[Paper Review] Random Shooting of Entangled Particles in Vacuum

Е. А. Новиков|ArXiv.org|Jul 23, 2007

Experimental and Theoretical Physics Studies3 references3 citations

TL;DR

This paper proposes that entangled particles in vacuum exhibit random shooting motion due to quantum vacuum-induced tachyonic impulses, modeled via imaginary diffusion in the Schrödinger equation and Wigner function formalism. The key result is that initial quantum correlations lead to high-velocity random trajectories, suggesting a potential mechanism for energy extraction via vacuum interactions.

ABSTRACT

The effect of random shooting of particles is considered on the basis of solution of the Schrodinger equation and in terms of the Wigner function. Two-particles description shows, in particular, that initial correlation leads to high velocities of particles. This could be a potential mechanism for obtaining energy. Evolution of the n-particle probability distribution is descibed analytically.

Motivation & Objective

• To investigate the dynamics of entangled particles in vacuum without external potentials, focusing on quantum vacuum-induced effects.
• To explain the emergence of random shooting motion in quantum systems through the Schrödinger equation and imaginary diffusion (ID).
• To analyze how initial quantum correlations between particles lead to enhanced velocities and non-trivial evolution of probability distributions.
• To provide a unified interpretation of quantum trajectories using both the Schrödinger and Wigner formalisms, emphasizing hidden complex trajectories.
• To explore the potential for energy extraction from vacuum fluctuations via correlation-induced high-velocity motion.

Proposed method

• Solves the free Schrödinger equation with imaginary diffusion coefficient q = ℏ/(2m), modeling vacuum-induced tachyonic impulses.
• Uses Fourier transforms to derive the time-evolved wave function Ψ(t,x), showing Gaussian form with complex variance.
• Derives the real-space probability density P(t,x) = ΨΨ* as a time-evolving Gaussian with quadratic dispersion, indicating random shooting with constant random velocity.
• Introduces complex-Gaussian stochastic processes to interpret the wave function as an effective probability density for complex trajectories.
• Applies the Wigner function formalism to describe the phase-space evolution, showing that P(t,x) arises from momentum integration of W(t,x,p).
• Generalizes results to n-particle systems using correlation matrices and covariance evolution, with velocity dependence on initial correlation structure.

Experimental results

Research questions

• RQ1 How does the quantum vacuum induce random shooting motion in entangled particles when no external potential is present?
• RQ2 What is the role of initial quantum correlations in generating high-velocity particle motion in vacuum?
• RQ3 How do the Schrödinger and Wigner formalisms jointly explain the emergence of random shooting trajectories?
• RQ4 Can the random shooting mechanism, driven by vacuum fluctuations, serve as a viable pathway for energy extraction?
• RQ5 How does the evolution of correlation coefficients between particles affect their collective velocity and dispersion in time?

Key findings

• The probability density P(t,x) evolves as a Gaussian with variance a² + w²t², where w = q/a, indicating motion with constant random velocity u, leading to random shooting x(t) = x₀ + ut.
• Initial quantum correlations between particles lead to a velocity enhancement factor proportional to (1 - ρ₀²)⁻¹, where ρ₀ is the initial correlation coefficient.
• The correlation coefficient evolves from ρ₀ to -ρ₀ asymptotically, indicating that the vacuum actively inverts imposed correlations.
• The effective velocity w is inversely proportional to particle mass, implying higher velocities for lighter particles, consistent with the uncertainty principle.
• The Wigner function formalism confirms the random shooting interpretation, with W(t,x,p) translating to a moving Gaussian in phase space, and P(t,x) recovered by momentum integration.
• For n ≥ 3 particles, the velocity of random shooting depends on the full structure of the initial correlation matrix, with the inverse covariance matrix amplifying motion when correlations are strong.