*Conducted in term:*2020L

*Erasmus code:*08.1

*ISCED code:*0223

*ECTS credits:*2

*Language:*English

*Organized by:*Faculty of Philosophy

# (in Polish) Identity and individuality in quantum mechanics 3501-IIQM20-M

Quantum mechanics changes radically the classical views of reality. One of the most important elements of the classical ontological view is the principle that all distinct objects must differ from one another with respect to some properties. This principle dates back to Leibniz, and is known as the Principle of the Identity of Indiscernibles (or, better yet, of the Discernibility of the Distinct). And yet the development of quantum mechanics that started at the beginning of the 20th century seems to challenge this well-entrenched view. Quantum mechanics imposes an important restriction on the states of groups of same-type particles, known as the Symmetrization Postulate. This postulate claims that only states with certain symmetry properties (invariant under the permutations of objects) are admissible for systems of ‘identical’ particles. From the Symmetrization Postulate many philosophers derive the Indiscernibility Thesis which claims that same-type particles cannot be distinguished by any properties. Thus some philosophers insist that quantum particles lose the status of individual objects, and even cease to be self-identical. On the other hand, others hope that the objecthood and some form of individuality may be restored by resorting to the concept of weak discernibility, or – more radically – by reconsidering the way we should individuate components of a greater mereological whole consisting of quantum particles. In this unorthodox approach quantum particles can be to a certain extent differentiated by their properties, however this individuation may be temporary only.

The plan of this lecture is as follows:

1. Introduction to the basic concepts and formal methods of quantum theory (the notions of a state vector, Hermitian operators representing properties, projectors, permutations, the distinction between bosons and fermions).

2. The Symmetrization Postulate and the proofs of the Indiscernibility Thesis.

3. The sources of the Symmetrization Postulate (the argument from exchange degeneracy).

4. The logic and metaphysics of discernibility (absolute, relative and weak discernibility and their connection with symmetries).

5. Weak discernibility in quantum mechanics. The apparent restoration of the Principle of the Identity of Indiscernibles.

6. The unorthodox approach to quantum individuation: the controversy regarding the physical interpretation of symmetric projectors of a certain kind.

7. The ambiguity of quantum qualitative individuation by symmetric operators.

8. Discernibility and entanglement. The notion of GMW-entanglement.

9. Synchronic identity and diachronic identity.

## Type of course

## Mode

## Prerequisites (description)

## Course coordinators

## Learning outcomes

Acquired knowledge

After completing the course the student should:

-know the basic concepts and methods used in the quantum-mechanical description of groups of identical particles,

-understand the key consequences of quantum mechanics for the philosophical reflection on the notion of identity and individuality,

-know basic conceptual problems of the quantum theory of many particles and of the logic of identity and discernibility,

-appreciate the role of scientific developments in philosophical investigations,

Acquired skills:

-ability to critically analyze problems that appear at the interface between scientific theories and philosophy,

-ability to connect philosophical problems with discoveries in natural sciences,

Acquired social competences:

-awareness of the importance of scientific problems for the development of worldview,

-awareness of the role that philosophy plays in shaping new scientific conceptions.

## Assessment criteria

The students’ progress will be assessed on the basis of short quizzes given throughout the course and a final essay.

Number of absences: 2

## Bibliography

The main literature for the course:

T. Bigaj, Identity and indiscernibility in quantum mechanics, preprint

Additional sources:

Caulton, A. (2014), “Qualitative individuation in permutation-invariant quantum mechanics”, arXive: 1409.0247v1 [quant-ph].

Dieks, D. and Lubberdink, A. (2011), “How classical particles emerge from the quantum world”, Foundations of Physics 41, 1051-1064.

Dieks, D., and Versteegh, M. (2008), “Identical quantum particles and weak discernibility”, Foundations of Physics, 38, 923-934.

French, S., and Krause, D. (2006). Identity and Physics: A Historical, Philosophical and Formal Analysis. Oxford: Clarendon Press.

French, S., and Redhead, M. (1988), “Quantum physics and the identity of indiscernibles”. British Journal for the Philosophy of Science 39: 233-246.

Ghirardi, G., Marinatto, L., & Weber, T. (2002), “Entanglement and Properties of Composite Quantum Systems: A Conceptual and Mathematical Analysis”, Journal of Statistical Physics , 108 (112), 49-122.

Hawley, K. (2006), “Weak discernibility”, Analysis, 66, 300-303.

Huggett, N. and Imbo, T. (2009), “Indistinguishability”, in: Friedel Weinert, Klaus Hentschel, Dan Greenberger, (eds.) Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, Springer-Verlag, 311-317

Ladyman, J., Linnebo, O., and Pettigrew, R. (2012), “Identity and discernibility in philosophy and logic”, The Review of Symbolic Logic, 5, 162-186

Muller, F.A. (2015), “The rise of relationals”, Mind, 124, 201-237.

Muller, F.A., and Saunders, S. (2008), “Discerning fermions”, British Journal for the Philosophy of Science, 59, 499-548.

Quine, W.V.O. (1976). Grades of Discriminability. Journal of Philosophy, 73: 113-116.

Saunders, S. (2006), “Are quantum particles objects?”, Analysis, 66, 52-63.

Saunders, S. (2009), “Identity of quanta” in: Friedel Weinert, Klaus Hentschel, Dan Greenberger, (eds.) Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, Springer-Verlag, 299-304.

Saunders, S. (2013), “Indistinguishability”, in: R. Batterman (ed.) Oxford Handbook of Philosophy of Physics, Oxford University Press, Oxford, 340-380.

## Additional information

Additional information (*registration* calendar, class conductors,
*localization and schedules* of classes), might be available in the USOSweb system: