Abstract
Turning from classical to quantum physics, new problems arise with regard to the traditional philosophical question of what a ‘physical object’ is. A recent ‘group-theoretical’ approach to the question as to whether it does make sense to speak of ‘quantum objects’ is illustrated, investigating the connection it affords with the traditional problem of the ‘objectivity’ of physical knowledge. The individuality issue for quantum particles is also taken into account.
“Mais ce que nous appelons la réalité objective c’est, en dernière analyse, ce qui est commun à plusieurs êtres pensants, et pourrait être commun à tous.”
(H. POINCARÉ, La valeur de la Science, 1905)
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Notes and References
Quine, W.V.O. (1976). ‘Whither Physical Objects?’, in R. S. Cohen et al. (eds.), Essays in Memory of Imre Lakatos, Reidel Publishing Company, Dordrecht, pp. 497–504.
Assuming that the objectifying role is not attributed to some kind of ‘substance’ or ‘essence’ trascending the entitys set of properties.
On this point, of particular interest is the contribute of Ernst Cassirer, ‘The Concept of Group and the Theory of Perception’, Philosophy and Phenomenological Research, Vol. V, No. 1 (1944), pp. 1–35, where the significance of the developments of the theory of transformation groups for the object problem is taken into consideration with regard to ‘objects’ in the context of geometry, physics and perception theory.
Max Born, in his ‘Physical Reality’ (Philosophical Quarterly 3, 39 (1953), pp. 139–149), offers a clear example of such a way of thinking, connecting his conception of ‘objects’ as “what is permanent in the flux of phenomena, the invariants”, with the view of the theory of relativity as “an extension of this programme [Klein‘s ’Erlanger Programm”] to the four-dimensional geometry of space-time.
Weyl, H. (1952). Symmetry, Princeton University press, Princeton, p. 132.
Wigner, E. (1939). ‘On unitary representations of the inhomogeneous Lorentz group’, Annals of Mathematics 40, No. 1, pp. 149–204.
Note that the concept of an ‘elementary system’is indeed broader than the intuitive concept of an ‘elementary particle’. The point was thoroughly discussed in Newton, T.D. and Wigner, E.P. (1949), Localized States for Elementary Systems, Review of Modern Physics, 21 pp. 400–406.
Or, to be more precise (if we want to stress the fact that what we get, in this way, is a class of equivalent elementary systems): a Galilean (Lorentz) particle is physical equivalence class of elementary Galilean (Lorentz) systems.
With regard to Galilean symmetry, a very thoroughly analysis of such programme of both classical and quantum particles can be found, in particular, in some contributes of J.M. Lévy-Leblond. See for instance his ‘Galilei Group and Galilean Invariance’, in Loebl, E.M. (ed.), Group Theory and Its Applications, Academic Press, New York (1971), Vol. II, pp. 221–299, and, for the quantum case, his ‘Galilei Group and Nonrelativistic Quantum Mechanics’, Journal of Mathematical Physics, 4 No. 6 (1963), pp. 776–788.
Taking into account, here, only the case of ‘pure’ states. A quite general treatment of representation spaces for the space-time symmetry groups including also the case of ‘mixed states’ is of course possible. See for example Currie, D.G., Jordan, T.F., Sudarshan, E.C.G. (1963), ‘Relativistic Invariance and Hamiltonian Theories of Interacting Particles’, Review of Modern Physics, 35 pp. 350–375.
Reichenbach, H. (1956). The Direction of Time, ed. by M. Reichenbach, University of California Press, Berkeley, p. 228.
With regard to this whole debate on identity, individuality and indistinguishability in quantum physics, see for example Van Fraassen, B., ‘Statistical Behaviour of Indistinguishable Particles: Problems of Interpretation’, in P. Mittelstaedt-E. W. Stachow (eds.), Recent Developments in Quantum Logic, Bibliographisches Institut, Mannheim (1985), pp. 189–202
which offers also a sort of revue of the related issues. For more recent contributes see, among others, French, S., ‘Identity and Individuality in Classical and Quantum Physics’, Australasian Journal of Philosophy, 67, No. 4 (1989), pp. 432–446
Van Fraassen, B., Quantum Mechanics: An Empiricist View, Clarendon Press, Oxford (1991)
whose chapter 11 is entirely devoted to the problem of ‘identical particles’; Redhead, M. and Teller, P., ‘Particles Labels and the Theory of Indistinguishable Particles in Quantum Mechanics’, British Journal for the Philosophy of Science, 43 (1992), pp. 201–218.
Piron, C. (1976). Foundations of Quantum Physics, W. A. Benjamin, Inc., Reading, Massachusetts, pp. 93 ff.
Piron, C. op. cit., pp. 93 ff.
See, in particular, by Busch, P., ‘Unsharp Reality and the Question of Quantum Systems’, in P. Lahti-P. Mittelstaedt (eds.), Symposium on the Foundations of Modern Physics 1987, World Scientific, Singapore (1987), pp. 105–125
Macroscopic Quantum Systems and the Objectification Problem’, in P. Lahti-P. Mittelstaedt (eds.), Symposium on the Foundations of Modern Physics 1990, World Scientific, Singapore (1990), pp. 62–76.
Such a programme was recently illustrated in Mittelstaedt, P., ‘The Constitution of Objects in Kant’s Philosophy and in Modern Physics’, in P. Parrini (ed.), Kant and Contemporary Epistemology, Kluwer Academic Publishers, Dordrecht (1994).
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Castellani, E. (1995). Quantum Mechanics, Objects and Objectivity. In: Garola, C., Rossi, A. (eds) The Foundations of Quantum Mechanics — Historical Analysis and Open Questions. Fundamental Theories of Physics, vol 71. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0029-8_9
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