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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?

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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. [2] 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[] . – 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

If you interpretate "particle" as a stable pattern in fluid motion, then the analogy between particles and solitons is quite reasonable, for example the equations describing the motion of fluids admit in some situations solitons solutions (for a visual demonstration, see for example 1 and 2).

Nevertheless, I would't consider it a quantum mechanical interpretation of waves in water, at limit it's the opposite as quantum mechanics is physically way more complex (in all senses) than fluid motion (mathematically are both hard).

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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.

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