System/apparatus superposition and the Born rule.

2008 ◽  
Vol 21 (1) ◽  
pp. 78-83
Author(s):  
S. L. Weinberg
Keyword(s):  
Born Rule

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.

scholarly journals The measure problem in no-collapse (many worlds) quantum mechanics

2017 ◽  
Vol 26 (03) ◽  
pp. 1730008 ◽  
Author(s):  
Stephen D. H. Hsu
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Probability Measure ◽  
Ab Initio ◽  
Subjective Probability ◽  
State Vector ◽  
A Priori ◽  
Born Rule ◽  
Many Worlds ◽  
Measure Problem

We explain the measure problem (cf. origin of the Born probability rule) in no-collapse quantum mechanics. Everett defined maverick branches of the state vector as those on which the usual Born probability rule fails to hold — these branches exhibit highly improbable behaviors, including possibly the breakdown of decoherence or even the absence of an emergent semi-classical reality. Derivations of the Born rule which originate in decision theory or subjective probability (i.e. the reasoning of individual observers) do not resolve this problem, because they are circular: they assume, a priori, that the observer occupies a non-maverick branch. An ab initio probability measure is sometimes assumed to explain why we do not occupy a maverick branch. This measure is constrained by, e.g. Gleason’s theorem or envariance to be the usual Hilbert measure. However, this ab initio measure ultimately governs the allocation of a self or a consciousness to a particular branch of the wave function, and hence invokes primitives which lie beyond the Everett wave function and beyond what we usually think of as physics. The significance of this leap has been largely overlooked, but requires serious scrutiny.

Cauchy–Born rule and stability of crystalline solids at finite temperature

2021 ◽  
Vol 19 (6) ◽  
pp. 1461-1490
Author(s):  
Tao Luo ◽  
Yang Xiang ◽  
Jerry Zhijian Yang ◽  
Cheng Yuan
Keyword(s):  
Finite Temperature ◽  
Crystalline Solids ◽  
Born Rule

scholarly journals Discrete Hilbert space, the Born Rule, and quantum gravity

2021 ◽  
Vol 36 (03) ◽  
pp. 2150013
Author(s):  
Stephen D. H. Hsu
Keyword(s):  
Hilbert Space ◽  
Quantum Gravity ◽  
Discrete Models ◽  
Born Rule ◽  
Gravitational Effects ◽  
Spacetime Geometry ◽  
Decoherent Histories ◽  
Lattice Quantum ◽  
Spacetime Interval ◽  
Matter Fields

Quantum gravitational effects suggest a minimal length, or spacetime interval, of order of the Planck length. This in turn suggests that Hilbert space itself may be discrete rather than continuous. One implication is that quantum states with norm below some very small threshold do not exist. The exclusion of what Everett referred to as maverick branches is necessary for the emergence of the Born Rule in no collapse quantum mechanics. We discuss this in the context of quantum gravity, showing that discrete models (such as simplicial or lattice quantum gravity) indeed suggest a discrete Hilbert space with minimum norm. These considerations are related to the ultimate level of fine-graining found in decoherent histories (of spacetime geometry plus matter fields) produced by quantum gravity.

How to Prove the Born Rule

Many Worlds? ◽  
2010 ◽  
pp. 227-263 ◽  
Author(s):  
David Wallace
Keyword(s):  
Born Rule

On the applicability of the Cauchy-Born rule

2009 ◽  
Vol 46 (2) ◽  
pp. 438-442 ◽  
Author(s):  
C. Pozrikidis
Keyword(s):  
Born Rule
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