Wave Function Realism in a Relativistic Setting

2020 ◽  
pp. 154-168
Author(s):  
Alyssa Ney
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Higher Dimensions ◽  
Recent Criticism ◽  
Interpretation Of Quantum Mechanics ◽  
Quantum Theories ◽  
Realist Interpretation ◽  
Wave Function Realism

The purpose of the present chapter is to respond to a thread of recent criticism against one candidate framework for interpreting quantum theories, a framework introduced and defended by David Albert and Barry Loewer: wave function realism, a framework for interpreting the ontology of quantum theories according to which what appears to be a nonseparable metaphysics ofentangled objects acting instantaneously across spatial distances is a manifestation of a more fundamental separable and local metaphysics in higher dimensions. Thechapterconsiders strategies for extending the wave function realist interpretation of quantum mechanics to the case of relativistic quantum theories, responding to arguments that this cannot be done.

The Virtues of Separability and Locality

2021 ◽  
pp. 80-132
Author(s):  
Alyssa Ney
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Bell’S Theorem ◽  
Bell's Theorem ◽  
Quantum Theories ◽  
Interpretations Of Quantum Mechanics ◽  
Realist Interpretation ◽  
Quantum Interpretation ◽  
Wave Function Realism

This chapter presents the argument for wave function realism that it is the only realist interpretation of quantum theories that can maintain a fundamentally separable and local metaphysics. It is commonly seen as a consequence of entanglement and Bell’s Theorem that quantum mechanics entails quantum nonseparability and nonlocality. Yet although all rival realist ontological interpretations of quantum mechanics involve either a nonseparable or a nonlocal fundamental metaphysics, the metaphysics of wave function realism is fundamentally both separable and local, although the view also makes room for nonfundamental nonseparability and nonlocality. The chapter considers several arguments that could explain why one should prefer interpretations of quantum theories that are separable and local, and concludes with a defense of intuitions in quantum interpretation.

Wave Function Realism in a Relativistic Setting

2021 ◽  
pp. 133-165
Author(s):  
Alyssa Ney
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Nonrelativistic Quantum ◽  
Important Lesson ◽  
Quantum Theories ◽  
Nonrelativistic Quantum Mechanics ◽  
Wave Function Realism

This chapter considers and responds to criticism that wave function realism is only plausible as an approach to the interpretation of nonrelativistic quantum mechanics and not relativistic quantum theories and quantum field theories. This critique gains traction as wave function realism has until now been formulated and defended solely within the context of idealized, nonrelativistic quantum mechanics. The chapter considers five such arguments and responds to each. An important lesson is that wave function realists should only adopt the wave-function-in-configuration-space picture as part of an interpretation of an idealized nonrelativistic quantum mechanics. More generally, the space the wave function inhabits will vary as the quantum theory the wave function realist is developing an interpretation of varies. The chapter develops a sketch of what wave function realism looks like in one relativistic context. It then discusses the issue of the interpretation of quantum theories in the limit of physical theorizing.

The Argument from Entanglement

2021 ◽  
pp. 49-79
Author(s):  
Alyssa Ney
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Entanglement ◽  
Structural Realism ◽  
Higher Dimensions ◽  
Quantum States ◽  
Central Issue ◽  
Entangled States ◽  
Field Approach ◽  
Wave Function Realism

In quantum mechanics, entangled states are not exotic or rare. Rather, entanglement is the norm and so the metaphysical consequences of entanglement are a central issue for anyone wishing to provide an ontological interpretation of the various formulations of quantum mechanics. This chapter presents the argument for wave function realism from quantum entanglement, which says that wave function realism is necessary if one wants an ontological interpretation that does not conflate distinct quantum states. It explains quantum entanglement and how postulating a wave function in higher dimensions can help to metaphysically ground the phenomenon. The chapter ultimately concludes that the argument from quantum entanglement fails as there are several rival positions that can also explain quantum entanglement and recover the distinctions between different entangled states. These include the primitive ontology approach, various other holisms, ontic structural realism, spacetime state realism, and the multi-field approach.

The World in the Wave Function

2021 ◽  
Author(s):  
Alyssa Ney
Keyword(s):  
Wave Function ◽  
Dimensional Space ◽  
Higher Dimensions ◽  
Quantum Nonlocality ◽  
High Dimensional ◽  
Material Objects ◽  
Quantum Theories ◽  
Quantum Wave Function ◽  
Quantum Wave ◽  
Wave Function Realism

What are the ontological implications of quantum theories, that is, what do they tell us about the fundamental objects that make up our world? How should quantum theories make us reevaluate our classical conceptions of the basic constitution of material objects and ourselves? Is there fundamental quantum nonlocality? This book articulates several rival approaches to answering these questions, ultimately defending the wave function realist approach. Wave function realism is a way of interpreting quantum theories so that the central object they describe is the quantum wave function, interpreted as a field in an extremely high-dimensional space. According to this approach, the nonseparability and nonlocality we seem to find in quantum mechanics are ultimately manifestations of a more intuitive, separable, and local picture in higher dimensions.

Density Functional Approaches to Relativistic Quantum Mechanics

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Electron Density ◽  
Density Functional ◽  
Relativistic Quantum ◽  
Electron System ◽  
State Density ◽  
Dft Methods ◽  
Particle Wave Function ◽  
Spatial Coordinates

The wave function is an elusive and somewhat mysterious object. Nobody has ever observed the wave function directly: rather, its existence is inferred from the various experiments whose outcome is most rationally explained using a wave function interpretation of quantum mechanics. Further, the N-particle wave function is a rather complicated construction, depending on 3N spatial coordinates as well as N spin coordinates, correlated in a manner that almost defies description. By contrast, the electron density of an N-electron system is a much simpler quantity, described by three spatial coordinates and even accessible to experiment. In terms of the wave function, the electron density is expressed as . . . ρ(r) = N ∫ Ψ* (r1,r2,...,rN)Ψ (r1,r2,...,rN)dr2dr3 ...drN (14.1) . . . where the sum over spin coordinates is implicit. It might be much more convenient to have a theory based on the electron density rather than the wave function. The description would be much simpler, and with a greatly reduced (and constant) number of variables, the calculation of the electron density would hopefully be faster and less demanding. We also note that given the correct ground state density, we should be able to calculate any observable quantity of a stationary system. The answer to these hopes is density functional theory, or DFT. Over the past decade, DFT has become one of the most widely used tools of the computational chemist, and in particular for systems of some size. This success has come despite complaints about arbitrary parametrization of potentials, and laments about the absence of a universal principle (other than comparison with experiment) that can guide improvements in the way the variational principle has led the development of wave-function-based methods. We do not intend to pursue that particular discussion, but we note as a historical fact that many important early contributions to relativistic quantum chemistry were made using DFT-like methods. Furthermore, there is every reason to try to extend the success of nonrelativistic DFT methods to the relativistic domain. We suspect that their potential for conquering a sizable part of this field is at least as large as it has been in the nonrelativistic domain.

INTERPRETATION AND PREDICTABILITY OF QUANTUM MECHANICS AND QUANTUM COSMOLOGY

1988 ◽  
Vol 03 (07) ◽  
pp. 645-651 ◽  
Author(s):  
SUMIO WADA
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Physical Meaning ◽  
Quantum Cosmology ◽  
Degrees Of Freedom ◽  
Interpretation Of Quantum Mechanics ◽  
Probabilistic Interpretation ◽  
The Universe ◽  
Classical Picture

A non-probabilistic interpretation of quantum mechanics asserts that we get a prediction only when a wave function has a peak. Taking this interpretation seriously, we discuss how to find a peak in the wave function of the universe, by using some minisuperspace models with homogeneous degrees of freedom and also a model with cosmological perturbations. Then we show how to recover our classical picture of the universe from the quantum theory, and comment on the physical meaning of the backreaction equation.

scholarly journals A Phenomenological Reading of the Many-Worlds Interpretation of Quantum Mechanics

2020 ◽  
Author(s):  
Joaquin Trujillo
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Measurement Problem ◽  
Copenhagen Interpretation ◽  
Interpretation Of Quantum Mechanics ◽  
Many Worlds ◽  
Standard Interpretation ◽  
Hermeneutic Phenomenological ◽  
Many Worlds Interpretation ◽  
The Many

The articles provides a phenomenological reading of the Many-Worlds Interpretation (MWI) of quantum mechanics and its answer to the measurement problem, or the question of “why only one of a wave function’s probable values is observed when the system is measured.” Transcendental-phenomenological and hermeneutic-phenomenological approaches are employed. The project comprises four parts. Parts one and two review MWI and the standard (Copenhagen) interpretation of quantum mechanics. Part three reviews the phenomenologies. Part four deconstructs the hermeneutics of MWI. It agrees with the confidence the theory derives from its (1) unforgiving appropriation of the Schrödinger equation and (2) association of branching universes with the evolution of the wave function insofar as that understanding comes from the formalism itself. Part four also reveals the hermeneutical shortcomings of the standard interpretation.

Constructing deterministic models for quantum mechanical systems

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040007
Author(s):  
Gerard ’t Hooft
Keyword(s):  
Quantum Mechanics ◽  
Essential Element ◽  
Quantum Mechanical ◽  
Interpretation Of Quantum Mechanics ◽  
Final States ◽  
Deterministic Models ◽  
Quantum Theories ◽  
Initial States ◽  
Quantum Mechanical Systems ◽  
Entire Theory

A sharper formulation is presented for an interpretation of quantum mechanics advocated by the author. We claim that only those quantum theories should be considered for which an ontological basis can be constructed. In terms of this basis, the entire theory can be considered as being deterministic. An example is illustrated: massless, noninteracting fermions are ontological. Subsequently, as an essential element of the deterministic interpretation, we put forward conservation laws concerning the ontological nature of a variable, and the uncertainties concerning the realization of states. Quantum mechanics can then be treated as a device that combines statistics with mechanical, deterministic laws, such that uncertainties are passed on from initial states to final states.

Probability relations between separated systems

1936 ◽  
Vol 32 (3) ◽  
pp. 446-452 ◽  
Author(s):  
E. Schrödinger
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Pure State ◽  
Relativistic Quantum ◽  
Present Theory ◽  
Relativistic Quantum Mechanics ◽  
Quantum Mechanical ◽  
Alternative Possibility ◽  
Linearly Independent ◽  
Statistical Operator

The paper first scrutinizes thoroughly the variety of compositions which lead to the same quantum-mechanical mixture (as opposed to state or pure state). With respect to a given mixture every state has a definite probability (or mixing fraction) between 0 and 1 (including the limits), which is calculated from the mixtures Statistical Operator and the wave function of the state in question.A well-known example of mixtures occurs when a system consists of two separated parts. If the wave function of the whole system is known, either part is in the situation of a mixture, which is decomposed into definite constituents by a definite measuring programme to be carried out on the other part. All the conceivable decompositions (into linearly independent constituents) of the first system are just realized by all the possible measuring programmes that can be carried out on the second one. In general every state of the first system can be given a finite chance by a suitable choice of the programme.It is suggested that these conclusions, unavoidable within the present theory but repugnant to some physicists including the author, are caused by applying non-relativistic quantum mechanics beyond its legitimate range. An alternative possibility is indicated.

On the completeness problem for the eigenfunction formulae of relativistic quantum mechanics

1961 ◽  
Vol 262 (1311) ◽  
pp. 489-502 ◽  
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Partial Differential ◽  
Completeness Problem ◽  
Complete Set

Dirac’s theory of relativistic quantum mechanics leads to the problem of solving a set of four partial differential equations for the four components of the wave function. Solutions of these equations in the case where the potential is a function of the radial co-ordinate only were obtained by Darwin. It is proved that these solutions form a complete set in the sense that we can simultaneously expand four arbitrary functions in terms of them.

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