Double-slit experiment simulated with water waves?

Question

We all know the explanation videos and other material using the water waves analogy to illustrate the propagation of electrons or photons and the interference patterns measured in the the single-slit and double-slits experiments.

Being just an analogy it misses for sure many attributes by which light/electron waves differ from water waves.

BUT: If limited only to use water-waves analogy would it be possible to simulate the impact of the observer/detector in the experiments by means of water waves (yes, i'm smiling my self at this a little ;)

What would be the properties of such a detector-by-means-of-waves needed to simulate the collapse of the interference pattern, for example?

In other words is it possible to rebuild the double-slit experiment with such a water-waves setup and with same known results?

How about in theory? What ("strange") requirements are there?

For starters maybe let's drop the switching the slit-result and let's assume when the observer is turned on the water wave shows to be originating always from the same slit...

At what earliest point does this "model" break? How?

Thanks!

Answer 1

You may wish to look at this article: Yves Couder, Emmanuel Fort, Single-Particle Diffraction and Interference at a Macroscopic Scale, Phys. Rev. Lett. 97, 154101 (2006).

Answer 2

It will be impossible to do what you want with water waves, because water waves are in physical space, and the effects of collapse and measurement only show up when the waves are propagating in enormous dimensional configuration spaces. The way to get the quantum effects in systems like this is to restrict the mechanical motion to a few quanta, but for water waves the quantum is essentially zero compared to the thermal energy.

You can see the interference pattern just fine with water waves, the issue is when you measure the position of the "particle". The number of elementary quanta in a water wave, or any other macroscopic wave, is so enormous, that you can measure the wave amplitude without disturbing the wave at all. In order to see the breakdown of interference in response to measurement, you would need to have only a few oscillation quanta of the water surface waves, so that measuring where the water was waving would localize the wave by entangling it with the measuring detector, and lead the remaining relative state of the water to show no interference.

The point is that the measurement effects are not due to the wave nature of matter, but due to the entangling nature of quantum mechanics, where waves travel in configuration space, so that they are waves over different possible worlds, not over the position of separate single particles. Without this enormous configuration space wave, you don't get a model for the measurement issues.

This is impossible in water, because the thermal energy at temperatures where water is liquid is essnetially infinitely larger than the energy of a single quantum of water oscillation. Because of this, the notion of a single quantum of water wave is difficult to define, and might not make coherent sense. You can't have a single quantum, because the thermal noise at any realistic wavelength and temperature is much larger than the quantum of energy.

But you might be able to pull off a double slit experiment at ultra-low temperature using a phonon in a solid, or a fluid excitation in liquid He, which might satisfy the criteria you want.