There are two visual aids I recently came across that i.m.o. can help to visualize what is happening at the sub atomic level. The first is about spin, and how it might be possible that a particle needs a turn of 4 pi to get back in its original position.
It is known as Dirac's belt trick (among many other names).
The second feature that mimics QM at a macroscopic level are the effects seen with walkers. Walkers are tiny droplets bouncing on a vibrating fluid. The droplets in combination with waves on the fluid simulate nicely some QM features, including the interference seen in the double slit experiment. A popularized version of the experiments can be seen here:
It appears that the Austrian Institute for Nonlinear Studies has taken up the challenge imposed by the findings of Yves Clouder and has come up with several computer simulations and calculations based on the walkers or 'bouncers' (3):
"On this basis, it has been explicitly shown how the following quantum mechanical features can be derived from purely classical physics: Planck‘s relation E = hw for the energy of a particle, the Schrödinger equation for conservative and non-conservative systems, the Heisenberg uncertainty relations, the quantum mechanical superposition principle, Born‘s rule, and the quantum mechanical ―decay of a Gaussian wave packet‖. Moreover, also the energy spectrum of a quantum mechanical harmonic oscillator has been derived classically, as well as that of a particle in a box."
I would like to finish with two statements I consider more or less true. I would like to hear your opinion on these:
"Apart from Theology Quantum Mechanics is the only branch in science in which there are observed phenomena postulated to be inexplicable" (wave-particle duality, Heisenberg’s uncertainty principle, wave function, entanglement, quantum randomness)
"Furthermore it's framework contains several ill- or circular defined objects (measurement, superposition, decoherence) and postulates that cannot even theoretically be disproved" (particle position nonexistent before measurement)
- Single-Particle Diffraction and Interference at a Macroscopic Scale 2006, Yves Couder and Emmanuel Fort, https://hekla.ipgp.fr/IMG/pdf/Couder-Fort_PRL_2006.pdf
- A macroscopic-scale wave-particle duality, Toronto 2011, http://www.physics.utoronto.ca/~colloq/Talk2011_Couder/Couder.pdf
- Sub-Quantum Thermodynamics as a Basis of Emergent Quantum Mechanics, Gerhard Grössing, Entropy 2010, 12, 1975-2044, http://www.mdpi.com/1099-4300/12/9/1975
- Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics Gerhard Groessing, 2013, http://arxiv.org/pdf/1304.3719.pdf