Properties , Statistics and the Identity of Quantum Particles

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

2. Introduction • What sort of things is quantum theory about? Starting points: 1) Entrenched intuition that reality is made of individual objects 2) Itis a widespreadbeliefthat quantum theoryrefutes the intuition, asitis a theory of non-individuals • ‘ReceivedView’, dating back to (some of) the foundingfathers 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

3. Introduction • Aimhere: to assess the widespreadbelief, via a criticalanalysis of options • ‘Naturalistic’ approachwhereby science and philosophycomplementeachother • Input coming from our best physicsisessential, butempirical data underdetermine the interpretation of the theory • Clarification of concepts and argumentsratherthanfinalanswers • Considerations re. non-relativistic quantum mechanics and (more briefly) quantum fieldtheory Properties, statistics and the identity of quantum particles

4. Plan • Definitions • (Non-relativistic) Quantum Mechanics: Properties, Statistics and the ReceivedView • Alternatives: A Theory of IndividualsafterAll? • Quantum Field Theory • Conclusions Properties, statistics and the identity of quantum particles

5. 1. Definitions • (Material/physical) entityxis an individualobjectiff: • xisathing/object • Notan event, property, factor… • xis self-identical • xisnumericallydistinct from everything else • xmayalsopossess: • Diachronic(in addition to synchronic) identity • Sharp localisability • Individualobject≠ objectaccording to classicalmechanics/common sense – Particle? Notobvious: think, e.g., of the differencebetween an actualcoin and a moneyunit in a bank account Properties, statistics and the identity of quantum particles

6. 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

7. 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

8. 2.2 Non-Relativistic QM: Properties • In classicalmechanics (althoughnot an axiom of the theory!), impenetrabilityguaranteesdifference in spatial location/trajectories • (The same in, e.g., BohmianMechanics) • Not in (standard) quantum mechanics! • Propertiescorrespond to probabilities (BornRule) • Twoentities can ‘have the same position’, i.e., share the samepossiblevalues for position measurements Properties, statistics and the identity of quantum particles

9. Properties, statistics and the identity of quantum particles

10. Properties, statistics and the identity of quantum particles

11. Underlyingintuition: things are individuatedby theirproperties • An importantphilosophicaltradition: • 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 notranging over propertiessuchas ‘isidentical to a’…) • QM statistics+violation of PIIReceivedView? Properties, statistics and the identity of quantum particles

12. 3. Alternatives (1) • Individuation via (qualitative) relations, notproperties • Consider, e.g., ‘…istallerthan…’, ‘… goes in the opposite direction to…’ • But, notreducible to monadicproperties of relata and symmetric • (Existence and features of relata notontologicallyprior) • Singlet state of two fermions 1/2(|>1|>2+|>1|>2) • No well-defined spin propertiesseparately • Yet, Prob=1 of opposite spins! Properties, statistics and the identity of quantum particles

13. 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

14. 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

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

16. 3. Alternatives (2) • An alternative philosophicalview: • Notnecessary to use PII as a principle of individuation • Individualityis a primitive, ‘brute’ fact • Duns Scotus: • Individualitybased on ‘transcendental’ identities «Common natures are ‘contracted’ in particular things by haecceitates» Properties, statistics and the identity of quantum particles

17. Whatabout primitive identities for quantum entities? • Makessense of violations of PII • Aswellas of the use of particlenames or ‘labels’ in QM • However, twoobjections: • 1) Seemsruled out by permutationsymmetry – quantum statistics • 2) Methodologicallysuspect • Whatis a primitive identity? How can such a thing be empiricallyrelevant? • Replies Properties, statistics and the identity of quantum particles

18. 1) Primitive identities are compatible with permutationsymmetry • 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 makea 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

19. 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

20. 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

21. 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

22. (Material/physical) entityxis an individualobjectiff: • xisathing/object • Notan event, property, factor… • xis self-identical • xisnumericallydistinct from everything else • xmayalsopossess: • Diachronic(in addition to synchronic) identity • Sharp localisability Properties, statistics and the identity of quantum particles

23. Thismayseem to leadusaway from individuals and particles • Notice, however, that: • The allegedlyproblematicresults are open to discussion • At any rate, theycarry over to an ontology of fields • More importantly, recallthatindividualobject(classical) particle • Ifwestick to 1.-3. and drop 4.-5., resultsconcerningnumber and localisabilitybecomeperhapslessworrisome • (Frame-dependent) individualobjectsbutnot (classical) particles? • The ontologicalquestionremains open… Properties, statistics and the identity of quantum particles

24. 5. Conclusions • Philosophicalissues with identity and individuality • Obviousrelevance 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

25. THANK YOU! Properties, statistics and the identity of quantum particles