We introduce an ultra high energy combined KAM-Rindler fractal spacetime quantum manifold, which increasingly resembles Einstein’s smooth relativity spacetime, with decreasing energy. That way we derive an effective ...We introduce an ultra high energy combined KAM-Rindler fractal spacetime quantum manifold, which increasingly resembles Einstein’s smooth relativity spacetime, with decreasing energy. That way we derive an effective quantum gravity energy-mass relation and compute a dark energy density in complete agreement with all cosmological measurements, specifically WMAP and type 1a supernova. In particular we find that ordinary measurable energy density is given by E1= mc2 /22 while the dark energy density of the vacuum is given by E2 = mc2 (21/22). The sum of both energies is equal to Einstein’s energy E = mc2. We conclude that E= mc2 makes no distinction between ordinary energy and dark energy. More generally we conclude that the geometry and topology of quantum entanglement create our classical spacetime and glue it together and conversely quantum entanglement is the logical consequence of KAM theorem and zero measure topology of quantum spacetime. Furthermore we show via our version of a Rindler hyperbolic spacetime that Hawking negative vacuum energy, Unruh temperature and dark energy are different sides of the same medal.展开更多
With a four-dimensional symplectic map we study numerically the break-up of three-frequency Kolmogorov-Arnold-Moser(KAM)tori.The locations and stabilities of a sequence of periodic orbits,whose winding numbers approac...With a four-dimensional symplectic map we study numerically the break-up of three-frequency Kolmogorov-Arnold-Moser(KAM)tori.The locations and stabilities of a sequence of periodic orbits,whose winding numbers approach the irrational winding number of the KAM torus,are examined.The break-up of quadratic frequency tori is characterized as the exponential growth of the residue means of the convergent periodic orbits.Critical parameters of the break-up of tori with different winding numbers are calculated,which shows that the spiral mean torus is the most robust one in our model.展开更多
1 Introduction Imagery of the Western United States typically evokes vast wheat fields,cowboys,and rolling mountain valleys.Few would associate the American West with Chinese medicine.This article describes a remote t...1 Introduction Imagery of the Western United States typically evokes vast wheat fields,cowboys,and rolling mountain valleys.Few would associate the American West with Chinese medicine.This article describes a remote town called John Day,which is located in a mountainous terrain in Oregon,and presents the remarkable story of the Kam Wah Chung Museum(Fig.1).展开更多
文摘We introduce an ultra high energy combined KAM-Rindler fractal spacetime quantum manifold, which increasingly resembles Einstein’s smooth relativity spacetime, with decreasing energy. That way we derive an effective quantum gravity energy-mass relation and compute a dark energy density in complete agreement with all cosmological measurements, specifically WMAP and type 1a supernova. In particular we find that ordinary measurable energy density is given by E1= mc2 /22 while the dark energy density of the vacuum is given by E2 = mc2 (21/22). The sum of both energies is equal to Einstein’s energy E = mc2. We conclude that E= mc2 makes no distinction between ordinary energy and dark energy. More generally we conclude that the geometry and topology of quantum entanglement create our classical spacetime and glue it together and conversely quantum entanglement is the logical consequence of KAM theorem and zero measure topology of quantum spacetime. Furthermore we show via our version of a Rindler hyperbolic spacetime that Hawking negative vacuum energy, Unruh temperature and dark energy are different sides of the same medal.
基金Supported by Hong Kong Baptist University Faculty Research Grants,Hong Kong Grant Council Grantsthe National Natural Science Foundation of China under Grant Nos.19903001 and 19633010the Special Funds for Major State Basic Research Projects.
文摘With a four-dimensional symplectic map we study numerically the break-up of three-frequency Kolmogorov-Arnold-Moser(KAM)tori.The locations and stabilities of a sequence of periodic orbits,whose winding numbers approach the irrational winding number of the KAM torus,are examined.The break-up of quadratic frequency tori is characterized as the exponential growth of the residue means of the convergent periodic orbits.Critical parameters of the break-up of tori with different winding numbers are calculated,which shows that the spiral mean torus is the most robust one in our model.
文摘1 Introduction Imagery of the Western United States typically evokes vast wheat fields,cowboys,and rolling mountain valleys.Few would associate the American West with Chinese medicine.This article describes a remote town called John Day,which is located in a mountainous terrain in Oregon,and presents the remarkable story of the Kam Wah Chung Museum(Fig.1).
基金Supported by NSFC(No.11126100)the Youth Science and Technology Innovation Fund of Nanjing Agricultural University(No.KJ2010025)the Fundamental Research Fund for the Central Universities(No.Y0201100265)
