Abstract
Nonassociative geometry provides an unified algebraic description of continuum and discrete spaces, making it a valuable candidate for the study of discrete spacetime. In the framework of the nonassociative geometry we propose the model of emergent spacetime. At the Planckian scales the spacetime is described by a so-called diodular discrete structure, but at large scales it ``looks like'' a differentiable manifold. In our model, the evolution of spacetime geometry is governed by a random/stochastic process. This leads to a natural appearance of causal structure and arrow of time. We apply our approach to study a toy model of $(2+1)$-D discrete spacetime and a discrete Friedmann-Robertson-Walker cosmological model. We show that in a continuous limit the evolution of the discrete spacetime corresponds to the radiation epoch of the standard cosmological model.
Highlights
Any attempt to create a quantum gravitation theory faces the challenge of comprehension the concept of quantizing of spacetime and of describing the quantum nature of space and time [1,2,3]
The preceding examples show how the framework of nonassociative geometry may describe the discrete structure of spacetime
At the Planckian scale the standard concept of spacetime is replaced by the nonassociative discrete structure
Summary
Any attempt to create a quantum gravitation theory faces the challenge of comprehension the concept of quantizing of spacetime and of describing the quantum nature of space and time [1,2,3]. A formulation of the quantum theory may require omitting use of continuum concepts a priori This means that at the Planck scale the standard concept of spacetime must be replaced by some discrete structure [10, 12]. Among advanced models that propose discreteness, two that will be relevant to our work are Causal Sets (CS)[19,20,21] and Causal Dynamical Triangulations (CDT)[14, 22,23,24,25,26,27,28] These approaches are based on the hypothesis that spacetime is discrete and causality is a fundamental principle. In the Supplemental Material, we present technical details of our method and algorithms
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
