Abstract
Duality behavior of photons in wave-particle property has posed challenges and opportunities to discover other frontiers of fundamental particles leading to the relativistic and quantum description of matter. The speed of particles faster than the speed of light could not be recognized, and matter was always described as a real number. A new fundamental view on matter as a complex value has been introduced by many authors who present a paradigm that is shifted from real or pure imaginary particles to Complex Matter Space. A new assumption will be imposed that matter has two intrinsic components: i) mass, and ii) charge. The mass will be measured by real number systems and charged by an imaginary unit. The relativistic concept of Complex Matter Space on energy and momentum is investigated and we can conclude that the new Complex Matter Space (CMS) theory will help get one step closer to a better understanding toward: 1) Un-Euclidean description of Minkowski Geometry in the context of the Complex Matter Space, 2) transformation from Euclidean to Minkowski space and its relativistic interpretation. Finally, geometrical foundations are essential to have a real picture of space, matter, and the universe.
Highlights
Several thousand years of human experiences in geometry, which was structured by Pythagoras and Euclid, has undergone challenges during the past few centuries
The relativistic concept of Complex Matter Space on energy and momentum is investigated and we can conclude that the new Complex Matter Space (CMS) theory will help get one step closer to a better understanding toward: 1) Un-Euclidean description of Minkowski Geometry in the context of the Complex Matter Space, 2) transformation from Euclidean to Minkowski space and its relativistic interpretation
In a small velocity for a shorter distance, Euclidean Geometry is a simplest model for our physical universe
Summary
Several thousand years of human experiences in geometry, which was structured by Pythagoras and Euclid, has undergone challenges during the past few centuries. Many were skeptical of the validity of this bizarre geometry which was axiomatically consistent and agreed with the models developed All these theories were not experimented physically to be consistent with the natural universe. In a small velocity for a shorter distance, Euclidean Geometry is a simplest model for our physical universe. It is not the proper model for the entire universe when the velocity of the object is near or approaches to the speed of light. It can be interpreted that light travels in a geodesic line This is a revolutionary conclusion that the physical space with the existing mass and gravity is not Euclidean (see Taylor et al, 2004 [3], and Feynman, 1963 [4]). The law of cosines is redeveloped in a hyperbolic triangle
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