The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos

2016

IJAA

Realizing the physical reality of 'tHooft's self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pythagoras and the larger than life man of theoretical physics Einstein, we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We started from the basic principles of self similarity which came to prominence in science with the advent of the modern theory of nonlinear dynamical systems, deterministic chaos and fractals. This fundamental logico-mathematical thread related to partially ordered sets is then applied to show how the classical Newton's kinetic energy E = 1/2mv 2 leads to Einstein's celebrated maximal energy equation E = mc 2 and how in turn this can be dissected into the ordinary energy density E(O) = mc 2 /22 and the dark energy density E(D) = mc 2 (21/22) of the cosmos where m is the mass; v is the velocity and c is the speed of light. The important role of the exceptional Lie symmetry groups and 'tHooft-Veltman-Wilson dimensional regularization in fractal spacetime played in the above is also highlighted. The author hopes that the unusual character of the analysis and presentation of the present work may be taken in a positive vein as seriously attempting to propose a different and new way of doing theoretical physics by treating number theory, set theory, group theory, experimental physics as well as conventional theoretical physics on the same footing and letting all these diverse tools lead us to the answer of fundamental questions without fear of being labelled in one way or another.

“…exactly as expected [26]- [34]. Note that this is the same result as that which we obtain for quantum gravity [26]- [34] [86].…”

Section: The Logarithmic Spiral Connection Between Quantum Fieldsupporting

confidence: 89%

“…[26]- [34]. Here we give only the analysis for a grand unification for non-super symmetric 1 ρ = and the super symmetric …”

Section: The Logarithmic Spiral Connection Between Quantum Fieldmentioning

confidence: 99%

Section: The Simplexity Of Quantum Complexity-an Informal Introductionmentioning

confidence: 99%

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Einstein’s Dark Energy via Similarity Equivalence, ‘tHooft Dimensional Regularization and Lie Symmetry Groups

2016

IJAA

“…Comparing these results with the actual cosmic measurements of WMAP, Planck and type 1a supernova [50]- [57] we find that they are in excellent agreement as well as being identical to the result obtained previously using many different methods and models [1]- [6].…”

Section: From Planck's Half Quantum To Dark Energy Via Ordinary and Csupporting

confidence: 88%

“…We start with stating the final result. This is first that the vacuum zero point energy is found from replacing w  by 5 φ and is consequently equal to the ordinary energy density of the cosmos [44]- [57] ( )…”

Section: From Planck's Half Quantum To Dark Energy Via Ordinary and Cmentioning

confidence: 99%

Max Planck Half Quanta as a Natural Explanation for Ordinary and Dark Energy of the Cosmos

2016

JMP

The work gives a natural explanation for the ordinary and dark energy density of the cosmos based on conventional quantum mechanical considerations which dates back as far as the early days of the quantum theory and specifically the work of Max Planck who seems to be the first to propose the possibility of a half quanta corresponding to the ground state, i.e. the energy zero point of the vacuum. Combining these old insights with the relatively new results of Hardy's quantum entanglement and Witten's topological quantum field theory as well as the fractal version of M-theory, we find a remarkably simple general theory for dark energy and the Casimir effect.

A Complementarity Resolution of the Black Hole Information Paradox

2015

AJAA

Self Cite

Abstract:The E-infinity theory particle-wave duality used to compute the density of ordinary and dark energy of the cosmos is extended to meet the black hole complementarity of Susskind and 'tHooft. A black hole is essentially a relativistic as well as a quantum object. Therefore the information paradox of black holes is a consequence of the clash between these two most fundamental theories of modern physics. It is logical to conclude that a resolution of the problem requires some form of a quantum gravity theory. The present work proposes such a resolution using set theory and pointless spacetime geometry coupled to the afore mentioned extension and the inbuilt self referential character of Cantorian fractal sets.