A Rindler-KAM Spacetime Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy

Abstract

We introduce an ultra high energy combined KAM-Rindler fractal spacetime quantum manifold, which increasingly resembles Einstein's smooth relativity spacetime, with decreasing energy. That way we derive an effective quantum gravity energy-mass relation and compute a dark energy density in complete agreement with all cosmological measurements, specifically WMAP and type 1a supernova. In particular we find that ordinary measurable energy density is given by 2 1 22 E mc  while the dark energy density of the vacuum is given by   2 2 21 22 E mc . The sum of both energies is equal to Einstein's energy. We conclude that makes no distinction between ordinary energy and dark energy. More generally we conclude that the geometry and topology of quantum entanglement create our classical spacetime and glue it together and conversely quantum entanglement is the logical consequence of KAM theorem and zero measure topology of quantum spacetime. Furthermore we show via our version of a Rindler hyperbolic spacetime that Hawking negative vacuum energy, Unruh temperature and dark energy are different sides of the same medal.

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

“…Since almost 95.5% of the energy density is due to the quantum wave, i.e. quantum energy of propagation and since the quantum wave is the cobordism of the quantum particle, then it follows that most of the energy will be located at the boundary of the holographic boundary of the universe that lies at the hyperbolic infinity [52] [53]. The same conclusion may also be reached by invoking Dvoretzky's theorem of measure concentration.…”

Quantum Disentanglement as the Physics behind Dark Energy

“…It is thus an elementary almost trivial step to conclude from this result that the probability of not being quantumly entangled must be 5φ is also a five-dimensional entropy [21]- [29]. The only difference between 5 φ and 2 5φ is that the first is multiplicative intersection and represents an entangled state, while 2 5φ is an additive union which represents a disentangled state [26] [248]. In fact even the reader who is not familiar with our previous work on fractal Cantorian spacetime and Dark Energy must have guessed by now that the entanglement probability …”

“…is the position or potential energy of the quantum wave modeled by the empty set [26] [28]. Now since any interference or measurement on an empty set quantum wave make the set non empty, we have to invite first quantum wave non-demolishing measuring devices before being in a position to measure dark energy directly [23] [26] [28].…”

Pinched Material Einstein Space-Time Produces Accelerated Cosmic Expansion

“…In fact we will show various completely unsuspected relations between metal forming engineering problems and the negative pressure behind the observed unexpected acceleration rather than deceleration of cosmic expansion [15]- [17]. To put it succinctly in a few sentences, we will show that anti-gravity is essentially the same phenomena as anti-curvature of a pinched long cylindrical shell once this cylinder is put in the projective hyperbolic plane corresponding to 4 and 5 dimensional fractal space-time.…”