Symmetries in Physics
Philosophical Reflections
Edited by Katherine Brading
Edited by Elena Castellani
Publisher: Cambridge University Press
Print Publication Year: 2003
Online Publication Date:October 2009
Online ISBN:9780511535369
Hardback ISBN:9780521821377
Paperback ISBN:9780521528894
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511535369.003
Subjects: General and Classical Physics
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I think the real situation has to be described as follows. Relative to a complete system of reference not only the points in space but also all physical quantities can be fixed by numbers. Two systems of reference are equally admissible if in both of them all universal geometric and physical laws of nature have the same algebraic expression. The transformations mediating between such equally admissible systems of reference form the group of physical automorphisms; the laws of nature are invariant with respect to the transformations of this group. It is a fact that a transformation of this group is uniquely determined by that part of it that concerns the coordinates of space points. Thus we can speak of the physical automorphisms of space. Their group does not include the dilatations, because the atomic laws fix an absolute length, but it contains the reflections because no law of nature indicates an intrinsic difference between left and right. Hence the group of physical automorphisms is the group of all proper and improper congruent mappings. If we call two configurations in space congruent provided they are carried over into each other by a transformation of this group, then bodies which are mirror images of each other are congruent. I think it is necessary to substitute this definition of congruence for that depending on the motion of rigid bodies, for reasons similar to those which induce the physicist to substitute the thermodynamical definition of temperature for an ordinary thermometer.
pp. i-iv
pp. v-vi
List of contributors : Read PDF
pp. vii-viii
pp. ix-x
Copyright acknowledgements : Read PDF
pp. xi-xii
pp. 1-18
Part I - Continuous symmetries : Read PDF
pp. 19-20
2 - Classic texts: extracts from Weyl and Wigner : Read PDF
pp. 21-28
3 - On continuous symmetries and the foundations of modern physics : Read PDF
pp. 29-60
4 - The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism : Read PDF
pp. 61-88
5 - Symmetries and Noether's theorems : Read PDF
pp. 89-109
6 - General covariance, gauge theories, and the Kretschmann objection : Read PDF
pp. 110-123
7 - The interpretation of gauge symmetry : Read PDF
pp. 124-139
8 - Tracking down gauge: an ode to the constrained Hamiltonian formalism : Read PDF
pp. 140-162
9 - Time-dependent symmetries: the link between gauge symmetries and indeterminism : Read PDF
pp. 163-173
10 - A fourth way to the Aharonov–Bohm effect : Read PDF
pp. 174-200
Part II - Discrete symmetries : Read PDF
pp. 201-202
11 - Classic texts: extracts from Leibniz, Kant, and Black : Read PDF
pp. 203-211
12 - Understanding permutation symmetry : Read PDF
pp. 212-238
13 - Quarticles and the identity of indiscernibles : Read PDF
pp. 239-249
14 - Handedness, parity violation, and the reality of space : Read PDF
pp. 250-280
15 - Mirror symmetry: what is it for a relational space to be orientable? : Read PDF
pp. 281-288
16 - Physics and Leibniz's principles : Read PDF
pp. 289-308
Part III - Symmetry breaking : Read PDF
pp. 309-310
17 - Classic texts: extracts from Curie and Weyl : Read PDF
pp. 311-314
18 - Cross fertilization in theoretical physics: the case of condensed matter and particle physics : Read PDF
pp. 315-320
19 - On the meaning of symmetry breaking : Read PDF
pp. 321-334
20 - Rough guide to spontaneous symmetry breaking : Read PDF
pp. 335-346
21 - Spontaneous symmetry breaking: theoretical arguments and philosophical problems : Read PDF
pp. 347-364
Part IV - General interpretative issues : Read PDF
pp. 365-366
22 - Classic texts: extracts from Wigner : Read PDF
pp. 367-370
23 - Symmetry as a guide to superfluous theoretical structure : Read PDF
pp. 371-392
24 - Notes on symmetries : Read PDF
pp. 393-412
25 - Symmetry, objectivity, and design : Read PDF
pp. 413-424
26 - Symmetry and equivalence : Read PDF
pp. 425-436
pp. 437-445