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.

Assigning Values and States

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum State ◽  
Density Operator ◽  
Entangled State ◽  
Physical Situation ◽  
Born Rule ◽  
Correct Assignment ◽  
Significant Magnitude ◽  
Good Advice ◽  
Empirical Significance ◽  
Important Idea

If a quantum state is prescriptive then what state should an agent assign, what expectations does this justify, and what are the grounds for those expectations? I address these questions and introduce a third important idea—decoherence. A subsystem of a system assigned an entangled state may be assigned a mixed state represented by a density operator. Quantum state assignment is an objective matter, but the correct assignment must be relativized to the physical situation of an actual or hypothetical agent for whom its prescription offers good advice, since differently situated agents have access to different information. However this situation is described, it is true, empirically significant magnitude claims that make the description correct, while others provide the objective grounds for the agent’s expectations. Quantum models of environmental decoherence certify the empirical significance of these magnitude claims while also licensing application of the Born rule to others without mentioning measurement.

Entanglement

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Physical Condition ◽  
Physical System ◽  
Polarization State ◽  
Quantum Systems ◽  
Ghz State ◽  
Mathematical Representation ◽  
Entangled State ◽  
Physical Relation

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

Losing Sight of the Forest for the ψ‎

2020 ◽  
pp. 185-211
Author(s):  
Alisa Bokulich
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Configuration Space ◽  
Mathematical Formalism ◽  
Alternative Formulation ◽  
Quantum Hydrodynamics ◽  
Many Body ◽  
Quantum Realism ◽  
The World ◽  
The Many

Traditionally \1 is used to stand for both the mathematical wavefunction (the representation) and the quantum state (thing in the world). This elision has been elevated to a metaphysical thesis by advocates of wavefunction realism. The aim of Chapter 10 is to challenge the hegemony of the wavefunction by calling attention to a littleknown formulation of quantum theory that does not make use of the wavefunction in representing the quantum state. This approach, called Lagrangian quantum hydrodynamics (LQH), is a full alternative formulation, not an approximation scheme. A consideration of alternative formalisms is essential for any realist project that attempts to read the ontology of a theory off the mathematical formalism. The chapter shows that LQH falsifies the claim that one must represent the many-body quantum state as living in 3n-dimensional configuration space. When exploring quantum realism, regaining sight of the proverbial forest of quantum representations beyond the \1 is just the beginning.

scholarly journals Is a time symmetric interpretation of quantum theory possible without retrocausality?

2017 ◽  
Vol 473 (2202) ◽  
pp. 20160607 ◽  
Author(s):  
Matthew S. Leifer ◽  
Matthew F. Pusey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
General Framework ◽  
Bell Inequalities ◽  
Time Symmetry ◽  
Causality Criterion ◽  
The Status ◽  
Interpretation Of Quantum Theory ◽  
Huw Price ◽  
New Interpretation

Huw Price has proposed an argument that suggests a time symmetric ontology for quantum theory must necessarily be retrocausal, i.e. it must involve influences that travel backwards in time. One of Price's assumptions is that the quantum state is a state of reality. However, one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no-go theorems, including recent proofs of the reality of the quantum state. Here, we show that this assumption can be replaced by a different assumption, called λ -mediation, that plausibly holds independently of the status of the quantum state. We also reformulate the other assumptions behind the argument to place them in a more general framework and pin down the notion of time symmetry involved more precisely. We show that our assumptions imply a timelike analogue of Bell's local causality criterion and, in doing so, give a new interpretation of timelike violations of Bell inequalities. Namely, they show the impossibility of a (non-retrocausal) time symmetric ontology.

scholarly journals Quantum Black Holes and (Re)Solution of the Singularity

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 478
Author(s):  
Roberto Casadio
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Quantum Theory ◽  
Quantum State ◽  
Spacetime Singularities ◽  
Classical General Relativity ◽  
Spacetime Geometry ◽  
Complete Quantum ◽  
General Conditions

Classical general relativity predicts the occurrence of spacetime singularities under very general conditions. Starting from the idea that the spacetime geometry must be described by suitable states in the complete quantum theory of matter and gravity, we shall argue that this scenario cannot be realised physically since no proper quantum state may contain the infinite momentum modes required to resolve the singularity.

scholarly journals The passage of neutrons through matter

1932 ◽  
Vol 138 (835) ◽  
pp. 460-469 ◽  
Keyword(s):  
Quantum Theory ◽  
Charged Particle ◽  
Hydrogen Atom ◽  
Experimental Method ◽  
Nuclear Structure ◽  
Quantum State ◽  
Mathematical Description ◽  
Elastic Collisions ◽  
Satisfactory Theory

The discovery of the neutron by Chadwick is of very great importance to the theory of nuclear structure for it is apparently a much simpler unit than the α-particle and so more amenable to mathematical description. It is, therefore, very necessary to obtain as much knowledge as possible of the field of force surrounding the particle. If this field be known a very strict test of any theory of the nature of the particle is provided. The experimental method used to determine the field of force consists in the observation of the collisions of neutrons with material particles such as electrons and protons. The interpretation of these results requires the development of a satisfactory theory of such collisions. Fortunately, in most cases the smallness of the field of interaction between a neutron and a charged particle leads to the possibility of applying the simple approximate quantum theory of collisions due to Born. In this paper we will discuss the application of the theory to the elastic collisions of neutrons with material particles. A neutron model consisting of a hydrogen atom in a nearly zero quantum state will be considered in particular and the probability of disintegration of such a model by nuclear impact estimated. It will be shown that the available experimental material indicates that the radius of such an atom must be less than 2·0 × 10 -13 cm.

scholarly journals Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 302
Author(s):  
Debashis Saha ◽  
Rafael Santos ◽  
Remigiusz Augusiak
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Three Dimensional ◽  
Sum Of Squares ◽  
Quantum Devices ◽  
Fundamental Feature ◽  
Quantum Contextuality ◽  
Sequential Measurement ◽  
Self Testing ◽  
Odd Cycle

Violation of a noncontextuality inequality or the phenomenon referred to `quantum contextuality' is a fundamental feature of quantum theory. In this article, we derive a novel family of noncontextuality inequalities along with their sum-of-squares decompositions in the simplest (odd-cycle) sequential-measurement scenario capable to demonstrate Kochen-Specker contextuality. The sum-of-squares decompositions allow us to obtain the maximal quantum violation of these inequalities and a set of algebraic relations necessarily satisfied by any state and measurements achieving it. With their help, we prove that our inequalities can be used for self-testing of three-dimensional quantum state and measurements. Remarkably, the presented self-testing results rely on weaker assumptions than the ones considered in Kochen-Specker contextuality.

scholarly journals General Probabilistic Theories with a Gleason-type Theorem

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 588
Author(s):  
Victoria J Wright ◽  
Stefan Weigert
Keyword(s):  
Quantum Theory ◽  
State Space ◽  
Quantum State ◽  
Type Theorem ◽  
General Probabilistic Theories ◽  
Probabilistic Theories

Gleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that (ii) there is a unique state for every such assignment. We identify the class of general probabilistic theories which also admit Gleason-type theorems. It contains theories satisfying the no-restriction hypothesis as well as others which can simulate such an unrestricted theory arbitrarily well when allowing for post-selection on measurement outcomes. Our result also implies that the standard no-restriction hypothesis applied to effects is not equivalent to the dual no-restriction hypothesis applied to states which is found to be less restrictive.

Sign in / Sign up

Export Citation Format

Share Document