By Robert B. Griffiths
Publisher: Cambridge University Press
Print Publication Year: 2001
Online Publication Date:December 2009
Online ISBN:9780511606052
Hardback ISBN:9780521803496
Paperback ISBN:9780521539296
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511606052.006
Subjects: Quantum Physics, Quantum Information and Quantum Computation, History, Philosophy and Foundations of Physics
Image View Extract Fullview: Text View | Enlarge Image ‹ Previous Chapter ›Next Chapter
Classical sample space and event algebra
Probability theory is based upon the concept of a sample space of mutually exclusive possibilities, one and only one of which actually occurs, or is true, in any given situation. The elements of the sample space are sometimes called points or elements or events. In classical and quantum mechanics the sample space usually consists of various possible states or properties of some physical system. For example, if a coin is tossed, there are two possible outcomes: H (heads) or T (tails), and the sample space S is {H, T}. If a die is rolled, the sample space S consists of six possible outcomes: s = 1, 2, 3, 4, 5, 6. If two individuals A and B share an office, the occupancy sample space consists of four possibilities: an empty office, A present, B present, or both A and B present.
Associated with a sample space S is an event algebra B consisting of subsets of elements of the sample space. In the case of a die, “s is even” is an event in the event algebra. So are “s is odd”, “s is less than 4”, and “s is equal to 2.” It is sometimes useful to distinguish events which are elements of the sample space, such as s = 2 in the previous example, and those which correspond to more than one element of the sample space, such as “s is even”. We shall refer to the former as elementary events and to the latter as compound events.
pp. i-vi
pp. vii-xii
pp. xiii-xvi
pp. 1-10
pp. 11-26
3 - Linear algebra in Dirac notation : Read PDF
pp. 27-46
4 - Physical properties : Read PDF
pp. 47-64
5 - Probabilities and physical variables : Read PDF
pp. 65-80
6 - Composite systems and tensor products : Read PDF
pp. 81-93
7 - Unitary dynamics : Read PDF
pp. 94-107
8 - Stochastic histories : Read PDF
pp. 108-120
pp. 121-136
10 - Consistent histories : Read PDF
pp. 137-147
11 - Checking consistency : Read PDF
pp. 148-158
12 - Examples of consistent families : Read PDF
pp. 159-173
13 - Quantum interference : Read PDF
pp. 174-191
14 - Dependent (contextual) events : Read PDF
pp. 192-201
15 - Density matrices : Read PDF
pp. 202-215
16 - Quantum reasoning : Read PDF
pp. 216-227
17 - Measurements I : Read PDF
pp. 228-242
18 - Measurements II : Read PDF
pp. 243-260
19 - Coins and counterfactuals : Read PDF
pp. 261-272
20 - Delayed choice paradox : Read PDF
pp. 273-283
21 - Indirect measurement paradox : Read PDF
pp. 284-295
22 - Incompatibility paradoxes : Read PDF
pp. 296-309
23 - Singlet state correlations : Read PDF
pp. 310-322
24 - EPR paradox and Bell inequalities : Read PDF
pp. 323-335
25 - Hardy's paradox : Read PDF
pp. 336-348
26 - Decoherence and the classical limit : Read PDF
pp. 349-359
27 - Quantum theory and reality : Read PDF
pp. 360-370
pp. 371-376
pp. 377-382
pp. 383-391