Abstract
Dark energy is shown to be the absolute value of the negative kinetic energy of the halo-like quantum wave modeled mathematically by the empty set in a five dimensional Kaluza-Klein (K-K) spacetime. Ordinary or position energy of the particle on the other hand is the dual of dark energy and is contained in the dynamic of the quantum particle modeled by the zero set in the same five dimensional K-K spacetime. The sum of both dark energy of the wave and the ordinary energy of the particle is exactly equal to the energy given by the well known formula of Einstein E=mc2 which is set in a four dimensional spacetime. Various interpretations of the results are presented and discussed based on the three fundamental energy density equations developed. In particular where E is the energy, m is the mass and c is the speed of light, is Hardy’s quantum entanglement and gives results in complete agreement with the cosmological measurements of WMAP and Supernova. On the other hand gives an intuitive explanation of negative gravity and the observed increased rate of cosmic expansion. Adding E (ordinary) to E (dark) one finds which as we mentioned above is Einstein’s famous relativity formula. We conclude that similar to the fact that the quantum wave interpreted generally as probability wave which is devoid of ordinary energy decides upon the location of a quantum particle, it also exerts a negative gravity effect on the cosmic scale of our clopen, i.e. closed and open universe. Analysis and conclusions are framed in a reader friendly manner in Figures 1-14 with detailed commentary.
Highlights
We utilize the wave-particle duality [1,2] and quantum entanglement [2,3,4,5,6,7,8] as fundamental features of quantum mechanics [1,8] as well as classical field, quantum set theory [3] and transfinite quantization [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] to develop an effective quantum gravity energy theory [1,2,3,4,5,6,7,8] that can convincingly resolve the problem of the accelerated rate of cosmic expansion and the missing dark energy of the cosmos and at the same time agrees with the accurate WMAP and Supernova cosmic energy density measurements and analysis [9,10,11,12,13,14,15,16,17,18]
From points discussed in the preceding sections we can conclude that Einstein’s formula E mc2 is blind to the difference between ordinary energy i.e. quantum particle energy and dark energy i.e. the quantum wave energy because it presupposes a continuous smooth spacetime and never addresses any questions related to fractality or sparseness of spacetime which is the cause of the constancy of the speed of light at the classical interface being a fractal average [8,12,13,30]
We conclude that while fractals i.e. the zero set or phenomenologically the quantum particle is behind ordinary energy, voids in spacetime corresponding to the empty set i.e. the quantum wave i.e. the halo of the quantum particle [8,23,33,44] are behind dark energy and are the cause of negative gravity and the increased rate of cosmic expansion [9,10,11,15,16]
Summary
We utilize the wave-particle duality [1,2] and quantum entanglement [2,3,4,5,6,7,8] as fundamental features of quantum mechanics [1,8] as well as classical field, quantum set theory [3] and transfinite quantization [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] to develop an effective quantum gravity energy theory [1,2,3,4,5,6,7,8] that can convincingly resolve the problem of the accelerated rate of cosmic expansion and the missing dark energy of the cosmos and at the same time agrees with the accurate WMAP and Supernova cosmic energy density measurements and analysis [9,10,11,12,13,14,15,16,17,18]. In turn the quantum particle is modeled by the zero set represented dimensionally by von Neumann-Connes dimensional function [8,44] of a Penrose quasicrystal fractal tiling space [21,22,23]. The broken mirror image of the quantum particle is the halo-like quantum probability wave which is the source of a negative energy anti-gravity (see Figures 9 and 11) stemming from modeling the quantum wave via the empty set of the same Penrose quasicrystals fractal tiling [21,22,23,30,31,32,33,34,44]. It was found to the Author’s delight that the sum of ordinary energy of the particle and absolute value of the negative dark energy of the wave added together is exactly the energy predicted by Einstein’s formula [2,3, 17]
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