Quantum Physics -- A Theory of Dynamics for "Space" on Space

TL;DR

The paper proposes a variant theory in which space itself is dynamic, giving rise to quantum and classical mechanics as emergent, phenomenological descriptions of an underlying changing-space framework. It introduces group-changing spaces and higher-order variability, presenting a tower-like structure where 0th-level variants set the vacuum, 1st-level variants yield matter, and 2nd-level variants produce motion, including emergent gauge fields. By projecting higher-order variants through K- and D-projections, the authors derive quantum states, wavefunctions, and gauge theories (QED, QCD) as effective descriptions of underlying nonlocal dynamics, and show how familiar phenomena like Schrödinger evolution, fermionic statistics, and decoherence arise from the geometry of zero lattices and knot projections. The framework also recasts classical mechanics as the long-wavelength limit of disordered variants and frames measurement, locality, and gauge interactions as manifestations of variability across multiple levels, with invariances interpreted as shadows of deeper variability. If borne out, this approach could unify quantum foundations, gauge theory, and the Standard Model in a single, space-centered formalism, potentially predicting new relations between topological invariants and particle properties. Overall, the work provides a mathematically rich, albeit speculative, path toward a complete theory where space and its changes drive all physical laws.

Abstract

Till now, the foundation of quantum physics is still mysterious. To explore the mysteries in the foundation of quantum physics, people always take it for granted that quantum processes must be some types of fields/objects on a rigid space. In this paper, we give a new idea that the space is no more rigid and the matter is the certain changing of "space" itself rather than extra things on it. Based on this starting point, we develop a new framework based on quantum and classical mechanics. Now, physical laws emerge from different changings of regular changings on spacetime. Then, both quantum mechanics and classical mechanics become phenomenological theories and are interpreted by using the concepts of the microscopic properties of a single physical framework. The expanding/contracting dynamics of "space" leads to quantum physics. In addition, when we consider a physical variant with 2-th order variability, quantum fields with gauge structure emerge. The 2-th order variability is reduced into U(1) local gauge symmetry and SU(N) non-Abelian gauge symmetry. The corresponding theory becomes QED and QCD. The belief of "symmetry induce interaction" is now updates to "Higher order variability induce interaction". After introducing chirality, a physical variant with 2-th order variability becomes the true physical reality of our universe. The low energy effective theory is just the Standard model -- an SU(3)*SU(2)*U(1) gauge theory. An important progress is about hidden topological structure for elementary particles of different generations -- chiral para-statistics. In particular, to obtain the entire mass spectra, we only need to use only one free parameter. This progress on the foundation of quantum physics will have a far-reaching impact on modern physics in the future.

Figures (50)

• Figure 1: (Color online) (a) An element of a compact U(1) group; (b) A mapping between the elements for the compact U(1) group to the points in the one-dimensional Cartesian space $C_{1}$. This is just the Geometry representation of it; (c) An illustration of the reference for U(1) group, $\phi(x)=\phi_{0}=0$; (d) The illustration of a general field of compact U(1) group under analytic representation.
• Figure 2: (Color online) (a) An element $\phi_{0}$ of a compact U(1) group that denotes the "non-changing" configuration of its field; (b) An element $\delta \phi$ (an infinitesimal group-changing operation) of non-compact Ũ(1) group that denotes the "changing" configuration of a variant.
• Figure 3: (Color online) (a) A group-changing space of a non-compact Ũ(1) group; (b) Globally shift of the group-changing space; (c) and (d) denote the global contraction and expansion of the group-changing space, respectively.
• Figure 4: (Color online) (a) A uniform variant of non-compact Ũ(1) group that is a mapping between the group-changing space to the one dimensional Cartesian space; (b) The constant changing rate $d\phi/dx$ of a uniform variant of non-compact Ũ(1) group on the one dimensional Cartesian space. $k_{0}$ denotes the constant changing rate; (c) The mapping between the group-changing space to one dimensional Cartesian space of a perturbative uniform variant of non-compact Ũ(1) group on the one dimensional Cartesian space; (d) The changing rate of the non-uniform variant.
• Figure 5: (Color online) (a) A variant $V_{\mathrm{\tilde{U}(1),}1}[\Delta \phi,\Delta x,k_{0}]$ of non-compact Ũ(1) group that is a mapping between the group-changing space to the one dimensional Cartesian space; (b) The changing rate $d\phi/dx$ of $V_{\mathrm{\tilde{U}(1),}1}[\Delta \phi,\Delta x,k_{0}]$; (c) The mapping of the complementary pair $V_{\mathrm{\tilde{U}(1),}1}^{\prime}[\Delta \phi,\Delta x,k_{0}]$ of $V_{\mathrm{\tilde{U}(1),}1}[\Delta \phi,\Delta x,k_{0}]$; (d) The changing rate $d\phi/dx$ of $V_{\mathrm{\tilde{U}(1),}1}^{\prime}[\Delta \phi,\Delta x,k_{0}].$