Abstract
Quantum particles are assumed to have a path constituting a random fluctuation super imposed on a classical one resulting in a golden mean spiral propagating in spacetime. Consequently, the dimension of the path of the quantum particle is given by one plus the random Cantor set Zitterbewegung, i.e. 1+O where O is the golden mean Hausdorff dimension of a random Cantor set. Proceeding in this way, we can derive the basic topological invariants of the corresponding spacetime which turned out to be that of E-infinity spacetime 4+O3 as well as a fractal Witten’s M-theory 11+O5. Setting O3 and O5 equal zero, we retrieve Einstein’s spacetime and Witten’s M-theory spacetime respectively where O3 is the latent Casimir topological pressure of spacetime and O5 is Hardy’s quantum entanglement of the same.
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