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.
We construct and study the simplest universal dissipative Lindblad master equation for many-body systems with the purpose of a new dissipative extension of existing nonrelativistic theories of fundamental spontaneous decoherence and spontaneous wave function collapse in nature. It is universal as it is written in terms of second-quantized mass density $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\varrho}}$ and current $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{J}}$, thus making it independent of the material structure and its parameters. Assuming linear friction in the current, we find that the dissipative structure is strictly constrained. Following the general structure of our dissipative Lindblad equation, we derive and analyze the dissipative extensions of the two most known spontaneous wave function collapse models, the Di\'osi-Penrose and the continuous spontaneous localization models.
We discuss a model of spontaneous collapse of the quantum state that does not require adding any stochastic processes to the standard dynamics. The additional ingredient with respect to the wave function is a position in the configuration space which drives the collapse in a completely deterministic way. This new variable is equivalent to a set of positions of all the particles, i.e., a set of Bohmian positions, which obey the usual guiding equation of Bohmian theory. Any superposition of quantum states of a macroscopic object occupying different regions of space is projected by a localization process onto the region occupied by the positions. Since the Bohmian positions are well defined in a single realization of the experiment, a space localization into one region is produced. The mechanism is based on the correlations between these positions arising from the cohesive forces inside macroscopic objects. The model introduces two collapse parameters which play a role very similar to those of the Ghirardi-Rimini-Weber (GRW) [Ghirardi et al., Phys. Rev. D 34, 470 (1986)] and continuous spontaneous localization (CSL) [Pearle, Phys. Rev. A 39, 2277 (1989); Ghirardi et al., Phys. Rev. A 42, 78 (1990)] theories. With appropriate values of these parameters, we check that the corresponding dynamics rapidly projects superpositions of macroscopic states localized in different regions of space into a single region, while it maintains a negligible effect in all situations where the predictions of standard quantum dynamics are known to be correct. We briefly speculate about the possible relations with gravity. We then study the evolution of the density operator and a mean-field approximation of the dynamical equations of this model, as well as the change of the evolution of the momentum introduced by the localization process. Possible theoretical interpretations are discussed. Generally speaking, this model introduces a sharper border between the quantum and classical worlds than the GRW and CSL theories and leaves a broader range of acceptable values for the parameters.
Collapse models explain the absence of quantum superpositions at the macroscopic scale, while giving practically the same predictions as quantum mechanics for microscopic systems. The Continuous Spontaneous Localization (CSL) model is the most refined and studied among collapse models. A well-known problem of this model, and of similar ones, is the steady and unlimited increase of the energy induced by the collapse noise. Here we present the dissipative version of the CSL model, which guarantees a finite energy during the entire system's evolution, thus making a crucial step toward a realistic energy-conserving collapse model. This is achieved by introducing a non-linear stochastic modification of the Schrödinger equation, which represents the action of a dissipative finite-temperature collapse noise. The possibility to introduce dissipation within collapse models in a consistent way will have relevant impact on the experimental investigations of the CSL model, and therefore also on the testability of the quantum superposition principle.
Models of dynamical wave function collapse consistently describe the breakdown of the quantum superposition with the growing mass of the system by introducing non-linear and stochastic modifications to the standard Schrödinger dynamics. Among them, Continuous Spontaneous Localization (CSL) was extensively investigated both theoretically and experimentally. Measurable consequences of the collapse phenomenon depend on different combinations of the phenomenological parameters of the model-the strength λ and the correlation length rC-and have led, so far, to the exclusion of regions of the admissible (λ-rC) parameters space. We developed a novel approach to disentangle the λ and rC probability density functions, which discloses a more profound statistical insight.
A Markovian wave-function collapse model is presented where the collapse-inducing operator, constructed from quantum fields, is a manifestly covariant generalization of the mass-density operator utilized in the nonrelativistic continuous spontaneous localization (CSL) wave-function collapse model. However, the model is not Lorentz invariant because two such operators do not commute at spacelike separation, i.e., the time-ordering operation in one Lorentz frame, the ``preferred'' frame, is not the time-ordering operation in another frame. However, the characteristic spacelike distance over which the commutator decays is the particle's Compton wavelength so, since the commutator rapidly gets quite small, the model is ``almost'' relativistic. This quasirelativistic CSL (QRCSL) model is completely finite: unlike previous, relativistic, models, it has no (infinite) energy production from the vacuum state. QRCSL calculations are given of the collapse rate for a single free particle in a superposition of spatially separated packets, and of the energy production rate for any number of free particles: these reduce to the CSL rates if the particle's Compton wavelength is small compared to the model's distance parameter. One motivation for QRCSL is the realization that previous relativistic models entail excitation of nuclear states which exceeds that of experiment, whereas QRCSL does not; an example is given involving quadrupole excitation of the
74Ge nucleus.