Newton Equations May be Treated as Diffusion Equations in the Real Time and Space Fields of Multifractal Universe (Masses are Diffusion Coefficients of Diffusion-like Equations)

2001/04/11 by L. Ya. Kobelev, Kobelev, L. Ya.
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Dynamics #Complex Systems and Time Series Analysis #FOS: Physical sciences #General Physics (physics.gen-ph) #Statistical Mechanics and Entropy #physics.gen-ph

paper · pdf · doi:10.48550/arxiv.physics/0104040

LaTex

arxiv created 2001/04/11 · openalex publication_date 2001/04/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In thirties years of last century Dirac proposed to treat Schrodinger equation as the equation of diffusion with imaginary diffusion coefficient. In the frame of multifractal theory of time and space (in this model our the multifractal universe is consisting of real time and space fields) in the works [1]-[16] was analyzed how the fractional dimensions of real fields of time and space influence on behavior of different physical phenomena. In this paper the Newton equations of the multifractal universe (considered for the first time in [1]-[3]) are generalized and is treated as the equations of diffusion with mass of bodies (depending of fractional dimension of place, where these bodies located) as a coefficient of diffusion. The realization of this point of view for inhomogeneous time equations (the analogies of Newton equations) is carried out too. The last leads to introducing of new sort of masses: the masses that characterize the inertia of inhomogeneous time flows with space coordinates changing. CONTENTS: 1. Introduction;2. Newton Equations in the Multifractal Universe; 3. Generalized Newton Equations and Its Diffusion Interpretation; 4. Generalized Inhomogeneous Time Equation and Its Diffusion Interpretation; 5. Conclusions

Citations

• Physical Consequences of Moving Faster than Light in Empty Space
• The Theory of Gravitation in the Space - Time with Fractal Dimensions and Modified Lorents Transformations
• The Fractal Geometry of Nature
• Multifractality of time and space, covariant derivatives and gauge invariance
• Generalized Riemann - Liouville fractional derivatives for multifractal sets
• Is it Possible to Transfer an Information with the Velocities Exceeding Speed of Light in Empty Space?

Related

• The Theory of Fractal Time: Field Equations (the Theory of Almost Inertial Systems and Modified Lorentz Transformations)
• Maxwell equation, Shroedinger equation, Dirac equation, Einstein equation defined on the multifractal sets of the time and the space
• What Dimensions Do the Time and Space Have: Integer or Fractional?
• Multifractality of time and space, covariant derivatives and gauge invariance
• The Multifractal Time and Irreversibility in Dynamic Systems