Gravity and the Collapse of the Wave Function: a Probe into Diósi-Penrose model

Abstract

We investigate the Diósi-Penrose (DP) proposal for connecting the collapse of the wave function to gravity. The DP model needs a free parameter, acting as a cut-off to regularize the dynamics, and the predictions of the model highly depend on the value of this cut-off. The Compton wavelength of a nucleon seems to be the most reasonable cut-off value since it justifies the non-relativistic approach. However, with this value, the DP model predicts an unrealistic high rate of energy increase. Thus, one either is forced to choose a much larger cut-off, which is not physically justified and totally arbitrary, or one needs to include dissipative effects in order to tame the energy increase. Taking the analogy with dissipative collisional decoherence seriously, we develop a dissipative generalization of the DP model. We show that even with dissipative effects, the DP model contradicts known physical facts, unless either the cut-off is kept artificially large, or one limits the applicability of the model to massive systems. We also provide an estimation for the mass range of this applicability.

arXiv comment15 pages, 1 figure; v2 updated references and fixed minor mistakes in Eqs.(18) and (31)-(34), thanks to Marko Toros for pointing them out

References in corpus (27)

• Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
• Dynamical Reduction Models
• Cavity optomechanics using an optically levitated nanosphere
• Testing the limits of quantum mechanical superpositions
• Gravitation and quantummechanical localization of macroobjects
• Lower and Upper Bounds on CSL Parameters from Latent Image Formation and IGM Heating
• The Schrödinger-Newton equation and its foundations
• The Schrödinger-Newton equation as non-relativistic limit of self-gravitating Klein-Gordon and Dirac fields
• Why Decoherence has not Solved the Measurement Problem: A Response to P. W. Anderson
• Quantum linear Boltzmann equation
• Completely Positive Quantum Dissipation
• Quantum Master Equation of Particle in Gas Environment
• Collapse of the State Vector
• Notes on Certain Newton Gravity Mechanisms of Wave Function Localisation and Decoherence
• Master equation for a quantum particle in a gas
• Ultimate decoherence border for matter-wave interferometry
• Gravity, energy conservation and parameter values in collapse models
• A General Argument Against the Universal Validity of the Superposition Principle
• Vacuum Birefringence in a Rotating Magnetic Field
• On the Energy Increase in Space-Collapse Models
• Monitoring derivation of the quantum linear Boltzmann equation
• Gravity-related spontaneous collapse in bulk matter
• Normalization of Collisional Decoherence: Squaring the Delta Function, and an Independent Cross-Check
• Dissipative extension of the Ghirardi-Rimini-Weber model
• On the precise connection between the GRW master-equation and master-equations for the description of decoherence
• Quantum master equation for collisional dynamics of massive particles with internal degrees of freedom
• Does gravity induce wavefunction collapse? An examination of Penrose's conjecture

Cited by in corpus (32)

• Gravitational Decoherence
• Underground test of gravity-related wave function collapse
• Present status and future challenges of non-interferometric tests of collapse models
• Sourcing semiclassical gravity from spontaneously localized quantum matter
• Bell's Theorem for Temporal Order
• Newton, entanglement, and the graviton
• Bounds on Collapse Models from Matter-Wave Interferometry: Calculational details
• Massive quantum systems as interfaces of quantum mechanics and gravity
• An ultra-narrow line width levitated nano-oscillator for testing dissipative wavefunction collapse
• A proposal for the experimental detection of CSL induced random walk
• Testing the foundations of quantum physics in space Interferometric and non-interferometric tests with Large Particles
• Roadmap on Quantum Thermodynamics
• Dissipative extension of the Ghirardi-Rimini-Weber model
• Testing Dissipative Collapse Models with a Levitated Micromagnet
• Gravitational interaction through a feedback mechanism
• Quantum enhanced estimation of diffusion
• On the effectiveness of the collapse in the Diósi-Penrose model
• Decoherence-Free Entropic Gravity: Model and Experimental Tests
• On the linear friction many-body equation for dissipative spontaneous wavefunction collapse
• Relativistic quantum field theory of stochastic dynamics in the Hilbert space
• Entanglement in Markovian hybrid classical-quantum theories of gravity
• Feasibility considerations for free-fall tests of gravitational decoherence
• Spontaneous Collapse Models
• Experimental bounds on linear-friction dissipative collapse models from levitated optomechanics
• Non-equilibrium thermodynamics of gravitational objective-collapse models
• Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility
• New avenues for testing collapse models
• Quantum Physics in Space
• Classifying deviation from standard quantum behavior using Kullback Leibler divergence
• Collapse models and gravitational decoherence at test: How far can we push the limits of quantum mechanics?
• Seven non-standard models coupling quantum matter and gravity
• Gravity-related collapse of the wave function and spontaneous heating: revisiting the experimental bounds