Summer school “Physics and
Philosophy of Time”, Saig, 24.7.13
Quantum non-locality and the
philosophy of time
Michael Esfeld
Université de Lausanne
Michael-Andreas.Esfeld@unil.ch
1
The lecture
1)
Bell‘s theorem and quantum
nonlocality
2) Proposals for a quantum ontology
of matter in space-time and their implications for the philosophy of time
a) Bohmian mechanics
b) The GRW mass density theory
c) The GRW flash theory
The EPR-experiment
3
Le théorème de Bell
4
Bell’s theorem (1964): non-locality
 “no conspiracy”: a and b are
independent of l
 locality: given l, 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, l) = P (Aa, l)
P (Ba, b, A, l) = P (Bb, l)
 There is no theory possible that
is in accord with the empirical
predictions of QM and that
satisfies locality.
 constraint on any future theory
5
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 Y
What does Y 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?
Y 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: Y 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 Y, motion of any particle at t
 ontology: particle configuration at t AND holistic
property of configuration represented by Y 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 Y, 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 Y
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 Y 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 Y 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 spacetime; 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 Lorentzinvariant way. Whether nature
chooses the space-time point fB
first, and fA 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
Y 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 Lorentzinvariance 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 nonseparability of Y = non-local correlations in spacetime  absolute simultaneity / preferred foliation of
space-time & presentism or growing block-universe