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arXiv:quant-ph/0001041

CSL Collapse Model And Spontaneous Radiation: An Update

Philip Pearle, Ring, James, J. I. Collar, Frank T. Avignone III

Published Jan 12, 2000• 61 citations
arXivHTMLPDF

Abstract

A brief review is given of the Continuous Spontaneous Localization (CSL) model in which a classical field interacts with quantized particles to cause dynamical wavefunction collapse. One of the model's predictions is that particles "spontaneously" gain energy at a slow rate. When applied to the excitation of a nucleon in a Ge nucleus, it is shown how a limit on the relative collapse rates of neutron and proton could be obtained, and a rough estimate is made from data. When applied to the spontaneous excitation of 1s electrons in Ge, by a more detailed analysis of more accurate data than previously given, an updated limit is obtained on the relative collapse rates of the electron and proton, suggesting that the coupling of the field to electrons and nucleons is mass proportional.

DOI
10.48550/arxiv.quant-ph/0001041

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A brief review is given of the Continuous Spontaneous Localization (CSL) model in which a classical field interacts with quantized particles to cause dynamical wavefunction collapse. One of the model's predictions is that particles "spontaneously" gain energy at a slow rate. When applied to the excitation of a nucleon in a Ge nucleus, it is shown how a limit on the relative collapse rates of neutron and proton could be obtained, and a rough estimate is made from data. When applied to the spontaneous excitation of 1s electrons in Ge, by a more detailed analysis of more accurate data than previously given, an updated limit is obtained on the relative collapse rates of the electron and proton, suggesting that the coupling of the field to electrons and nucleons is mass proportional.
One way to solve the long-standing ``measurement''problem in quantum mechanics is to modify Schr\"odinger's equation so that the collapse of a state vector is the result of some intrinsic physical dynamics. The introduction of such collapse dynamics often results in energy nonconservation. In this paper, we first derive a general expression for the rate of change in the expectation value of energy in a general collapse model that supports a linear evolution of the density matrix. In particular, we show, under certain plausible assumptions, that energy nonconservation is an inevitable consequence of collapse. We then work with a specific model, namely, the nonrelativistic continuous spontaneous localization (CSL) model, to derive further consequences of collapse. In CSL, in a nonunitary evolution, a particle interacts with a fluctuating scalar field, leading to the collapse of the state vector. One consequence of this interaction is that a free electron can radiate spontaneously. We calculate the spectrum of this radiation. The result is then compared with the observed upper bound on spontaneous radiation in Ge and a constraint on the parameters of CSL is obtained.
The Majorana Demonstrator neutrinoless double-beta decay experiment comprises a 44 kg (30 kg enriched in ^{76}Ge) array of p-type, point-contact germanium detectors. With its unprecedented energy resolution and ultralow backgrounds, Majorana also searches for rare event signatures from beyond standard model physics in the low energy region below 100 keV. In this Letter, we test the continuous spontaneous localization (CSL) model, one of the mathematically well-motivated wave function collapse models aimed at solving the long-standing unresolved quantum mechanical measurement problem. While the CSL predicts the existence of a detectable radiation signature in the x-ray domain, we find no evidence of such radiation in the 19-100 keV range in a 37.5 kg-y enriched germanium exposure collected between December 31, 2015, and November 27, 2019, with the Demonstrator. We explored both the non-mass-proportional (n-m-p) and the mass-proportional (m-p) versions of the CSL with two different assumptions: that only the quasifree electrons can emit the x-ray radiation and that the nucleus can coherently emit an amplified radiation. In all cases, we set the most stringent upper limit to date for the white CSL model on the collapse rate, λ, providing a factor of 40-100 improvement in sensitivity over comparable searches. Our limit is the most stringent for large parts of the allowed parameter space. If the result is interpreted in terms of the Diòsi-Penrose gravitational wave function collapse model, the lower bound with a 95% confidence level is almost an order of magnitude improvement over the previous best limit.
{The Continuous Spontaneous Localization (CSL) theory alters the Schrodinger equation. It describes wave function collapse as a dynamical process instead of an ill-defined postulate, thereby providing macroscopic uniqueness and solving the so-called measurement problem of standard quantum theory. CSL contains a parameter λ\lambdaλ giving the collapse rate of an isolated nucleon in a superposition of two spatially separated states and, more generally, characterizing the collapse time for any physical situation. CSL is experimentally testable, since it predicts some behavior different from that predicted by standard quantum theory. One example is the narrowing of wave functions, which results in energy imparted to particles. Here we consider energy given to trapped ultra-cold atoms. Since these are the coldest samples under experimental investigation, it is worth inquiring how they are affected by the CSL heating mechanism. We examine the CSL heating of a BEC in contact with its thermal cloud. Of course, other mechanisms also provide heat and also particle loss. From varied data on optically trapped cesium BEC's, we present an energy audit for known heating and loss mechanisms. The result provides an upper limit on CSL heating and thereby an upper limit on the parameter λ\lambdaλ. We obtain λ≲1(±1)×10−7\lambda\lesssim 1(\pm1)\times 10^{-7}λ≲1(±1)×10−7sec−1^{-1}−1.}
In this paper new upper limits on the parameters of the Continuous Spontaneous Localization (CSL) collapse model are extracted. To this end the X-ray emission data collected by the IGEX collaboration are analyzed and compared with the spectrum of the spontaneous photon emission process predicted by collapse models. This study allows to obtain the most stringent limits within a relevant range of the CSL model parameters, with respect to any other method. The collapse rate λ\lambdaλ and the correlation length rCr_CrC​ are mapped, thus allowing to exclude a broad range of the parameter space.
The work presented in this paper aimed to obtain new, more stringent, limits on the parameters of the Continuous Spontaneous Localization collapse model. The result is accomplished by performing a Bayesian analysis of the X-ray emission data collected by the IGEX collaboration, compared with the spontaneous photon emission which is predicted by collapse models. The most stringent limits on the collapse rate λ\lambdaλ and the correlation length rCr_CrC​ of the CSL model are obtained , with respect to any other method, over a broad range of the parameters space.
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^{74}\mathrm{Ge}74Ge nucleus.