A simple means for deriving quantum mechanics

TL;DR

This work proposes positional mechanics as a simple, intuitive foundation from which quantum mechanics can be derived, challenging the view that quantum phenomena are inherently mysterious. By modeling systems with continuous particle paths and discrete, non-deterministic momentum-changing events governed by environmental information, the framework reproduces the Madelung form and, in the appropriate limit, Schrödinger dynamics for Schrödinger distributions. It also clarifies how different quantum-world interpretations—Bohmian, stochastic, many-worlds, and physical collapse—arise as distinct limits or reconstructions of the same underlying positional framework, including a relativistic extension that preserves covariance. The approach offers a unifying ontological view, providing a constructive path to understand quantum phenomena across non-relativistic and relativistic regimes and to relate to established interpretations.

Abstract

A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable predictions of non-relativistic quantum mechanics. Within it, particles exist at points in space, follow continuous, piecewise differentiable paths, and their linear momentum is equal to their mass times their velocity along their path. Yet the probabilities for position and momentum, conditioned on the state of the particle's environment, follow the rules of quantum theory. Indeed, all observable consequences of quantum theory are satisfied; particles can be entangled, have intrinsic spin, this spin is not local to the particle, particle identity can effect probabilities, and so forth. All the rules of quantum mechanics are obeyed, and all arise in a straightforward fashion. After this is established, connections will be drawn out between this type of mechanics and other types of quantum worlds; those that obey Bohmian mechanics, stochastic mechanics, the many worlds interpretation, and physical collapse. In the final section, a relativistic version of the mechanics will be presented.