In 2005, Couder, Protière, Fort and Badouad showed that oil droplets bouncing on a vibrating tray of oil can display nonlocal interactions reminiscent of the particle-wave associations in quantum mechanics; in particular they can move, attract, repel and orbit each other. Subsequent experimental work by Couder, Fort, Protière, Eddi, Sultan, Moukhtar, Rossi, Moláček, Bush and Sbitnev has established that bouncing drops exhibit single-slit and double-slit diffraction, tunnelling, quantised energy levels, Anderson localisation and the creation/annihilation of droplet/bubble pairs.In this paper we explain why. We show first that the surface waves guiding the droplets are Lorentz covariant with the characteristic speed c of the surface waves; second, that pairs of bouncing droplets experience an inverse-square force of attraction or repulsion according to their relative phase, and an analogue of the magnetic force; third, that bouncing droplets are governed by an analogue of Schrödinger's equation where Planck's constant is replaced by an appropriate constant of the motion; and fourth, that orbiting droplet pairs exhibit spin-half symmetry and align antisymmetrically as in the Pauli exclusion principle. Our analysis explains the similarities between bouncing-droplet experiments and the behaviour of quantum-mechanical particles. It also enables us to highlight some differences, and to predict some surprising phenomena that can be tested in feasible experiments.

SummaryThis case report describes the presentation, treatment and outcome of an adult German shepherd dog with gastroesophageal intussusception (GEI). The dog’s presenting complaint included acute lethargy, and a single bout of excessive drinking followed by immediate regurgitation. After patient stabilisation, radiographs were taken which revealed a soft tissue opacity in the caudodorsal thorax and lack of a gastric silhouette in the abdomen. The patient was diagnosed with GEI, a laparotomy was performed and the stomach and spleen were surgically reduced. A right-sided incisional gastropexy, left-sided tube gastropexy, splenectomy and narrowing of the oesophageal hiatus were performed. The patient developed aspiration pneumonia postoperatively, likely secondary to megaoesophagus, which responded to antimicrobials. The gastric tube was removed 31 days after surgery and the patient had no further clinical signs eight months postoperatively.

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