Three qRules governing wave collapse are given in this paper that provide a foundation theory of quantum mechanics. They are empirical regularities that are known to be valid in macroscopic situations. When projected theoretically into the microscopic domain they predict a novel ontology, including the frequent collapse of atomic wave functions. Future experiments can potentially discriminate between this and other foundation theories of quantum mechanics. Important features of the qRules are: (1) they apply to individual trials not just to ensembles of trials, (2) they are valid independent of size or mass (microscopic or macroscopic), (3) they allow all observers to be continuously included in the system without ambiguity, (4) they account for the collapse of the wave function without introducing new or using old physical constants, (5) they allow energy and momentum to be conserved in an individual collapse, (6) they generate wave reductions that are independent of any outside observer or measuring device, (7) they provide a high frequency of stochastic localizations of microscopic objects independent of macroscopic objects, and (8) they are formulated in a covariant language that makes them useful beyond non-relativistic quantum mechanics. Keywords: foundation theory, measurement, qRules, state reduction, wave collapse.
The nRules are empirical regularities that were discovered in macroscopic situations where the outcome is known. When they are projected theoretically into the microscopic domain they predict a novel ontology including the frequent collapse of an atomic wave function, thereby defining an nRule based foundation theory. Future experiments can potentially discriminate between this and other foundation theories of (non‐relativistic) quantum mechanics. Important features of the nRules are: (1) they introduce probability through probability current rather than the Born rule, (2) they are valid independent of size (micro or macroscopic), (3) they apply to individual trials as well as to ensembles of trials. (4) they allow all observers to be continuously included in the system without ambiguity, (5) they account for the collapse of the wave function without introducing new or using old physical constants, and (6) in dense environments they provide a high frequency of stochastic localizations of quantum mechanical objects.
Three qRules governing the collapse of a wave function are given in another paper. In most situations the predictions of this theory are identical with the predictions of other foundation theories. However, there is at least one experiment in which the qRules predict results that are characteristically different from other theories. These results are shown to be a function of molecular collisions in an experiment proposed by Collett and Pearle. Wave reductions in other collapse theories are distinctly not a function of collisions. Keywords: foundation theory, measurement, qRules, state reduction, wave collapse.
The basic strategy underlying models of spontaneous wave function collapse (collapse models) is to modify the Schrödinger equation by including nonlinear stochastic terms, which tend to localize wave functions in space in a dynamical manner. These terms have negligible effects on microscopic systems—therefore their quantum behaviour is practically preserved. On the other end, since the strength of these new terms scales with the mass of the system, they become dominant at the macroscopic level, making sure that wave functions of macro-objects are always well-localized in space. We will review these basic features. By changing the dynamics of quantum systems, collapse models make predictions, which are different from standard quantum mechanical predictions. Although they are difficult to detect, we discuss the most relevant scenarios, where such deviations can be observed.
It is claimed in another paper that the collapse of a quantum mechanical wave function is more than invariant, it is trans-representational. It must occur along a fully invariant surface. The obvious surface available for this purpose is that of the backward time cone of the collapse event as proposed by Hellwig and Kraus. This collapse is widely believed to result in paradoxical causal loops that cannot be removed by special relativistic or standard quantum mechanical considerations alone. However, the paradox is resolved when we apply the qRule foundation theory that is developed in the other paper. The causal and temporal orders of state reduction are then found to be in agreement with one another, and the resulting boundaries in Minkowski space are shown to have a novel architecture that limits the range of a Hellwig-Kraus reduction in space and time. Although these boundaries have been worked out using the qRules, they should be the same for any foundation theory that treats the collapse of a wave in an invariant way, and requires that a collapse destroys the possibility of any further influence on itself, as do the qRules. Keywords: measurement, state reduction, wave collapse.
Standard quantum mechanics relies on an observer-dependent measurement postulate and an artificial linear-nonlinear dichotomy to resolve the superposition of macroscopically distinct states. While objective collapse models---such as Continuous Spontaneous Localization (CSL), Ghirardi-Rimini-Weber (GRW), and Di\'{o}si-Penrose gravitationally induced models---introduce stochastic non-linearities to achieve objective state reduction, they suffer from three fundamental pathologies: continuous energy non-conservation (spontaneous heating), reliance on memoryless white-noise approximations, and unphysical infinite spatial tails. In this work, I present Quantum Wave Function (QWF) Theory, a comprehensive non-perturbative framework that elevates the state functional
Ψ to an exact physical ontology. QWF introduces a non-Markovian colored noise memory kernel
K(t−τ) governed by a finite high-frequency cutoff, capturing realistic vacuum and environmental back-action times. To resolve the long-standing spontaneous heating anomaly, I incorporate a momentum-dependent dissipative counter-term
D^diss into the stochastic differential equation, strictly enforcing energy conservation
dtd⟨H^⟩=0 in closed isolated systems. Furthermore, I eliminate the infinite tail pathology by introducing a state-dependent stochastic amplitude filtering protocol where the microscopic collapse coupling dynamically increases in the asymptotic regime to enforce exponential tail damping below a physical threshold
ϵ, without breaking density matrix linearity. Extending beyond non-relativistic domains, I formulate a fully covariant quantum field description on arbitrary spacelike hypersurfaces
Σ using a Tomonaga-Schwinger stress-energy framework, ensuring causality and preventing superluminal signaling. Finally, I prove via martingale analysis that standard Born-rule statistics (
P=∣Ψ∣2) emerge naturally as a dynamical attractor of the stochastic localization process. QWF provides a mathematically rigorous, falsifiable, and complete resolution to the quantum measurement problem with explicit, testable signatures for modern gravitational wave and optomechanical experiments.