论文标题
使用爱德华·尼尔森（Edward Nelson
Classical Elastic Two-Particle Collision Energy Conservation using Edward Nelson's Energy, Double Diffusion and Special Relativity
论文作者
论文摘要
本文表明，爱德华·尼尔森（Edward Nelson）的随机力学方法可以从两个经典的弹性碰撞颗粒中得出，并满足保持碰撞动量保留方程的粒子。经典弹性动量碰撞表达的特性决定了这两个颗粒的完整Edward Nelson Energy Collision Energy。这种经典的总能量表达不需要统计期望，因为没有为能量定义的过程，并且完美地模拟了主要和入射粒子速度。量子力学可以通过将入射粒子建模为非随机过程，使用随机过程对主要粒子的前进，碰撞后和向后填充速度进行建模。这列出了Schroedinger方程的准确，尼尔森在1966年提出的方式除了扩散常数外。在这种情况下，平均能量是在时间上保存的，并且使用统计方法相关的系统的正向，碰撞后和向后的固定速度是相关的。如果入射粒子没有潜在的入射粒子运动的其他约束，则会导致另一个Schroedinger方程。最后，在适当的条件下，将表明碰撞颗粒在特殊相对论中满足Minkowski度量。最后一个示例显示了如何使用此能量表达的细节对重力进行量化。
The present paper shows that Edward Nelson's stochastic mechanics approach for quantum mechanics can be derived from the two classical elastically colliding particles with masses M and m satisfying a collision momentum preserving equation. The properties of the classical elastic momentum collision expression determine the full Edward Nelson energy collision energy for both particles. This classical total energy expression does not require a statistical expectation since no process was defined for the energy and it models the main and incident particle velocities perfectly. Quantum mechanics can be obtained by modelling the incident particle as a non-random potential using stochastic processes modelling the forward, post-collision and backward pre-collision velocities of the main particle. This presents the Schroedinger equation exactly the way that Nelson proposed in 1966 except for the diffusion constant. In this case the average energy is conserved in time and the forward, post-collision and backward pre-collision velocities of the system are related using statistical methods. If the incident particle does not have a potential the additional constraints for the movement of the incident particle leads to another Schroedinger equation. Finally, under suitable conditions it will be shown that the colliding particles satisfy Minkowski metric in special relativity. This last example shows how gravity can be quantized using details of this energy expression.
