The Gap Labelling Integrated Density of States for a Quasi Crystal Universe Is Identical to the Observed 4.5 Percent Ordinary Energy Density of the Cosmos

Condense matter methods and mathematical models used in solving problems in solid state physics are transformed to high energy quantum cosmology in order to estimate the magnitude of the missing dark energy of the universe. Looking at the problem from this novel viewpoint was rewarded by a rather unexpected result, namely that the gap labelling method of integrated density of states for three dimensional icosahedral quasicrystals is identical to the previously measured and theoretically concluded ordinary energy density of the universe, namely a mere 4.5 percent of Einstein’s energy density, i.e. E(O) = mc2/22 where E is the energy, m is the mass and c is the speed of light. Consequently we conclude that the missing dark energy density must be E(D) = 1 - E(O) = mc2(21/22) in agreement with all known cosmological measurements and observations. This result could also be interpreted as a strong evidence for the self similarity of the geometry of spacetime, which is an expression of its basic fractal nature.

On a Fractal Version of Witten’s M-Theory

Starting from Witten’s eleven dimensional M-theory, the present work develops in an analogous way a corresponding dimensional fractal version where . Subsequently, the new fractal formalism is utilized to determine the measured ordinary energy density of the cosmos which turns out to be intimately linked to the new theory’s fractal dimension via non-integer irrational Lorentzian-like factor: where is Hardy’s probability of quantum entanglement. Consequently, the energy density is found from a limiting classical kinetic energy to be Here, is ‘tHooft’s renormalon of dimensional regularization. The immediate logical, mathematical and physical implication of this result is that the dark energy density of the cosmos must be in astounding agreement with cosmic measurements and observations.

Spacetime from Zitterbewegung

Quantum particles are assumed to have a path constituting a random fluctuation super imposed on a classical one resulting in a golden mean spiral propagating in spacetime. Consequently, the dimension of the path of the quantum particle is given by one plus the random Cantor set Zitterbewegung, i.e. 1+Øwhere Øis the golden mean Hausdorff dimension of a random Cantor set. Proceeding in this way, we can derive the basic topological invariants of the corresponding spacetime which turned out to be that of E-infinity spacetime 4+Ø3 as well as a fractal Witten’s M-theory 11+Ø5. Setting Ø3 and Ø5 equal zero, we retrieve Einstein’s spacetime and Witten’s M-theory spacetime respectively where Ø3 is the latent Casimir topological pressure of spacetime and Ø5 is Hardy’s quantum entanglement of the same.

Quantum Fractals and the Casimir-Dark Energy Duality—The Road to a Clean Quantum Energy Nano Reactor

Based on Witten’s T-duality and mirror symmetry we show, following earlier work, the fundamental complimentarity of the Casimir energy and dark energy. Such a conclusion opens new vistas in cold fusion technology in the wider sense of the word which we tackle via fractal nano technologies leading to some design proposals for a nano Casimir-dark energy reactor.

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

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.