Abstract
Previous work by Sigalotti in 2006 and recently by Hendi and Sharifzadeh in 2012 showed that all the fundamental equations of special relativity may be derived from a golden mean proportioned classical-Euclidean triangle and confirmed Einstein’s famous equation E=mc2. In the present work it is shown that exchanging the Euclidean triangle with a hyperbolic one an extended quantum relativity energy equation, namely , is obtained. The relevance of this result in understanding the true nature of the “missing” so-called dark energy of the cosmos is discussed in the light of the fact that the ratio of to E=mc2 is which agrees almost completely with the latest supernova and WMAP cosmological measurements. To put it succinctly what is really missing is a quantum mechanical factor equal 1/22 in Einstein’s purely relativistic equation. This factor on the other hand is derivable from the intrinsic hyperbolic Cantor set nature of quantum entanglement.
Highlights
Introduction and Background InformationIn a remarkable paper by Hendi and Sharifzadeh [1] the authors used Sigalotti’s insight regarding the connection between Einstein’s special relativity and the golden mean triangle [2] to derive all the fundamental equations of Lorentz and Einstein [2,3]
Previous work by Sigalotti in 2006 and recently by Hendi and Sharifzadeh in 2012 showed that all the fundamental equations of special relativity may be derived from a golden mean proportioned classical-Euclidean triangle and confirmed Einstein’s famous equation E mc2
Special relativity is based on the extension of Euclidean 3D spacetime geometry to a Euclidean but 4D spacetime geometry [1,2,3,4]
Summary
In a remarkable paper by Hendi and Sharifzadeh [1] the authors used Sigalotti’s insight regarding the connection between Einstein’s special relativity and the golden mean triangle [2] to derive all the fundamental equations of Lorentz and Einstein [2,3]. 5 1 2 0.61803398 is the golden mean [5,6] This particular form of Klein modular curve is basically a collection of an infinite number of hierarchical hyperbolic triangles [5,6] and here is the deceptively simple connection. It is the geometry of these hyperbolic traingles of the compactified Klein modular curve which in an analogous way leads to the quantum-relativity extension of Einstein’s E mc to the relatively well known result of the ordinary energy of a quantum particle [4].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
