A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) ...A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) how a subsequent 2-1 mapping (projection) of P16 onto a 8D-hyperplane might furnish the 2160 vertices of the uniform 241 polytope in 8-dimensions, and such that one can capture the chain sequence of polytopes 241,231,221,211in D=8,7,6,5dimensions, leading, respectively, to the sequence of Coxeter groups E8,E7,E6,SO(10)which are putative GUT group candidates. An embedding of the E8⊕E8and E8⊕E8⊕E8lattice into the Barnes-Wall Λ16 and Leech Λ24 lattices, respectively, is explicitly shown. From the 16D lattice E8⊕E8one can generate two separate families of Elser-Sloane 4D quasicrystals (QC’s) with H4 (icosahedral) symmetry via the “cut-and-project” method from 8D to 4D in each separate E8 lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC’s Q×Qspanning an 8D space. Similarly, from the 24D lattice E8⊕E8⊕E8one can generate the Cartesian product of three Elser-Sloane 4D quasicrystals (QC’s) Q×Q×Qwith H4 symmetry and spanning a 12D space.展开更多
The multiverse is a hypothesis created to solve certain problems in cosmology. Currently, this scheme is still largely ad hoc, rather than derived from fundamental laws and principles. Because of this, the predictive ...The multiverse is a hypothesis created to solve certain problems in cosmology. Currently, this scheme is still largely ad hoc, rather than derived from fundamental laws and principles. Because of this, the predictive power of this theory is rather limited. Furthermore, there are concerns that this theory will make it impossible to calculate some measured quantities, such as the masses of quarks and the electron. In this paper, we will show that a new development in string theory, the universal wave function interpretation of string theory, provides a way to derive the mathematical expression of the multiverse. We will demonstrate that the Weyl invariance existing in string theory indicates that our observed universe is a projection from a hologram. We will present how the laws of physics can be derived from this fact. Furthermore, we suggest it may also provide a way to calculate the masses of fundamental particles such as quarks and the electron.展开更多
The understanding about the creation of our universe is explored in many philosophies, natural sciences, religions, ideologies, traditions, and disciplines. Current natural science cannot answer this question at the f...The understanding about the creation of our universe is explored in many philosophies, natural sciences, religions, ideologies, traditions, and disciplines. Current natural science cannot answer this question at the fundamental level. In this work, we combine the ancient Chinese Tao wisdom about the creation with quantum physics. We propose that everything comes from the emptiness. Our universe is manifested from the emptiness through two pairs of duality measurements： space and time duality pair and inclusion and exclusion duality pair. From this understanding, we are able to derive one mathematic formula describing our universe. It also yields a new metaphysical approach to derive and interpret string theory as well as produce more testable predictions from string theory. This work gives a new way to understand and mathematically describe how our universe is created and evolved. It provides another way to comprehend the meaning and function of space and time. It indicates that our universe is manifested from the emptiness through human actions. Space and time is a pair of duality action and codes that help manifest our universe. It provides answer to an important philosophical question about whether and why we can understand and mathematically describe our universe.展开更多
Inflation is the most commonly accepted theory in cosmology to explain why the universe appears flat, homogeneous, and isotropic, as well as the origin of the large-scale structure of the cosmos and why no magnetic mo...Inflation is the most commonly accepted theory in cosmology to explain why the universe appears flat, homogeneous, and isotropic, as well as the origin of the large-scale structure of the cosmos and why no magnetic monopoles have been detected. However, so far, the origin of the inflation epoch and what is the hypothetical field, the inflation, giving rise to inflation, remains unknown. String theory is one of the promising candidates for the grand unification theory. Grand unification theory is to use one mathematic formula to describe everything. In this work, we study the inflation scheme in a new development in string theory, UWFIST （universal wave function interpretation of string theory）. We show that from UWFIST we can derive from the fundamental theory that the long-range vibration is the possible candidate of inflation. We estimate the vacuum energy created by the long-range vibration and show that it can indeed drive the inflation.展开更多
We reexamine the dynamical generation of mass for fermions charged under various Lie groups with equal charge and mass at a high Grand Uni?cation scale, extending the Renormalization Group Equations in the perturbativ...We reexamine the dynamical generation of mass for fermions charged under various Lie groups with equal charge and mass at a high Grand Uni?cation scale, extending the Renormalization Group Equations in the perturbative regime to two loops and matching to the Dyson-Schwinger Equations in the strong coupling regime.展开更多
文摘A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) how a subsequent 2-1 mapping (projection) of P16 onto a 8D-hyperplane might furnish the 2160 vertices of the uniform 241 polytope in 8-dimensions, and such that one can capture the chain sequence of polytopes 241,231,221,211in D=8,7,6,5dimensions, leading, respectively, to the sequence of Coxeter groups E8,E7,E6,SO(10)which are putative GUT group candidates. An embedding of the E8⊕E8and E8⊕E8⊕E8lattice into the Barnes-Wall Λ16 and Leech Λ24 lattices, respectively, is explicitly shown. From the 16D lattice E8⊕E8one can generate two separate families of Elser-Sloane 4D quasicrystals (QC’s) with H4 (icosahedral) symmetry via the “cut-and-project” method from 8D to 4D in each separate E8 lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC’s Q×Qspanning an 8D space. Similarly, from the 24D lattice E8⊕E8⊕E8one can generate the Cartesian product of three Elser-Sloane 4D quasicrystals (QC’s) Q×Q×Qwith H4 symmetry and spanning a 12D space.
文摘The multiverse is a hypothesis created to solve certain problems in cosmology. Currently, this scheme is still largely ad hoc, rather than derived from fundamental laws and principles. Because of this, the predictive power of this theory is rather limited. Furthermore, there are concerns that this theory will make it impossible to calculate some measured quantities, such as the masses of quarks and the electron. In this paper, we will show that a new development in string theory, the universal wave function interpretation of string theory, provides a way to derive the mathematical expression of the multiverse. We will demonstrate that the Weyl invariance existing in string theory indicates that our observed universe is a projection from a hologram. We will present how the laws of physics can be derived from this fact. Furthermore, we suggest it may also provide a way to calculate the masses of fundamental particles such as quarks and the electron.
文摘The understanding about the creation of our universe is explored in many philosophies, natural sciences, religions, ideologies, traditions, and disciplines. Current natural science cannot answer this question at the fundamental level. In this work, we combine the ancient Chinese Tao wisdom about the creation with quantum physics. We propose that everything comes from the emptiness. Our universe is manifested from the emptiness through two pairs of duality measurements： space and time duality pair and inclusion and exclusion duality pair. From this understanding, we are able to derive one mathematic formula describing our universe. It also yields a new metaphysical approach to derive and interpret string theory as well as produce more testable predictions from string theory. This work gives a new way to understand and mathematically describe how our universe is created and evolved. It provides another way to comprehend the meaning and function of space and time. It indicates that our universe is manifested from the emptiness through human actions. Space and time is a pair of duality action and codes that help manifest our universe. It provides answer to an important philosophical question about whether and why we can understand and mathematically describe our universe.
文摘Inflation is the most commonly accepted theory in cosmology to explain why the universe appears flat, homogeneous, and isotropic, as well as the origin of the large-scale structure of the cosmos and why no magnetic monopoles have been detected. However, so far, the origin of the inflation epoch and what is the hypothetical field, the inflation, giving rise to inflation, remains unknown. String theory is one of the promising candidates for the grand unification theory. Grand unification theory is to use one mathematic formula to describe everything. In this work, we study the inflation scheme in a new development in string theory, UWFIST （universal wave function interpretation of string theory）. We show that from UWFIST we can derive from the fundamental theory that the long-range vibration is the possible candidate of inflation. We estimate the vacuum energy created by the long-range vibration and show that it can indeed drive the inflation.
基金Spanish Grant MINECO:FPA2016-75654-C2-1-P and Carried out in the Inspiring Atmosphere of the IPARCOS Institute for Particles and Cosmology
文摘We reexamine the dynamical generation of mass for fermions charged under various Lie groups with equal charge and mass at a high Grand Uni?cation scale, extending the Renormalization Group Equations in the perturbative regime to two loops and matching to the Dyson-Schwinger Equations in the strong coupling regime.
