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.
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