Crystallization of space: Space-time fractals from fractal arithmetic

被引：10

作者：

Aerts, Diederik ^{[1
]}

Czachor, Marek ^{[1
,2
]}

Kuna, Maciej ^{[1
,2
]}

机构：

[1] Vrije Univ Brussel, Ctr Leo Apostel CLEA, B-1050 Brussels, Belgium

[2] Gdansk Tech Univ, Wydziai Fizyki Tech & Matematyki Stosowanej, PL-80233 Gdansk, Poland

来源：

CHAOS SOLITONS & FRACTALS | 2016年 / 83卷

关键词：

Fractals; Arithmetic; Space-time; DIMENSIONS; RELATIVITY; GALAXIES; SCALE;

D O I：

10.1016/j.chaos.2015.12.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetic allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated with appropriate Lie groups. The construction is illustrated by explicit examples. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：201 / 211

页数：11

共 46 条

[1] DIMENSION OF A QUANTUM-MECHANICAL PATH [J].

ABBOTT, LF ;

WISE, MB .

AMERICAN JOURNAL OF PHYSICS, 1981, 49 (01) :37-39

[2] Reconstructing the Universe [J].

Ambjorn, J ;

Jurkiewicz, J ;

Loll, R .

PHYSICAL REVIEW D, 2005, 72 (06)

[3] Doubly-special relativity: First results and key open problems [J].

Amelino-Camelia, G .

INTERNATIONAL JOURNAL OF MODERN PHYSICS D, 2002, 11 (10) :1643-1669

[4]

[Anonymous], 1998, Lecture notes Math

[5] Fractal dimensions of a weakly clustered distribution and the scale of homogeneity [J].

Bagla, J. S. ;

Yadav, Jaswant ;

Seshadri, T. R. .

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 2008, 390 (02) :829-838

[6] GALAXIES - FRACTAL DIMENSIONS, COUNTS IN CELLS, AND CORRELATIONS [J].

BALIAN, R ;

SCHAEFFER, R .

ASTROPHYSICAL JOURNAL, 1988, 335 (02) :L43-L46

[7]

Beck C., 1993, Thermodynamics of Chaotic Systems

[8] Fractal Properties of Quantum Spacetime [J].

Benedetti, Dario .

PHYSICAL REVIEW LETTERS, 2009, 102 (11)

[9]

Benioff P., 2015, QUANTUM STUD MATH FD, V2, P289

[10] New Gauge Field from Extension of Space Time Parallel Transport of Vector Spaces to the Underlying Number Systems [J].

Benioff, Paul .

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2011, 50 (06) :1887-1907

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