着名家获英国绍多大奖，因早逝而失诺奖的何款搜论力量与分形多维告间和爱因斯坦能量的分配，completely empty, with a Menger-Urysohn dimension -1, but nevertheless possesses a Hasudorff fractal dimension f2. The empty set is de facto two identical things at the very same time, the surface or the topological neighbourhood of the zero set as well as being the guiding quantum wave. The zero set is a Cantorian fractal point as well as the quantum particle guided by the ‘ghost’ wave. This may be understood in a very elementary manner, according to El Naschie, by recalling that the wave is the surface of the particle and it is evident that the smaller, say a sphere, the larger is the ratio between its surface area and its volume. When the volume tends to zero, the ratio will tend to infinity.
Now, on taking measurement on this particle-wave packet, we inevitably enter into the wave and consequently into the domain of the empty set. So the empty set becomes non-empty and “practically reduced or jumps to at best, a zero set.”
Wave particle duality and dark energy
Continuing in the same vein, El Naschie proposes that Einstein’s famous formula E = mc2 consists of two parts. The first part is the positive energy of the quantum particle modeled by the topology of the zero set. The second is the absolute value of the negative energy of the quantum Schrödinger wave modeled by the topology of the empty set [3] (see above). The latter is the missing dark energy (actually dark energy and dark matter) of the universe accounting for 95.45 % of the total energy-matter in agreement with the findings from the Wilkinson Microwave Anisotropy Probe and the supernova cosmic measurement awarded the 2011 Nobel Prize in Physics. The dark energy of the quantum wave cannot be detected in the normal way because measurement collapses the quantum wave. Several recent attempts to detect dark matter with sophisticated detectors have failed [4] No Dark Matter Detected Yet (SiS 62), which is potentially devastating for the standard model of cosmology that depends on postulates of dark matter and dark energy.
The Menger-Urysohn dimension and Hausdorff dimension of a random Cantor set are [o, f] [3]. The dimensions of the complement (gaps) are [-1, and 1 – f = f2], as established above.
Raising both the f (points) and f2 (gaps) set to the Kaluza-Klein 5 dimensional spacetime gives f5 (volume) and 5f2 (boundary) and respectively equal to 4.5 % and 95.5 % of Einstein’s energy, the latter
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