1. Michael Esfeld Université de Lausanne Michael-Andreas.Esfeld@unil.ch
New directions in the foundations of physics, Washington DC, 24 April 15 The measurement problem and the primitive ontology of quantum physics
Michael Esfeld
Université de Lausanne

2. The methodology
physis: the domain of what exists in itself (Aristotle)
physics: the science of that domain
natural philosophy: physics and philosophy coming in one in the quest for understanding the natural world: physics on the basis of fundamental concepts about nature
Newton: Philosophiae naturalis principia mathematica
against both a priori metaphysics &
operationalism in physics

3. The paper 1) The quantum measurement problem: state of the art
2) Primitive (= fundamental) ontology: matter points: spatial structure
change: dynamical structure
 atomism & holism / structural realism

4. The measurement problem (Tim Maudlin 1995)
A The wave-function of a system is complete, i.e. the wave-function specifies (directly or indirectly) all of the physical properties of a system.
B The wave-function always evolves in accord with a linear dynamical equation (e.g. the Schrödinger equation).
C Measurements of, e.g., the spin of an electron always (or at least usually) have determinate outcomes, i.e., at the end of the measurement the measuring device is either in a state which indicates spin up (and not down) or spin down (and not up).
A ∧ B  not C
Problem touches any quantum theory: concerns link between theory and data

5. The ontology of quantum physics: state of the art
EITHER not C: quantum state realism
formalism refers to quantum state = physical object: e.g. field in high-dimensional space, represented by Y
 problem how to account for empirical data
OR not A / not B: primitive ontology
physical objects in 3d space or 4d space-time as referent of quantum formalism
 primitive = not derived from formalism, has to be put in as referent of formalism; provides the link between theory and data
dualism implausible

6. Primitive ontology
If C endorsed, then not important whether not A or not B. QM formalism in any case incomplete in the sense that it does not specify what the distribution of matter in space-time is; specifies only quantum state = dynamics of that distribution
de Broglie-Bohm: not A: particles & guiding equation
GRW: not B: Schrödinger equation + collapse parameters
How does the GRW equation link up with the distribution of matter in space-time?
GRWm (Ghirardi): matter density field described by Y
GRWf (Bell): collapse of Y (spontaneous localization in configu-ration space) describes single events (flashes) in physical space
In any case, no radical change from classical to quantum physics: objects the same, dynamics changes: non-local dynamics by Y

7. Primitive ontology as solution to measurement problem
distribution of matter in 3d space (or 4d space-time) (no superpositions) necessary condition
& dynamics of that distribution (that includes entanglement) sufficient condition
task: develop primitive ontology that is most parsimonious and most general

8. Democritus (about 460-370 before J.C.)
“There is an infinite number of impenetrable atoms, without qualities and indestructible, which move in the void where they are distributed. But when they come close to each other or collide, their aggregation results in water, in fire, in a plant, or in a human being.”

9. Newton, Opticks (1704)
“… it seems probable to me, that God in the Beginning form'd Matter in solid, massy, hard, impenetrable, moveable Particles … the Changes of corporeal Things are to be placed only in the various Separations and new Associations and motions of these permanent Particles."

10. First approximation discrete (particles)
inserted into absolute background space; 3d, Euclidean
 particle = what occupies a point of space
 variation: points of space occupied or empty
change in which points of space are empty and which ones are occupied as time passes
If change such that continuous lines of occupation of points of space, then worldlines = continuous sequences of events = particles (QM: Bohmian mechanics)
If not, then only single events (QM: GRW flash theory)

11. Problem
What makes up the difference between a point of space being occupied and a point of space being empty?
no intrinsic properties such as mass or charge (dynamical parameters in CM; situated on level of Y in QM)
no primitive thisness (haecceity)
bare substrata with primitive stuff-essence mysterious

12. Contra gunk
continuous fundamental ontology (gunk) instead of discrete objects (particles) (QM: GRW matter density theory)
Allori et al. (2014): “Moreover, the matter that we postulate in GRWm and whose density is given by the m function does not ipso facto have any such properties as mass or charge; it can only assume various levels of density.”
What does constitute the various levels of density of matter at points of space, if there are no properties such as mass or charge available?
 primitive stuff-essence that can assume various levels of density at points of space

13. Fundamental ontology
no cogent answer to the question of what distinguishes matter from space available
 abandon dualism of matter and space: no absolute space into which matter is inserted
relationalism about space (Leibniz): matter points connected by spatial relations (non-vanishing distance and direction)
only matter points and spatial relations, no points of space: spatial structure
background independence
Cartesianism: matter points, because connected by spatial relations (res extensa); standing in spatial relations distinguishes matter points from (hypothetical) mind points.

14. Matter points
fundamental: matter points not composed of anything, compose everything else
primitive objects: no intrinsic physical properties, but not bare substrata; spatial relations their essence.
factual: configuration of matter points simply there
 most parsimonious and most general way to conceive fundamental ontology of the natural world that is able to account for familiar macroscopic domain: matter points connected by spatial relations
All experimental evidence is evidence of particles.

15. Dynamics change in the spatial relations among the matter points
 time from change as suitable parametrization
relationalism: motion = change of spatial relations among the matter points: interaction
 velocity has to be specified for each transition from one configuration of matter points to another one
task: fix velocity such that specifying initial conditions at an arbitrary time and plugging them into velocity law is sufficient to determine the motion of the matter points at any time
further dynamical parameters necessary: mass, charge, energy, spin, wave function, etc.  dynamical structure

16. Newtonian mechanics
Newton‘s gravitational constant G and masses of matter points as determining the potential V (given the spatial relations) & the initial velocities: dynamical structure of Newtonian classical mechanics

17. Bohmian quantum mechanics
Newton’s gravitational constant G and and masses of matter points as determining the potential V, Planck’s constant & the initial wave function Ψ0: dynamical structure of Bohmian quantum mechanics

18. Dynamical structure spatial structure: permutation invariant
dynamical structure: distinguishes matter points; sorts them into various particle species
 particle species through dynamics, not intrinsic
dynamical structure defined only for particle configuration as a whole: to solve the equations, initial data for entire configuration required
dynamical relations that couple motion of particles to one another interaction = correlated change of velocities
no properties needed, structures sufficient: spatial structure individuating material objects, dynamical structure fixing change of spatial relations

19. Dynamical structure spatial structure: factual
dynamical structure: modal: fixes for any configuration of matter points given as initial condition how the world would evolve if that configuration were the actual one
Humeanism: nothing modal in the world
 dynamical structure only structure of theory that describes change in spatial relations in most simple & informative way (best system); only spatial relations and change that happens to occur in their configuration in the world
modal realism: dynamical structure real physical relations like spatial structure
 power that literally determines change in spatial relations

20. Dynamical structure: classical & quantum
in any case non-local correlations
stronger in quantum physics than in classical physics: one wave-function Y for whole particle configuration  correlates in principle the velocity of all matter points independently of their distance
small deviations in initial conditions will lead to widely divergent trajectories ( no sense to calculate real trajectories)
 more prominent role for probabilistic descriptions
only difference between classical and quantum
 objects the same through theory change, dynamical structure varies

21. Conclusion
primitive ontology: link between theory and data; solves measurement problem
spatial configuration of matter points; persisting, substances; structurally individuated by spatial relations
change persisting: dynamical structure to capture change
spatial structure: permutation invariant; dynamical structure: sorts matter points into different kinds of particles
spatial structure: factual; dynamical structure: modal, power that determines correlated change in spatial relations (interaction)
dynamical structure applies in any case to the configuration of matter points as a whole; correlations between motions of matter points stronger in quantum physics than in classical physics
objects the same through theory change; dynamical structure varies