Properties, Statistics and the Identity of Quantum Particles Matteo Morganti INFN Training School 19-21 December 2016 Frascati 19/12/2016

Introduction What sort of things is quantum theory about? Starting points: 1) Entrenched intuition that reality is made of individual objects 2) It is a widespread belief that quantum theory refutes the intuition, as it is a theory of non-individuals ‘Received View’, dating back to (some of) the founding fathers of the theory - e.g., Born, Heisenberg «It is impossible for either of these individuals to retain his identity so that one of them will always be able to say ‘I’m Mike’ and the other ‘I’m Ike.’ Even in principle one cannot demand an alibi of an electron!» (Weyl, 1931) Properties, statistics and the identity of quantum particles

Introduction Aim here: to assess the widespread belief, via a critical analysis of options ‘Naturalistic’ approach whereby science and philosophy complement each other Input coming from our best physics is essential, but empirical data underdetermine the interpretation of the theory Clarification of concepts and arguments rather than final answers Considerations re. non-relativistic quantum mechanics and (more briefly) quantum field theory Properties, statistics and the identity of quantum particles

Plan Definitions (Non-relativistic) Quantum Mechanics: Properties, Statistics and the Received View Alternatives: A Theory of Individuals after All? Quantum Field Theory Conclusions Properties, statistics and the identity of quantum particles

1. Definitions (Material/physical) entity x is an individual object iff: x is a thing/object Not an event, property, fact or… x is self-identical x is numerically distinct from everything else x may also possess: Diachronic (in addition to synchronic) identity Sharp localisability Individual object ≠ object according to classical mechanics/common sense – Particle? Not obvious: think, e.g., of the difference between an actual coin and a money unit in a bank account Properties, statistics and the identity of quantum particles

2.1 Non-Relativistic QM: Statistics Individuality a problem with respect to statistics: Assume two systems 1 and 2 and two available states x and y Available arrangements, classically: |x>1|x>2 |y>1|y>2 |x>1|y>2 |y>1|x>2 Properties, statistics and the identity of quantum particles

2.1 Non-Relativistic QM: Statistics Individuality a problem with respect to statistics: Assume two systems 1 and 2 and two available states x and y Available arrangements, quantum case: |x>1|x>2 |y>1|y>2 1/2(|x>1|y>2|y>1|x>2) Only (anti-)symmetric states available in QM Permutation Symmetry Confirmation of the Received View? ‘Particles’ more like money units in a bank than real coins BOSONS FERMIONS Properties, statistics and the identity of quantum particles

2.2 Non-Relativistic QM: Properties In classical mechanics (although not an axiom of the theory!), impenetrability guarantees difference in spatial location/trajectories (The same in, e.g., Bohmian Mechanics) Not in (standard) quantum mechanics! Properties correspond to probabilities (Born Rule) Two entities can ‘have the same position’, i.e., share the same possible values for position measurements Properties, statistics and the identity of quantum particles

Properties, statistics and the identity of quantum particles

Properties, statistics and the identity of quantum particles

xy((xy)P(Px&Py)) Underlying intuition: things are individuated by their properties An important philosophical tradition: Leibniz  Quine, Hilbert and Bernays, etc. Principle of the Identity of Indiscernibles (PII): xyP(PxPy)(x=y)  xy((xy)P(Px&Py)) (P not ranging over properties such as ‘is identical to a’…) QM statistics+violation of PIIReceived View? Properties, statistics and the identity of quantum particles

1/2(|>1|>2+|>1|>2) 3. Alternatives (1) Individuation via (qualitative) relations, not properties Consider, e.g., ‘…is taller than…’, ‘… goes in the opposite direction to…’ But, not reducible to monadic properties of relata and symmetric (Existence and features of relata not ontologically prior) Singlet state of two fermions 1/2(|>1|>2+|>1|>2) No well-defined spin properties separately Yet, Prob=1 of opposite spins! Properties, statistics and the identity of quantum particles

Mass x Charge y Spin probability z … Opposite spin! Mass x Charge y Spin probability z … Encoded in states like 1/2(|>1|>2+|>1|>2) Properties, statistics and the identity of quantum particles

The result is good news for Leibnizians Some remarks: The result is good news for Leibnizians Individuation via qualitative physical features Due to the Exclusion Principle, ‘identical’ fermions in the same physical system can only be found in states such as the one just described Basic ontological distinction between bosons and fermions? Actually a controversial result: Can relations be prior to their relata? Are the relevant properties always physically meaningful? Are weakly discernible entities individuals? Do we really have a relation between parts? Properties, statistics and the identity of quantum particles

A ? B Spin  Spin correlation Spin  Time t1 Time t2 (after measurement) Properties, statistics and the identity of quantum particles

«Common natures are ‘contracted’ in particular things by haecceitates» 3. Alternatives (2) An alternative philosophical view: Not necessary to use PII as a principle of individuation Individuality is a primitive, ‘brute’ fact Duns Scotus: Individuality based on ‘transcendental’ identities «Common natures are ‘contracted’ in particular things by haecceitates» Properties, statistics and the identity of quantum particles

What about primitive identities for quantum entities? Makes sense of violations of PII As well as of the use of particle names or ‘labels’ in QM However, two objections: 1) Seems ruled out by permutation symmetry – quantum statistics 2) Methodologically suspect What is a primitive identity? How can such a thing be empirically relevant? Replies Properties, statistics and the identity of quantum particles

1) Primitive identities are compatible with permutation symmetry For instance, state-dependent properties of many-particle quantum systems (of identical particles) may be holistic Notice that this accounts for the impossibility of non- symmetric states, which must be explained anyway Obvious difference: |x>1|y>2 and 1/2(|x>1|y>2|y>1|x>2) 2) Indiscernibles could in fact make a qualitative difference For example, a system with n indiscernible fermions has n times the unit mass (Compare with the Leibniz vs. Newton dispute on the nature of space (and time)) Primitive identities need not be ‘mysterious metaphysics’ Properties, statistics and the identity of quantum particles Identity, Indiscernibility and Naturalised Metaphysics

4. Quantum Field Theory More elements to take into account: QFT has no ‘labels’ for particles, but rather occupation numbers and annihilation/creation operators The number operator N can be in a superposition of states! How many ‘things’?? The relativistic theory makes things even worse: Not clear that we have a fully consistent theory of both free and interacting fields (Haag’s Theorem) Expectation values for certain quantities do not vanish for the vacuum state Properties, statistics and the identity of quantum particles

4. Quantum Field Theory Moreover, in relativistic QFT: Local measurements do not allow to distinguish a ‘vacuum state’ from any n-particle state (Reeh-Schlieder Theorem) An accelerated observer in a vacuum detects a ‘thermal bath’ of particles (Unruh Effect) Particles cannot be localised in finite regions (Malament’s Theorem) In short, facts about numbers of ‘things’ fail to be completely determinate in QFT Even the distinction between vacuum and non- vacuum is not clear-cut Localisation cannot be taken for granted either Properties, statistics and the identity of quantum particles

This may seem to lead us away from individuals and particles Notice, however, that: The allegedly problematic results are open to discussion At any rate, they carry over to an ontology of fields More importantly, recall that individual object(classical) particle Properties, statistics and the identity of quantum particles

(Material/physical) entity x is an individual object iff: x is a thing/object Not an event, property, fact or… x is self-identical x is numerically distinct from everything else x may also possess: Diachronic (in addition to synchronic) identity Sharp localisability Properties, statistics and the identity of quantum particles

This may seem to lead us away from individuals and particles Notice, however, that: The allegedly problematic results are open to discussion At any rate, they carry over to an ontology of fields More importantly, recall that individual object(classical) particle If we stick to 1.-3. and drop 4.-5., results concerning number and localisability become perhaps less worrisome (Frame-dependent) individual objects but not (classical) particles? The ontological question remains open… Properties, statistics and the identity of quantum particles

5. Conclusions Philosophical issues with identity and individuality Obvious relevance of science - naturalism Individuals vs. non-individuals, particles vs. fields vs. … Non-relativistic quantum mechanics and quantum field theories Issues not settled: Received View with non-individual entities not an obvious winner Need for further study of: Empirical evidence Physical theory Philosophical assumptions Underlying methodology This case study indicates the importance of the interplay between physics and philosophy: empirical data do not determine a unique interpretation Properties, statistics and the identity of quantum particles

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