Stability Analysis of the two-slit experiment with quantum particles

An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy

“…The only somewhat similar theories are those of the Canadian physics Professor G.N. Ord and the French cosmologist Dr. L. Nottale but both used continuous Peano-like fractals unlike the totally disjointed Cantor sets of El Naschie [17][18][19][20][21][22][23][24][25]. There is some correspondence between Richard Feynman and G. Ord which indicates that Feynman was tinkering with the idea of space filling fractal curves but he published nothing on the subject [26].…”

“…One very interesting point about El Naschie's spacetime is that viewed at macroscopic resolution it appears as if it were only three plus one or four dimensional, thus mimicking the space-time of classical mechanics and relativity and which agrees in the three plus one case with our daily experience with the macroscopic world [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. In other words the dimensionality of this space-time is resolution dependent and the invariance theorem of dimensions must be relaxed [20][21][22][23][24][25][26][27]. The high dimensional character of space-time starts to become noticeable only at sub-microscopic resolution [25,27].…”

The golden mean in the topology of four-manifolds, in conformal field theory, in the mathematical probability theory and in Cantorian space-time

“…In other mathematical fields such as in mathematical analysis, in conformal field theory, in the topology of four-manifold the golden mean is also of great importance. In the present work we presented the connections between random Cantor set and the two-slit gedanken experiment following [6][7][8]. It is extremely important to notice that in our discussion of the two-slit experiment we do not use anywhere wave equations of any type.…”

“…Following [6][7][8] we see that classical probability is involved in the two-slit experiment. The probability to observe a wave like or a particle like behavior is identical and so we can conclude that particles and waves are fundamentally indistinguishable in quantum space-time.…”

“…The probability that the particle goes through slit 1 is P 1 and the probability of going through slit 2 is P 2 . Following [6][7][8] the total probability is given by the union or subtraction of the two events as…”