Can Pragmatism about Quantum Theory Handle Objectivity about Explanations?

2020 ◽  
pp. 147-167
Author(s):  
Lina Jansson
Keyword(s):  
Quantum Theory ◽  
Explanatory Power ◽  
Quantum States ◽  
Target System ◽  
Born Rule ◽  
Accurate Representation

Richard Healey’s pragmatist approach to quantum theory promises a middle road between realism and anti-realism. However, in order to capture quantum theory’s explanatory power the pragmatist approach gives up a putative truism about explanation. Namely, that explanation demands accurate representation of the target system. This threatens to undermine our ability to distinguish explanations from nonexplanations in an objective way. Chapter 8 develops a criterion internal to explanation that puts a systematic restriction on the explanatory roles of non-representational (or not adequately representing) explanatory resources. It shows that this allows the pragmatist approach to keep the realist commitment to objective explanation even while weakening the typical realist commitment to the putative truism about explanation. However, the chapter also argues that this way of tackling the problem does not allow us to have a middle road without some explanatory sacrifices. Quantum states and the Born rule can be part of explanations but no longer the explanatory initial input.

scholarly journals The Born rule as a statistics of quantum micro-events

2020 ◽  
Vol 476 (2244) ◽  
pp. 20200282
Author(s):  
Yurii V. Brezhnev
Keyword(s):  
Hilbert Space ◽  
Quantum Theory ◽  
Vector Space ◽  
Scalar Product ◽  
Mathematical Structure ◽  
Quantum States ◽  
Born Rule ◽  
Statistical Nature ◽  
Quadratic Character ◽  
Quantum Superpositions

We deduce the Born rule from a purely statistical take on quantum theory within minimalistic math-setup. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics—a linear, not Hilbert’, vector space—and empirical notion of the Statistical Length of a state. Its statistical nature comes from the lab micro-events (detector-clicks) being formalized into the C -coefficients of quantum superpositions. We also comment that not only has the use not been made of quantum axioms (scalar-product, operators, interpretations , etc.), but that the involving thereof would be, in a sense, inconsistent when deriving the rule. In point of fact, the quadratic character of the statistical length, and even not (the ‘physics’ of) Born’s formula, represents a first step in constructing the mathematical structure we name the Hilbert space of quantum states.

Probability and Explanation

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Causal Explanation ◽  
Born Rule ◽  
Correct Application

We can use quantum theory to explain an enormous variety of phenomena by showing why they were to be expected and what they depend on. These explanations of probabilistic phenomena involve applications of the Born rule: to accept quantum theory is to let relevant Born probabilities guide one’s credences about presently inaccessible events. We use quantum theory to explain a probabilistic phenomenon by showing how its probabilities follow from a correct application of the Born rule, thereby exhibiting the phenomenon’s dependence on the quantum state to be assigned in circumstances of that type. This is not a causal explanation since a probabilistic phenomenon is not constituted by events that may manifest it: but each of those events does depend causally on events that actually occur in those circumstances. Born probabilities are objective and sui generis, but not all Born probabilities are chances.

“Non-locality”

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum Entanglement ◽  
Quantum States ◽  
Entangled States ◽  
Entangled Quantum States ◽  
Action At A Distance ◽  
Insight Into ◽  
Non Locality

Quantum entanglement is popularly believed to give rise to spooky action at a distance of a kind that Einstein decisively rejected. Indeed, important recent experiments on systems assigned entangled states have been claimed to refute Einstein by exhibiting such spooky action. After reviewing two considerations in favor of this view I argue that quantum theory can be used to explain puzzling correlations correctly predicted by assignment of entangled quantum states with no such instantaneous action at a distance. We owe both considerations in favor of the view to arguments of John Bell. I present simplified forms of these arguments as well as a game that provides insight into the situation. The argument I give in response turns on a prescriptive view of quantum states that differs both from Dirac’s (as stated in Chapter 2) and Einstein’s.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

scholarly journals The Strange (Hi)story of Particles and Waves

2016 ◽  
Vol 71 (3) ◽  
pp. 195-212
Author(s):  
H. Dieter Zeh
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Excited States ◽  
Configuration Space ◽  
Historical Context ◽  
Quantum States ◽  
Wave Functions ◽  
General Readership ◽  
Boson Fields

AbstractThis is an attempt of a non-technical but conceptually consistent presentation of quantum theory in a historical context. While the first part is written for a general readership, Section 5 may appear a bit provocative to some quantum physicists. I argue that the single-particle wave functions of quantum mechanics have to be correctly interpreted as field modes that are “occupied once” (i.e. first excited states of the corresponding quantum oscillators in the case of boson fields). Multiple excitations lead to apparent many-particle wave functions, while the quantum states proper are defined by wave function(al)s on the “configuration” space of fundamental fields, or on another, as yet elusive, fundamental local basis.

scholarly journals Schrödinger-like quantum dynamics in loop quantized black holes

2016 ◽  
Vol 25 (08) ◽  
pp. 1642006 ◽  
Author(s):  
Rodolfo Gambini ◽  
Javier Olmedo ◽  
Jorge Pullin
Keyword(s):  
Black Holes ◽  
Quantum Theory ◽  
Quantum Dynamics ◽  
Local Information ◽  
Quantum States ◽  
Spherically Symmetric ◽  
Definition Of ◽  
Symmetric Spacetime ◽  
Spherically Symmetric Spacetime

We show, following a previous quantization of a vacuum spherically symmetric spacetime carried out in [R. Gambini, J. Olmedo and J. Pullin, Class. Quantum Grav. 31 (2014) 095009.] that this setting admits a Schrödinger-like picture. More precisely, the technique adopted there for the definition of parametrized Dirac observables (that codify local information of the quantum theory) can be extended in order to accommodate different pictures. In this new picture, the quantum states are parametrized in terms of suitable gauge parameters and the observables constructed out of the kinematical ones on this space of parametrized states.

THE EINSTEIN–PODOLSKY–ROSEN PROPOSITION ON QUANTUM THEORY AND ITS IMPLICATIONS FOR INTUITIVE CLASSICAL LOGIC

2010 ◽  
Vol 19 (06) ◽  
pp. 799-807 ◽  
Author(s):  
ALI ESKANDARIAN
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Information Content ◽  
Classical Logic ◽  
Quantum States ◽  
Einstein Podolsky Rosen ◽  
Completeness Of Quantum Mechanics ◽  
Shed Light ◽  
Intense Research

Einstein, Podolsky and Rosen raised foundational questions about the completeness of quantum mechanics, if certain intuitive logical statements regarding the nature of reality were assumed to be true. These questions are ultimately of significance to the information content of the theory, which is currently the focus of intense research. In this presentation, selected investigations that have made progress in addressing the EPR concerns and that shed light on the nature of quantum states are surveyed. The implications for intuitive classical logic are speculated in the concluding remarks.

scholarly journals The type-independent resource theory of local operations and shared randomness

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 262 ◽  
Author(s):  
David Schmid ◽  
Denis Rosset ◽  
Francesco Buscemi
Keyword(s):  
Quantum Theory ◽  
Quantum Information Processing ◽  
Full Range ◽  
Quantum States ◽  
Resource Theory ◽  
Independent Manner ◽  
Common Cause ◽  
Entanglement Witnesses ◽  
Different Types ◽  
Common Resource

In space-like separated experiments and other scenarios where multiple parties share a classical common cause but no cause-effect relations, quantum theory allows a variety of nonsignaling resources which are useful for distributed quantum information processing. These include quantum states, nonlocal boxes, steering assemblages, teleportages, channel steering assemblages, and so on. Such resources are often studied using nonlocal games, semiquantum games, entanglement-witnesses, teleportation experiments, and similar tasks. We introduce a unifying framework which subsumes the full range of nonsignaling resources, as well as the games and experiments which probe them, into a common resource theory: that of local operations and shared randomness (LOSR). Crucially, we allow these LOSR operations to locally change the type of a resource, so that players can convert resources of any type into resources of any other type, and in particular into strategies for the specific type of game they are playing. We then prove several theorems relating resources and games of different types. These theorems generalize a number of seminal results from the literature, and can be applied to lessen the assumptions needed to characterize the nonclassicality of resources. As just one example, we prove that semiquantum games are able to perfectly characterize the LOSR nonclassicality of every resource of any type (not just quantum states, as was previously shown). As a consequence, we show that any resource can be characterized in a measurement-device-independent manner.

scholarly journals Obscure Qubits and Membership Amplitudes

2021 ◽  
Author(s):  
Steven Duplij ◽  
Raimund Vogl
Keyword(s):  
Hilbert Space ◽  
Quantum Computing ◽  
Density Matrix ◽  
Tensor Product ◽  
Quantum Computation ◽  
Membership Function ◽  
Quantum Probability ◽  
Quantum States ◽  
Born Rule ◽  
Quantum Amplitude

We propose a concept of quantum computing which incorporates an additional kind of uncertainty, i.e. vagueness (fuzziness), in a natural way by introducing new entities, obscure qudits (e.g. obscure qubits), which are characterized simultaneously by a quantum probability and by a membership function. To achieve this, a membership amplitude for quantum states is introduced alongside the quantum amplitude. The Born rule is used for the quantum probability only, while the membership function can be computed from the membership amplitudes according to a chosen model. Two different versions of this approach are given here: the “product” obscure qubit, where the resulting amplitude is a product of the quantum amplitude and the membership amplitude, and the “Kronecker” obscure qubit, where quantum and vagueness computations are to be performed independently (i.e. quantum computation alongside truth evaluation). The latter is called a double obscure-quantum computation. In this case, the measurement becomes mixed in the quantum and obscure amplitudes, while the density matrix is not idempotent. The obscure-quantum gates act not in the tensor product of spaces, but in the direct product of quantum Hilbert space and so called membership space which are of different natures and properties. The concept of double (obscure-quantum) entanglement is introduced, and vector and scalar concurrences are proposed, with some examples being given.

scholarly journals Any modification of the Born rule leads to a violation of the purification and local tomography principles

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 104 ◽  
Author(s):  
Thomas D. Galley ◽  
Lluis Masanes
Keyword(s):  
Quantum Theory ◽  
Born Rule ◽  
Mixed States ◽  
Many Worlds ◽  
Local Tomography ◽  
Local Measurements ◽  
State Tomography ◽  
Quantum Phenomena ◽  
The Many

Using the existing classification of all alternatives to the measurement postulates of quantum theory we study the properties of bi-partite systems in these alternative theories. We prove that in all these theories the purification principle is violated, meaning that some mixed states are not the reduction of a pure state in a larger system. This allows us to derive the measurement postulates of quantum theory from the structure of pure states and reversible dynamics, and the requirement that the purification principle holds. The violation of the purification principle implies that there is some irreducible classicality in these theories, which appears like an important clue for the problem of deriving the Born rule within the many-worlds interpretation. We also prove that in all such modifications the task of state tomography with local measurements is impossible, and present a simple toy theory displaying all these exotic non-quantum phenomena. This toy model shows that, contrarily to previous claims, it is possible to modify the Born rule without violating the no-signalling principle. Finally, we argue that the quantum measurement postulates are the most non-classical amongst all alternatives.

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