УДК 530.145.65 MACROSCOPIC MODEL OF QUANTUM MECHANICS Atknin I.I. Language adviser: Alekseenko I. V. Siberian Federal University The article describes macroscopic quantum effects, which are difficult or even impossible to visualise. For the last decade there was no any experimental proof of quantum effects, which could be apparent in macro world. The pilot wave theory was developed by Louis de Broglie and David Bohm, then later overtaken by the Copenhagen interpretation as a standard view of quantum mechanics, thus, there was no macroscopic pilot wave analog to draw upon. Now there is one. A droplet bouncing on a liquid bath can self-propel due to its interaction with the wave it generates. The resulting “walker” is a dynamical association where, at a macroscopic scale, a particle (the droplet) is driven by pilot - wave field. We know, that the idea of the wave - particle duality was originated when Isaac Newton and Christian Huygens suggested conflicting theories. The Newton applied that light consist of corpuscles in contrast to the Huygens, who determined the wave theory of light. Concepts of light theory have changed a lot since the last century. Today light particles are known as photons. Reviewing the investigations of many scientists, we conclude, that current scientific theory holds such microparticles as photons, electrons and even molecules, which are able to be particles and waves at the same time. According to this idea, de Broglie proposed the pilot wave theory and later it was developed by David Bohm. Due to this theory, particles are guided by waves. The pilot wave theory restores determinism and realism in quantum mechanics, but the physical nature of the guiding wave field remains unclear. So, at that time the theory of de Broglie - Bohm was overtaken by the interpretation of probabilistic approach, because there was no macroscopic pilot wave analog to draw upon. Now there is one. Yves Couder and colleagues found a macroscopic pilot system that demonstrates properties, which previously were peculiar to the microscopic world When a bath with a fluid is vibrated in the periodic mode, we are able to find the critical vibration frequency, above which the flat hydrostatic surface becomes unstable to a regular pattern of standing millimetric Faraday waves (fig. 1). The critical value of acceleration depends on the depth of liquid, surface tension and viscosity. Fig. 1. Snapshot of Faraday waves on a the fluid surface induced by driving the bath vertically in a periodic mode Here is investigated the situation when a droplet of the same fluid is placed on the surface (fig. 2) of the vertically oscillating (1) bath . The diameter of the droplet is about 1 mm. g (t) = g m cos(wt) where w = 2p f0 ; g m = -Aw2 - amplitude of acceleration. (1) Fig. 2. Small cell containing a liquid is subjected to a vertical sinusoidal acceleration (1) Liquid droplet usually disappears rapidly (a few tenth of a second) when it falls on the same liquid surface. The forcing acceleration is made to exceed g (the gravitational acceleration) in order to avoid this coalescence. The collide period of time becomes shorter than the time, which is required to break the air film between the droplet and fluid surface. Thus, before the distance becomes critical to merger by van der Waals forces, the droplet lifts off again and can be maintained for an unlimited time in a kind of “levitation” on the surface . The experiment includes a droplet, placed on a bath of silicone oil in the vibrating regime between the Faraday threshold and threshold of bouncing. Depending on the droplet size, it is possible to achieve the result, when a droplet could remain bouncing infinitely. Its bouncing emits damped surface waves (fig. 3). Fig. 3. Three photographs demonstrate a droplet, bouncing on the surface of a bath, when the same liquid oscillating vertically. These waves are able to be a mediator among multiple bouncers on the surface. When pair of neighbouring walkers stuck together, they may be locked into orbit around each other (fig. 4 Left). This set of equal - sized droplets can form structure corresponding to Archimedean tilings (fig 4 right) . Fig 4. Left: A pair of walkers lock into collective orbit. Right: Side-view snapshot of a hexagonal lattice aggregate of bouncing droplets. The waves, which are generated by the bouncer, create an irregularity of the surface (waves). When the droplet lands on the sloping surface, it rebounds out of the vertical bouncing state and slides along the horizontal plane . As a result, the droplet is piloted by its wave field (fig. 5). We should, also, notice that this motion depends on the depth of the liquid, the bigger the height of these waves, which are generated, more readily the droplet moves. Fig. 5. The droplet, touching the sloping surface of the wave, generated by the previous collisions. If a metal strip is put on the bottom of the bath so that the liquid layer is above the strip (subsurface barrier), creating the equivalent of the barrier for the moving bouncer (walker). It replicates the single - particle single- and double-slit experiments in macroscopic realm (fig. 6). The experiment demonstrates the way the droplet is launched into the direction of the slit. Fig. 6. A walker passes through the slit. The complex pilot wave field when the droplet is in the slit region. When the droplet gets closer to the slit region, the wave propagation is distorted by interference between the reflected and direct waves, as depicted in fig. 6. The statistics of the deviations is investigated in fig. 7 in terms of many independent realization, where it duplicates the classical diffraction pattern of microscopic particle proved by Taylor in 1909. Fig. 7. The droplet trajectory passes through the slit and the histogram for 125 successive events. In the double - slit experiment while the droplet passes through the first slit, the generated wave has time to pass through the both slits, where the wave velocity is higher than the velocity of the moving droplet .These waves interact after the slits, creating the interference. Quantum tunneling is a quantum mechanic phenomenon when a particle tunnels through a barrier that it classically could not surmount. Exploring a droplet interaction with a barrier, we can see a macroscopic model of quantum tunneling. In the macroscopic experiment a bouncing droplet is confined by walls around, above which the droplet could jump over, but not walk (fig. 8). However, the probability of tunneling decreases exponentially with increasing width of the barrier . Fig. 8. The recorded path of the droplet inside the square trap, e – barrier width (2,5 mm), P – probability of escape. V – velocity of motion. a) V=11,8 mm/s, P≈10% ; b) V=13,2 mm/s, P≈30%; In conclusion, we should notice that scientists are fully confident, that quantum and classical realms are totally different. Due to the experiment with vibrating droplet, which demonstrates the similarity of the wave - particle duality between quantum and classical scales. The system remains deterministic in contrast to quantum world. The system is two dimensional, but the system is received energy by the third dimension. Here may be the clue for solving the problem of probabilistic understanding of current quantum theory. Probably the solving is hidden in one more dimension whose nature remains unclear. This system provides a great number of questions which are difficult or even impossible to answer. REFERENCES 1. Particle–wave association on a fluid interface // J. Fluid Mech. (2006), vol. 554, pp. 85– 108. 2. Y. Couder, E. Fort, C.-H. Gautier, and A. Boudaoud // From Bouncing to Floating: Noncoalescence of Drops on a Fluid Bath, PRL 94, 177801 (2005) 3. Eddi A, Decelle A, Fort E, Couder Y (2009) // Archimedean lattices in the bound states of wave interacting particles. Europhys Lett 87:56002-p1–56002-p6. 4. Protiere S., Boudaoud A. and Couder Y., J. Fluid Mech., 554 (2006) 85. 5. A. Eddi, E. Fort, F. Moisy, and Y. Couder // Unpredictable Tunneling of a Classical WaveParticle Association.