Abstract
The final chapter takes into account two further aspects of the identity and identification of quantum particles: diachronic (across temporal instances) and counterfactual (across possible worlds). The problem of diachronic identifications is analyzed with the help of scattering processes involving same-type particles. The differences between the orthodox and heterodox approaches to individuation are highlighted. Counterfactual identifications are discussed within three philosophical conceptions of modality de re: Kripke’s approach, Lewis’s counterpart theory and Lewis’s cheap haecceitism. Finally we try to sketch a future metaphysical theory of objects that could account for the revealed facts regarding various types of identity in the quantum regime.
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Notes
- 1.
Compare the standard analysis of events by Jaegwon Kim in Kim (1976), where events are defined as triples consisting of an object, a property and a temporal point at which the object possesses the property.
- 2.
A more sophisticated variant of this problem is known as the “amputation case” (van Inwagen 1981; Heller 1984). If the particle in question is genuinely elementary, that is, does not possess any parts smaller than itself, then the “splitting” is better thought of as a process of decay where new particles are created. Sill, from the classical perspective the condition of temporal continuity is satisfied.
- 3.
As Nick Huggett and Tom Imbo (Huggett and Imbo 2009) point out, the non-existence of continuous spatiotemporal trajectories in quantum mechanics follows precisely from the fact that the Schrödinger evolution of quantum systems is continuous in Hilbert spaces. Since classical trajectories in space consist of points corresponding to eigenstates of the position operator, and since distinct eigenvectors are orthogonal to each other, it follows that the continuous evolution of a quantum system from one eigenvector to another must take the system through states with no well-defined position.
- 4.
Here is a quick proof: 〈Uλa|Uλb〉 = 〈λa|U†U|λb〉 = 〈λa|λb〉 = 0, since U† = U−1 for unitary operators.
- 5.
More general processes, such as rearrangement collisions, lead to the creation of new particles and thus belong to the category of reactions (see Cohen-Tannoudji et al. 1978, pp. 903–904).
- 6.
For more details on that, see, for example, Cohen-Tannoudji et al. (1978, p. 903ff).
- 7.
- 8.
This assumption is not necessary for the subsequent discussion, but it simplifies appropriate formulas.
- 9.
See Liu et al. (1998) for a detailed description of a real collision experiment involving electrons that gives rise to interference effects.
- 10.
- 11.
This argument against the possibility of diachronic identifications for objects that are synchronically indistinguishable is similar to the argument against the possibility of history-based individuation of objects that share their momentary properties, as presented in Cortes (1976, pp. 503–504).
- 12.
- 13.
- 14.
That is, any sentence expressed with the help of individual constants (names) true in the original world will remain true in the “switched” world.
- 15.
- 16.
Another proposal for an ontological theory of quantum particles as bundles of properties is outlined in Friebe (2014). It is notable that Friebe formulates his proposal in the context of the GMW conception of entanglement (as presented in Chap. 6), and thus broadly in terms of what we call the heterodox approach (even though he does not make the distinction between two alternative conceptions of individuation in the quantum theory of many particles). A detailed critical analysis of Friebe’s approach has to be left for another occasion.
- 17.
Thus I am not a proponent of one of many eliminative ontologies of the physical world that dispense with the concept of a physical object as a fundamental entity, replacing it, for instance, with more fundamental abstract structures. See French (1998), French and Ladyman (2003, 2011) and Rickles and Bloom (2016).
- 18.
It is quite possible that we could use equivalence here instead of implication, which would mean that the relation denoted by GI is actually definable in terms of St.
- 19.
In a fully developed metaphysical theory of quantum particles, we would have to find a way to indicate that the existence of momentary objects xi and yi composing system a at a time ti is relativized to the choice of an orthogonal basis.
- 20.
Apart from that we have to solve the following conceptual conundrum: how is it possible that object a (the system of two particles) retains its identity while its components do not? The whole temporal slices of a at times t1 and t2 should be connected by the relation of full genidentity GI, and yet the spatial parts of these slices are linked by mere partial genidentities PI. Clearly, some intuitions regarding the relations between components and their diachronic identities must be abandoned. It is advisable to spell out these intuitions and show precisely why they fail.
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Bigaj, T. (2022). The Metaphysics of Quantum Objects: Transtemporal and Transworld Identities. In: Identity and Indiscernibility in Quantum Mechanics. New Directions in the Philosophy of Science. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-74870-8_8
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