Citations of:
Quantum Mechanics and 3 N  Dimensional Space
Philosophy of Science 73 (5):778789 (2006)
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A century after the discovery of quantum mechanics, the meaning of quantum mechanics still remains elusive. This is largely due to the puzzling nature of the wave function, the central object in quantum mechanics. If we are realists about quantum mechanics, how should we understand the wave function? What does it represent? What is its physical meaning? Answering these questions would improve our understanding of what it means to be a realist about quantum mechanics. In this survey article, I review (...) 

It has been widely thought that the wave function describes a real, physical field in a realist interpretation of quantum mechanics. In this paper, I present a new analysis of the field ontology for the wave function. First, I argue that the nonexistence of selfinteractions for a quantum system such as an electron poses a puzzle for the field ontologists. If the wave function represents a physical field, then it seems odd that there are interactions between the fields of two (...) 

Philosophy is unsolved. My forthcoming book sets forth the final resolution, with some exceptions, to this 2,500 year crisis. I am currently close to finishing page 983. 

I argue that space has three dimensions, and quantum mechanics does not show otherwise. Specifically, I argue that the mathematical wave function of quantum mechanics corresponds to a property that an Nparticle system has in threedimensional space. 

I will defend two claims. First, Schaffer's priority monism is in tension with many research programs in quantum gravity. Second, priority monism can be modified into a view more amenable to this physics. The first claim is grounded in the fact that promising approaches to quantum gravity such as loop quantum gravity or string theory deny the fundamental reality of spacetime. Since fundamental spacetime plays an important role in Schaffer's priority monism by being identified with the fundamental structure, namely the (...) 

The paper points out that the modern formulation of Bohm’s quantum theory known as Bohmian mechanics is committed only to particles’ positions and a law of motion. We explain how this view can avoid the open questions that the traditional view faces according to which Bohm’s theory is committed to a wavefunction that is a physical entity over and above the particles, although it is defined on configuration space instead of threedimensional space. We then enquire into the status of the (...) 

What ontology does realism about the quantum state suggest? The main extant view in contemporary philosophy of physics is wavefunction realism . We elaborate the sense in which wavefunction realism does provide an ontological picture, and defend it from certain objections that have been raised against it. However, there are good reasons to be dissatisfied with wavefunction realism, as we go on to elaborate. This motivates the development of an opposing picture: what we call spacetime state realism , a view (...) 

According to a radical account of quantum metaphysics that I label ‘highdimensionalism’, ordinary objects are the ‘shadows’ of highdimensional fundamental ontology. Critics—especially Maudlin —allege that highdimensionalism cannot provide a satisfactory explanation of the manifest image. In this paper, I examine the two main ideas behind these criticisms: that highdimensionalist connections between fundamental and nonfundamental are 1) inscrutable, and 2) arbitrary. In response to the first, I argue that there is no metaphysically significant contrast regarding the scrutability of low and highdimensionalist (...) 

In a quantum universe with a strong arrow of time, we postulate a lowentropy boundary condition to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a unique initial condition in such a world. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix that represents something objective. This stands in sharp contrast to Wave Function (...) 

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostatethe special lowentropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two (...) 

Scientific realism is the view that our best scientific theories can be regarded as (approximately) true. This is connected with the view that science, physics in particular, and metaphysics could (and should) inform one another: on the one hand, science tells us what the world is like, and on the other hand, metaphysical principles allow us to select between the various possible theories which are underdetermined by the data. Nonetheless, quantum mechanics has always been regarded as, at best, puzzling, if (...) 

‘Space does not exist fundamentally: it emerges from a more fundamental nonspatial structure.’ This intriguing claim appears in various research programs in contemporary physics. Philosophers of physics tend to believe that this claim entails either that spacetime does not exist, or that it is derivatively real. In this article, I introduce and defend a third metaphysical interpretation of the claim: reductionism about space. I argue that, as a result, there is no need to subscribe to fundamentality, layers of reality and (...) 

The article sets out a primitive ontology of the natural world in terms of primitive stuff—that is, stuff that has as such no physical properties at all—but that is not a bare substratum either, being individuated by metrical relations. We focus on quantum physics and employ identitybased Bohmian mechanics to illustrate this view, but point out that it applies all over physics. Properties then enter into the picture exclusively through the role that they play for the dynamics of the primitive (...) 

This paper defends wave function realism against the charge that the view is empirically incoherent because our evidence for quantum theory involves facts about objects in threedimensional space or spacetime . It also criticizes previous attempts to defend wave function realism against this charge by claiming that the wave function is capable of grounding local beables as elements of a derivative ontology. 

Monism is roughly the view that there is only one fundamental entity. One of the most powerful argument in its favor comes from quantum mechanics. Extant discussions of quantum monism are framed independently of any interpretation of the quantum theory. In contrast, this paper argues that matters of interpretation play a crucial role when assessing the viability of monism in the quantum realm. I consider four different interpretations: modal interpretations, Bohmian mechanics, many worlds interpretations, and wavefunction realism. In particular, I (...) 

One of Julian Barbour’s main aims is to solve the problem of time that appears in quantum geometrodynamics (QG). QG involves the application of canonical quantization procedure to the Hamiltonian formulation of General Relativity. The problem of time arises because the quantization of the Hamiltonian constraint results in an equation that has no explicit time parameter. Thus, it appears that the resulting equation, as apparently timeless, cannot describe evolution of quantum states. Barbour attempts to resolve the problem by allegedly eliminating (...) 

Spacetime functionalism is the view that spacetime is a functional structure implemented by a more fundamental ontology. Lam and Wüthrich have recently argued that spacetime functionalism helps to solve the epistemological problem of empirical coherence in quantum gravity and suggested that it also (dis)solves the hard problem of spacetime, namely the problem of offering a picture consistent with the emergence of spacetime from a nonspatiotemporal structure. First, I will deny that spacetime functionalism solves the hard problem by showing that it (...) 

In this paper I review three different positions on the wave function, namely: nomological realism, dispositionalism, and configuration space realism by regarding as essential their capacity to account for the world of our experience. I conclude that the first two positions are committed to regard the wave function as an abstract entity. The third position will be shown to be a merely speculative attempt to derive a primitive ontology from a reified mathematical space. Without entering any discussion about nominalism, I (...) 

I defend a pragmatist reinterpretation of Sellars’s famous manifestscientific distinction. I claim that in order to do justice to this important distinction we must first recognize, despite what philosophers—including, arguably, Sellars—often make of it, that the distinction does not draw an epistemological or metaphysical boundary between different kinds of objects and events, but a pragmatic boundary between different ways in which we interact with objects and events. Put differently, I argue that the manifestscientific distinction, in my view, can be best (...) 

The aim of this thesis dissertation is to propose a novel position in the debate on scientific realism, modal empiricism, and to show its fruitfulness when it comes to interpreting the cognitive content of scientific theories. Modal empiricism is an empiricist position, according to which the aim of science is to produce empirically adequate theories rather than true theories. However, it suggests adopting a broader comprehension of experience than traditional versions of empiricism, through a commitment to natural modalities. Following modal (...) 

Suppose that God exists, and that God does not violate the laws of nature he created for the world. God can nevertheless act in the world, by acting at the indeterministic quantum level. This chapter makes two specific points about God’s quantum action. First, on some ways of understanding quantum mechanics (specifically, the GRW theory, and the associated Continuous Spontaneous Localization theories), God’s actions are almost unlimited, contrary to those who say that God would be quite constrained in his action, (...) 

In this paper, I critically assess different interpretations of Bohmian mechanics that are not committed to an ontology based on the wave function being an actual physical object that inhabits configuration space. More specifically, my aim is to explore the connection between the denial of configuration space realism and another interpretive debate that is specific to Bohmian mechanics: the quantum potential versus guidance approaches. Whereas defenders of the quantum potential approach to the theory claim that Bohmian mechanics is better formulated (...) 

The main claim of the paper is that one can be ‘realist’ (in some sense) about quantum mechanics without requiring any form of realism about the wave function. We begin by discussing various forms of realism about the wave function, namely Albert’s configurationspace realism, Dürr Zanghi and Goldstein’s nomological realism about Ψ, Esfeld’s dispositional reading of Ψ Pusey Barrett and Rudolph’s realism about the quantum state. By discussing the articulation of these four positions, and their interrelation, we conclude that instrumentalism (...) 

The ManyWorlds Interpretation (MWI) is an approach to quantum mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds which exist in parallel at the same space and time. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics. 

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. Being realist 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 (...) 

In the first part of the paper I argue that an ontology of events is precise, flexible and general enough so as to cover the three main alternative formulations of quantum mechanics as well as theories advocating an antirealistic view of the wave function. Since these formulations advocate a primitive ontology of entities living in fourdimensional spacetime, they are good candidates to connect that quantum image with the manifest image of the world. However, to the extent that some form of (...) 

The problem of the 3N dimensions of the wave function is of particular interest in the philosophy of physics. In this work, we will recall the main positions about the nature and dimensionality of the wave function and we will introduce a new perspective, coming from quantum chemistry. For this, we will bring to light the formal operations that underlie the independent electron approximation. On this basis, we will point out how quantum chemistry can offer new arguments that contribute to (...) 

This article analyzes the implications of protective measurement for the meaning of the wave function. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wave function. It is shown that the mass and charge density is not real but effective, formed by the ergodic motion of a localized particle with the total mass and charge of the system. Moreover, it is argued that the ergodic motion is not continuous but (...) 

This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics.In it, I aim to review, in a way accessible to foundationally interested physicists as well as physicsinformed philosophers, just where we have got to in the quest for a solution to the measurement problem. I don't advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence theory to (...) 

In my dissertation I analyze the structure of fundamental physical theories. I start with an analysis of what an adequate primitive ontology is, discussing the measurement problem in quantum mechanics and theirs solutions. It is commonly said that these theories have little in common. I argue instead that the moral of the measurement problem is that the wave function cannot represent physical objects and a common structure between these solutions can be recognized: each of them is about a clear threedimensional (...) 

In this article, I briefly explain the quantum measurement problem and the Everett interpretation, in a way that is faithful to modern physics and yet accessible to readers without any physics training. I then consider the metaphysical lessons for ontology from quantum mechanics under the Everett interpretation. My conclusions are largely negative: I argue that very little can be said in full generality about the ontology of quantum mechanics, because quantum mechanics, like abstract classical mechanics, is a framework within which (...) 

This thesis is an attempt to reconstruct the conceptual foundations of quantum mechanics. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear nonrelativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation (...) 

The paper has two aims: (1) it sets out to show that it is well motivated to seek for an account of quantum nonlocality in the framework of ontic structural realism (OSR), which integrates the notions of holism and nonseparability that have been employed since the 1980s to achieve such an account. However, recent research shows that OSR on its own cannot provide such an account. Against this background, the paper argues that by applying OSR to the primitive ontology theories (...) 

The paper seeks to make progress from stating primitive ontology theories of quantum physics – notably Bohmian mechanics, the GRW matter density theory and the GRW flash theory – to assessing these theories. Four criteria are set out: internal coherence; empirical adequacy; relationship to other theories; explanatory value. The paper argues that the stock objections against these theories do not withstand scrutiny. Its focus then is on their explanatory value: they pursue different strategies to ground the textbook formalism of quantum (...) 

The world looks threedimensional unless one looks closely, when it looks 3Ndimensional. But which appearance is veridical, and which the illusion? Albert contends that the threedimensionality of the everyday world is illusory, and that 3Ndimensional wavefunction one discerns in quantum phenomena is the reality behind the illusion. What I try to do here is to argue for the converse of Albert's position; the world really is three dimensional, and the 3Ndimensional appearance of quantum phenomena is the theoretical analog of an (...) 

Primitive ontology is a program which seeks to make explicit the ontological commitments of physical theories in terms of a distribution of matter in ordinary spacetime. This program targets wavefunction realism, which interprets the highdimensional configuration space on which wavefunctions are defined as our fundamental physical space. Wavefunction realism allegedly fails to account for a correspondence between the ontology it postulates and the ‘manifest image’ of the world in which experimental tests of the theory are performed, and therefore the wavefunction (...) 

The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this longstanding question. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical (...) 

In recent literature, it has become clear that quantum physics does not refute Humeanism: Lewis’s thesis of Humean supervenience can be literally true even in the light of quantum entanglement. This point has so far been made with respect to Bohm’s quantum theory. Against this background, this paper seeks to achieve the following four results: to generalize the option of quantum Humeanism from Bohmian mechanics to primitive ontology theories in general; to show that this option applies also to classical mechanics; (...) 

Spontaneous collapse theories provide a promising solution to the measurement problem. But they also introduce a number of problems of their own concerning dimensionality, vagueness, and locality. In response to these problems, advocates of collapse theories have proposed various accounts of the primitive ontology of collapse theories—postulated underlying entities governed by the collapse theory and underwriting our observations. The most prominent of these are a mass density distribution over threedimensional space, and a set of discrete “flash” events at spacetime points. (...) 

The fact that physical laws often admit certain kinds of spacetime symmetries is often thought to be problematic for substantivalism  the view that spacetime is as real as the objects it contains. The most prominent alternative, relationism, avoids these problems but at the cost of giving abstract objects (rather than spacetime points) a pivotal role in the fundamental metaphysics. This incurs related problems concerning the relation of the physical to the mathematical. In this paper I will present a version (...) 

Under socalled primitive ontology approaches, in fully describing the history of a quantum system, one thereby attributes interesting properties to regions of spacetime. Primitive ontology approaches, which include some varieties of Bohmian mechanics and spontaneous collapse theories, are interesting in part because they hold out the hope that it should not be too difficult to make a connection between models of quantum mechanics and descriptions of histories of ordinary macroscopic bodies. But such approaches are dualistic, positing a quantum state as (...) 



The literature on physicalism often fails to elucidate, I think, what the word physical in physical ism precisely means. Philosophers speak at times of an ideal set of fundamental physical facts, or they stipulate that physical means nonmental , such that all fundamental physical facts are fundamental facts pertaining to the nonmental. In this article, I will probe physicalism in the very much tangible framework of quantum mechanics. Although this theory, unlike “ideal physics” or some “final theory of nonmentality”, is (...) 

We investigate the validity of the field explanation of the wave function by analyzing the mass and charge density distributions of a quantum system. It is argued that a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. This is also a consequence of protective measurement. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously (...) 

It has been widely thought that the ontology of quantum mechanics is real, physical fields. In this paper, I will present a new argument against the field ontology of quantum mechanics by analyzing onebody systems such as an electron. First, I argue that if the physical entity described by the wave function of an electron is a field, then this field is massive and charged. Next, I argue that if a field is massive and charged, then any two parts of (...) 

The aim of this paper is to summarize a particular approach of doing metaphysics through physics  the primitive ontology approach. The idea is that any fundamental physical theory has a welldefined architecture, to the foundation of which there is the primitive ontology, which represents matter. According to the framework provided by this approach when applied to quantum mechanics, the wave function is not suitable to represent matter. Rather, the wave function has a nomological character, given that its role in (...) 

Different realistic attitudes towards wavefunctions and quantum states are as old as quantum theory itself. Recently Pusey, Barret and Rudolph on the one hand, and Auletta and Tarozzi on the other, have proposed new interesting arguments in favor of a broad realistic interpretation of quantum mechanics that can be considered the modern heir to some views held by the fathers of quantum theory. In this paper we give a new and detailed presentation of such arguments, propose a new taxonomy of (...) 

There are three possible interpretations of the wave function in the de BroglieBohm theory: taking the wave function as corresponding to a physical entity or a property of the Bohmian particles or a law. In this paper, we argue that the first interpretation is favored by an analysis of protective measurements. 

Quantum mechanics has always been regarded as, at best, puzzling, if not contradictory. The aim of the paper is to explore a particular approach to fundamental physical theories, the one based on the notion of primitive ontology. This approach, when applied to quantum mechanics, makes it a paradoxfree theory. 