Some experimental implications of the recent progress on wave function collapse are calculated. Exact results are derived for the center-of-mass wave function collapse caused by random scatterings and applied to a range of specific examples. The results show that recently proposed experiments to measure the GRW effect are likely to fail, since the effect of naturally occurring scatterings is of the same form as the GRW effect but generally much stronger. The same goes for attempts to measure the collapse caused by quantum gravity as suggested by Hawking and others. The results also indicate that macroscopic systems tend to be found in states with ∆x∆p = ¯h / √ 2, but microscopic systems in highly tiltedly squeezed states with ∆x∆p ≫ ¯h.
Some experimental implications of the recent progress on wave function collapse are calculated. Exact results are derived for the center-of-mass wave function collapse caused by random scatterings and applied to a range of specific examples. The results show that recently proposed experiments to measure the GRW effect are likely to fail, since the effect of naturally occurring scatterings is of the same form as the GRW effect but generally much stronger. The same goes for attempts to measure the collapse caused by quantum gravity as suggested by Hawking and others. The results also indicate that macroscopic systems tend to be found in states with ∆x∆p = ¯h / √ 2, but microscopic systems in highly tiltedly squeezed states with ∆x∆p ≫ ¯h.
We study the effect that the state-vector reduction of Ghirardi, Rimini, and Weber (GRW) [Phys. Rev. D 34, 470 (1986)] has on the quantum fluctuation-dissipation process. A conventional fluctuation-dissipation process stems from the interaction between a system of interest and a macroscopic number of microscopic variables, thereby suggesting the possible occurrence of an enhancement of the GRW wave-function collapse. We carry out an exact treatment of the joint action of conventional quantum dissipation and GRW wave-function collapse in the special case where the system of interest is a harmonic oscillator. We prove that the GRW dynamics does not lead to any significant departure from the predictions of ordinary quantum mechanics, if the region of astronomically large times is disregarded, where the energy of the system diverges as an effect of a slow but steady increase caused by the GRW collapses.
Abstract When about half a century ago the concept of universal spontaneous collapse of the wave function was conceived it was an attempt to alter standard non-relativistic quantum physics. As such, it was largely ignored by relativistic field theory and quantum gravity communities. A central motivation of spontaneous collapse community has been to replace the standard collapse-by-measurement that annoyed many. With few exceptions, it did not annoy the field theory and quantum gravity communities. Concept of certain general-relativity-related universal irreversibility in quantum field theory had been initiated very long ago by Wheeler, Hawking and a few others independently from the concept of spontaneous collapse. Lately the two concepts started to converge and support each other.
Among several possibilities for what reality could be like in view of the empirical facts of quantum mechanics, one is provided by theories of spontaneous wave function collapse, the best known of which is the Ghirardi–Rimini–Weber (GRW) theory. We show mathematically that in GRW theory (and similar theories) there are limitations to knowledge, that is, inhabitants of a GRW universe cannot find out all the facts true of their universe. As a specific example, they cannot accurately measure the number of collapses that a given physical system undergoes during a given time interval; in fact, they cannot reliably measure whether one or zero collapses occur. Put differently, in a GRW universe certain meaningful, factual questions are empirically undecidable. We discuss several types of limitations to knowledge and compare them with those in other (no-collapse) versions of quantum mechanics, such as Bohmian mechanics. Most of our results also apply to observer-induced collapses as in orthodox quantum mechanics (as opposed to the spontaneous collapses of GRW theory). 1 Introduction 1.1 Known examples of limitations to knowledge 1.2 Remarks2 Brief Review of GRW Theories 2.1 The GRW process 2.2 GRWm 2.3 GRWf3 First Examples of Limitations to Knowledge in GRW Theories4 Measurements of Flashes in GRWf, or of Collapses in GRWm 4.1 An example in which ψ is known 4.2 Other choices of ψ 4.3 Experiments beginning before t 2 4.4 If ψ is random 4.5 Optimal way of distinguishing two density matrices 4.6 If ψ is unknown5 Measurements of m(x) in GRWmAppendix
Quantum mechanics is an extremely successful theory that agrees with every experimental test. However, the principle of linear superposition, a central tenet of the theory, apparently contradicts a commonplace observation: macroscopic objects are never found in a linear superposition of position states. Moreover, the theory does not explain why during a quantum measurement, deterministic evolution is replaced by probabilistic evolution, whose random outcomes obey the Born probability rule. In this article a review is given of an experimentally falsifiable phenomenological proposal, known as continuous spontaneous collapse: a stochastic nonlinear modification of the Schr\"odinger equation, which resolves these problems, while giving the same experimental results as quantum theory in the microscopic regime. Two underlying theories for this phenomenology are reviewed: trace dynamics and gravity-induced collapse. As the macroscopic scale is approached, predictions of this proposal begin to differ appreciably from those of quantum theory and are being confronted by ongoing laboratory experiments that include molecular interferometry and optomechanics. These experiments, which test the validity of linear superposition for large systems, are reviewed here, and their technical challenges, current results, and future prospects summarized. It is likely that over the next two decades or so, these experiments can verify or rule out the proposed stochastic modification of quantum theory.
Abstract Inspired by an ontic view of the wave function in quantum mechanics and motivated by the universal interaction of gravity, we discuss a possible gravity implication in the state collapse mechanism. Concretely, we investigate the stability of the spatial superposition of a massive quantum state under the gravity effect. In this context, we argue that the stability of the spatially superposed state , depends on its gravitational self-energy originating from the effective mass density distribution through the spatially localized eigenstates . We reveal that the gravitational self-interaction between the different spacetime curvatures created by the eigenstate effective masses leads to the reduction of the superposed state to one of the possible localized states . Among others, we discuss such a gravity-driven state reduction. Then, we approach the corresponding collapse time and the induced effective electric current in the case of a charged state, as well as the possible detection aspects.
The basic strategy underlying models of spontaneous wave function collapse (collapse models) is to modify the Schrödinger equation by including nonlinear stochastic terms, which tend to localize wave functions in space in a dynamical manner. These terms have negligible effects on microscopic systems—therefore their quantum behaviour is practically preserved. On the other end, since the strength of these new terms scales with the mass of the system, they become dominant at the macroscopic level, making sure that wave functions of macro-objects are always well-localized in space. We will review these basic features. By changing the dynamics of quantum systems, collapse models make predictions, which are different from standard quantum mechanical predictions. Although they are difficult to detect, we discuss the most relevant scenarios, where such deviations can be observed.