Depending on the values of the parameters, the liquid drop is surfing, bouncing at a fixed position, or "walking" along the surface wave. The surface wave is created by the interaction of particle with the surface. These findings suggest that macrosopic quantum coherence could be involved and quantum phenomena have also classical description. There is energy feed to the systems.

The findings of the group led by Bush and describe in his Youtube lecture (see this) give a nice overall view about the quantum analogs. Bush also suggests a generalization of theory of Vigier involving two pilot waves, which correspond to those associated with wave function and to classical system and theory of Bohm involving single pilot wave assigned to wave function.

The article of Bush et al (see this) describes the findings about the analog of quantum corral. The latter involves electrons inside a circular corral defined by negative ions.

"* Bouncing droplets can self-propel laterally along the surface of a vibrated fluid bath by virtue of a resonant interaction with their own wave field . The resulting walking droplets exhibit features reminiscent of microscopic quantum particles. Here we present the results of an experimental investigation of droplets walking in a circular corral. We demonstrate that a coherent wavelike statistical behavior emerges from the complex underlying dynamics and that the probability distribution is prescribed by the Faraday wave mode of the corral. The statistical
behavior of the walking droplets is demonstrated to be analogous to that of electrons in quantum corrals.*

The key questions are following.

- Could quantum classical correspondence (QCC) be more than an approximation (stationary phase approximation). Note that in TGD QCC is in a well-defined sense exact.
- Can a macroscopic system can exhibit quantal looking behavior and is there a genuine quantum behavior behind it? In the TGD framework, the hierarchy of effective Planck constants h
_{eff}=nh_{0}labelling phases of ordinary matter located at magnetic body (MB). MB has a hierarchical structure and defines a master slave hierarchy.A given level of the hierarchy controls the physics at the lower levels. h

_{eff}hierarchy makes quantum coherence possible in arbitrarily long scales at MB and this induces coherence at the level of ordinary matter and makes possible self-organization. The increase of h_{eff}requires however the analogy of metabolic energy feed quite generally.There is indeed energy feed to the studied system at frequency of f=50 Hz of the vibrating cylindrical shaker. The standing wave resonance occurs at Faraday frequency f

_{F}= f/2. The Faraday frequency has slow time variation with the frequency f and slightly below f_{F}.The system system should be near criticality for the generation of h

_{eff}phases. These phases at MB would induce long range correlations of ordinary matter near criticality. The system studied is indeed near criticality for the generation of standing Faraday waves. - What could the value of h
_{eff}be? The Faraday wave length λ_{F}= 2\pi\sqrt{2ν/μ should be equal to the analog of Compton wavelength λ_{c}=ℏ_{eff}/m, m the mass of the water droplet. λ_{F}does not however depend on the mass of the droplet and in the model of the Faraday waves hydrodynamical is determined in the model considered by the properties of the fluid that is friction and kinematic viscosity.The only possibility is that one has ℏ

_{eff}= ℏ_{gr}= GMm/v_{0}, where ℏ_{gr}is the gravitational Planck constant introduced by Nottale and also appearing in the TGD based model of superconductivity. This would give λ_{F}= λ_{>gr}= GM/v_{0}= r_{s}(M)/2v_{0}, where r_{s}(M) is Schartschild radius. M is naturally the mass of Earth. The minimum value of λ_{gr}corresponds to v_{0}/c=1 and is λ_{gr}= r_{s}/2. Earth's Scwartschild radius is 8.7 mm so that one would have λ_{F}= 4.35 mm.The value of λ

_{F}for the system studied in the analog of quantum corral by Bush et al is 4.75 mm \cite{bcond/qcorral} and about 10 per cent larger than the minimal value suggesting that β_{0}=v_{0}/c\simeq .92!If this single testable prediction is not a nasty coincidence, it would mean an instantaneous breakthrough for the TGD view about quantum gravitation as macroscopic and even astrophysical phenomenon. The only parameter that can be varied in the prediction is β

_{0}. One could measure λ_{F}=2\pi (2ν/μ)^{1/2}for different liquids to see whether v_{0}codes for the properties of the liquid or whether λ_{F}is independent of the liquid so that the classical model for Faraday waves could be wrong. - The system has a memory in the sense that the induced Faraday wave interpreted as an analog of pilot wave is affected by the bouncing particle and in turns determines particle behavior but not quite completely: an analog of non-deterministic "zitterbewegung" seems to be present for strong enough acccelerations. The observations about the double slit experiment and also about approach to chaotic behavior indeed suggests that the system is not completely deterministic. The findings also suggest that the statistical description of this non-determinism is analogous that in quantum systems.
In ZEO quantum state as time= constant snapshot is replaced with a space-time surface as preferred extremal (PE) analogous to Bohr orbit. What comes in mind, is that the bouncing corresponds to "small" SFRs (SSFRs). The determinism of PEs is not quite exact that it would serve as correlate for what I call cognitive measurements as SSFRs. In the TGD inspired theory of consciousness, the loci of non-determism for space-time surfaces as analogs of soap filmds would serve as the seats of mental images quite universally and also represent conscious memories.

- In this talk Bush interprets the Faraday wave induced by the motion of the droplet along the surface as a kind of pilot wave. In the TGD framework the counterpart of the pilot wave would be the magnetic body (MB) carrying h
_{eff}=nh_{0}phases quantum controlling the behavior of ordinary matter. The magnetic flux tubes assignable to the exteriors of vortex cores are proposed to be present in microscopic scale also below turbulence and to serve as correlates for the vorticity caused by the boundary conditions at the boundary of flowing liquid. Now these boundaries correspond to the boundary between air and liquid bath and air and liquid droplet and could explain how the gravitational magnetic body characterized by ℏ_{gr}enters into the physics of the moving water droplet.

See the article TGD and condensed matter.

For a summary of earlier postings see Latest progress in TGD.