Abstract
The formula for the quantum amplitude of the Veneziano dual resonance model is shown to be formally analogous to the dimensionality of a K-theoretical fractal quotient manifold of the non-commutative geometrical type. Subsequently this analogy is used to deduce the ordinary energy of the quantum particle and the dark energy of the quantum wave. The results agree completely with cosmological measurements. Even more surprisingly the sum of both energy expressions turned out to be exactly equal to Einstein’s iconic formula E = mc2. Consequently Einstein’s formula makes no distinction between ordinary and dark energy.
Highlights
We utilize a formal analogy between Veneziano’s formula for the amplitude of the dual resonance model and that for the Hausdorff fractal dimensionality of quotient manifold to develop an energy-mass quantum relativity equation which where E mc2 turned to be of the form is the famous formula of entanglement and 2 5 1
Einstein’s E mc2 maximal total energy density is the hypothetical dark energy which is in turn a confirmation of the real existence of dark energy and of the exactness of the cosmological measurements of WMAP and certain supernova analysis by the three 2011
In this paper we will be concerned with revising the interpretation of E mc2 where E is the energy, m is the mass and c is the velocity of light by including quantum particle physics [7,8,9,10,11] as well as quantum entanglement [12], topological quantum field theory [13], effective quantum gravity [14] and superstrings [15,16] in our deterministic chaos-fractal analysis [17,18,19,20,21,22,23,24,25,26,27,28]
Summary
Einstein’s E mc maximal total energy density is the hypothetical dark energy which is in turn a confirmation of the real existence of dark energy and of the exactness of the cosmological measurements of WMAP and certain supernova analysis by the three 2011. More importantly the analysis clearly shows the inadequacy of the traditional interpretation of the energy-mass relationship of special relativity when applied to the problem of immensely large distance scales of the order of magnitude of Hubble radius. The correct way to understand E mc is to realize that only E O mc is ordinary energy, which can be measured and corresponds to the energy of the quantum particle. The rest, i.e. E D 21 22 mc is the dark energy of the quantum wave and cannot be measured in a direct way because of quantum wave collapse.
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