The paper presents an exact analysis leading to an accurate theoretical prediction of the amount of the mysteriously missing hypothetical dark energy density in the cosmos. The value found, namely 95.4915028% is in fu...The paper presents an exact analysis leading to an accurate theoretical prediction of the amount of the mysteriously missing hypothetical dark energy density in the cosmos. The value found, namely 95.4915028% is in full agreement with earlier analysis, the WMAP and the supernova cosmic measurements. The work follows first the strategy of finding a critical point which separates a semi-classical regime from a fully relativistic domain given by topological unit interval velocity parameter then proceeds to wider aspects of a topological quantum field of fractal unit interval. This idea of a critical velocity parameter was first advanced by Sigalotti and Mejias in 2006 who proposed a critical value equal . A second interesting proposal made in 2012 by Hendi and Sharifzadeh set the critical point at 0.8256645. The present analysis is based upon a light cone velocity quantized coordinate. This leads to the same quantum relativity energy mass relation found in earlier publications by rescaling that of Einstein’s special relativity. Two effective quantum gravity formulae are obtained. The first is for the ordinary measurable energy of the quantum particle while the second is for dark energy density of the quantum wave which we cannot measure directly and we can only infer its existence from the measured accelerated expansion of the universe E(D) = where . The critical velocity parameter in this case arises naturally to be . The results so obtained are validated using a heuristic Lorentzian transformation. Finally the entire methodology is put into the wider perspective of a fundamental scaling theory for the Planck scale proposed by G. Gross.展开更多
Following an inspiring idea due to D. Gross, we arrive at a topological Planck energy Ep and a corresponding topological Planck length effectively scaling the Planck scale from esoterically large and equally esoterica...Following an inspiring idea due to D. Gross, we arrive at a topological Planck energy Ep and a corresponding topological Planck length effectively scaling the Planck scale from esoterically large and equally esoterically small numbers to a manageably where P(H) is the famous Hardy’s probability for quantum entanglement which amounts to almost 9 percent and Based on these results, we conclude the equivalence of Einstein-Rosen “wormhole” bridges and Einstein’s Podolsky-Rosen’s spooky action at a distance. In turn these results are shown to be consistent with distinguishing two energy components which results in , namely the quantum zero set particle component which we can measure and the quantum empty set wave component which we cannot measure , i.e. the missing dark energy. Together the two components add to where E is the total energy, m is the mass and c is the speed of light. In other words, the present new derivation of the world’s most celebrated formula explains in one stroke the two most puzzling problems of quantum physics and relativistic cosmology, namely the physicomathematical meaning of the wave function and the nature of dark energy. In essence they are one and the same when looked upon from the view point of quantum-fractal geometry.展开更多
Using powerful concepts and tools borrowed from the seminal arsenal connecting physics fundamentals with esoteric set theoretical operations developed in recent years by Alexandria E-infinity theoretician M. S. El Nas...Using powerful concepts and tools borrowed from the seminal arsenal connecting physics fundamentals with esoteric set theoretical operations developed in recent years by Alexandria E-infinity theoretician M. S. El Naschie, this paper explores the deep implications of some of the dualities Dr El Naschie has identified and analyzed in his exposes, connecting them with our own Xonic Quantum Physics (XQP) which places dynamical action rather than spacetime and energy at the core of the System of the World.展开更多
Haug has recently introduced a new theory of unified quantum gravity coined “<em>Collision Space-Time</em>”. From this new and deeper understanding of mass, we can also understand how a grandfather pendu...Haug has recently introduced a new theory of unified quantum gravity coined “<em>Collision Space-Time</em>”. From this new and deeper understanding of mass, we can also understand how a grandfather pendulum clock can be used to measure the world’s shortest time interval, namely the Planck time, indirectly, without any knowledge of G. Therefore, such a clock can also be used to measure the diameter of an indivisible particle indirectly. Further, such a clock can easily measure the Schwarzschild radius of the gravity object and what we will call “Schwarzschild time”. These facts basically prove that the Newton gravitational constant is not needed to find the Planck length or the Planck time;it is also not needed to find the Schwarzschild radius. Unfortunately, there is significant inertia towards new ideas that could significantly alter our perspective on the fundamentals in the current physics establishment. However, this situation is not new in the history of science. Still, the idea that the Planck time can be measured totally independently of any knowledge of Newton’s gravitational constant could be very important for moving forward in physics. Interestingly, an old instrument that today is often thought of as primitive instrument can measure the world’s shortest possible time interval. No atomic clock or optical clock is even close to be able to do this.展开更多
The first part of this article develops [1] a closed universe model deploying by identical multiplication a Friedmann-Planck micro-universe;thus this one constitutes the grains of the vacuum of this universe. The quan...The first part of this article develops [1] a closed universe model deploying by identical multiplication a Friedmann-Planck micro-universe;thus this one constitutes the grains of the vacuum of this universe. The quantum initial expansion of this is quadratic as a function of time. Using this model, calculating the density of matter at the present time gives a correct numerical result. The essential point is that during periods of expansion following the initial quadratic period, this model reveals a surprising phenomenon. The function expressing the radius curvature as a function of time depends on the individual mass of the heaviest elementary particles created at the end of the quadratic period. The model also leads to reflection on the dark matter. The second part imagines a new type of Big Rip based on the following hypothesis: when the acceleration of the Universe, caused by dark energy, reaches the value of Planck acceleration, destruction of the microscopic structure of the Universe occurs and is replaced by a macroscopic structure (photon spheres) identical to that of the initial Planck element. Thus a new Big Bang could begin on an immensely larger scale. This reasoning eventually leads to reflection on the origins of the Big Bang.展开更多
We have recently suggested a new quantum gravity theory that can be unified with quantum mechanics. We have coined this theory collision space-time. This new theory seems to be fully consistent with a 3-dimensional sp...We have recently suggested a new quantum gravity theory that can be unified with quantum mechanics. We have coined this theory collision space-time. This new theory seems to be fully consistent with a 3-dimensional space-time, that is, three space dimensions and three time-dimensions, so some would call it six-dimensional. However, we have shown that collision-time and collision-length (space) are just two different sides of the same “coin” (space-time), so it is more intuitive to think of them as 3-dimensional space-time. In previous papers, we have not laid out a geometric coordinate system for our theory that also considers gravity, but we will do that here. We are pointing out that Einstein’s negative attitude towards relativistic mass can perhaps cause a weakness in the foundation of general relativity theory. When a relativistic mass is incorporated in the theory, this mass also seems to indicate one needs to move to three-dimensional space-time. Then, for example, our new theory matches fully up with all the properties of the Planck scale in relation to the mathematical properties of micro black holes, not only mathematically but also logically, something we demonstrate clearly that it is not the case of general relativity theory. Our new metric has many benefits as an alternative to the Schwarzschild metric and general relativity theory. It seems to be more consistent with the Planck units than the Schwarzschild metric. Most importantly, it seems to be fully consistent with a new quantum gravity theory that seems to unify gravity with quantum mechanics.展开更多
The paper introduces Planck scale into the Newtonian law of gravity for the model simplification. The terms of Newtonian gravitational force can be separated into two parts, namely Dark Matter and Dark Energy respecti...The paper introduces Planck scale into the Newtonian law of gravity for the model simplification. The terms of Newtonian gravitational force can be separated into two parts, namely Dark Matter and Dark Energy respectively. They are inverse relation to the distance. In the very early Universe, the novel model gives the sum “attractive force” of all matters in the cosmos. It indicates that Inflationary Universe firstly and then Universe expands slowly on condition that the accelerated velocity is slowing down for ever. In the galaxy scale, the paper gets the local “attractive force” of different galaxies by using the novel interaction model. It shows the intercommunity property in the formation process of different galaxies, where the matter suppresses firstly, sharp inflates secondly, slowly expands finally. Otherwise, the novel interaction model solves the problem about the flat rotation curves of galaxy by considering the change of the mass ratio of Dark Energy and Dark Matter. All results of simulation show that the core of our Universe is hollow now.展开更多
This paper discovers the secret codes of the scale distribution from Planck scale to the Sun-scale by using Planck length derived from three fundamental physics constants, i.e., gravitation constant G, light speed c a...This paper discovers the secret codes of the scale distribution from Planck scale to the Sun-scale by using Planck length derived from three fundamental physics constants, i.e., gravitation constant G, light speed c and Plank constant, and starting from the global consideration of treating the whole universe as a well unified entity in all scales. According to this symmetric scale distribution law of different scale regions: (a) we naturally give a possibility overcoming the difficulty of the desert effect between the grand unification scale and electroweak unification scale relevant to quarks and leptons, and it is really surprising to discover that the scales of quarks & electrons, protons & neutrons and atoms again all sequentially locate at the predicted points of the scale space;(b) we closely uncover the scale of the cells, which is the basic unit constructing the human bodies;(c) even the average height of human being is naturally deduced;(d) further, it is very surprising that the scales of the celestial bodies tightly related to us human beings, including the earth and the sun, also exactly fall at the predicted points in scale space in order. Therefore, all these scales with 105n cm order (n = 0, 1, 2, …, 9) above just give a proof of very key anthropic principle for whole mankind (which just makes the anthropic principle be reduced as anthropic theorem), i.e., matter stratums (a) and (b) are inorganic and organic bases of constructing human being respectively;matter stratum (c) is just human being;matter stratums (d) are the living environments of human being. Namely, everything is for or relevant to the existence of human being. Consequently, the experimentally checked scale ladder of well-known matter levels just coincides with the scale ladder predicted by the deduced distribution law. From Planck scale to the Sun scale, people may systematically build up the exact scientific theories corresponding ten matter stratums, may set up the different sciences among the different cross stratums, further, can systematically understand all the different sciences and their relations in the deepest way up to now.展开更多
The singularity at distance r → 0 at the center of a spherically symmetric non-rotating, uncharged mass of radius R, is considered here. Under inverse square law force, the Schwarzschild metric, needs to be modified,...The singularity at distance r → 0 at the center of a spherically symmetric non-rotating, uncharged mass of radius R, is considered here. Under inverse square law force, the Schwarzschild metric, needs to be modified, to include Newton’s Shell Theorem (NST). By including NST for r, both Schwarzschild singularity at r = 2GM/c2 and at r → 0 singularities are removed from the metric. Near R → 0, the question of maximal density is considered based on Schwarzschild’s modified metric, and compared to the quantum limit of maximal mass density put by Planck’s quantum-based universal units. It is asserted, that General relativity, when combined with Planck’s universal units, inevitably leads to quantization of gravity.展开更多
It is shown that the fine structure constant at Planck times tends to one as well as those of the weak and strong interactions. This results by constraining them at the Planck force. That seems to provide interesting ...It is shown that the fine structure constant at Planck times tends to one as well as those of the weak and strong interactions. This results by constraining them at the Planck force. That seems to provide interesting new results which confirm that at the beginning of space time (Planck scale) all fundamental forces converge to the same unit value.展开更多
We present a Machian model of Quantum Cosmology with full dark matter and light speed expansion and rotation. During galaxy formation and evolution, fraction of dark matter transforms to visible matter with a relation...We present a Machian model of Quantum Cosmology with full dark matter and light speed expansion and rotation. During galaxy formation and evolution, fraction of dark matter transforms to visible matter with a relation of the form, m_vis = constant * (m_dark)<sup>2/3</sup>. Using this relation and replacing MOND’s “critical acceleration” with “current cosmic maximum angular acceleration”, galactic flat rotation speed range of (50 to 500) km/sec can be fitted well. Estimated flat rotation speeds of DD168, Milky Way and UGC12591 are 49.96 km/sec, 199.66 km/sec and 521.75 km/sec respectively. Based on these striking coincidences, it is possible to say that, MOND’s approach is implicitly connected with cosmological estimation of 95% invisible matter. With reference to SPARC data for flat rotation speeds and current cosmic maximum angular acceleration, galactic total mass can be estimated. Considering galactic total mass, galactic visible mass and dark mass can be estimated. Proceeding further, galactic working radii, angular velocity and visible matter density can be estimated. Estimated Milky Way’s effective radius is 293 kpc. Even though, this model is free from “big bang”, “inflation”, “dark energy”, “flatness” and “red shift” issues, at 2.722 K, estimated present Hubble parameter is 66.24 km/sec/Mpc, cosmic radius is 146.3 times of the Hubble radius, angular velocity is 146.3 times lower than the Hubble parameter and cosmic age is 146.3 times of the Hubble age. With future observations and advanced telescopes, it may be possible to see far distant galaxies and very old stars far beyond the current observable cosmic radius.展开更多
We reason that in quantum cosmology there are two kinds of energy. The first is the ordinary energy of the quantum particle which we can measure. The second is the dark energy of the quantum wave by quantum duality. B...We reason that in quantum cosmology there are two kinds of energy. The first is the ordinary energy of the quantum particle which we can measure. The second is the dark energy of the quantum wave by quantum duality. Because measurement collapses the Hawking-Hartle quantum wave of the cosmos, dark energy cannot be detected or measured in any conventional manner. The quantitative results are confirmed using some exact solutions for the hydrogen atom. In particular the ordinary energy of the quantum particle is given by E(0) = (/2)(mc2) where is Hardy’s probability of quantum entanglement, =( - 1)/2 is the Hausdorff dimension of the zero measure thin Cantor set modeling the quantum particle, while the dark energy of the quantum wave is given by E(D) = (5/2)(mc2) where is the Hausdorff dimension of the positive measure thick empty Cantor set modeling the quantum wave and the factor five (5) is the Kaluza-Klein spacetime dimension to which the measure zero thin Cantor set D(0) = (0,) and the thick empty set D(-1) = (1,) must be lifted to give the five dimensional analogue sets namely and 5 needed for calculating the energy density E(0) and E(D) which together add to Einstein’s maximal total energy density E(total) = E(0) + E(D) = mc2 = E(Einstein). These results seem to be in complete agreement with the WMAP, supernova and recent Planck cosmic measurement as well as the 2005 quantum gravity experiments of V. V. Nesvizhersky and his associates. It also confirms the equivalence of wormhole solutions of Einstein’s equations and quantum entanglement by scaling the Planck scale.展开更多
文摘The paper presents an exact analysis leading to an accurate theoretical prediction of the amount of the mysteriously missing hypothetical dark energy density in the cosmos. The value found, namely 95.4915028% is in full agreement with earlier analysis, the WMAP and the supernova cosmic measurements. The work follows first the strategy of finding a critical point which separates a semi-classical regime from a fully relativistic domain given by topological unit interval velocity parameter then proceeds to wider aspects of a topological quantum field of fractal unit interval. This idea of a critical velocity parameter was first advanced by Sigalotti and Mejias in 2006 who proposed a critical value equal . A second interesting proposal made in 2012 by Hendi and Sharifzadeh set the critical point at 0.8256645. The present analysis is based upon a light cone velocity quantized coordinate. This leads to the same quantum relativity energy mass relation found in earlier publications by rescaling that of Einstein’s special relativity. Two effective quantum gravity formulae are obtained. The first is for the ordinary measurable energy of the quantum particle while the second is for dark energy density of the quantum wave which we cannot measure directly and we can only infer its existence from the measured accelerated expansion of the universe E(D) = where . The critical velocity parameter in this case arises naturally to be . The results so obtained are validated using a heuristic Lorentzian transformation. Finally the entire methodology is put into the wider perspective of a fundamental scaling theory for the Planck scale proposed by G. Gross.
文摘Following an inspiring idea due to D. Gross, we arrive at a topological Planck energy Ep and a corresponding topological Planck length effectively scaling the Planck scale from esoterically large and equally esoterically small numbers to a manageably where P(H) is the famous Hardy’s probability for quantum entanglement which amounts to almost 9 percent and Based on these results, we conclude the equivalence of Einstein-Rosen “wormhole” bridges and Einstein’s Podolsky-Rosen’s spooky action at a distance. In turn these results are shown to be consistent with distinguishing two energy components which results in , namely the quantum zero set particle component which we can measure and the quantum empty set wave component which we cannot measure , i.e. the missing dark energy. Together the two components add to where E is the total energy, m is the mass and c is the speed of light. In other words, the present new derivation of the world’s most celebrated formula explains in one stroke the two most puzzling problems of quantum physics and relativistic cosmology, namely the physicomathematical meaning of the wave function and the nature of dark energy. In essence they are one and the same when looked upon from the view point of quantum-fractal geometry.
文摘Using powerful concepts and tools borrowed from the seminal arsenal connecting physics fundamentals with esoteric set theoretical operations developed in recent years by Alexandria E-infinity theoretician M. S. El Naschie, this paper explores the deep implications of some of the dualities Dr El Naschie has identified and analyzed in his exposes, connecting them with our own Xonic Quantum Physics (XQP) which places dynamical action rather than spacetime and energy at the core of the System of the World.
文摘Haug has recently introduced a new theory of unified quantum gravity coined “<em>Collision Space-Time</em>”. From this new and deeper understanding of mass, we can also understand how a grandfather pendulum clock can be used to measure the world’s shortest time interval, namely the Planck time, indirectly, without any knowledge of G. Therefore, such a clock can also be used to measure the diameter of an indivisible particle indirectly. Further, such a clock can easily measure the Schwarzschild radius of the gravity object and what we will call “Schwarzschild time”. These facts basically prove that the Newton gravitational constant is not needed to find the Planck length or the Planck time;it is also not needed to find the Schwarzschild radius. Unfortunately, there is significant inertia towards new ideas that could significantly alter our perspective on the fundamentals in the current physics establishment. However, this situation is not new in the history of science. Still, the idea that the Planck time can be measured totally independently of any knowledge of Newton’s gravitational constant could be very important for moving forward in physics. Interestingly, an old instrument that today is often thought of as primitive instrument can measure the world’s shortest possible time interval. No atomic clock or optical clock is even close to be able to do this.
文摘The first part of this article develops [1] a closed universe model deploying by identical multiplication a Friedmann-Planck micro-universe;thus this one constitutes the grains of the vacuum of this universe. The quantum initial expansion of this is quadratic as a function of time. Using this model, calculating the density of matter at the present time gives a correct numerical result. The essential point is that during periods of expansion following the initial quadratic period, this model reveals a surprising phenomenon. The function expressing the radius curvature as a function of time depends on the individual mass of the heaviest elementary particles created at the end of the quadratic period. The model also leads to reflection on the dark matter. The second part imagines a new type of Big Rip based on the following hypothesis: when the acceleration of the Universe, caused by dark energy, reaches the value of Planck acceleration, destruction of the microscopic structure of the Universe occurs and is replaced by a macroscopic structure (photon spheres) identical to that of the initial Planck element. Thus a new Big Bang could begin on an immensely larger scale. This reasoning eventually leads to reflection on the origins of the Big Bang.
文摘We have recently suggested a new quantum gravity theory that can be unified with quantum mechanics. We have coined this theory collision space-time. This new theory seems to be fully consistent with a 3-dimensional space-time, that is, three space dimensions and three time-dimensions, so some would call it six-dimensional. However, we have shown that collision-time and collision-length (space) are just two different sides of the same “coin” (space-time), so it is more intuitive to think of them as 3-dimensional space-time. In previous papers, we have not laid out a geometric coordinate system for our theory that also considers gravity, but we will do that here. We are pointing out that Einstein’s negative attitude towards relativistic mass can perhaps cause a weakness in the foundation of general relativity theory. When a relativistic mass is incorporated in the theory, this mass also seems to indicate one needs to move to three-dimensional space-time. Then, for example, our new theory matches fully up with all the properties of the Planck scale in relation to the mathematical properties of micro black holes, not only mathematically but also logically, something we demonstrate clearly that it is not the case of general relativity theory. Our new metric has many benefits as an alternative to the Schwarzschild metric and general relativity theory. It seems to be more consistent with the Planck units than the Schwarzschild metric. Most importantly, it seems to be fully consistent with a new quantum gravity theory that seems to unify gravity with quantum mechanics.
文摘The paper introduces Planck scale into the Newtonian law of gravity for the model simplification. The terms of Newtonian gravitational force can be separated into two parts, namely Dark Matter and Dark Energy respectively. They are inverse relation to the distance. In the very early Universe, the novel model gives the sum “attractive force” of all matters in the cosmos. It indicates that Inflationary Universe firstly and then Universe expands slowly on condition that the accelerated velocity is slowing down for ever. In the galaxy scale, the paper gets the local “attractive force” of different galaxies by using the novel interaction model. It shows the intercommunity property in the formation process of different galaxies, where the matter suppresses firstly, sharp inflates secondly, slowly expands finally. Otherwise, the novel interaction model solves the problem about the flat rotation curves of galaxy by considering the change of the mass ratio of Dark Energy and Dark Matter. All results of simulation show that the core of our Universe is hollow now.
文摘This paper discovers the secret codes of the scale distribution from Planck scale to the Sun-scale by using Planck length derived from three fundamental physics constants, i.e., gravitation constant G, light speed c and Plank constant, and starting from the global consideration of treating the whole universe as a well unified entity in all scales. According to this symmetric scale distribution law of different scale regions: (a) we naturally give a possibility overcoming the difficulty of the desert effect between the grand unification scale and electroweak unification scale relevant to quarks and leptons, and it is really surprising to discover that the scales of quarks & electrons, protons & neutrons and atoms again all sequentially locate at the predicted points of the scale space;(b) we closely uncover the scale of the cells, which is the basic unit constructing the human bodies;(c) even the average height of human being is naturally deduced;(d) further, it is very surprising that the scales of the celestial bodies tightly related to us human beings, including the earth and the sun, also exactly fall at the predicted points in scale space in order. Therefore, all these scales with 105n cm order (n = 0, 1, 2, …, 9) above just give a proof of very key anthropic principle for whole mankind (which just makes the anthropic principle be reduced as anthropic theorem), i.e., matter stratums (a) and (b) are inorganic and organic bases of constructing human being respectively;matter stratum (c) is just human being;matter stratums (d) are the living environments of human being. Namely, everything is for or relevant to the existence of human being. Consequently, the experimentally checked scale ladder of well-known matter levels just coincides with the scale ladder predicted by the deduced distribution law. From Planck scale to the Sun scale, people may systematically build up the exact scientific theories corresponding ten matter stratums, may set up the different sciences among the different cross stratums, further, can systematically understand all the different sciences and their relations in the deepest way up to now.
文摘The singularity at distance r → 0 at the center of a spherically symmetric non-rotating, uncharged mass of radius R, is considered here. Under inverse square law force, the Schwarzschild metric, needs to be modified, to include Newton’s Shell Theorem (NST). By including NST for r, both Schwarzschild singularity at r = 2GM/c2 and at r → 0 singularities are removed from the metric. Near R → 0, the question of maximal density is considered based on Schwarzschild’s modified metric, and compared to the quantum limit of maximal mass density put by Planck’s quantum-based universal units. It is asserted, that General relativity, when combined with Planck’s universal units, inevitably leads to quantization of gravity.
文摘It is shown that the fine structure constant at Planck times tends to one as well as those of the weak and strong interactions. This results by constraining them at the Planck force. That seems to provide interesting new results which confirm that at the beginning of space time (Planck scale) all fundamental forces converge to the same unit value.
文摘We present a Machian model of Quantum Cosmology with full dark matter and light speed expansion and rotation. During galaxy formation and evolution, fraction of dark matter transforms to visible matter with a relation of the form, m_vis = constant * (m_dark)<sup>2/3</sup>. Using this relation and replacing MOND’s “critical acceleration” with “current cosmic maximum angular acceleration”, galactic flat rotation speed range of (50 to 500) km/sec can be fitted well. Estimated flat rotation speeds of DD168, Milky Way and UGC12591 are 49.96 km/sec, 199.66 km/sec and 521.75 km/sec respectively. Based on these striking coincidences, it is possible to say that, MOND’s approach is implicitly connected with cosmological estimation of 95% invisible matter. With reference to SPARC data for flat rotation speeds and current cosmic maximum angular acceleration, galactic total mass can be estimated. Considering galactic total mass, galactic visible mass and dark mass can be estimated. Proceeding further, galactic working radii, angular velocity and visible matter density can be estimated. Estimated Milky Way’s effective radius is 293 kpc. Even though, this model is free from “big bang”, “inflation”, “dark energy”, “flatness” and “red shift” issues, at 2.722 K, estimated present Hubble parameter is 66.24 km/sec/Mpc, cosmic radius is 146.3 times of the Hubble radius, angular velocity is 146.3 times lower than the Hubble parameter and cosmic age is 146.3 times of the Hubble age. With future observations and advanced telescopes, it may be possible to see far distant galaxies and very old stars far beyond the current observable cosmic radius.
文摘We reason that in quantum cosmology there are two kinds of energy. The first is the ordinary energy of the quantum particle which we can measure. The second is the dark energy of the quantum wave by quantum duality. Because measurement collapses the Hawking-Hartle quantum wave of the cosmos, dark energy cannot be detected or measured in any conventional manner. The quantitative results are confirmed using some exact solutions for the hydrogen atom. In particular the ordinary energy of the quantum particle is given by E(0) = (/2)(mc2) where is Hardy’s probability of quantum entanglement, =( - 1)/2 is the Hausdorff dimension of the zero measure thin Cantor set modeling the quantum particle, while the dark energy of the quantum wave is given by E(D) = (5/2)(mc2) where is the Hausdorff dimension of the positive measure thick empty Cantor set modeling the quantum wave and the factor five (5) is the Kaluza-Klein spacetime dimension to which the measure zero thin Cantor set D(0) = (0,) and the thick empty set D(-1) = (1,) must be lifted to give the five dimensional analogue sets namely and 5 needed for calculating the energy density E(0) and E(D) which together add to Einstein’s maximal total energy density E(total) = E(0) + E(D) = mc2 = E(Einstein). These results seem to be in complete agreement with the WMAP, supernova and recent Planck cosmic measurement as well as the 2005 quantum gravity experiments of V. V. Nesvizhersky and his associates. It also confirms the equivalence of wormhole solutions of Einstein’s equations and quantum entanglement by scaling the Planck scale.
