2001/03/26 by Manoelito M. de Souza, de Souza, Manoelito M.
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Astrophysics (astro-ph) #Complex Systems and Time Series Analysis #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #astro-ph #cond-mat.stat-mech #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.hep-th/0103218
30 pages, 3 figures
arxiv created 2001/03/26 · openalex publication_date 2001/03/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The physical meaning, the properties and the consequences of a discrete scalar field are discussed; limits for the validity of a mathematical description of fundamental physics in terms of continuous fields are a natural outcome of discrete fields with discrete interactions. The discrete scalar field is ultimately the gravitational field of general relativity, necessarily, and there is no place for any other fundamental scalar field, in this context. Part of the paper comprehends a more generic discussion about the nature, if continuous or discrete, of fundamental interactions. There is a critical point defined by the equivalence between the two descriptions. Discrepancies between them can be observed far away from this point as a continuous-interaction is always stronger below it and weaker above it than a discrete one. It is possible that some discrete-field manifestations have already been observed in the flat rotation curves of galaxies and in the apparent anomalous acceleration of the Pioneer spacecrafts. The existence of a critical point is equivalent to the introduction of an effective-acceleration scale which may put Milgrom's MOND on a more solid physical basis. Contact is also made, on passing, with inflation in cosmological theories and with Tsallis generalized one-parameter statistics which is regarded as proper for discrete-interaction systems. The validity of Botzmann statistics is then reduced to idealized asymptotic states which, rigorously, are reachable only after an infinite number of internal interactions . Tsallis parameter is then a measure of how close a system is from its idealized asymptotic state.