Yves Couder’s (and others) experiments with small (in the human sense) and absolutely huge (in the quantum sense) silicon oil droplets and baths have proven to be a wonderful analog for quantum mechanics.

There are many researchers who think that these experiments show something much more – they hint at what the microscopic quantum world is really like. The quantum like effects occur when the driving force and frequency of the system are carefully tuned. When the conditions are right, the drops interact with their own waves – long after the waves have been emitted. Couder calls this behaviour the ‘high memory regime’ – its where all the quantum like behaviour emerges.

So the question becomes – what is the memory of a real quantum system? The answer to that question is surprisingly simple. Its infinite. Quantum states can entangle and ‘live’ forever. This fact is the foundation of Quantum Computing, the Many Worlds Theory and many other absurdities (Schrödinger’s cat…). Indeed the only point in QM where memory is not complete and infinite is at the point of measurement. But measurement is in the eye of beholder, and thus we need not worry about the measurement problem here. Or rather we will attempt to solve the measurement problem with a new hypothesis – that the memory of real quantum systems are limited, and that this limit is responsible for the collapse of the wave function.

This of course could kill or seriously limit the reach of quantum computing, and would provide a quick end to the Many Worlds Theory, and many many other consequences of quantum mechanics. Indeed Hilbert Space itself would lose its ‘reality’ – becoming nothing more than a mere mathematical trick for ‘memory intact’ (AKA pre-collapse) states.

What is the form of the memory? In Couder’s experiments its simply the range of an emitted wave in meters. Since his test trays are small, this means that the waves can bounce off the walls and interact with the emitter again.

We can look at such a system as a particle in a well. In Couder’s experiments you can see excited states decay after a time, and this time is increased as the memory of the system is increased.

So if we look at the simplest physical analog of this – a particle in a well that can quantum tunnel out – we have Alpha – emission. These particles are trapped in the nucleus, but sooner or later they tunnel out.

Thus tunnelling is a collapse of the wave function – these alpha particles leave fossil traces in rocks for instance, so they have been emitted in a very real sense.

Of course the pure QM follower will tell you that each emitted alpha is just another cat in a box - and that the entire history of the world hinges on you (or is that any smart person?) looking at the actual billion year old track - only then does the linear superposition of uncountable 10^{Millions}of state vectors collapse. Kind of hilarious, but that is what a truly linear system will do to you if you push it!

What causes the emission? The wave function has presence inside and outside of the barrier, so it can ‘feel’ that there is a lower energy state out there waiting for it. In a real pilot wave sense the pilot wave extends into the region beyond the barrier. We have a series of waves inside a femto metre sphere or so, and they bounce around for a few years (or 10^{24}) years, or 10^{-6} seconds.

So a large variation of lifetimes – yet the playground is almost the same size, its the energy levels that are different, but only by a small factor. The greater amount of the wave function that is outside the nucleus, the shorter half life.

What really happens? Is it that the particle keeps inside the nucleus, and as soon as it randomly happens to walk out it is released? In ‘real QM’ the wave function only gives a probability for finding the alpha outside the nucleus, so in some sense its ‘constantly’ out there. But in a realist theory the alpha has a real velocity inside and around the nucleus. This could perhaps be a real difference – perhaps if we postulate a fixed speed of the alpha on a random walk through the probability field, we can connect the lifetime to the percentage of the wave function that is outside the nucleus. See

Unpredictable Tunneling of a Classical Wave-Particle Association

So if a certain percentage of paths is outside, and the particle covers … do the calculation – random walk – step length is some distance much less than the nucleus size, speed v, then typical time to get out would be defined. perhaps with the speed held constant, we can determine step length by looking at the size of the region of probability outside the nucleus, we can determine the speed/step length that is implied. Someone must have done this?

http://demonstrations.wolfram.com/GamowModelForAlphaDecayTheGeigerNuttallLaw/

So in the playtime circa 1900 flat spacetime where QM currently works, there are no non – local effects and QM makes sense. This is why most theorists like the quantization of gravitation program – it would bury the annoying real 4D version of spacetime underneath many levels of obscure mathematics.