Possible role of gravity in collapse of the wave-function: a brief survey of some ideas
Tejinder P. Singh
备注:
16 pages, one figure, submitted to J. Phys. Conf. Series [proceedings of the conference DICE2014: Spacetime - Matter - Quantum Mechanics, Castiglioncello (Tuscany) September 15-19, 2014 Eds. H-T. Elze et al.]
This article is a brief survey of some approaches to implementing the suggestion that collapse of the wave function is mediated by gravity. These approaches include: a possible connection between the problem of time and problem of quantum measurement, decoherence models based on space-time uncertainty, the Schrödinger-Newton equation, attempts to introduce gravity into collapse models such as CSL, ideas based on the black hole - elementary particle complementarity, and the possible role of a complex space-time metric.
Roger Penrose and the author share the proposal that the spatial superposition $|x_1\rangle+|x_2\rangle$ of a massive object collapses into its localized components $|x_1\rangle$ or $|x_2\rangle$ with the characteristic time $\hbar/E_Δ$ where $E_Δ$ is the gravitational self-energy excess of the superposition versus the localized states. Underlying arguments of such radical departure from standard quantum mechanics and different derivations of the rate equation are briefly recapitulated and discussed.
This paper is a brief overview of the concepts involved in measuring the degree of contextuality and detecting contextuality in systems of binary measurements of a finite number of objects. We discuss and clarify the main concepts and terminology of the theory called "contextuality-by-default," and then discuss a possible generalization of the theory from binary to arbitrary measurements.
Does consciousness collapse the quantum wave function? This idea was taken seriously by John von Neumann and Eugene Wigner but is now widely dismissed. We develop the idea by combining a mathematical theory of consciousness (integrated information theory) with an account of quantum collapse dynamics (continuous spontaneous localization). Simple versions of the theory are falsified by the quantum Zeno effect, but more complex versions remain compatible with empirical evidence. In principle, versions of the theory can be tested by experiments with quantum computers. The upshot is not that consci…
Inspired by possible connections between gravity and foundational question in quantum theory, we consider an approach for the adaptation of objective collapse models to a general relativistic context. We apply these ideas to a list of open problems in cosmology and quantum gravity, such as the emergence of seeds of cosmic structure, the black hole information issue, the problem of time in quantum gravity and, in a more speculative manner, to the nature of dark energy and the origin of the very special initial state of the universe. We conclude that objective collapse models offer a rather prom…
Proposed derivations of the Born rule for Everettian theory are controversial. I argue that they are unnecessary but may provide justification for a simplified version of the Principal Principle. It's also unnecessary to replace Everett's idea that a subject splits in measurement contexts with the idea that subjects have linear histories which partition: Deutsch 1985, 2011; Saunders and Wallace 2008; Saunders 2010; Wallace 2012, Chapter 7; Wilson 2013, forthcoming. Linear histories were introduced to provide a concept of pre-measurement uncertainty and I explain why pre-measurement uncertainty…
Starting from an idea of S.L. Adler~\cite{Adler2015}, we develop a novel model of gravity-induced spontaneous wave-function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After deriving the fundamental equations, we prove the collapse and amplification mechanism, the two most important features of a consistent collapse model. Under reasonable simplifying assumptions, we constrain the strength $ξ$ of the complex metric fluctuations with available experimental data. We show that $ξ\geq 10^{-26}$ in order for the model to guarantee classicality of mac…
The goal of machine learning is to facilitate a computer to execute a specific task without explicit instruction by an external party. Quantum foundations seeks to explain the conceptual and mathematical edifice of quantum theory. Recently, ideas from machine learning have successfully been applied to different problems in quantum foundations. Here, we compile the representative works done so far at the interface of machine learning and quantum foundations. We conclude the survey with potential future directions.
We address the impossibility of achieving exact time reversal in a system with many degrees of freedom. This is a particular example of the difficult task of "aiming" an initial classical state so as to become a specific final state. We also comment on the classical-to-quantum transition in any non-separable closed system of $n \geq 2$ degrees of freedom. Even if the system is initially in a well defined WKB, semi-classical state, quantum evolution and, in particular, multiple reflections at classical turning points make it completely quantum mechanical with each particle smeared almost unifor…