_{1}

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+
Ø where
Ø 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+
Ø^{3}
^{ } as well as a fractal Witten’s M-theory 11+
Ø^{5}. Setting
Ø^{3} and
Ø^{5} equal zero, we retrieve Einstein’s spacetime and Witten’s M-theory spacetime respectively where
Ø^{3} is the latent Casimir topological pressure of spacetime and
Ø^{5} is Hardy’s quantum entanglement of the same.

There is an excellent model for Zitterbewegung due to Arend Niehaus, University of Utrecht Physics Professor [

As mentioned in the present Introduction earlier on, the basic idea of the Niehaus Zitterbewegung model [

Now starting from Newtonian three dimensional classical space, we see that the corresponding dimension must be the triadic intersection given by

This is clearly the Hausdorff dimension of a

so that

The connection to Zitterbewegung of the Niehaus model and the associated theory [

It is a well known mathematical-geometrical fact that except for the straight line and the perfect circle, only the logarithmic spiral is infinitely self similar homogeneous. In addition the spiral in two dimensions arises from the construction of a random one dimensional Cantor dust (set) with uniform distribution [

Before concluding this section let us show using the above result a remarkable derivation connecting superstrings

where

with which we conclude this compressed, very short analysis. For in depth study of the ideas and theories discussed here, the reader is directed to Refs. [

The effort of what might be called the Utrecht Dutch School of G. ‘tHooft in inventing or discovering a quantum physics without the unintuitive and/or at least classically paradoxical orthodox quantum mechanics seems to have some considerable success by the non-mainstream efforts of people like Gerard ‘tHooft himself [

“Nur in der fuller Liegt die Klarkeit”, i.e. only in the abundance lies clarity.

This does not only apply to the physical phenomena but also to the mathematical models and theories which we apply [

El Naschie, M.S. (2017) Spacetime from Zitterbewegung. Open Journal of Modelling and Simula- tion, 5, 169-173. https://doi.org/10.4236/ojmsi.2017.53012