
D. Dolce. chapter 4 in "Beyond Peaceful Coexistence The Emergence of Space, Time and Quantum", IMPERIAL COLLEGE PRESS (2016)(2017)cite arxiv:1707.00677Comment: Revised version of the published chapter 4 in "Beyond Peaceful Coexistence The Emergence of Space, Time and Quantum", IMPERIAL COLLEGE PRESS (2016).
Elementary Cycles Theory is a self-consistent, unified formulation of quantum
and relativistic physics. Here we introduce its basic quantum aspects. On one
hand, Newton's law of inertia states that every isolated particle has
persistent motion, i.e. constant energy and momentum. On the other hand, the
wave-particle duality associates a space-time recurrence to the elementary
particle energy-momentum. Paraphrasing these two fundamental principles,
Elementary Cycles Theory postulates that every isolated elementary constituent
of nature (every elementary particle) must be characterized by persistent
intrinsic space-time periodicity. Elementary particles are the elementary
reference clocks of Nature. The space-time periodicity is determined by the
kinematical state (energy and momentum), so that interactions imply
modulations, and every system is decomposable in terms of modulated elementary
cycles. Undulatory mechanics is imposed as constraint överdetermining"
relativistic mechanics, similarly to Einstein's proposal of unification.
Surprisingly this mathematically proves that the unification of quantum and
relativistic physics is fully achieved by imposing an intrinsically cyclic (or
compact) nature for relativistic space-time coordinates. In particular the
Minkowskian time must be cyclic. The resulting classical mechanics are in fact
fully consistent with relativity and reproduces all the fundamental aspects of
quantum-relativistic mechanics without explicit quantization. This
överdetermination" just enforces both the local nature of relativistic
space-time and the wave-particle duality. It also implies a fully
geometrodynamical formulation of gauge interactions which, similarly to gravity
and general relativity, is inferred as modulations of the elementary space-time
clocks. This brings novel elements to address most of the fundamental open
problems of modern physics.