In this paper, a new symmetry and its conserved quantities of a mechanical system in phase space are studied. The defition of this new symmetry, i.e., a unified one is presented, and the criterion of this symmetry is ...In this paper, a new symmetry and its conserved quantities of a mechanical system in phase space are studied. The defition of this new symmetry, i.e., a unified one is presented, and the criterion of this symmetry is also given. The Noether, the generalized Hojman and the Mei conserved quantities of the unified symmetry of the system are obtained. The unified symmetry contains the Noether, the Lie and the Mei symmetries, and has more generalized significance.展开更多
The consequence of the wave-particle duality is a pointer to the fact that everything in the universe, including light and gravity, can be described in terms of particles. These particles have a property called spin. ...The consequence of the wave-particle duality is a pointer to the fact that everything in the universe, including light and gravity, can be described in terms of particles. These particles have a property called spin. What the spin of a particle really tells us is what the particle looks like from different directions, in other words it is nothing more than a geometrical property. The motivation for this work stems from the fact that geometry has always played a fundamental role in physics, macroscopic and microscopic, relativistic and non-relativistic. Our belief is that if a GUT （Grand Unified Theory） is to be established at all, then geometry must be the common thread connecting all the different aspects of the already known theories. We propose a new way to visualize the concept of four-dimensional space-time in simple geometrical terms. It is observed that our time frame becomes curved, just as the space-frame, in the presence of a massive gravitating body. Specifically, in the event horizon of a black hole, where time seems to grind to a halt for external observers, the time frame appears to curve in on itself, forming an imaginary loop. This results in extreme time dilation, due to the strong gravitational field. Finally we adopt a descriptive view of a GUT called Quantum Necklace GUT which attempts to connect gravity together the other three fundamental forces of nature, namely the strong, weak and electromagnetic interactions.展开更多
文摘In this paper, a new symmetry and its conserved quantities of a mechanical system in phase space are studied. The defition of this new symmetry, i.e., a unified one is presented, and the criterion of this symmetry is also given. The Noether, the generalized Hojman and the Mei conserved quantities of the unified symmetry of the system are obtained. The unified symmetry contains the Noether, the Lie and the Mei symmetries, and has more generalized significance.
文摘The consequence of the wave-particle duality is a pointer to the fact that everything in the universe, including light and gravity, can be described in terms of particles. These particles have a property called spin. What the spin of a particle really tells us is what the particle looks like from different directions, in other words it is nothing more than a geometrical property. The motivation for this work stems from the fact that geometry has always played a fundamental role in physics, macroscopic and microscopic, relativistic and non-relativistic. Our belief is that if a GUT （Grand Unified Theory） is to be established at all, then geometry must be the common thread connecting all the different aspects of the already known theories. We propose a new way to visualize the concept of four-dimensional space-time in simple geometrical terms. It is observed that our time frame becomes curved, just as the space-frame, in the presence of a massive gravitating body. Specifically, in the event horizon of a black hole, where time seems to grind to a halt for external observers, the time frame appears to curve in on itself, forming an imaginary loop. This results in extreme time dilation, due to the strong gravitational field. Finally we adopt a descriptive view of a GUT called Quantum Necklace GUT which attempts to connect gravity together the other three fundamental forces of nature, namely the strong, weak and electromagnetic interactions.
