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SUMMARY:Why bouncing droplets are a pretty good model of quantum mechanics
  - Robert Brady\, Computer Laboratory
DTSTART:20140613T150000Z
DTEND:20140613T160000Z
UID:TALK52233@talks.cam.ac.uk
CONTACT:Dr C. P.  Caulfield
DESCRIPTION:In 2005\, Couder\, Protiere\, Fort and Badouad showed that oi
 l droplets bouncing on a vibrating tray of oil can display nonlocal intera
 ctions reminiscent of the particle-wave associations in quantum mechanics\
 ; in particular they can move\, attract\, repel and orbit each other. Subs
 equent experimental work by Couder\, Fort\, Protiere\, Eddi\, Sultan\, Mo
 ukhtar\, Rossi\, Molacek\, Bush and Sbitnev has established that bouncing
  drops exhibit single-slit and double-slit diffraction\, tunnelling\, quan
 tised 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 cha
 racteristic speed c of the surface waves\; second\, that pairs of bouncing
  droplets experience an inverse-square force of attraction or repulsion ac
 cording to their relative phase\, and an analogue of the magnetic force\; 
 third\, that bouncing droplets are governed by an analogue of Schrodinger
 's equation where Planck's constant is replaced by an appropriate constant
  of the motion\; and fourth\, that orbiting droplet pairs exhibit spin-hal
 f symmetry and\nalign antisymmetrically as in the Pauli exclusion principl
 e. Our analysis explains the similarities between bouncing-droplet experim
 ents 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.
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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