The Quantum Newton's Law

Relativistic Quantum Newton's Law and photon trajectories

Using the relativistic quantum Hamilton-Jacobi equation within the framework of the equivalence postulate, and grounding one self on both relativistic and quantum Lagrangians, we construct a Lagrangian of relativistic quantum system in one dimension and derive a third order equation of motion representing a first integral of the relativistic quantum Newton's law. Then, we investigate the free particle case and establish the photon's trajectories.

Third Newton Law in the Mean and Perturbations of Noise

We analyze an isothermal Brownian motion of particle ensembles in the Smoluchowski approximation. Contrary to standard procedures, the environmental recoil effects associated with locally induced heat flows are not completely disregarded. The main technical tool in the study of such weakly-out-of equilibrium systems is a consequent exploitation of the Hamilton-Jacobi equation. The third Newton law in the mean is utilised to generate diffusion-type processes which are either anomalous (enhanced), or generically non-dispersive.

A Method for Deriving the Dirac Equation from the Relativistic Newton's Second Law

The derivation becomes possible when we find a new formalism which connects the relativistic mechanics with the quantum mechanics. In this paper, we explore the quantum wave nature from the Newtonian mechanics by using a concept: velocity field. At first, we rewrite the relativistic Newton's second law as a field equation in terms of the velocity field, which directly reveals a new relationship connecting to the quantum mechanics. Next, we show that the Dirac equation can be derived from the field equation in a rigorous and consistent manner.

Quantum Mechanics from Newton's Second Law and the Canonical Commutation Relation [X,P]=i

Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian or Lagrangian formulations of mechanics. Here, we first derive the existing Heisenberg equations of motion from Newton's laws and the uncertainty principle using only the equations $F=\frac{dP}{dt}$, $P=m\frac{dV}{dt}$, and $\left[X,P\right]=i$. Then, a new expression for the propagator is derived that makes a connection between time evolution in quantum mec…

On the microscopic basis of Newton's law of cooling and beyond

The microscopic basis of Newton's law of cooling and its modification when the difference in temperature between the system and the surroundings is very large is discussed. When the system of interest is interacting with a small bath, the effect of the dynamical evolution of the bath variables is important to find out its dynamical feedback on the system. As in the usual system-bath approach, however, the bath is finally considered to be in thermal equilibrium and thereby provides an effective generalization of the Born-Markov master equation. It is shown that the cooling at early time is fast…

源于牛顿第三定律的量子概率玻恩（Born）规则

The Born rule for quantum probabilities from Newton's third law

本研究针对玻恩规则缺乏公认推导的问题，构建物理图景提出粒子与测量装置作用等效于产生波函数镜像，借牛顿第三定律致镜像相位反转，自然推导出量子概率的玻恩规则。

Microscopic foundations of the Second Law of Thermodynamics within Nonunitary Newtonian Gravity

The quest for a microscopic foundation of Thermodynamics is addressed within the Nonunitary Newtonian Gravity model through the study of a specific closed system, namely a three-dimensional harmonic nanocrystal. A numerical calculation of the nanocrystal von Neumann entropy as a function of time is performed, showing a sharp monotonic increase, followed by a stabilization at late times. This behavior is consistent with the emergence of a micro-canonical ensemble within the initial energy levels, signaling, in this way, the establishment of a non-unitary gravity-induced thermal equilibrium.