Abstract
Following an inspiring idea due to D. Gross, we arrive at a topological Planck energy Ep and a corresponding topological Planck length effectively scaling the Planck scale from esoterically large and equally esoterically small numbers to a manageably where P(H) is the famous Hardy’s probability for quantum entanglement which amounts to almost 9 percent and Based on these results, we conclude the equivalence of Einstein-Rosen “wormhole” bridges and Einstein’s Podolsky-Rosen’s spooky action at a distance. In turn these results are shown to be consistent with distinguishing two energy components which results in , namely the quantum zero set particle component which we can measure and the quantum empty set wave component which we cannot measure , i.e. the missing dark energy. Together the two components add to where E is the total energy, m is the mass and c is the speed of light. In other words, the present new derivation of the world’s most celebrated formula explains in one stroke the two most puzzling problems of quantum physics and relativistic cosmology, namely the physicomathematical meaning of the wave function and the nature of dark energy. In essence they are one and the same when looked upon from the view point of quantum-fractal geometry.
Highlights
In a remarkable essay [1] the founding father of Heterotic superstring theory and Nobel Laureate in physics D
In the present work which tackles one of the currently most researched and hotly debated problems in quantum physics and cosmology [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72], we take this idea literally and seriously to mean a mathematical topological formulation of physics starting from a unit interval spacetime with non-classical and non-smooth transfinite discrete geometry and topology [2,3,4,5]
In other words when we look at the two dimensional projection of a ramified i.e. compactified Klein modular curve or a fractal Penrose universe [65], at the edges being in the hyperbolic plane at infinity surrounded by a Cantorian circle we have anticlastic curvature, i.e. negative curvature producing negative dark energy causing negative gravity pushing the universe apart rather than pulling it together
Summary
In a remarkable essay [1] the founding father of Heterotic superstring theory and Nobel Laureate in physics D. Finkelstein who introduced the notion of quantum relativity [69]
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