• Introduction
• General Overviews and Introductory Texts
• Historical Background
• Transcendental Identity
• Metaphysical Underdetermination and OSR

# Identity in PhysicsbyDécio Krause, Jonas R. B. ArenhartLAST REVIEWED: 08 October 2015LAST MODIFIED: 30 January 2014DOI: 10.1093/obo/9780195396577-0174

## Introduction

Traditionally, the problem of identity is closely associated with the problem of individuality: What is it that makes something being what it is? Approaches to the problem may be classified into two classes: reductionism and transcendental identity. The first group tries to reduce identity to some qualitative feature of the entities dealt with, while the second either grounds identity on some feature other than qualitative properties or else take it to be primitive. The debate is generally centred on the validity of the Principle of the Identity of Indiscernibles (PII), which states that qualitative indiscernibility amounts to numerical identity. If PII is valid, then reductionism concerning identity is at least viable; if PII is invalid, then reductionism seems less plausible and some form of transcendental identity seems required. It is common to say that objects in classical mechanics are individuals. This fact is exhibited by postulating that physical objects obey Maxwell-Boltzmann statistics; if we have containers A and B to accommodate two objects a and b, there are four equiprobable situations: (1) both objects in A, (2) both in B, (3) a in A and b in B, and finally (4) a in B and b in A. Since situations (3) and (4) differ, there may be something that makes the difference—a transcendental individuality or some quality. In quantum mechanics, assuming that we have two containers A and B to accommodate objects a and b, there are just three equiprobable situations for bosons: (1) both objects in A, (2) both in B, (3) one object in A and one in B. It makes no sense to say that it is a or b that is in A: Switching them makes no difference. For fermions we have only one possibility due to the exclusion principle: (1) one object in A and one in B. Again, switching them makes no difference whatsoever. The dispute in quantum mechanics concerns non-individuality on the one side and individuality (be it reductionism or transcendental individuality) on the other. That distinction was grounded on the fact that quantum particles may be qualitatively indiscernible, and, as the statistics show, permutations are unobservable. The actual debate concerns whether some form of reductionism may survive in quantum mechanics or whether some form of transcendental identity should be adopted on the one hand and whether non-individuality is a viable option. Furthermore, a third option, Ontic Structural Realism (OSR), proposes that we transcend the debate and choose a metaphysics of structures and relations, leaving the controversial topic individuals × non-individuals behind.

## General Overviews and Introductory Texts

The discussion on identity in physics appears frequently mixed with metaphysical discussions on identity or within more technical discussions on the philosophy of physics. The general reader with philosophical background will benefit from French 2011 in which the discussion is completely focused on the problem on identity in physics. A very useful (once again, philosophically demanding) general introduction to the theme may also be found in French and Rickles 2003 and Ghirardi 2005. A very comprehensive textbook on the philosophy of quantum mechanics that touches on ontology and identity of quantum particles is Bitbol 1996. For a philosophy of science textbook-like introduction, see Dalla Chiara and Toraldo di Francia 2000, and for an introductory article dealing with the main novelties of the quantum world, see Toraldo di Francia 1998.

• Bitbol, M. Mécanique Quantique: Une introduction philosophique. Paris: Flammarion, 1996.

An introduction to quantum theory designed for philosophers. The book discusses the main novelties of the theory from a philosophical point of view, in particular the implications for the very concepts of object and identity.

• Dalla Chiara, M. L., and G. Toraldo di Francia. Introduzione alla filosofia della scienza. Rome: Bari, 2000.

This textbook discusses in a very introductory fashion the role of statistics and names in physics, presenting the trouble created by quantum mechanics to the traditional approaches on identity, naming, and individuality.

• French, S. Identity and Individuality in Quantum Theory. In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. 2011.

This is an encyclopaedia article devoted especially to the topic of identity in physics. It contains a general presentation of the major positions and problems concerning the theme, relating them to the role of statistics in quantum mechanics. It covers most of the actual controversies of the field with a generous list of references.

• French, S., and D. Rickles. “Understanding Permutation Symmetry.” In Symmetries in Physics: Philosophical Reflections. Edited by K. Brading and E. Castellani, 212–238. Cambridge, UK: Cambridge University Press, 2003.

This paper introduces the topic of permutation invariance in quantum mechanics and discusses its mathematical, physical, and philosophical aspects in a general fashion, relating permutation invariance with the discussion on identity and individuality. Contains the major arguments presented for the majority of positions available so far in the debate.

• Ghirardi, G. Sneaking a Look at God’s Cards. Princeton, NJ: Princeton University Press, 2005.

This is an introductory book on the main problems of quantum mechanics. It presents the topic of identity in quantum mechanics in the context of a reader-friendly presentation of the technical aspects of the theory. The approach is highly based on the view that quantum mechanics casts doubts on the universality of identity.

• Toraldo di Francia, G. “A World of Individual Objects?” In Interpreting Bodies: Classical and Quantum Objects in Modern Physics. Edited by E. Castellani, 21–29. Princeton, NJ: Princeton University Press, 1998.

This paper presents in general terms the situation of objects in quantum physics. It illustrates the idea that identity breaks in the quantum case, so that one cannot count quantum entities. However, cardinal attribution remains in the sense that one may always know how many entities there are in any context.