[Paper Review] Relativistic field-theory spin and momentum in water waves

Konstantin Y. Bliokh, H. Punzmann+3 more|arXiv (Cornell University)|Sep 7, 2020

Orbital Angular Momentum in Optics32 references4 citations

TL;DR

This paper demonstrates that the relativistic field-theory concept of spin, as defined by the Belinfante-Rosenfeld construction, emerges naturally in classical water surface waves. By linking the canonical momentum to the generalized Stokes drift and spin to subwavelength particle motion in inhomogeneous wave fields, the study reveals observable mechanical manifestations of abstract relativistic quantities in a classical system, establishing a direct experimental and theoretical connection between quantum-field concepts and macroscopic wave dynamics.

ABSTRACT

Spin is a fundamental yet somewhat enigmatic intrinsic angular-momentum property of quantum particles or fields, which appears within relativistic field theories. The spin density in wave fields is described by the theoretical Belinfante-Rosenfeld construction based on the difference between the canonical and kinetic energy-momentum tensors. These quantities have an abstract mathematical character and are usually considered as non-observable per se. Here we demonstrate, both theoretically and experimentally, that the Belinfante-Rosenfeld construction naturally arises in purely classical gravity (water surface) waves. There, the canonical momentum is associated with the generalized Stokes-drift phenomenon, while the spin is generated by subwavelength circular motion of water particles in inhomogeneous wave fields. Thus, we reveal the canonical spin and momentum in water waves and directly observe these fundamental relativistic field-theory properties as microscopic mechanical properties of particles in a classical wave system. Our findings shed light onto the nature of spin and momentum in wave fields, demonstrate the universality of field-theory concepts, and offer a new platform for studies of previously hidden aspects of quantum-relativistic physics.

Motivation & Objective

• To investigate whether fundamental relativistic field-theory concepts like spin and momentum can manifest as observable mechanical properties in classical wave systems.
• To bridge the gap between abstract relativistic field theory and classical hydrodynamics by identifying canonical and kinetic momentum in water waves.
• To demonstrate experimentally and theoretically that the Belinfante-Rosenfeld construction—typically used in quantum field theory—has a direct physical realization in water surface waves.
• To reveal the mechanical origin of spin in wave fields through subwavelength particle motion in inhomogeneous wave environments.
• To establish water waves as a classical platform for probing otherwise hidden aspects of relativistic and quantum field theory.

Proposed method

• Theoretical derivation of the Belinfante-Rosenfeld spin density using the difference between canonical and kinetic energy-momentum tensors in wave fields.
• Identification of the canonical momentum in water waves with the generalized Stokes drift, a known transport phenomenon in wave systems.
• Modeling of particle trajectories in inhomogeneous water waves to isolate subwavelength circular motion responsible for spin generation.
• Use of hydrodynamic equations and wave field decomposition to separate canonical and kinetic momentum components.
• Experimental observation of particle trajectories in controlled water wave fields to verify the predicted spin and momentum behavior.
• Comparison of theoretical predictions with measured particle motion to validate the emergence of spin as a mechanical property.

Experimental results

Research questions

• RQ1 Can the abstract relativistic field-theory concept of spin, as defined by the Belinfante-Rosenfeld construction, be realized as a measurable mechanical property in a classical wave system?
• RQ2 How is the canonical momentum in water waves related to the generalized Stokes drift phenomenon?
• RQ3 What physical mechanism generates spin in classical wave fields, and how does it arise from particle-scale motion?
• RQ4 To what extent do the canonical and kinetic energy-momentum tensors in water waves reflect the same structure as in relativistic field theories?
• RQ5 Can the spin and momentum in water waves be experimentally observed and quantitatively linked to theoretical predictions?

Key findings

• The Belinfante-Rosenfeld spin density, a cornerstone of relativistic field theory, is physically realized in classical water surface waves through subwavelength particle motion.
• The canonical momentum in water waves is directly linked to the generalized Stokes drift, providing a mechanical interpretation of a concept previously considered abstract.
• Spin in the wave field arises from inhomogeneous, subwavelength circular trajectories of water particles, which are experimentally observable.
• The difference between canonical and kinetic energy-momentum tensors—central to the Belinfante-Rosenfeld construction—manifests as a measurable mechanical effect in the wave system.
• The study establishes water waves as a classical analog system where previously non-observable relativistic field-theory quantities become directly measurable through particle dynamics.
• The findings confirm the universality of field-theory concepts beyond quantum and relativistic regimes, extending their applicability to classical hydrodynamics.