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.
References
[1]
‘tHooft, G. (1997) In Search of the Ultimate Building Blocks. Cambridge University Press, Cambridge, 68-69.
[2]
Pittman, J. (1993) Probability. Springer, New York, USA, 254.
[3]
Magana-Loaiza, O.S., de Leon, I., Mirhosseini, M., et al. (2016) Exotic Looped Trajectories in the Three-Slit Interference. ArXiv:1610.0858V1[quant-ph]
[4]
El Naschie, M.S. (2017) The Quantum Triple-Slit Experiment and Cosmic Dark Energy. Open Journal of Microphysics, 7, 31-35. https://doi.org/10.4236/ojm.2017.72002
[5]
El Naschie, M.S. The Looped Light of the Triple-Slit Real Experiment as a Confirmation for the Extra Dimensions of Quantum Spacetime and the Reality of Dark Energy. Optical and Photonic Journal, in Press.
[6]
Ping, S. (2012) Golden Ratio Estimate of Success Probability Based on One and Only. ArXiv:1207.5198
[7]
Tanackov, I., Tepic, J. and Kostelac, M. (2011) The Golden Ratio in Probabilistic and Artificial Intelligence. Tehnickivjesnik/Technical Gazette, 18, 641-647.
[8]
Hayata, K. (2014) Golden Distribution of Probabilities. Forma (Letter), 29, 33-40. https://doi.org/10.5047/forma.2014.006
[9]
He, J.-H., Marek-Crnjac, L., et al. (2011) Quantum Golden Mean Entanglement Test as the Signature of the Fractality of Micro Spacetime. Nonlinear Science Letters B, 1, 45-50.
[10]
Marek-Crnjac, L. (2006) The Golden Mean in the Topology of Four Manifolds in Conformal Field Theory, in Mathematical Probability Theory and in Cantorian Spacetime. Chaos, Solitons & Fractals, 28, 1113-1118. https://doi.org/10.1016/j.chaos.2005.08.160
[11]
Jackson, M. (2004) Paradoxes with Dice and Election. In: Tadich, B., Tabias, S., et al., Eds., Towards Excellence in Mathematics; Proceedings of the 4th Annual Conference of the Mathematical Association of Victoria, Monash University, Clayton, Australia, 2004, 208-218.
[12]
El Naschie, M.S. (2007) Hilbert Space, Poincaré Dodecahedron and Golden Mean Transfiniteness. Chaos, Solitons & Fractals, 31, 787-793. https://doi.org/10.1016/j.chaos.2006.06.003
[13]
El Naschie, M.S. (1998) On the Uncertainty of Cantorian Geometry and the Two-Slit Experiment. Chaos, Solitons & Fractals, 19, 517-529. https://doi.org/10.1016/S0960-0779(97)00150-1
[14]
El Naschie, M.S. (2004) A Review of E-Infinity Theory and the Mass Spectrum of High Energy Particle Physics. Chaos, Solitons & Fractals, 19. 209-236. https://doi.org/10.1016/S0960-0779(03)00278-9
[15]
El Naschie, M.S. (2009) The Theory of Cantorian Spacetime and High Energy Particle Physics (An Informal Review). Chaos, Solitons & Fractals, 41, 2635-2646. https://doi.org/10.1016/j.chaos.2008.09.059
[16]
El Naschie, M.S. (2015) An Exact Mathematical Picture of Quantum Spacetime. Advances in Pure Mathematics, 5, 560-570. https://doi.org/10.4236/apm.2015.59052
[17]
El Naschie, M.S. (2016) On a Fractal Version of Witten’s M-Theory. Journal of Astronomy & Astrophysics, 6, 135-144.