[Paper Review] Space-time Symmetry Transformations of Elementary Particles realized in Optics Laboratories

D. Han, Y. S. Kim+1 more|ArXiv.org|Apr 19, 1999

Experimental and Theoretical Physics Studies4 references3 citations

TL;DR

This paper demonstrates that space-time symmetry transformations of elementary particles—specifically Wigner rotations and Iwasawa decompositions—can be experimentally realized using optical setups based on polarization optics. By leveraging the six-parameter Lorentz group structure in polarization systems, the authors construct optical filters that mimic internal space-time symmetries of massive and massless particles, enabling laboratory simulation of relativistic quantum symmetries.

ABSTRACT

The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations can generate group representations applicable to different branches of physics. It is pointed out that polarization optics can be formulated in terms of the six-parameter Lorentz group. This allows us to construct optical instruments corresponding to the subgroups of the Lorentz groups. It is shown possible to produce combinations of optical filters that exhibit transformations corresponding to Wigner rotations and Iwasawa decompositions, which are manifestations of the internal space-time symmetries of massive and massless particles.

Motivation & Objective

• To establish a bridge between relativistic quantum mechanics and optical systems by exploiting shared mathematical structures in space-time symmetries.
• To demonstrate that optical polarization setups can emulate the internal space-time symmetries of elementary particles, such as Wigner rotations and Iwasawa decompositions.
• To show that the Lorentz group's subgroup structure can be physically realized in optical laboratories using combinations of waveplates and polarizers.
• To provide a laboratory-based model for studying the symmetry properties of massive and massless particles using accessible optical components.
• To unify the description of harmonic oscillators and LCR circuits with relativistic particle symmetries through group-theoretic formalism in optics.

Proposed method

• Utilize the six-parameter Lorentz group to describe polarization transformations in optics, mapping its subgroups to physical optical components.
• Construct optical filter combinations (e.g., waveplates and polarizers) that realize specific Lorentz group transformations, such as Wigner rotations.
• Apply the Iwasawa decomposition of the Lorentz group to design optical systems that simulate the decomposition of boosts and rotations in relativistic particle states.
• Use the closed commutation relations of the Lorentz algebra to model the symmetry transformations of elementary particles in optical systems.
• Leverage the mathematical equivalence between second-order differential equations in harmonic oscillators and LCR circuits to extend the analogy to relativistic symmetries in optics.
• Map the internal space-time symmetries of massive and massless particles onto polarization states via group representation theory applied to optical systems.

Experimental results

Research questions

• RQ1 Can space-time symmetry transformations of elementary particles be physically realized in optical laboratories?
• RQ2 How can the Lorentz group's subgroups be implemented using optical components like waveplates and polarizers?
• RQ3 To what extent do optical polarization systems reproduce the Wigner rotation and Iwasawa decomposition phenomena of relativistic particles?
• RQ4 What is the role of the six-parameter Lorentz group in unifying the description of harmonic oscillators, LCR circuits, and relativistic particle symmetries in optics?
• RQ5 Can optical setups serve as analog simulators for the internal space-time symmetries of massive and massless elementary particles?

Key findings

• Optical systems based on polarization optics can simulate the internal space-time symmetries of elementary particles, including Wigner rotations.
• The Iwasawa decomposition of the Lorentz group can be physically realized in optical setups using combinations of waveplates and polarizers.
• The six-parameter Lorentz group provides a unifying framework that connects polarization optics, harmonic oscillators, and LCR circuits through shared group-theoretic structures.
• Optical filters can be engineered to reproduce the transformation properties of massive and massless particles under Lorentz boosts and rotations.
• The mathematical structure of the Lorentz group allows for the experimental realization of abstract relativistic symmetry operations in a controlled laboratory environment.
• The study establishes a direct correspondence between the symmetry transformations of elementary particles and measurable optical phenomena, enabling analog simulation of relativistic quantum systems.