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In a short, neat and credible analysis , it is established that time is a fractal effect of the Cantor set-like topology of micro spacetime. This effect as well as the ordinary cosmic energy density of the universe is shown to be a direct consequence of Hardy’s probability of quantum entanglement. Finally and as a general conclusion, we point out the importance of understanding the fractal origin of time as well as spacetime for resolving certain types of paradoxes arising in quantum information science.

To show how the title of this short letter is true, we start by using stringent mathematics to demonstrate how the time dimension is actually a fractal effect that may be called a real and persistent illusion without being inconsistent or esoteric [

〈 n 〉 = 1 + d c ( O ) 1 − d c ( O ) (1)

where d c ( O ) is the Hausdorff dimension of the backbone fractal-Cantor unit set forming the space of the physical-mathematical E-infinity theory [

〈 n 〉 = 1 + ( 3 / 5 ) 1 − ( 3 / 5 ) = ( 8 / 5 ) ( 2 / 5 ) = 4 (2)

The result means that for d c ( O ) = 3 / 5 = 0.6 which is the first rational approximation found from continued fraction expansion of the irrational golden mean ϕ = ( 5 − 1 ) / 2 = 0.618033989 one finds the dimensionality of Einstein’s spacetime [

〈 n 〉 = 1 + ( 1 / 2 ) 1 − ( 1 / 2 ) = 3 (3)

which is the topological dimensionality of classical Newtonian space [3, 8, 13]. Remembering that d c ( O ) = 0.6 is the first approximation of d c ( O ) = ϕ and that f is nothing but ( d c ( O ) = 0.6 ) plus ‘tHooft’s renormalon divided by superstring dimensionality D = 10 [

d c ( n ) = ( d c ( O ) ) n − 1 (4)

Consequently for d c ( O ) = ( d c ( O ) ) = 1 / 2 and n = 3 one finds [

d c ( 3 ) = [ 1 / ( 1 / 2 ) ] 3 − 1 = ( 2 ) 2 = 4 (5)

That means that for n = 3 we find d_{c} = 4 which means that 4 - 3 = 1 is the difference between the fractal Hausdorff dimension of spacetime, i.e. d_{c} = 4 and the corresponding topological dimension n = 3 so that we may interpret d = 4 not as the union of n = 3 plus a time dimension n (time) = 1 leading to 3 + 1 = 4 spacetime dimension but rather the difference on average between n = 3 and d c ( 3 ) = 4 , i.e. the effect of hidden on average fractality [

〈 d c 〉 = 1 d c ( O ) ( 1 − d c ( O ) ) (6)

and find

〈 d c 〉 = 1 ( 1 / 2 ) ( 1 − ( 1 / 2 ) ) = ( 1 / 4 ) − 1 = 4 (7)

where we saw from Equation (3) that 〈 n 〉 = 3 [

It is highly instructive and insightful that while we do not see but simply “feel” the time dimension, there is another effect that we can “see” and feel due to a fractality effect, namely the ordinary energy density of the cosmos [

ϕ 3 / ( 5 + ϕ 3 ) = ϕ 5 / 2 (8)

in full agreement with all actual cosmic measurements and observations [

From the preceding analysis and conclusion, we can draw the profound conclusion that one of the most important components of our universe and existence is its chaotic fractal dynamics, geometry and topology [

El Naschie, M.S. (2018) Time Dimension and Ordinary Cosmic Energy Density Are Fractal Effects. Journal of Quantum Information Science, 8, 47-51. https://doi.org/10.4236/jqis.2018.82004