Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Wave functions
- 3 Linear algebra in Dirac notation
- 4 Physical properties
- 5 Probabilities and physical variables
- 6 Composite systems and tensor products
- 7 Unitary dynamics
- 8 Stochastic histories
- 9 The Born rule
- 10 Consistent histories
- 11 Checking consistency
- 12 Examples of consistent families
- 13 Quantum interference
- 14 Dependent (contextual) events
- 15 Density matrices
- 16 Quantum reasoning
- 17 Measurements I
- 18 Measurements II
- 19 Coins and counterfactuals
- 20 Delayed choice paradox
- 21 Indirect measurement paradox
- 22 Incompatibility paradoxes
- 23 Singlet state correlations
- 24 EPR paradox and Bell inequalities
- 25 Hardy's paradox
- 26 Decoherence and the classical limit
- 27 Quantum theory and reality
- Bibliography
- References
- Index
8 - Stochastic histories
Published online by Cambridge University Press: 10 December 2009
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Wave functions
- 3 Linear algebra in Dirac notation
- 4 Physical properties
- 5 Probabilities and physical variables
- 6 Composite systems and tensor products
- 7 Unitary dynamics
- 8 Stochastic histories
- 9 The Born rule
- 10 Consistent histories
- 11 Checking consistency
- 12 Examples of consistent families
- 13 Quantum interference
- 14 Dependent (contextual) events
- 15 Density matrices
- 16 Quantum reasoning
- 17 Measurements I
- 18 Measurements II
- 19 Coins and counterfactuals
- 20 Delayed choice paradox
- 21 Indirect measurement paradox
- 22 Incompatibility paradoxes
- 23 Singlet state correlations
- 24 EPR paradox and Bell inequalities
- 25 Hardy's paradox
- 26 Decoherence and the classical limit
- 27 Quantum theory and reality
- Bibliography
- References
- Index
Summary
Introduction
Despite the fact that classical mechanics employs deterministic dynamical laws, random dynamical processes often arise in classical physics, as well as in everyday life. A stochastic or random process is one in which states-of-affairs at successive times are not related to one another by deterministic laws, and instead probability theory is employed to describe whatever regularities exist. Tossing a coin or rolling a die several times in succession are examples of stochastic processes in which the previous history is of very little help in predicting what will happen in the future. The motion of a baseball is an example of a stochastic process which is to some degree predictable using classical equations of motion that relate its acceleration to the total force acting upon it. However, a lack of information about its initial state (e.g., whether it is spinning), its precise shape, and the condition and motion of the air through which it moves limits the precision with which one can predict its trajectory.
The Brownian motion of a small particle suspended in a fluid and subject to random bombardment by the surrounding molecules of fluid is a well-studied example of a stochastic process in classical physics. Whereas the instantaneous velocity of the particle is hard to predict, there is a probabilistic correlation between successive positions, which can be predicted using stochastic dynamics and checked by experimental measurements. In particular, given the particle's position at a time t, it is possible to compute the probability that it will have moved a certain distance by the time t + Δt.
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- Consistent Quantum Theory , pp. 108 - 120Publisher: Cambridge University PressPrint publication year: 2001