Protective measurement and the nature of the wave function within the primitive ontology approach

2015 ◽  
pp. 195-210
Author(s):  
Vincent Lam
Keyword(s):  
Wave Function ◽  
Primitive Ontology

scholarly journals Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 594
Author(s):  
Antoine Tilloy ◽  
Howard M. Wiseman
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Initial Conditions ◽  
Hidden Variables ◽  
Bohmian Mechanics ◽  
Primitive Ontology ◽  
Collapse Model ◽  
Collapse Models

Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise term to the Schrödinger equation, and extract definite measurement outcomes either from the wave function (e.g. mass density ontology) or the noise itself (flash ontology). Bohmian mechanics keeps the Schrödinger equation intact but uses the wave function to guide particles (or fields), which comprise the primitive ontology. Collapse models modify the predictions of orthodox quantum mechanics, whilst Bohmian mechanics can be argued to reproduce them. However, it turns out that collapse models and their primitive ontology can be exactly recast as Bohmian theories. More precisely, considering (i) a system described by a non-Markovian collapse model, and (ii) an extended system where a carefully tailored bath is added and described by Bohmian mechanics, the stochastic wave-function of the collapse model is exactly the wave-function of the original system conditioned on the Bohmian hidden variables of the bath. Further, the noise driving the collapse model is a linear functional of the Bohmian variables. The randomness that seems progressively revealed in the collapse models lies entirely in the initial conditions in the Bohmian-like theory. Our construction of the appropriate bath is not trivial and exploits an old result from the theory of open quantum systems. This reformulation of collapse models as Bohmian theories brings to the fore the question of whether there exists `unromantic' realist interpretations of quantum theory that cannot ultimately be rewritten this way, with some guiding law. It also points to important foundational differences between `true' (Markovian) collapse models and non-Markovian models.

Scientific Realism without the Wave Function

2020 ◽  
pp. 212-228
Author(s):  
Valia Allori
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Scientific Realism ◽  
Theory Construction ◽  
Scientific Theories ◽  
Primitive Ontology ◽  
Theory Evaluation ◽  
Spatio Temporal ◽  
True Quantum

Scientific realism assumes that our best scientific theories can be regarded as (approximately) true. Quantum mechanics has long been regarded as at odds with scientific realism. It is now known that this is not true. However, scientific realists usually assume that the wave function represents physical entities. Chapter 11 discusses a particular approach which makes quantum mechanics compatible with scientific realism without assuming this: matter is instead represented by some spatio-temporal entity dubbed the primitive ontology. It argues how within this framework one developsa distinctive theory-construction schema, which allows us to perform a more informed theory evaluation by analyzing the various ingredients of the approach and their inter-relations.

scholarly journals Scientific Realism and Primitive Ontology Or: The Pessimistic Induction and the Nature of the Wave Function

2018 ◽  
Vol 5 (1) ◽  
pp. 69-76 ◽  
Author(s):  
Valia Allori
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Philosophy Of Science ◽  
Scientific Realism ◽  
Pessimistic Induction ◽  
Physical Entity ◽  
Primitive Ontology ◽  
Induction Argument ◽  
Quantum Domain ◽  
Recent Debate

In this paper, I wish to connect the recent debate in the philosophy of quantum mechanics concerning the nature of the wave function to the historical debate in the philosophy of science regarding the tenability of scientific realism. Advocating realism about quantum mechanics is particularly challenging when focusing on the wave function. According to the wave function ontology approach, the wave function is a concrete physical entity. In contrast, according to an alternative viewpoint, namely the primitive ontology approach, the wave function does not represent physical objects. In this paper, I argue that the primitive ontology approach can naturally be interpreted as an instance of the so-called explanationist realism, which has been proposed as a response to the pessimistic-meta induction argument against scientific realism. If my arguments are sound, then one could conclude that: (1) contrary to what is commonly thought, if explanationism realism is a good response to the pessimistic-meta induction argument, it can be straightforwardly extended also to the quantum domain; (2) the primitive ontology approach is in better shape than the wave function ontology approach in resisting the pessimistic-meta induction argument against scientific realism.

Analytic integration of contrast transfer functions

1988 ◽  
Vol 46 ◽  
pp. 822-823
Author(s):  
Peter Rez
Keyword(s):  
Wave Function ◽  
Transfer Function ◽  
Transfer Functions ◽  
Spherical Aberration ◽  
Continuous Distribution ◽  
Objective Lens ◽  
Direction Parallel ◽  
Scattering Angle ◽  
Analytic Integration ◽  
Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

Atomic Imaging of Crystals using Large-Angle Electron Scattering in STEM

1990 ◽  
Vol 48 (1) ◽  
pp. 74-75
Author(s):  
D.E. Jesson ◽  
S. J. Pennycook
Keyword(s):  
Wave Function ◽  
Electron Scattering ◽  
Numerical Solutions ◽  
Large Angle ◽  
Real Space ◽  
High Angle ◽  
Analytical Treatment ◽  
Order Zero ◽  
Experimental Conditions ◽  
Ewald Sphere

It is well known that conventional atomic resolution electron microscopy is a coherent imaging process best interpreted in reciprocal space using contrast transfer function theory. This is because the equivalent real space interpretation involving a convolution between the exit face wave function and the instrumental response is difficult to visualize. Furthermore, the crystal wave function is not simply related to the projected crystal potential, except under a very restrictive set of experimental conditions, making image simulation an essential part of image interpretation. In this paper we present a different conceptual approach to the atomic imaging of crystals based on incoherent imaging theory. Using a real-space analysis of electron scattering to a high-angle annular detector, it is shown how the STEM imaging process can be partitioned into components parallel and perpendicular to the relevant low index zone-axis.It has become customary to describe STEM imaging using the analytical treatment developed by Cowley. However, the convenient assumption of a phase object (which neglects the curvature of the Ewald sphere) fails rapidly for large scattering angles, even in very thin crystals. Thus, to avoid unpredictive numerical solutions, it would seem more appropriate to apply pseudo-kinematic theory to the treatment of the weak high angle signal. Diffraction to medium order zero-layer reflections is most important compared with thermal diffuse scattering in very thin crystals (<5nm). The electron wave function ψ(R,z) at a depth z and transverse coordinate R due to a phase aberrated surface probe function P(R-RO) located at RO is then well described by the channeling approximation;

DEUTERON: WAVE FUNCTION AND PARAMETERS

2014 ◽  
Vol 36 (0) ◽  
pp. 100-106 ◽  
Author(s):  
І. І. Гайсак ◽  
В. І. Жаба
Keyword(s):  
Wave Function ◽  
Deuteron Wave Function

Operators and meaning of wave function

2016 ◽  
pp. 4039-4042
Author(s):  
Viliam Malcher
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
State Vector ◽  
The State ◽  
Physical Significance ◽  
Central Problem ◽  
Quantum Mechanical ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Interpretation Of Quantum Theory

The interpretation problems of quantum theory are considered. In the formalism of quantum theory the possible states of a system are described by a state vector. The state vector, which will be represented as |ψ> in Dirac notation, is the most general form of the quantum mechanical description. The central problem of the interpretation of quantum theory is to explain the physical significance of the |ψ>. In this paper we have shown that one of the best way to make of interpretation of wave function is to take the wave function as an operator.

The build of nonlinear quantum mechancs and variations of feature of microscopic particles as well as their experimental affirmation

2014 ◽  
Vol 5 (3) ◽  
pp. 871-981 ◽  
Author(s):  
Pang Xiao Feng
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Lagrange Equation ◽  
Minimum Principle ◽  
Superposition Principle ◽  
Type Equation ◽  
Experimental Results ◽  
Traditional Concept ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

We establish the nonlinear quantum mechanics due to difficulties and problems of original quantum mechanics, in which microscopic particles have only a wave feature, not corpuscle feature, which are completely not consistent with experimental results and traditional concept of particle. In this theory the microscopic particles are no longer a wave, but localized and have a wave-corpuscle duality, which are represented by the following facts, the solutions of dynamic equation describing the particles have a wave-corpuscle duality, namely it consists of a mass center with constant size and carrier wave, is localized and stable and has a determinant mass, momentum and energy, which obey also generally conservation laws of motion, their motions meet both the Hamilton equation, Euler-Lagrange equation and Newton-type equation, their collision satisfies also the classical rule of collision of macroscopic particles, the uncertainty of their position and momentum is denoted by the minimum principle of uncertainty. Meanwhile the microscopic particles in this theory can both propagate in solitary wave with certain frequency and amplitude and generate reflection and transmission at the interfaces, thus they have also a wave feature, which but are different from linear and KdV solitary wave’s. Therefore the nonlinear quantum mechanics changes thoroughly the natures of microscopic particles due to the nonlinear interactions. In this investigation we gave systematically and completely the distinctions and variations between linear and nonlinear quantum mechanics, including the significances and representations of wave function and mechanical quantities, superposition principle of wave function, property of microscopic particle, eigenvalue problem, uncertainty relation and the methods solving the dynamic equations, from which we found nonlinear quantum mechanics is fully new and different from linear quantum mechanics. Finally, we verify further the correctness of properties of microscopic particles described by nonlinear quantum mechanics using the experimental results of light soliton in fiber and water soliton, which are described by same nonlinear Schrödinger equation. Thus we affirm that nonlinear quantum mechanics is correct and useful, it can be used to study the real properties of microscopic particles in physical systems.

Holographic wave function and space-time

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Function ◽  
Space Time

Holographic wave function and space-time

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