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We give a mathematical golden mean distribution based probabilistic confirmation of a recent spectacular experiment with light. The experiment in question is a three-slit variant of the well known two-slit set up of quantum mechanics. The outcome of the sophisticated experiment revealed the looped path of light on the quantum scale and consequently the Peano-Hilbert geometry of spacetime, ergo its fractal-Cantorian nature. The mathematics used here on the other hand is the remarkably simple and insightful golden mean probability distribution known from a famous paradox known in social sciences as the voter paradox.

In [

“… The physics of elementary particles has nothing to do with the physics of low temperature, but the mathematics is very, very similar… What a nice feature of theoretical physics! Totally different worlds can be compared with each other, just because they happen to obey similar mathematical equations.”

In the present letter we take ‘tHooft’s words much further than we could have thought possible by comparing the voter paradox of political sciences [

The voter paradox with its golden mean distribution [

We start with the probabilistic mathematics of the voter paradox [

Let X, Y and Z be random variables and the corresponding probabilities are denoted by P(X), P(Y) and P(Z).

Theorem:

For independent X, Y and Z all the three probabilities P(X), P(Y) and P(Z) can be as large as the

For details the reader is referred to the relevant literature [

In this part we give a short account of the analogical correspondence between the voter paradox and the looped light experiment [

where

Note that Equation (2) corresponds to the counterfactual part of Hardy’s quantum entanglement

where

From the preceding simple chain of thought it is obvious that we may interpret the results of Equation (2) as a confirmation of the fractal-Cantorian nature of spacetime [

Interestingly we could take a special case of the voter paradox namely the Steinhaus-Trybula paradox [

which is the two Brane of a string world sheet [

is our classical spacetime and finally

which is super space of super symmetry [

The golden mean probability resolution of the voter paradox is applied in the present work to the triple-slit experiment of looped light. In a nutshell our analysis lends a firm probabilistic underpinning of a highly non-classical quantum phenomenon without direct reference to quantum mechanics. In general we hope that we showed with utter simplicity that measurement naturally converts an empty set to a zero set which means a quantum wave to a quantum particle. In other words, it is all nothing more than the topological density of spacetime. That is exactly why we think the looped light is an experimental proof for the fractal nature of quantum spacetime and that dark energy and dark matter are real consequences of the topology and geometry of quantum spacetime.

The first time I learned of the voter paradox was from my then Ph.D. supervisor, Prof. J. M. T. Thompson, FRS around 1970. Amazingly the subject remained dormant in my subconscious for almost 47 years. I am grateful in all events to Prof. Thompson for expanding my horizons beyond civil engineering.

El Naschie, M.S. (2017) Looped Light on Dark Energy. Journal of Quantum Information Science, 7, 43- 47. https://doi.org/10.4236/jqis.2017.72004