Valia Allori

Huskie Commons

     1 Primitive Ontology and the Structure of Fundamental Physical TheoriesValia AlloriNorthern Illinois UniversityOctober 8th 2007or August 24th?  2the non-Vulcanian side of Shelly  3Fundamental Physical Theories Physical: a theory of the physical world describe the world/ behaviour of things postulate the existence of some invisible/counter-intuitive/not obvious entities Examples: ancient Greek atomism classical mechanics quantum mechanics  4Fundamental Physical Theories Fundamental: explain the behaviour of all things physics vs chemistry vs biology ...  Reductionism: description of the behaviour of macroscopic things in three-dimensional space statistical mechanics vs thermodynamics explanation ofhow we think there are things that actually aren't there example: color  5Fundamental Physical Theories Theory:  conjectural nature creative element role of explanation   6 what a FPT can/should be able to explain:  the behaviour of everything (=motion of macroscopic objects in ordinary space) FPT: Common Structure     7 what a FPT cannot explain:  the mind-body problem ex: perception of color vs colorFPT: Common Structure  8 They need to be about something: they should have a clear ontology What they are fundamentally about is what Shelly (and Nino and Detlef) called the primitive ontology  (PO) They also need dynamical variablesFPT: Common Structure 1 9The need for a clear ontology If one wants to be a REALIST w.r.t. a Fundamental Physical Theory, then it must be clear what the theory is about:  What are the entities that are out there in the world and and what is their mathematical representation? If we do not specify the ontology, the theory is only empty mathematics 1 10The notion of Primitive Ontology The primitive ontology of the theory is what the theory is fundamentally about A bunch of variables in the FPT: The primitive ontology is the stuff physical things are made of as opposed to the dynamical variable(s) 1 11The dynamics of the PO It is not sufficient to specify only what is the PO - we also need to specify how it behaves:   What is the law of motion for the PO? The variables describing  the PO must be distinguished from the other auxiliary (or nomological) variables that allow for the implementation of a dynamical law for the primitive variables  1 12The PO and its dynamics(what there is) & (how it behaves) (Primitive) & (nomological) variables    1 13Decorations Dual structure: (X; Φ) X (=PO): decoration of space-time Φ : governing the motion of Xtx 1 14FPT: Common Structure X (primitive ontology): what matter is  Φ (the dynamical variable): how matter moves  µ (measure of typicality): what the majority of histories of X are doing 1 15FPT: Common Structure in a space-time setting the description is in terms of (, µ):: the space of histories µ: the measure of typicality   16Fundamental Physical Theories FPT are what physicists should be looking for Examples of FPT: classical mechanics classical electrodynamics General relativity String theory ... quantum mechanics ? 1 17 What is Quantum Mechanics? It is supposed to be a FPT The fundamental object of the theory is the wave function Ψ: it completely describes the state of a physical system  The wave function lives in configuration space (dimension d~1023) The wave function evolves in time according to an equation called Schrödinger's equation  1 18The equation is Linear: If Ψ1 and Ψ2 describe possible physical states at a given time t, also Ψ1+Ψ2 does State: all you need to specify in order to completely describe the systemΨ1Ψ2Ψ1+Ψ2 What is Quantum Mechanics?    1 19Impossible cats Because of linearity of the evolution equation, the wave function evolves into a superposition state: It is the sum of two macroscopically distinct states of affairs of the system under consideration (cat alive and cat dead) + 1 20 From experience we know that macroscopic systems are NEVER in a superposition. Rather, they are always in well defined states                        orImpossible cats 1 21 But we just saw that IF the wave function provides a complete description of a system AND it evolves according to Schrödinger's equation, THEN it produces such superpositions Therefore, IF we want quantum mechanics to describe what really happens (that is, if we want measurements to have results), THEN ....Impossible cats 1 22 Bell's famous alternatives:Either the wave function does not provide the complete descriptionOR it does not evolve according to Schrödinger's equationImpossible cats 1 23Impossible cats Moral of the story: The three claims 1:The wave function provides a complete description  2:The wave function evolves according to Schrödinger's equation  3:Measurements have results  Are incompatible 1 24Solutions to the measurement problem  (without the observer) Deny claim 1 (the wave function provides a complete description) Add particles positions  (Bohmian Mechanics, BM) Deny claim 2 (the wave function evolves according to Schrödinger's equation) The wave function evolves according to a stochastic equation  (GRW theory) Deny claim 3 (measurements don't have results) There is a multiverse of different worlds (Many Worlds, MW)     25Bohmian Mechanics Complete description  (Q,Ψ):   Q=(Q1, ... , QN) , Qk in R3, k=1,...,N Ψ(Q)=Ψ(Q1, ... , QN)  26Bohmian MechanicsGuide equation Schrödinger equation  27Bohmian metaphysics BM is about particles in 3-dimensional space :  The microscopic description of reality is discrete (particle-like)   28GRW Theory Ψ(Q)=Ψ(Q1, ... , QN) Q=(Q1, ... , QN) , Qk in R3, k=1,...,N particles are not really there  29GRW Theory For any point x in R3 The evolution for ψ is Schrödinger interrupted by collapses A collapse center with center x and label i will occur at rate When this happens:  30GRW metaphysics? In GRW there seem to be just the wave function.  Is GRW a theory about the wave function?  is Ψ the PO of GRW? Problems of considering tables and chairs as made of wave functions: The wave function lives in a space with a very large number of dimensions (~1023) Where is three-dimensional space?     31GRW metaphysics? [...] the wave function as a whole lives in a much bigger space, of 3N dimensions. It makes no sense to ask for the amplitude or phase or whatever of the wave function at a point in ordinary space. It has neither amplitude nor phase nor anything else until a multitude of points in ordinary three-space are specified.  [Bell, 1987]  32Mass density GRW - GRWm GRWm is a theory about the behaviour of a field m(x, t) on three-dimensional space This is reminiscent of Schrödingers early view of the wave function as representing a continuous matter field.  33GRWm metaphysics The microscopic description of reality provided by the matter density field m(x, t)  is  continuous (in contrast with the particle ontology of BM)  34Flashy GRW - GRWf GRWf is a theory about a set of events in space-time, the flashes = the points in s-t corresponding to the collapses of the wave function    The wave function evolves in a random way F is a random set of space-time  35GRWf metaphysics The microscopic description of reality provided by GRWf is discrete in space-time the world is a galaxy of such events  [Bell 1976]  1 36The notion of Primitive Ontology The wave function in GRWf and GRWm do not belong to the primitive ontology: according to these theories, physical objects are not made of wave functions    1 37The common structure of BM and GRW  the POThey both have a Primitive Ontology  (PO) Bohmian Mechanics: PO=  Positions of particles GRW theory:  PO=  GRWf: flashes (random events in space-time) GRWm: 3-d density of mass field Different choices of PO define different physical theories  1 38The common structure of BM and GRW  PO's dynamics Dynamics for the PO: the wave function Bohmian Mechanics: Deterministic evolution for Ψ (Schrödinger's equation) GRW theory: The wave function evolves randomly In both cases, the wave function induces a law for the PO  1 39The role of the wave function PO=output of a FPT Nomological variables: algorithm to generate the output Different algorithms can produce the very same output EX: different sorting algorithms Selection sort: find the minimum value in the list, swap it with the value in the first position, repeat the steps for rest of the list Bubble sort: stepping through the list to be sorted, comparing two items at a time and swapping them if in the wrong order  1 40PO and Physical Equivalence Theories with the same output are physically equivalent Two theories are physically equivalent if they lead to the same histories for the PO (regardless to the evolution for the nomological variable) 1 41PO and Physical Equivalence Gauge transformation: Heisenberg picture: The history of the PO does not change 1 42The flexible wave function Since what is important is the history of the PO and not the variable used to implement the law for the PO, we have a lot of flexibility:  Formulation of GRWf in which the wave function does not collapse Physically equivalent to GRWf with stochastically evolving wave function Formulation of BM in terms of a collapsed wave function Physically equivalent to BM with linearly evolving wave function    1 43Problems with Ψ as nomological ?   Ψ evolves in time Quantum cosmology suggests the universal wave function is static (Shelly and Stefan) Ψ is controllable Not the universal wave function There are different degrees of reality If one is nominalists wrt laws, the wave function does not exist If one is realist, it exists as an abstract entity Fay have tried to eliminate the wave function 1 44PO and symmetries Symmetries are  properties of the law which governs the dynamics of the PO 1 45 Lψ(X): (probability) law for X X     Xg  natural geometrical action of g on X  The law is symmetric under g if                Lψg(Xg )=Lψ(X)for suitable action ψ     ψg of g on ψPO and symmetries 1 46 Easy part: X transform the right way Novelty: ψ is allowed to transform in any fancy way EX: Galilean boosts in BMPO and symmetries 1 47PO and relativity The flashy ontology was invented by Bell [1987] as a step toward a relativistic GRW theory:I am particularly struck by the fact that the model is as Lorentz invariant as it could be in the non relativistic version. It takes away the ground of my fear that any exact formulation of quantum mechanics must conflict with fundamental Lorentz invariance.      1 49Quantum state and the PO                   PO stateBM        x  (x,Ψ)GRWm      m(x)   Ψ GRWf      F={(xi,ti)}   Ψ   In GRWf, GRWm the PO is determined by the state Ψ :   Ex: m(x)=f(Ψ) , Flashes = f '(Ψ)    1 50The measurement problem revisited The moral of the measurement problem  is NOT the one of Bell in terms of the wave function Rather, it is that the wave function should  not be regarded as representing physical objects in terms of the PO 1 51The measurement problem revisited Bohm-like solutions of the measurement problem:PO independent on Ψ GRW-like solutions of the measurement problem:PO is a function of Ψ  1 52The measurement problem revisited - Bohmianization?Ψ                          cat problem  (Ψ, Q)  Ψ             mass density                    flashes                         (Ψ, X)                             X                 X=f(Ψ)                                          X=Q 1 53The measurement problem revisited - Bohmianization?Ψ                 the wf is not the POX       (X,Ψ)                  X=f(Ψ) GRW-like                                         X=Q     Bohmian                                            

Primitive Ontology and the Structure of Fundamental Physical Theories

http://commons.lib.niu.edu/bitstream/handle/10843/16154/primitive-ontology-structure.pdf?sequence=1&isAllowed=y

Primitive Ontology and the Structure of Fundamental Physical Theories

Abstract

Similar works

Full text

Available Versions

Huskie Commons