# Quantum Mechanical Interpretation of Water Waves?

So I have been exploring the idea of wave-particle duality and came across and interesting idea.

Could water waves, be interpreted as particles in some context? If so, how would you observe their particle-like properties?

• See ref,find : analogy between water waves (in a ripple tank) and light waves. This is a fairly harmless analogy. Many classical light phenomena are demonstrable in a mathematically correct way using water, with some obvious exceptions: The water waves have only one polarization direction. The water waves require a medium, light doesn't. In the essentially two-dimensional ripple tank, the wave energy propagates by an inverse first power law, not an inverse square law.  The water waves are rapidly damped; light waves usually aren't. – Trimok May 27 '13 at 19:01
• Is water describeable (i'm srry that doesn't look like a word but you know what i mean), using the wave equation? From there can you describe it in term of the Schrodinger Equation? Not the indivdual particles but rather the entire wave itself...if its possible – frogeyedpeas May 27 '13 at 19:22
• I am not at all a specialist. But the text in the reference says clearly that there is no relation between analysis of water waves and a possible analogy with light-waves (that is particles-like properties) In fact, water waves are clearly a macroscopic problem (but not cosmological...), and should not be analyzed with fundamental tools as Quantum Mechanics or wave-particle duality. But maybe somebody has a more clever answer... – Trimok May 27 '13 at 19:32
• You may find something interesting here[ web.mit.edu/newsoffice/2010/quantum-mechanics-1020.html] . – gatsu May 27 '13 at 21:24
• You may be interested in Phonons which are particle-like waves. I think most water waves would be considered "off shell" though. – Brandon Enright May 27 '13 at 21:25

I don't think this works. If it did, then $p=h/\lambda$ would have to give something reasonable, but it doesn't -- it gives something unmeasurably small. Water waves can transmit momentum (e.g., think of someone doing a cannonball dive into a pool -- there is net outward flow). Even in cases that should have a relatively small momentum transport (a well-behaved sine wave), the momentum transport is not going to be exactly zero, and it's going to be much, much greater than $h/\lambda$.
You'd also have a fundamental problem because the wavelength of a water wave is invariant when you change frames of reference (do a boost), but $p$ isn't. (In quantum mechanics, $\lambda$ isn't invariant under boosts, and this is possible because the wavefunction's phase isn't measurable.)
A body of water does have a quantum-mechanical wavelength given by $\lambda=h/p$, but this wavelength is unmeasurably small, and is interpreted as the wavelength corresponding to the water's center of mass motion, regardless of whether there are surface waves or not.