A joint Model of Particles and Spacetime

The emergent character of space-time is a main topic in different approaches to Quantum Gravity. This article connects the emergence of space-time and the emergence of particles, capable to translate in space-time. A model is proposed which describes the structure and dynamics of fundamental particles as well as the properties of space-time, emerging due to the structural development and the motion of particles. Particles are assumed to be composed and spatially extended in a circular extra space, called basic space, however fundamental and nearly point-like in space-time. The connected development of particles and space-time is realized in two stages. During the one-particle stage, intrinsic particle properties such as invariant mass, charge, angular momentum (spin) and magnetic dipole moment are formed by a force-free circular motion of masses and charges. An isolated piece of space-time emerges as the translational state space of a particle, where a local mode and a nonlocal mode of translation appear. The deterministic circular motion is accompanied by stochastic linear steps, both performed with the velocity of light. The probabilistic description of intermittent translation leads to the laws of the Special Relativity Theory. During the second, multi-particle stage, the particle structure shows capabilities of interaction, and space-time develops from isolated pieces to a general space-time spanned by spatial distances between different particles. The relativistic addition of velocities and the special Lorentz transformation follow naturally from the probabilistic expressions. In the nonlocal mode of translation, the particle model has six dimensions (D = 5 + 1). Two subcomponents of a particle, called rotons, have D = 3 +1 dimensions and different inobservable positions in space-time. The nonlocal mode of translation corresponds to a superposion of quantum states (quantum nonlocality) and represents possibly the origin of nonlocal Newtonian gravity.