1 Summer school “Physics and Philosophy of Time”, Saig, Quantum non-locality and the philosophy of time Michael Esfeld Université de Lausanne

The lecture 1)Bell‘s theorem and quantum non-locality 2) Proposals for a quantum ontology of matter in space-time and their impli- cations for the philosophy of time a) Bohmian mechanics b)The GRW mass density theory c) The GRW flash theory

3 The EPR-experiment

4 Le théorème de Bell

5 Bell’s theorem (1964): non-locality  “no conspiracy”: a and b are independent of  locality: given, a and A are independent of b and B (and vice versa); the probability for a certain value of A does not change, if b and B are given (and vice versa) P (A  a, b, B, ) = P (A  a, ) P (B  a, b, A, ) = P (B  b, )  There is no theory possible that is in accord with the empirical predictions of QM and that satisfies locality.  constraint on any future theory

Physical theory  What are the physical objects? classical mechanics: particles  What is the law of their behaviour (temporal development, motion)? What are the properties of these objects so that a certain law describes their behaviour? classical mechanics: mass, charge  force laws  How do the physical objects and their properties explain the observable phenomena? classical mechanics: macroscopic objects composed of microscopic particles; form of motion of particles due to forces explains variations in observable phenomena

Primitive ontology  textbook QM formalism: law for temporal development of  What does  represent? (Schrödinger equation cannot even accommodate measurement outcomes)  primitive ontology: ontology of matter distributed in space-time as referent of the quantum formalism cannot be inferred from the formalism of QM  motivation: obtain an ontology that can account for the existence of measurement outcomes (and the familiar macroscopic objects in general)  discussion of the relationship between QM and relativistic space-time possible only once primitive ontology of QM specified

Primitive ontology two possibilities:  recognize Schrödinger equation as law for the temporal development of the wave-function and provide additional law that links wave-function up with distribution of matter in space-time and its temporal development  Bohmian mechanics  change the Schrödinger equation so that a law is achieved that can accommodate the fact of there being measurement outcomes (and localized macroscopic objects in general)  theory of Ghirardi, Rimini & Weber (GRW)

Bohmian mechanics  What are the physical objects? particles localized in physical space  What is the law of their behaviour (temporal development, motion)? What are the properties of these objects so that a certain law describes their behaviour?  plays the role, given the position of the particles at t, to fix their velocity at t  first order equation: velocity instead of acceleration by means of forces  velocity of each particle at t depends on position of all the other particles at t  holism:  describes property of the whole particle configuration that determines temporal development (instead of intrinsic properties of particles such as mass, charge  local forces)  non-local correlations explained  no interaction among particles at t, no “spooky” action at a distance

Bohmian mechanics  How do the physical objects and their properties explain the observable phenomena? macroscopic objects composed of microscopic particles form of motion of particles explains variations in observable phenomena (including QM observables such as spin) decoherence (effective wave-functions) explains classical behaviour  ignorance of exact initial conditions (exact initial particle positions) & initial distribution typical  QM probability calculus deduced from Bohmian mechanics

Bohmian mechanics and the philosophy of time  absolute simultaneity: position of all the particles at t influences, via , motion of any particle at t  ontology: particle configuration at t AND holistic property of configuration represented by  at t  particles: endurants  philosophy of time: presentism  Bohmian QFT, QG: configuration of matter & holistic property of configuration that determines transition from one configuration to next one (represented by , figuring in guiding equation)  one actual configuration at a time & holistic property of that configuration

GRW  Ghirardi, Rimini, Weber (1986): amendment of Schrödinger equation so that “collapse of the wave-function” is included (probability for “collapse” & width of “collapse”)  still law for temporal development of   What is the primitive ontology?

GRWm  What are the physical objects? Ghirardi: one object: mass density field in space = gunk  What is the law of their behaviour (temporal development, motion)? What are the properties of these objects so that a certain law describes their behaviour? GRW equation; holistic property of mass density that fixes probabilities for its temporal development, propensity for spontaneous contraction at certain location  spontaneous delocation of mass density  non-local correlations explained  How do the physical objects and their properties explain the observable phenomena? microscopic objects literally smeared out in space, macroscopic objects well localized due to spontaneous contraction of mass density; shape of mass density explains variations in observable phenomena (including QM observables such as spin)

GRWm and the philosophy of time  absolute simultaneity: mass density field in entire physical space at t, holistic property at t that determines motion of mass density  ontology: mass density at t & holistic property BOTH represented by  at t  mass density: endurant or perdurant  philosophy of time: presentism or growing block universe

GRWf  What are the physical objects? Bell, Tumulka: flashes = events centred at space-time points, sparse distribution  What is the law of their behaviour (temporal development, motion)? What are the properties of these objects so that a certain law describes their behaviour? GRW equation; flash iff spontaneous localization of  in configuration space; holistic property of configuration of flashes that fixes probabilities for occurrence of further flashes  How do the physical objects and their properties explain the observable phenomena? macroscopic objects composed of flashes; where flashes occur in space-time explains variations in observable phenomena (including QM observables such as spin)

GRWf and the philosophy of time  rGRWf, Tumulka: initial configuration of seed flashes & GRW equation  Lorentz-invariant law  calculation of probabilities for entire distributions (histories) of flashes in space- time; each of these distributions as a whole can be described in a Lorentz-invariant manner  one actual distribution, given as primitive ontology

GRWf and the philosophy of time  But: How does actual distribution of flashes come into being (develop in time), given initial configuration of seed flashes?  no Lorentz-invariant answer to that question possible: no local, relativistic becoming possible (= becoming along a worldline) due no non-local correlations = how further flashes occur depends on where at spacelike separated locations other flashes occur  coming into being / temporal development of flash distribution requires absolute simultaneity (preferred foliation of space-time)

Rodi Tumulka (2007) “Who influences whom is frame dependent. There is no objective fact about who “really” influenced whom. There is no need for such a fact. The objective facts are where-when the flashes occur, and it is enough if a theory prescribes, as does rGRWf, their joint distribution in a Lorentz- invariant way. Whether nature chooses the space-time point f B first, and f A afterwards, or the other way around, does not seem like a meaningful question to me”

John Bell “The theory of local beables” (1976) “One of the apparent non-localities of quantum mechanics is the instantaneous, over all space, ‘collapse of the wave function’ on ‘measurement’. But this does not bother us if we do not grant beable status to the wave function. We can regard it simply as a convenient but inessential mathematical device for formulating correlations between experimental procedures and experimental results, i.e., between one set of beables and another.”

GRWf and the philosophy of time  ontology I: only primitive ontology flashes = primitive matter in space-time (flash at a point = point occupied instead of empty), events, neither endurants nor perdurants no properties / no quantum state instantiated in space-time  part of law that achieves most economical description of entire distribution of flashes in space-time  Lorentz-invariant; block universe  ontology II: primitive ontology & quantum state flashes quantum state instantiated in space-time: holistic property of configuration of flashes that fixes probabilities for further occurrence of flashes  coming into being / temporal development of actual distribution of flashes not Lorentz-invariant; growing block universe

Conclusion  primitive ontology: particles, gunk, events  philosophy of time:  if events and these only primitive stuff in space-time & account of becoming renounced, then Lorentz- invariance possible & block universe  if primitive stuff in space-time & quantum state instantiated by that stuff = holistic property that fixes its temporal development, then, due to non- separability of  = non-local correlations in space- time  absolute simultaneity / preferred foliation of space-time & presentism or growing block-universe