Abstract
Dark energy is explained using familiar notions and concepts used in quantum field theory, string theory and the exact mathematical theory of spacetime. The main result of the present work is first a new mathematical definition of pre-quantum spacetime (QST) as a multiset made of infinitely many empty Cantor sets connected to pre-quantum wave empty set (QW) and the pre-quantum particle (QP) zero set via the cobordism equation ∂(QW) = (QP)U(QST). Second, and in turn, this new path of reasoning is used to validate the quantum splitting of Einstein’s E = mc2 into the sum of the ordinary energy E = mc2/22 of the quantum particle and the dark energy E = mc2(21/22) of the quantum wave, used predominantly to explain the observed accelerated expansion of the universe.
Highlights
Introduction and MotivationThe theme of the present scientific essay is aptly captured by a remark ascribed to Wolfgang E
One step is still missing to come to the quantitative result that confirms what is transpiring from the preceding toy model of our universe, namely that the “boundary” energy is nothing but the energy of the quantum wave and that is what we call dark energy
Remembering that for a simple two-dimensional square area A is multiplicative A = a2 while the length of the four border lines L is additive L = 4a generalizing to five dimensions we find that the quantum particle quasi volume must be φ5 while the quantum wave quasi volume must be 5φ2 [8]-[31]
Summary
The theme of the present scientific essay is aptly captured by a remark ascribed to Wolfgang E. The second set is a spacetime-like non-substance fat Cantor set with a Hausdorff dimension 1−φ =φ 2 and a topological dimension minus one (−1) indicating that it is essentially an empty set [7]-[9] This will be shown later to give rise to the quantum wave which harbours what has been dubbed the missing dark energy of the cosmos [9]-[29]. One step is still missing to come to the quantitative result that confirms what is transpiring from the preceding toy model of our universe, namely that the “boundary” energy is nothing but the energy of the quantum wave and that is what we call dark energy This step is the following realization gained from the cobordism theory of spacetime [33] which put, means that Einstein’s D = 4 spacetime is cobodent to Kaluza-Klein spacetime D = 5. That dilemma was solved as usual by including a large number of references [1]-[99]
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