The hydrodynamics of quantum spacetime - The minimal essentials of a new quantum theory
Keywords:
Hydrodynamics of quantum spacetime, new quantum theory
Abstract
This is a somewhat long and extended abstract of a paper that presents a relatively short and concise review of a new quantum mechanics. This new theory is anchored in the hydrodynamical paradigm first introduced by L. Prandtl in his famous boundary layer theory. In addition the original ideas of L. Prandtl are expanded to encompass and combine with ideas from von Neumann-Connes’ pointless noncommutative geometry, Penrose-like fractal tiling cosmology, E-infinity Cantorian theory and the platonic golden mean number system based transfinite set theory. Proceeding in this way it is reasoned that while the pre-quantum particle and the pre-quantum wave may be best described as a multi dimensional zero set and empty set respectively in stringent mathematical terms, in physical terms however the new picture of a bluff body modelling the quantum particle and a surrounding Prandtl boundary layer modelling the quantum wave is virtually a quantum jump in our understanding of quantum physics in general and quantum wave collapse in particular. In that respect the work has some resemblance to that pilot wave theory of de Broglie and Bohm but is by no means more than that. The work is naturally connected to very specialized hydrodynamics related fields apart of Batchelor’s law and the important earthquake engineering subject of liquefaction which is of paramount importance for designing buildings with high resistance to earthquakes among other things. The concerted use of all these mathematical, experimental and number theoretical tools combine in the present paper to give a new synthesis for a deeper understanding of what we label the classical and quantum world predominantly for simplicity rather than logical, mandatory reasons.
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References
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2. L. Marek-Crnjac, On El Naschie’s fractal-Cantorian spacetime and dark energy – A tutorial review. Natural Science, 7(13), 2015, pp. 581-598.
3. L. Marek-Crnjac, J. H. He, An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy. International Journal of Astronomy and Astrophysics,3(4), 2013, pp. 464-471.
4. L. Marek-Crnjac, M.S. El Naschie and J.H. He, Chaotic fractals at the root of relativistic quantum physics and cosmology. International Journal of Modern Nonlinear Theory and Application, 2(1), 2013, pp.78-88.
5. M. A. Helal, L. Marek-Crnjac, J.H. He, The threepage guide to the most important results of M. S. El Naschie’s research in E-infinity quantum physics and cosmology. Open Journal of Microphysics, 3(4), 2013, pp. 141-145.
6. J. H. He, A tutorial review on fractal spacetime and fractional calculus. International Journal of Theoretical Physics, 53(11), 2014, pp. 3698-3718.
7. J. H. He and L. Marek-Crnjac,Mohamed El Naschie’s Revision of Albert Einstein’s E = m0c2: A Definite Resolution of The Mystery of The Missing Dark Energy of The Cosmos. International Journal of Modern Nonlinear Theory and Application,2(1), 2013, pp. 55-59.
8. M.S. El Naschie, L. Marek-Crnjac, and J.H. He, On the mathematical philosophy of being and nothingness in quantum physics. Fractal Space-Time & Non-Commutative Geometry in Quantum and High Energy Physics, 2(2), 2012, pp.103-106.
9. J. H. He, New promises and future challenges of fractal calculus from two-scale thermodynamics to fractal variational principles. Thermal Sciences, 24(2), 2020, Part A. pp. 659-681.
10. S. Olsen, L. Marek-Crnjac, Ji-Huan He and M.S. El Naschie, A grand unification of science, art and consciousness: Rediscovering the Pythagorean-Plato’s golden mean number system. Journal of Progressive Research in Mathematics, 16(2), 2020, pp. 2888-2931.
11. S. Olsen, Golden ratio beauty as scientific function. Lebenswelt Aesthetics and Philosophy of Experience, No. 11, 2018, pp. 46-60.
12. A.Stakhov (assisted by Scott Olsen), The Mathematics of Harmony, World Scientific, Singapore, 2009.
13. Scott Olsen, The Indefinite Dyad: Uncovering Plato’s Second Principle. Nexus Network Journal, 2002, pp. 97-110.
14. S. Olsen, The Golden Section: Nature’s Greatest Secret. Wooden Books (Walker & Co), New York, USA, 2006.
15. M.S. El Naschie, Platonic quantum set theory proposal and fractal-Cantorian Heterotic Kaluza-Klein spacetime. Global Journal of Science Frontier Research A – Physics & Space Science, 20(3), 2020, pp. 29-37.
16. M. S. El Naschie, Fluid turbulence road to quantum Cantorianspacetime via nested solitoniceddies chaos implied by Batchelor’s law – A possible rationale for the mysterious fine tuning of the cosmos. International Journal of Applied Science and Mathematics, 7(4), 2020, pp. 98-108.
17. M. S. El Naschie, Fluid turbulence Batchelor’s law implies spacetime unification of classical and quantum physics, International Journal of Applied Science and Mathematics, 7(3), 2020, pp. 85-91.
18. M. S. El Naschie, Demonstrating the basic equivalence of a wide class of fundamental theories of high energy physics and quantum cosmology via transfinite number theoretical fine-tuning. International Journal of Innovation in Science & Mathematics, 8(4), 2020, pp. 145-153.
19. M.S. El Naschie, A review of E-infinity and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals, 19(1), 2004, pp. 209-236.
20. M.S. El Naschie, Superstrings, knots and noncommutative geometry in E-infinity space. International Journal of Theoretical Physics, 37(12), 1998, pp. 2935-2951.
21. J. H. He, Application of E-infinity theory to turbulence. Chaos, Solitons & Fractals, 30(2), 2006, pp. 506-511.
22. M.S. El Naschie, On turbulence and complex dynamics in a four dimensional Peano-Hilbert space. Journal of The Franklin Institute, 330, 1993, pp. 183-198.
23. M.S. El Naschie, Kolmogorov turbulence, Apollonian fractals and the Cantorian model of quantum spacetime. Chaos, Solitons & Fractals, 7(1), 1996, pp. 147-149.
24. M. Agop, Cantorian E-infinity spacetime, a hydrodynamical model and unified super conductivity. Chaos, Solitons & Fractals, 16(2), 2003, pp. 321-338.
25. M. Agop, P. Nica, P.D. Ionnou, O. Malandraki, El Naschie’s E-infinity spacetime, hydrodynamical model of scale relativity theory and some applications. Chaos, Solitons & Fractals, 34(5), 2007, pp. 1704-1723.
26. M. S. El Naschie, An elastic model for Lagrangian turbulence and diffusion. ActaPhysicaPolonica A, 6(79), 1991, pp. 757-764.
27. D. Wang, Wave-particle duality” and soil liquefaction in geotechnical engineering. IOP Conference Series: Materials Science and Engineering, 250, 2017. 3rd International workshop on Materials Science & Engineering, September, 2017, China.
28. M. Agop, A. Harabagu, P. Nica, Wave particle duality through a dydrodynamic model of the fractal spacetime theory. ActaPhysicaPolonica – series A, 113(6), 2008, pp. 1571-1588.
29. I. Gottlieb, M. Agop, G. Ciobanu, A. Stue, E-infinity space-time and new results in scale relativity theories. Chaos, Solitons & Fractals, 30(2), 2006, pp. 380-398.
30. M. Agop, P.D. Ioannou, C.G. Buzea, P. Nica, Hydrodynamic formulation of scale relativity theory and unified super conductivity by means of fractal strings. Super Conductivity, 390(1), 2003, pp. 37-55.
31. M. Agop, P.D. Ioannou, P. Nica, G. Gallusca,El Naschie’s coherence on subquantum medium.Chaos, Solitons & Fractals, 23(5), 2005, pp. 1497-1500.
32. M. Agop, P.D. Ioannou, P. Nica, El Naschie’sCantorian strings and duality in Weyl-Dirac theory. Chaos, Solitons & Fractals, 19(5), 2004, pp. 1057-1070.
33. M.S. El Naschie, S. Al Athel, T. Kapitaniak, A note on elastic turbulence and diffusion. Journal of Sound and Vibration, 155(3), 1992, pp. 515-522.
34. T. Kapitaniak, Soliton chaos in elastic chains and turbulence. Hamiltonian Mechanics, NATA Science Series B, 331, 1994, pp. 341-344.
35. M.S. El Naschie and S.S.E.H. Elnashaie, On the connection between fluid and elastostatical turbulence in Hamiltonian and flatter sets, ZAMM, 70(3), 1993, pp. 182-184.
36. T Kapitaniak and J. Brindly (Editors), Chaos and Nonlinear Mechanics, 1994, pp. 1-322. World Scientific, Singapore. Proceedings of Euromech Colloquium, 308 ‘Chaos and noise in dynamical systems’.
37. J. Brindley, T. Kapitaniak and M.S. El Naschie, Analytical condition for strange chaotic and non-chaotic attractors of the quasi periodically forced van der Pol equation. Physica D, Nonlinear Phenomena, 51(1-3), 1991, pp. 28-38.
38. J. H. He, A fractal variational theory for one dimensional compressible flow in microgravity space. Fractals, 28(2), 2020.
39. J. H. He, Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics. International Journal of Turbo and Jet Engines, 4(1), 1997.
40. L. Biferale and ItamarProcaccia, Anistrotropy in turbulent flow and turbulent transport. Physics Reports, 414(2-3), 2005, pp. 43-164.
41. H. E.Hentchel and I. Procaccia, Fractal nature of turbulence as manifested in turbulent diffusion. Physics Review A, 27(2), 1993, pp. 1266.
42. D. Khomenko, V. L’Vov, A. Pomyalov and ItamarProcaccia, Counterflow induced decoupling in super fluid turbulence. Physical Review B 93.1, 014516, 2016.
43. L. Kondaurova, V. L’Vov, AnazaPomyalov and ItamarProcaccia, Structure of quantum vortex tangle in He(4) counterflows turbulence. Physical Review B 89, 014502, 2014.
44. G.N. Ord, Bohr, Bohm and the entwined path. Chaos, Solitons & Fractals, 25(4), 2005, pp. 769-774.
45. G.N. Ord, Gravity and the spiral model. Chaos, Solitons & Fractals, 10(2), 1999, pp. 499-512.
46. P. Weibel, G. Ord, O. Rössler (Editors): Spacetime Physics and Fractality. Festschrift in honour of Mohamed El Naschie on the occasion of his 60th birthday. Springer, Vienna-New York (2005).
47. L. Nottale and T. Lehner, Turbulence and scale relativity. Physics of Fluids, 31, 105109, 2019.
48. M.S. El Naschie, Speculation in science and technology: Is the quantum wave nothing more than Prandtl’s boundary layer. International Journal of Engineering Innovation and Research, 9(3), 2020, pp. 137-141.
49. M.Heideger, Sein und Zeit (Beingand Time), Max Niemeyer Verlag, Tubingen, Germany, 2006.
50. M. S. El Naschie, Elements of a new set theory based quantum mechanics with applications in high energy quantum physics and cosmology. International Journal of High Energy Physics, 24, 2017, pp.65-74.
51. M.S. El Naschie, On certain ‘empty’ Cantor sets and their dimensions. Chaos, Solitons & Fractals, 4(2), 1994, pp. 293-296.
52. M.S. El Naschie: On the universality class of all universality classes and E-infinity spacetime physics. Chaos, Solitons & Fractals, 32(3), 2007, pp. 927-936.
53. M. S. El Naschie, From Pythagorean mathematical music theory to the density of the dark energy sector of the cosmos and unification of art with science. International Journal of Engineering Innovation and Research, 8(6), 2019, pp. 249-261.
54. M.S. El Naschie, Simulating the quantum Universe via the golden mean number expert-like -system, International Journal of Artificial Intelligence and Mechatronics, 7(4), 2019, pp.15-18.
55. W. Heisenberg, Der Teil und das Ganze. Piper-Verlag, Munich, Germany, 1969.
56. J. Polchinski, String Theory Vol. I, Cambridge University Press, Cambridge, 1999. (See in particular pp. 22, equation (1.3.32)).
57. M. S. El Naschie, S. Olsen, J. H. He, S. Nada, L. Marek-Crnjac, A. Helal: On the Need for Fractal Logic in High Energy Quantum Physics. International Journal of Modern Nonlinear Theory and Application, 21(3), 2012, pp. 84-92.
58. M. S. El Naschie, Computational fractal logic for quantum physics and cosmology. American Journal of Astronomy and Astrophysics, 4(4), 2016, pp. 42-53.
59. M.S. El Naschie, On a fractal version of Witten's M-theory. International Journal of Astronomy and Astrophysics, 6, 2016, pp.135-144.
60. M.S. El Naschie, Symmetria massima of the fractal M-theory via the golden mean number system-A new language for a deep dialogue between man and nature. International Journal of Artificial Intelligence and Mechatronics, 7(3), 2018, pp.11-14.
61. M. S. El Naschie, A combined Heterotic string and Kähler manifold elucidation of ordinary energy, dark matter, Olbers’s paradox and pure dark energy density of the cosmos. Journal of Modern Physics, 8(7), 2017, pp. 1101-1118.
62. X. S. Yang, Multiple integrals and special integrals. Science Direct, 2017. https://www.sciencedirect.com/topics/mathematics/gaussian-integral/pdf
63. I. Kant, Der Kategorishe Imperative. Philosophie der Fürüng, Springer, Berlin, Germany. 2013.
64. A.J. Babchin, and M.S. El Naschie, On the real Einstein beauty E= kmc2. World Journal of Condensed Matter Physics, 6(1), 2016, pp.1-6.
65. M.S. El Naschie, From Nikolay Umov E= kmc2 via Albert Einstein's E= mc2 to the dark energy density of the cosmos E=(21/22) mc2. World Journal of Mechanics, 8, 2018, pp.73-81.
66. M. S. El Naschie, Scott Olsen, M.A. Helal, L. Marek-Crnjac and S. Nada, On the missing link between cosmology and biology. International Journal of Innovation in Science and Mathematics, 6(1), 2018, pp. 11-13.
67. M.Salvam, Self-organized criticality and predictability in atmospheric flow – The quantum world of clouds and rain. Springer Atmospheric Sciences, 2017, pp. 75-106.
68. M. Salvam and S. Fadnavis, Superstrings, Cantorian-fractal space-time and quantum-like chaos in atmospheric flow. Chaos, Solitons & Fractals, 10(8), 1999, pp. 1321-1334.
69. M. Salvam and S. Fadnavis, Cantorian-fractal space-time, quantum-like chaos and scale relativity in atmospheric flow. Chaos, Solitons & Fractals, 10(9), 1999, pp. 1579-1582.
70. A.Valentini, On the pilot-wave theory of classical, quantum and sub-quantum physics. PHD Thesis, International School of Advanced Studies, Trieste, Italy (Supervisor Prof. D.W. Sciama), 1991-1992.
2. L. Marek-Crnjac, On El Naschie’s fractal-Cantorian spacetime and dark energy – A tutorial review. Natural Science, 7(13), 2015, pp. 581-598.
3. L. Marek-Crnjac, J. H. He, An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy. International Journal of Astronomy and Astrophysics,3(4), 2013, pp. 464-471.
4. L. Marek-Crnjac, M.S. El Naschie and J.H. He, Chaotic fractals at the root of relativistic quantum physics and cosmology. International Journal of Modern Nonlinear Theory and Application, 2(1), 2013, pp.78-88.
5. M. A. Helal, L. Marek-Crnjac, J.H. He, The threepage guide to the most important results of M. S. El Naschie’s research in E-infinity quantum physics and cosmology. Open Journal of Microphysics, 3(4), 2013, pp. 141-145.
6. J. H. He, A tutorial review on fractal spacetime and fractional calculus. International Journal of Theoretical Physics, 53(11), 2014, pp. 3698-3718.
7. J. H. He and L. Marek-Crnjac,Mohamed El Naschie’s Revision of Albert Einstein’s E = m0c2: A Definite Resolution of The Mystery of The Missing Dark Energy of The Cosmos. International Journal of Modern Nonlinear Theory and Application,2(1), 2013, pp. 55-59.
8. M.S. El Naschie, L. Marek-Crnjac, and J.H. He, On the mathematical philosophy of being and nothingness in quantum physics. Fractal Space-Time & Non-Commutative Geometry in Quantum and High Energy Physics, 2(2), 2012, pp.103-106.
9. J. H. He, New promises and future challenges of fractal calculus from two-scale thermodynamics to fractal variational principles. Thermal Sciences, 24(2), 2020, Part A. pp. 659-681.
10. S. Olsen, L. Marek-Crnjac, Ji-Huan He and M.S. El Naschie, A grand unification of science, art and consciousness: Rediscovering the Pythagorean-Plato’s golden mean number system. Journal of Progressive Research in Mathematics, 16(2), 2020, pp. 2888-2931.
11. S. Olsen, Golden ratio beauty as scientific function. Lebenswelt Aesthetics and Philosophy of Experience, No. 11, 2018, pp. 46-60.
12. A.Stakhov (assisted by Scott Olsen), The Mathematics of Harmony, World Scientific, Singapore, 2009.
13. Scott Olsen, The Indefinite Dyad: Uncovering Plato’s Second Principle. Nexus Network Journal, 2002, pp. 97-110.
14. S. Olsen, The Golden Section: Nature’s Greatest Secret. Wooden Books (Walker & Co), New York, USA, 2006.
15. M.S. El Naschie, Platonic quantum set theory proposal and fractal-Cantorian Heterotic Kaluza-Klein spacetime. Global Journal of Science Frontier Research A – Physics & Space Science, 20(3), 2020, pp. 29-37.
16. M. S. El Naschie, Fluid turbulence road to quantum Cantorianspacetime via nested solitoniceddies chaos implied by Batchelor’s law – A possible rationale for the mysterious fine tuning of the cosmos. International Journal of Applied Science and Mathematics, 7(4), 2020, pp. 98-108.
17. M. S. El Naschie, Fluid turbulence Batchelor’s law implies spacetime unification of classical and quantum physics, International Journal of Applied Science and Mathematics, 7(3), 2020, pp. 85-91.
18. M. S. El Naschie, Demonstrating the basic equivalence of a wide class of fundamental theories of high energy physics and quantum cosmology via transfinite number theoretical fine-tuning. International Journal of Innovation in Science & Mathematics, 8(4), 2020, pp. 145-153.
19. M.S. El Naschie, A review of E-infinity and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals, 19(1), 2004, pp. 209-236.
20. M.S. El Naschie, Superstrings, knots and noncommutative geometry in E-infinity space. International Journal of Theoretical Physics, 37(12), 1998, pp. 2935-2951.
21. J. H. He, Application of E-infinity theory to turbulence. Chaos, Solitons & Fractals, 30(2), 2006, pp. 506-511.
22. M.S. El Naschie, On turbulence and complex dynamics in a four dimensional Peano-Hilbert space. Journal of The Franklin Institute, 330, 1993, pp. 183-198.
23. M.S. El Naschie, Kolmogorov turbulence, Apollonian fractals and the Cantorian model of quantum spacetime. Chaos, Solitons & Fractals, 7(1), 1996, pp. 147-149.
24. M. Agop, Cantorian E-infinity spacetime, a hydrodynamical model and unified super conductivity. Chaos, Solitons & Fractals, 16(2), 2003, pp. 321-338.
25. M. Agop, P. Nica, P.D. Ionnou, O. Malandraki, El Naschie’s E-infinity spacetime, hydrodynamical model of scale relativity theory and some applications. Chaos, Solitons & Fractals, 34(5), 2007, pp. 1704-1723.
26. M. S. El Naschie, An elastic model for Lagrangian turbulence and diffusion. ActaPhysicaPolonica A, 6(79), 1991, pp. 757-764.
27. D. Wang, Wave-particle duality” and soil liquefaction in geotechnical engineering. IOP Conference Series: Materials Science and Engineering, 250, 2017. 3rd International workshop on Materials Science & Engineering, September, 2017, China.
28. M. Agop, A. Harabagu, P. Nica, Wave particle duality through a dydrodynamic model of the fractal spacetime theory. ActaPhysicaPolonica – series A, 113(6), 2008, pp. 1571-1588.
29. I. Gottlieb, M. Agop, G. Ciobanu, A. Stue, E-infinity space-time and new results in scale relativity theories. Chaos, Solitons & Fractals, 30(2), 2006, pp. 380-398.
30. M. Agop, P.D. Ioannou, C.G. Buzea, P. Nica, Hydrodynamic formulation of scale relativity theory and unified super conductivity by means of fractal strings. Super Conductivity, 390(1), 2003, pp. 37-55.
31. M. Agop, P.D. Ioannou, P. Nica, G. Gallusca,El Naschie’s coherence on subquantum medium.Chaos, Solitons & Fractals, 23(5), 2005, pp. 1497-1500.
32. M. Agop, P.D. Ioannou, P. Nica, El Naschie’sCantorian strings and duality in Weyl-Dirac theory. Chaos, Solitons & Fractals, 19(5), 2004, pp. 1057-1070.
33. M.S. El Naschie, S. Al Athel, T. Kapitaniak, A note on elastic turbulence and diffusion. Journal of Sound and Vibration, 155(3), 1992, pp. 515-522.
34. T. Kapitaniak, Soliton chaos in elastic chains and turbulence. Hamiltonian Mechanics, NATA Science Series B, 331, 1994, pp. 341-344.
35. M.S. El Naschie and S.S.E.H. Elnashaie, On the connection between fluid and elastostatical turbulence in Hamiltonian and flatter sets, ZAMM, 70(3), 1993, pp. 182-184.
36. T Kapitaniak and J. Brindly (Editors), Chaos and Nonlinear Mechanics, 1994, pp. 1-322. World Scientific, Singapore. Proceedings of Euromech Colloquium, 308 ‘Chaos and noise in dynamical systems’.
37. J. Brindley, T. Kapitaniak and M.S. El Naschie, Analytical condition for strange chaotic and non-chaotic attractors of the quasi periodically forced van der Pol equation. Physica D, Nonlinear Phenomena, 51(1-3), 1991, pp. 28-38.
38. J. H. He, A fractal variational theory for one dimensional compressible flow in microgravity space. Fractals, 28(2), 2020.
39. J. H. He, Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics. International Journal of Turbo and Jet Engines, 4(1), 1997.
40. L. Biferale and ItamarProcaccia, Anistrotropy in turbulent flow and turbulent transport. Physics Reports, 414(2-3), 2005, pp. 43-164.
41. H. E.Hentchel and I. Procaccia, Fractal nature of turbulence as manifested in turbulent diffusion. Physics Review A, 27(2), 1993, pp. 1266.
42. D. Khomenko, V. L’Vov, A. Pomyalov and ItamarProcaccia, Counterflow induced decoupling in super fluid turbulence. Physical Review B 93.1, 014516, 2016.
43. L. Kondaurova, V. L’Vov, AnazaPomyalov and ItamarProcaccia, Structure of quantum vortex tangle in He(4) counterflows turbulence. Physical Review B 89, 014502, 2014.
44. G.N. Ord, Bohr, Bohm and the entwined path. Chaos, Solitons & Fractals, 25(4), 2005, pp. 769-774.
45. G.N. Ord, Gravity and the spiral model. Chaos, Solitons & Fractals, 10(2), 1999, pp. 499-512.
46. P. Weibel, G. Ord, O. Rössler (Editors): Spacetime Physics and Fractality. Festschrift in honour of Mohamed El Naschie on the occasion of his 60th birthday. Springer, Vienna-New York (2005).
47. L. Nottale and T. Lehner, Turbulence and scale relativity. Physics of Fluids, 31, 105109, 2019.
48. M.S. El Naschie, Speculation in science and technology: Is the quantum wave nothing more than Prandtl’s boundary layer. International Journal of Engineering Innovation and Research, 9(3), 2020, pp. 137-141.
49. M.Heideger, Sein und Zeit (Beingand Time), Max Niemeyer Verlag, Tubingen, Germany, 2006.
50. M. S. El Naschie, Elements of a new set theory based quantum mechanics with applications in high energy quantum physics and cosmology. International Journal of High Energy Physics, 24, 2017, pp.65-74.
51. M.S. El Naschie, On certain ‘empty’ Cantor sets and their dimensions. Chaos, Solitons & Fractals, 4(2), 1994, pp. 293-296.
52. M.S. El Naschie: On the universality class of all universality classes and E-infinity spacetime physics. Chaos, Solitons & Fractals, 32(3), 2007, pp. 927-936.
53. M. S. El Naschie, From Pythagorean mathematical music theory to the density of the dark energy sector of the cosmos and unification of art with science. International Journal of Engineering Innovation and Research, 8(6), 2019, pp. 249-261.
54. M.S. El Naschie, Simulating the quantum Universe via the golden mean number expert-like -system, International Journal of Artificial Intelligence and Mechatronics, 7(4), 2019, pp.15-18.
55. W. Heisenberg, Der Teil und das Ganze. Piper-Verlag, Munich, Germany, 1969.
56. J. Polchinski, String Theory Vol. I, Cambridge University Press, Cambridge, 1999. (See in particular pp. 22, equation (1.3.32)).
57. M. S. El Naschie, S. Olsen, J. H. He, S. Nada, L. Marek-Crnjac, A. Helal: On the Need for Fractal Logic in High Energy Quantum Physics. International Journal of Modern Nonlinear Theory and Application, 21(3), 2012, pp. 84-92.
58. M. S. El Naschie, Computational fractal logic for quantum physics and cosmology. American Journal of Astronomy and Astrophysics, 4(4), 2016, pp. 42-53.
59. M.S. El Naschie, On a fractal version of Witten's M-theory. International Journal of Astronomy and Astrophysics, 6, 2016, pp.135-144.
60. M.S. El Naschie, Symmetria massima of the fractal M-theory via the golden mean number system-A new language for a deep dialogue between man and nature. International Journal of Artificial Intelligence and Mechatronics, 7(3), 2018, pp.11-14.
61. M. S. El Naschie, A combined Heterotic string and Kähler manifold elucidation of ordinary energy, dark matter, Olbers’s paradox and pure dark energy density of the cosmos. Journal of Modern Physics, 8(7), 2017, pp. 1101-1118.
62. X. S. Yang, Multiple integrals and special integrals. Science Direct, 2017. https://www.sciencedirect.com/topics/mathematics/gaussian-integral/pdf
63. I. Kant, Der Kategorishe Imperative. Philosophie der Fürüng, Springer, Berlin, Germany. 2013.
64. A.J. Babchin, and M.S. El Naschie, On the real Einstein beauty E= kmc2. World Journal of Condensed Matter Physics, 6(1), 2016, pp.1-6.
65. M.S. El Naschie, From Nikolay Umov E= kmc2 via Albert Einstein's E= mc2 to the dark energy density of the cosmos E=(21/22) mc2. World Journal of Mechanics, 8, 2018, pp.73-81.
66. M. S. El Naschie, Scott Olsen, M.A. Helal, L. Marek-Crnjac and S. Nada, On the missing link between cosmology and biology. International Journal of Innovation in Science and Mathematics, 6(1), 2018, pp. 11-13.
67. M.Salvam, Self-organized criticality and predictability in atmospheric flow – The quantum world of clouds and rain. Springer Atmospheric Sciences, 2017, pp. 75-106.
68. M. Salvam and S. Fadnavis, Superstrings, Cantorian-fractal space-time and quantum-like chaos in atmospheric flow. Chaos, Solitons & Fractals, 10(8), 1999, pp. 1321-1334.
69. M. Salvam and S. Fadnavis, Cantorian-fractal space-time, quantum-like chaos and scale relativity in atmospheric flow. Chaos, Solitons & Fractals, 10(9), 1999, pp. 1579-1582.
70. A.Valentini, On the pilot-wave theory of classical, quantum and sub-quantum physics. PHD Thesis, International School of Advanced Studies, Trieste, Italy (Supervisor Prof. D.W. Sciama), 1991-1992.
Published
2020-11-02
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Marek-Crnjac, L., & El Naschie, M. (2020). The hydrodynamics of quantum spacetime - The minimal essentials of a new quantum theory. Journal of Progressive Research in Mathematics, 17(1), 41-53. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1949
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