Zhai Xiaobo, Huang Changyu, Ren Gang
The Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA, 94720, USA.
College of Science, Xi'an University of Science and Technology, Xi'an, 710054, Shaanxi, China.
Sci Rep. 2020 Oct 26;10(1):18281. doi: 10.1038/s41598-020-75211-5.
One potential pathway to find an ultimate rule governing our universe is to hunt for a connection among the fundamental equations in physics. Recently, Ren et al. reported that the harmonic maps with potential introduced by Duan, named extended harmonic mapping (EHM), connect the equations of general relativity, chaos and quantum mechanics via a universal geodesic equation. The equation, expressed as Euler-Lagrange equations on the Riemannian manifold, was obtained from the principle of least action. Here, we further demonstrate that more than ten fundamental equations, including that of classical mechanics, fluid physics, statistical physics, astrophysics, quantum physics and general relativity, can be connected by the same universal geodesic equation. The connection sketches a family tree of the physics equations, and their intrinsic connections reflect an alternative ultimate rule of our universe, i.e., the principle of least action on a Finsler manifold.
寻找支配我们宇宙的终极规则的一条潜在途径是探寻物理学基本方程之间的联系。最近，任等人报告称，段引入的带势调和映射，即扩展调和映射（EHM），通过一个通用测地线方程将广义相对论、混沌和量子力学的方程联系起来。该方程表示为黎曼流形上的欧拉 - 拉格朗日方程，它是从最小作用量原理推导出来的。在此，我们进一步证明，包括经典力学、流体物理学、统计物理学、天体物理学、量子物理学和广义相对论在内的十多个基本方程都可以通过同一个通用测地线方程联系起来。这种联系勾勒出了物理方程的族谱，它们的内在联系反映了我们宇宙的另一种终极规则，即在芬斯勒流形上的最小作用量原理。
