Implications of a scale invariant model of statistical mechanics to nonstandard analysis and the wave equation

Siavash H. Sohrab*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

A scale-invariant model of statistical mechanics is applied to examine the physical foundation of nonstandard analysis and to identify the nature and the range (0β, 0β-1) of nonstandard numbers and to establish the existence of infinitesimals (0β> Lβ-2> Xβ > 0β-2). An invariant logarithmic definition of coordinate is presented and the concept of "measureless" or "dimensionless" numbers (L′β, λβ, 0β) = (Lβ, 1β, 0β) is described. Also, a scale-invariant definition of fractal dimension is introduced that suggest exceedingly large values 107 of fractal dimension. A scale invariant form of the wave equation is derived that applies to acoustic waves that propagate at speed of sound vm = 350 m/s, gravitational waves that propagate at the speed of light vt = c, and gravitational radiation that propagates at superluminal speeds vg > 2 × 1010 C.

Original languageEnglish (US)
Pages (from-to)95-103
Number of pages9
JournalWSEAS Transactions on Mathematics
Volume7
Issue number3
StatePublished - Mar 1 2008

Keywords

  • Gravitational radiation
  • Gravitational waves
  • Infinitesimals
  • Nonstandard analysis

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Endocrinology, Diabetes and Metabolism
  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Management Science and Operations Research
  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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