[Paper Review] To Enjoy the Morning Flower in the Evening -- Is Special Relativity a Classical Theory?

Guang-jiong Ni|ArXiv.org|Mar 14, 1998

Relativity and Gravitational Theory3 references3 citations

TL;DR

This paper investigates whether special relativity (SR) can be considered a classical theory by postulating that space-time inversion is equivalent to particle-antiparticle transformation. Using this principle, the author derives a relativistic modification of the stationary Schrödinger equation, suggesting that SR's foundations may be reinterpreted through quantum field theory principles, implying a deeper unification between relativity and quantum mechanics at a fundamental level.

ABSTRACT

The relation between the special relativity and quantum mechanics is discussed. Based on the postulate that space-time inversion is equavalent to particle-antiparticle transformation, the essence of special relativity is explored and the relativistic modification on Stationary Schrödinger Equation is derived.

Motivation & Objective

• To examine the foundational status of special relativity within the framework of quantum mechanics.
• To investigate whether space-time inversion symmetry implies particle-antiparticle duality.
• To derive a relativistic correction to the stationary Schrödinger equation based on this duality postulate.
• To assess whether special relativity emerges from quantum field principles rather than being purely classical.
• To explore the unification potential between relativity and quantum theory through symmetry principles.

Proposed method

• Postulating that space-time inversion is equivalent to particle-antiparticle transformation as a fundamental symmetry.
• Applying this duality principle to derive the relativistic form of the stationary Schrödinger equation.
• Using Lorentz invariance and CPT symmetry as guiding principles in the derivation.
• Analyzing the implications of this transformation for the structure of relativistic quantum mechanics.
• Employing theoretical field-theoretic reasoning to connect space-time symmetries with quantum particle-antiparticle behavior.
• Formulating the relativistic Hamiltonian and wave equation using the duality postulate.

Experimental results

Research questions

• RQ1 Can special relativity be understood as emerging from quantum field symmetries rather than classical spacetime?
• RQ2 Does space-time inversion symmetry imply a fundamental equivalence to particle-antiparticle transformation?
• RQ3 How does the stationary Schrödinger equation transform under this duality principle?
• RQ4 What is the relativistic modification of the Schrödinger equation derived from this symmetry?
• RQ5 Does this approach suggest a deeper unification between quantum mechanics and special relativity?

Key findings

• The paper derives a relativistic modification of the stationary Schrödinger equation based on the postulate of space-time inversion equivalence to particle-antiparticle transformation.
• The derived equation exhibits Lorentz invariance and incorporates relativistic energy-momentum relations.
• The transformation symmetry implies that antiparticles can be interpreted as particles moving backward in time, consistent with Feynman-Stueckelberg interpretation.
• The approach suggests that special relativity is not purely classical but emerges from quantum field symmetry principles.
• The formalism provides a unified framework where relativistic quantum mechanics arises naturally from CPT-like symmetries.
• The result implies that the classical nature of special relativity may be an emergent property rather than fundamental.