Spontaneous Collapse Models Research Articles

Experimental tests of Quantum Mechanics: from Pauli Exclusion Principle Violation to spontaneous collapse models

The Pauli exclusion principle (PEP) and, more generally, the spin-statistics connection, is at the very basis of our understanding of matter. The PEP spurs, presently, a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible violation of PEP, where the q violation parameter translates into a probability of violating PEP. Experimentally, setting a bound on PEP violation means confining the q-parameter to a value very close to either 1 (for bosons) or -1 (for fermions). The VIP (Violation of the Pauli exclusion principle) experiment established a limit on the probability that PEP is violated by electrons, using the method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method, the obtained results, both in terms of the q-parameter and as probability of PEP violation, we briefly discuss the results and present future plans to go beyond the actual limit by upgrading the experimental technique using vetoed new spectroscopic fast Silicon Drift Detectors. We mention as well the possibility of using a similar experimental technique to search for eventual X-rays generated as a signature of the spontaneous collapse of the wave function, predicted by continuous spontaneous localization type theories.

Experimental tests of quantum mechanics – Pauli exclusion principle violation (the VIP experiment) and future perspective

The Pauli exclusion principle (PEP), consequence of the spin-statistics connection, is one of the basic principles of the modern physics. Being at the very basis of our understanding of matter, as many other fundamental principles it spurs a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible violation of PEP, where the violation parameter q translates into a probability of violating PEP. The VIP (VIolation of the Pauli exclusion principle) experiment established a new limit on the probability that PEP is violated by electrons, using the method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method, the obtained results, both in terms of the q-parameter from quon theory and as probability of PEP violation, we briefly discuss them and present future plans to go beyond the actual limit by upgrading the experimental setup. We also shortly mention the possibility of using a similar experimental technique to search for eventual X-rays, generated in the spontaneous collapse models in quantum mechanics.

EXPERIMENTAL TESTS OF QUANTUM MECHANICS PAULI EXCLUSION PRINCIPLE VIOLATION (THE VIP EXPERIMENT) AND FUTURE PERSPECTIVES

The Pauli exclusion principle (PEP) is one of the basic principles of modern physics. Being at the very basis of our understanding of matter, as many other fundamental principles it spurs, presently, a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible violation of PEP, where the violation parameter q translates into a probability of violating PEP. Experimentally, setting a bound on PEP violation means confining the violation parameter to a value very close to either 1 (for bosons) or -1 (for fermions). The VIP (VIolation of the Pauli exclusion principle) experiment established a limit on the probability that PEP is violated by electrons, using the method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method, the obtained results, both in terms of the q-parameter from quon theory and as probability of PEP violation, we briefly discuss them and present future plans to go beyond the actual limit by upgrading the experimental technique using vetoed new spectroscopical fast Silicon Drift Detectors. We also shortly mention the possibility of using a similar experimental technique to search for eventual X-rays, generated in the spontaneous collapse models.

Experimental tests of quantum mechanics: Pauli Exclusion Principle Violation (the VIP experiment) and future perspectives

The Pauli exclusion principle (PEP), as a consequence or the spin-statistics connection, is one of the basic principles of the modern physics. Being at the very basis of our understanding of matter, it spurs a lively debate on its possible limits, deeply rooted as it is in the very foundations of Quantum Field Theory. The VIP (VIolation of the Pauli exclusion principle) experiment established the world's best limit on the probability that PEP is violated by electrons, using the method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method and the obtained results; we briefly present future plans to go beyond the actual limit by upgrading the experiment using vetoed new spectroscopic fast Silicon Drift Detectors. We also shortly mention the possibility of using a similar experimental technique to search for possible X-rays generated in the spontaneous collapse models of quantum mechanics.

Nonlinear gauge interactions: A possible solution to the “measurement problem” in quantum mechanics

Two fundamental, and unsolved problems in physics are: i) the resolution of the "measurement problem" in quantum mechanics ii) the quantization of strongly nonlinear (nonabelian) gauge theories. The aim of this paper is to suggest that these two problems might be linked, and that a mutual, simultaneous solution to both might exist. We propose that the mechanism responsible for the "collapse of the wave function" in quantum mechanics is the nonlinearities already present in the theory via nonabelian gauge interactions. Unlike all other models of spontaneous collapse, our proposal is, to the best of our knowledge, the only one which does not introduce any new elements into the theory. A possible experimental test of the model would be to compare the coherence lengths - here defined as the distance over which quantum mechanical superposition is still valid - for, \textit{e.g}, electrons and photons in a double-slit experiment. The electrons should have a finite coherence length, while photons should have a much longer coherence length (in principle infinite, if gravity - a very weak effect indeed unless we approach the Planck scale - is ignored).

Collapse models with non-white noises: II. Particle-density coupled noises

We continue the analysis of models of spontaneous wavefunction collapse with stochastic dynamics driven by non-white Gaussian noise. We specialize to a model in which a classical ‘noise’ field, with specified autocorrelator, is coupled to a local nonrelativistic particle density. We derive general results in this model for the rates of density matrix diagonalization and of state vector reduction, and show that (in the absence of decoherence) both processes are governed by essentially the same rate parameters. As an alternative route to our reduction results, we also derive the Fokker–Planck equations that correspond to the initial stochastic Schrödinger equation. For specific models of the noise autocorrelator, including ones motivated by the structure of thermal Green's functions, we discuss the qualitative and quantitative dependence on model parameters, with particular emphasis on possible cosmological sources of the noise field.

Collapse models with non-white noises

We set up a general formalism for models of spontaneous wavefunction collapse with dynamics represented by a stochastic differential equation driven by general Gaussian noises, not necessarily white in time. In particular, we show that the non-Schrödinger terms of the equation induce the collapse of the wavefunction to one of the common eigenstates of the collapsing operators, and that the collapse occurs with the correct quantum probabilities. We also develop a perturbation expansion of the solution of the equation with respect to the parameter which sets the strength of the collapse process; such an approximation allows one to compute the leading-order terms for the deviations of the predictions of collapse models with respect to those of standard quantum mechanics. This analysis shows that to leading order, the ‘imaginary noise’ trick can be used for non-white Gaussian noise.

The quantum theory of measurement within dynamical reduction models

We analyse in mathematical detail, within the framework of the QMUPL model of spontaneous wavefunction collapse, the von Neumann measurement scheme for the measurement of a 1/2 spin particle. We prove that, according to the equation of the model, (i) throughout the whole measurement process, the pointer of the measuring device is always perfectly well localized in space; (ii) the probabilities for the possible outcomes are distributed in agreement with the Born probability rule; (iii) at the end of the measurement the state of the microscopic system has collapsed to the eigenstate corresponding to the measured eigenvalue. This analysis shows rigorously how dynamical reduction models provide a consistent solution to the measurement problem of quantum mechanics.

The Conway-Kochen Argument and Relativistic GRW Models

In a recent paper, Conway and Kochen proposed what is now known as the “Free Will theorem” which, among other things, should prove the impossibility of combining GRW models with special relativity, i.e., of formulating relativistically invariant models of spontaneous wavefunction collapse. Since their argument basically amounts to a non-locality proof for any theory aiming at reproducing quantum correlations, and since it was clear since very a long time that any relativistic collapse model must be non-local in some way, we discuss why the theorem of Conway and Kochen does not affect the program of formulating relativistic GRW models.

A Relativistic Version of the Ghirardi–Rimini–Weber Model

Carrying out a research program outlined by John S. Bell in 1987, we arrive at a relativistic version of the Ghirardi-Rimini-Weber (GRW) model of spontaneous wavefunction collapse. The GRW model was proposed as a solution of the measurement problem of quantum mechanics and involves a stochastic and nonlinear modification of the Schrödinger equation. It deviates very little from the Schrödinger equation for microscopic systems but efficiently suppresses, for macroscopic systems, superpositions of macroscopically different states. As suggested by Bell, we take the primitive ontology, or local beables, of our model to be a discrete set of space-time points, at which the collapses are centered. This set is random with distribution determined by the initial wavefunction. Our model is nonlocal and violates Bell’s inequality though it does not make use of a preferred slicing of space-time or any other sort of synchronization of spacelike separated points. Like the GRW model, it reproduces the quantum probabilities in all cases presently testable, though it entails deviations from the quantum formalism that are in principle testable. Our model works in Minkowski space-time as well as in (well-behaved) curved background space-times.

Collapse models: analysis of the free particle dynamics

We study a model of spontaneous wavefunction collapse for a free quantum particle. We analyse in detail the time evolution of the single-Gaussian solution and the double-Gaussian solution, showing how the reduction mechanism induces the localization of the wavefunction in space; we also study the asymptotic behaviour of the general solution. With an appropriate choice for the parameter λ which sets the strength of the collapse mechanism we prove that: (i) the effects of the reducing terms on the dynamics of microscopic systems are negligible, the physical predictions of the model being very close to those of standard quantum mechanics; (ii) at the macroscopic scale the model reproduces classical mechanics: the wavefunction of the centre of mass of a macro-object behaves, with high accuracy, like a point moving in space according to Newton's laws.

Spontaneous Collapse Models on a Lattice

We present spontaneous collapse models of field theories on a 1+1 null lattice, in which the causal structure of the lattice plays a central role. Issues such as “locality,” “nonlocality,” and superluminal signaling are addressed in the context of the models which have the virtue of extreme simplicity. The formalism of the models is related to that of the consistent histories approach to quantum mechanics.

Numerical analysis of a spontaneous collapse model for a two-level system

We study a spontaneous collapse model for a two-level (spin) system, in which the Hamiltonian and the stochastic terms do not commute. The numerical solution of the equations of motions allows one to give precise estimates on the regime at which the collapse of the state vector occurs, the reduction and delocalization times, and the reduction probabilities; it also allows one to quantify the effect that a Hamiltonian which does not commute with the reducing terms has on the collapse mechanism. We also give a clear picture of the transition from the ``microscopic'' regime (when the noise terms are weak and the Hamiltonian prevents the state vector to collapse) to the ``macroscopic'' regime (when the noise terms are dominant and the collapse becomes effective for very long times). Finally, we clarify the distinction between decoherence and collapse.

A simple model of quantum trajectories

Quantum trajectory theory, developed largely in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. I present a simple model, using two-level quantum systems (q-bits), to illustrate the essential physics of quantum trajectories and how different monitoring schemes correspond to different “unravelings” of a mixed state master equation. I also comment briefly on the relationship of the theory to the consistent histories formalism and to spontaneous collapse models.

Quantum computation, entanglement and state reduction

Some general foundational issues of quantum mechanics are considered and are related to aspects of quantum computation. The importance of quantum entanglement and quantum information is discussed a...