Spontaneous wave-function collapse models, like continuous spontaneous localization, are designed to suppress macroscopic superpositions while preserving microscopic quantum phenomena. An observable consequence of collapse models is spontaneous heating of massive objects. We calculate the collapse-induced heating rate of astrophysical objects, and the corresponding equilibrium temperature. We apply these results to neutron stars, the densest phase of baryonic matter in the Universe. Stronger collapse model parameters imply greater heating, allowing us to derive competitive bounds on model parameters using neutron star observational data, and to propose speculative bounds based on the capabilities of current and future astronomical surveys.
Models of spontaneous wave function collapse modify the linear Schr\"odinger equation of standard quantum mechanics by adding stochastic nonlinear terms to it. The aim of such models is to describe the quantum (linear) nature of microsystems along with the classical nature (violation of superposition principle) of macroscopic ones. The addition of such nonlinear terms in the Schr\"odinger equation leads to nonconservation of energy of the system under consideration. Thus, a striking feature of collapse models is to heat nonrelativistic particles with a constant rate. If such a process is physical, then it has the ability to perturb the well-understood thermal history of the universe. In this article we will try to investigate the impacts of such heating terms, according to the continuous spontaneous localization model, on the standard evolution of nonrelativistic matter and on the formation of cosmic microwave background radiation. We will also put constraints on the continuous spontaneous localization collapse rate $\ensuremath{\lambda}$ by considering that the standard evolution of nonrelativistic matter is not hampered and the observed precise blackbody spectrum of cosmic microwave background radiation would not get distorted (in the form of $\ensuremath{\mu}$-type and
y-type distortions) so as to violate the observed bounds.
Abstract Among the open problems in fundamental physics, few are as conceptually significant as the “measurement problem” in Quantum Mechanics. One of the proposed solutions to this problem is the Continuous Spontaneous Localization (CSL) model, which introduces a non-linear and stochastic modification of the Schrödinger equation. This model incorporates two parameters that can be subjected to experimental constraints. One of the most notable consequences of this theory is the spontaneous heating of massive objects; this anomalous heating is dependent on the CSL parameters. In this work, we will revisit some astrophysical bounds previously found, and introduce new methods for testing the spontaneous heating in a variety of compact objects. Finally, we will compare our different bounds and discuss the benefits and shortcomings of each one.
The possibility that the collapse of the wave function in quantum mechanics is real and ultimately connected to (classical) gravity has been debated for decades with main contributions by Diósi and Penrose (DP). In particular, Diósi proposed a noise-based dynamical reduction model, which captures the same order of magnitudes for the collapse time suggested by Penrose based on heuristic arguments. This is known in the literature as the DP model (Diósi–Penrose). A peculiarity of the DP model is the prediction of spontaneous heating of matter, which can be tested without the need for massive quantum superpositions. Notably, a very similar effect is predicted by recent theoretical approaches to gravity as a classical-only information channel. Here, we reconsider the current constraints on the DP model from spontaneous heating by analyzing experimental situations not properly considered before. We argue that the parameter-free version of the DP model is close to be ruled out by standard heat leak measurements at ultralow temperatures with a conclusive exclusion likely within reach with existing technology. This result would strengthen a recent claim of exclusion inferred by spontaneous x-ray emission experiments, which relies on the somewhat stronger assumption that the DP noise field is white up to x-ray frequencies.
Abstract This paper proposes a parameter-free objective reduction theory where wavefunction collapse is induced by gravitational self-energy differences between mass distributions. Unlike Continuous Spontaneous Localization (CSL) models, which rely on phenomenological parameters, the collapse rate in this model (Γ = Eg/ħ) is uniquely determined by universal constants G and ħ. Key Highlights: Dynamical Derivation of the Born Rule: The model demonstrates that the Born probability rule emerges naturally from the martingale property of the stochastic dynamics, rather than being postulated. Experimental Consistency: The theory is shown to be consistent with current laboratory constraints, including double-slit interference experiments with large molecules (mcrit ≈ 10⁻¹⁴ kg) and loophole-free Bell inequality tests. Astrophysical Stability: Analysis confirms the stability of compact objects like neutron stars and the preservation of primordial fluctuations in the Cosmic Microwave Background (CMB). Relativistic Extension: A Lorentz-covariant field-theoretic generalization is provided, using the energy-momentum tensor to source collapse noise while respecting microcausality. The results suggest a self-contained, falsifiable framework for the transition from quantum to classical spacetime without the need for adjustable parameters.
Heating induced by the noise postulated in wave function collapse models leads to a lower bound to the temperature of solid objects. For the noise parameter values
λ=coupling strength∼10−8s−1 and
rC=correlation length∼10−5cm, which were suggested \cite{adler1} to make latent image formation an indicator of wave function collapse and which are consistent with the recent experiment of Vinante et al. \cite{vin}, the effect may be observable. For metals, where the heat conductivity is proportional to the temperature at low temperatures, the lower bound (specifically for RRR=30 copper) is $\sim 5\times 10^{-11} (L/r_C) $K, with L the size of the object. For the thermal insulator Torlon 4203, the comparable lower bound is
∼3×10−6(L/rc)0.63 K. We first give a rough estimate for a cubical metal solid, and then give an exact solution of the heat transfer problem for a sphere.
The Gravitational Poissonian Spontaneous Localization (GPSL) model is a hybrid classical-quantum framework in which Newtonian gravity emerges from stochastic collapses of a smeared mass-density operator. Consistency of the hybrid dynamics entails momentum diffusion and, hence, spontaneous heating. Without smearing, which enters both the collapse (measurement) and gravitational-feedback components of the dynamics, the heating rate would be divergent. Previous work assumed identical smearings for both components. Here, we treat the general case of distinct spatial smearings
grC(x) and
grG(x), characterized, respectively, by length scales
rC and
rG. We characterize the spontaneous heating rate for arbitrary
grC(x) and
grG(x), and then discuss which smearing profiles minimize the spontaneous heating rate in relevant physical situations. Remarkably, there are situations in which, while the measurement noise remains the same, allowing
grG(x)=grC(x) may reduce the feedback-induced spontaneous heating by more than 60 orders of magnitude already for
rG=10rC. Finally, we use our results to estimate the spontaneous heating rate of neutron stars and to set new lower bounds on the model's parameters by comparing the theoretical predictions with astronomical data on temperature, radius, and mass of neutron stars.