📝 SummarXiv

Abstract

It is quite familiar that Schr\"{o}dinger equation can be rewritten in terms of fluid-type equations, called Madelung equations. However one term in these fluid equations, the so called `quantum potential` is quite complicated. Indeed, D\"{u}rr complains that the quantum potential is `neither simple nor natural` \cite{Durr1996}. Thus it may appear a hopeless task to imagine a fluid with such properties that would lead to the Madelung equations, and more specifically, to the quantum potential. We prove the opposite. We make a model with \textit{two} interacting fluids, instead of one. Then we consider a process of mutual diffusion between the fluids. This leads quite naturally to the Madelung fluid equations \textit{including} the quantum potential for one of the fluids. In addition, we model the particle as a point-like object, that moves inside this particular fluid. We require that it moves with the \textit{same} velocity as the \textit{local velocity of this fluid}. Then the guiding equation of Bohmian mechanics follows directly. From this equation we derive Born's rule. Our interpretation of that result is that \textit{the particle is part of the fluid, a kind of singularity in it}. Finally, we answer several possible objections against the model.