The paper “Quantum Field Derivation of the Superluminal Schrödinger Equation and Deuteron Potential” by E.J. Betinis, published in Physics Essays in 2002, explores the theoretical foundations and implications of superluminal quantum mechanics. Here’s a summary:

Abstract:

  • The paper builds on the author’s previous work on the superluminal Schrödinger equation, which addresses kinetic energy forms that do not become singular at the speed of light.
  • It re-derives this equation using quantum field theory approaches, including constructing Lagrangian and Hamiltonian densities.
  • The paper solves the superluminal Schrödinger equation for eigenfunctions and iteratively finds the superluminal potential for the deuteron.
  • The iterative method shows convergence, yielding a potential similar to subluminal potentials, supporting the validity of the superluminal theories.
  • The study implies that particles within the nucleus may exceed the speed of light, challenging traditional physics boundaries.

Key Points:

  1. Introduction:
    • The nuclear force is treated analogously to the electrostatic force in Yukawa’s theory, focusing on spherical symmetry to find superluminal eigenfunctions and potentials.
    • The study proposes a boson, with mass equal to the deuteron’s reduced mass, is exchanged between nucleons, leading to the nuclear force and potential.
  2. Superluminal Schrödinger Equation:
    • The superluminal form of kinetic energy does not become singular at v=cv = c and increases indefinitely as velocity increases.
    • The paper shows that Lagrangian and Hamiltonian densities can re-derive this superluminal Schrödinger equation via quantum field theory.
  3. Eigenfunctions and Potentials:
    • The spherically symmetric superluminal Schrödinger equation is solved for eigenfunctions.
    • An iterative Laplace transform method finds the superluminal potential for the deuteron, with convergence observed after the fourth iteration.
  4. Comparison with Subluminal Potentials:
    • The superluminal potentials closely resemble those found by subluminal approaches, like the Reid potential.
    • The potentials have a “hard” core nature, indicating nucleons are not point particles but have a finite size.
  5. Implications for Nuclear Physics:
    • The superluminal approach suggests the existence of particles moving faster than light within the nucleus.
    • If experimentally verified, this challenges the speed-of-light limitation in other physics branches.

Conclusion:

  • The paper demonstrates the feasibility of constructing a superluminal Schrödinger equation through quantum field theory.
  • The derived potentials support the concept of superluminal interactions in nuclear physics.
  • This work opens the possibility for future studies and experimental verification of faster-than-light particles in the nucleus.

Overall, Betinis’ work extends quantum mechanics into the superluminal regime, providing theoretical tools and results that could reshape our understanding of nuclear forces and particle physics.