Abstract We propose a space-time interaction principle (StIP) which states any particle with mass m will involve a random motion without friction, due to random impacts from space-time. Every impact changes the amount \hbar for an action of the particle. According to the principle, firstly, we prove the interaction coefficient must be \Re=\frac{\hbar}{2m_{ST}} deriving from Langevin's equation to the corresponding Fokker-Planck Hamiltonian, where m_{ST} is a space-time sensible mass of the particle. We can derive that an equation of motion for the particle will be the Schr\ddot{o} dinger equation, and prove that the space-time sensible mass m_{ST} reduce to the inertial mass in the non-relativistic quantum mechanics. Secondly, we show that there must exist the smallest mass \bar{m}_{ST} as the minimum of space-time sensible mass, provided the speed of light in vacuum as the maximum speed due to the postulation of special relativity. Furthermore, we estimate a magnitude of this \bar{m}_{ST} from microwave background radiation. Thirdly, an interpretation of Heisenberg's uncertainty principle is suggested, with a stochastic origin of Feynman's path integral formalism. It is shown that we can construct a physical picture distinct from Copenhagen interpretation, and reinvestigate the nature of space-time and reveal the origin of quantum behaviours from the materialistic point of view.
The Feynman path integral formalism for non-relativistic quantum mechanics is revisited. A comparison is made with cases of light propagation (Huygens' principle) and Brownian motion. The difficulties for a physical model applying Feynman's formalism are pointed out. A reformulation is proposed, where the transition probability of a particle from one space-time point to another one is the sum of probabilities of the possible paths. As an application, Born approximation for scattering is derived within the formalism, which suggests an interpretation involving the stochastic motion of a particle rather than the square of a wavelike amplitude.
Since Newton's time, deterministic causality has been considered a crucial prerequisite in any fundamental theory in physics. In contrast, the present work investigates stochastic dynamical models for motion in one spatial dimension, in which Newtonian mechanics becomes an emergent property: We present a coherent theory in which a Hamilton-Jacobi equation (HJE) emerges in a description of the evolution of entropy
−ϕ(x,t)=εlog(Probability) of a system under observation and in the limit of large information extent
ε−1 in homogeneous space and time. The variable
ϕ represents a non-random high-order statistical concept that is distinct from probability itself as
ε=0; the HJE embodies an emergent law of deterministic causality in continuous space and time with an Imaginary Scale symmetry
(t,x,ϕ)↔(it,ix,−iϕ).
ϕ(x,t) exhibits a nonlinear wave phenomenon with a mathematical singularity in finite time, overcoming which we introduce viscosity
ε(∂2ϕ/∂x2) and wave
iε(∂2ϕ/∂x2) perturbations, articulating dissipation and conservation, which break the Imaginary Scale symmetry: They lead to the Brownian motion and Schrödinger's equation of motion, respectively. Last but not least, Lagrange's action in classical mechanics acquires an entropic interpretation and Hamilton's principle is established.