静电引力振荡器
Electrostatic-gravitational oscillator
摘要：
本文用相对论性运动方程研究了两个带相同电荷的粒子在库仑排斥力和引力作用下的一维运动。我们发现，当两个粒子的静止质量足够小（~ 0.4 eV/c ~ 2）和初始库仑势能足够高（~ mpc ~ 2，其中mp是质子质量）时，那么由相对论粒子速度产生的强引力吸引力足以抵消库仑排斥力，并导致两个粒子稳定的周期运动。通过研究粒子的德布罗意波长和克莱因-戈登方程以及薛定谔方程，证明了这种静止质量等于质子静止质量的受限振荡态的产生与量子力学是一致的。结果表明，引力常量可以用质子的质量和电荷、真空介电常数、普朗克常量和光速来表示。它还表明，重力可以导致限制轻（~ 0.1 eV/c2）中性粒子（中微子），或对中性和带电轻粒子，在圆形轨道的大小为0.9 fm和周期10-24 s形成束缚中性或带电强子状态。
英文摘要：
We examine the one-dimensional motion of two similarly charged particles under the influence of only two forces, i.e. their Coulombic repulsion and their gravitational attraction, using the relativistic equation of motion. We find that when the rest mass of the two particles is sufficiently small (~ 0.4 eV/c2) and the initial Coulombic potential energy is sufficiently high (~ mpc2, where mp is the proton mass), then the strong gravitational attraction resulting from the relativistic particle velocities suffices to counterbalance the Coulombic repulsion and to cause stable periodic motion of the two particles. The creation of this confined oscillatory state, with a rest mass equal to that of a proton, is shown to be consistent with quantum mechanics by examining the particle de Broglie wavelength and the Klein-Gordon and Schrodinger equations. It is shown that the gravitational constant can be expressed in terms of the proton mass and charge, the vacuum dielectric constant, the Planck constant and the speed of light. It is also shown that gravity can cause confinement of light (~ 0.1 eV/c2) neutral particles (neutrinos), or pairs of a neutral and a charged light particle, in circular orbits of size 0.9 fm and period 10-24 s forming bound neutral or charged hadron states.
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