Transcript Do dispositions and propensities have a role in the

Do dispositions and
propensities have a role in the
philosophy of QM?
Mauro Dorato
Dept. of Philosophy
University of Rome 3
[email protected]
Two main answers:
1 In collapse theories à la GRW, they do, as
they have explanatory, unifying power,
despite their irreducibility to categorical
properties;
2 In no-collapse interpretations, dispositions
are either reducible (Bohm), or lack any
explanatory power, as their ascription is a
sign that we still do not understand the
theory (no clear ontological picture)
Plan
1) Overview of the metaphysics of dispositions:
no distinction with categorical properties;
their predictive role;
2) Linking dispositions with QM’s formalism;
3) Dispositions in “flashy” GRW: why they
explain;
4) Dispositions in no collapse interpretations:
why they don’t explain.
1.1 Is there a clear-cut criterion to
distinguish the dispositional from the
categorical?
• No, the distinction is vague, and the following
are unpromising strategies
i) Dispositional
ii) Dispositional
Relational
Occasional Manifestation
i) Dispositions are not relational, but intrinsic properties
- exactly like categorical properties – and only their
manifestation, an event, calls for a relation.
ii) Constant manifestation vs manifestation under
special circumstances. But gravitational fields never
stop…
Coextensionality of the disp. and the cat. (the former
describes a functional role, the latter is the realizer of
the role).
Inapplicable whenever dispositions are irreducible
and lack a categorical basis
An objection and a possible reply
• Any distinction between Cat. and Disp. that one
can draw in QM cannot rely on clear intuitions
coming from our experience. If there is no clear
distinction to begin with, what do we gain in QM
by introducing dispositions?
• But one could find a clear distinction in QM terms,
accepting that the metaphyical debate on
dispositions and the philosophy of QM cannot be
used to shed light on each other
1.2
The predictive role of dispositions
• the function of dispositional predicates in ordinary
language is predictive. Consider the evolutionary
advantage of classifying animals or people
around our ancestors as “peaceful” or “ferocious”.
• This anticipates a possible link with QM:
dispositions in QM might simply refer to the
predictive content of the quantum state,
coherently with a merely instrumentalist
understanding of the theory
2) Dispositions in QM
• Within QM, the distinction between disp. and cat.
is clearer. Replace “dispositional properties” with
“indefinite properties”, i.e. properties that before
measurement lack a precisely possessed value,
as in pure, superposed states.
• So the passage from dispositional to the
categorical in measurement interactions is a
mind-independent
passage
from
the
indefiniteness to the definiteness of the relevant
property
• [“Therefore, the transition from the ‘possible’
(dispositional) to the ‘actual’ (categorical) takes place
during the act of observation (measurement). If we want
to describe what happens in an atomic event, we have to
realise that the word ‘happens’ can apply only to the
observation (measurement), not to the state of affairs
between two observations. It applies to the physical, not
the psychical act of observation, and we may say that
the transition from the ‘possible’ to the ‘actual’ takes
place as soon as the interaction of the object with the
measuring device, and thereby with the rest of the world,
has come into play; it is not connected with the act of
registration of the result by the mind of the observer. The
discontinuous change in the probability function,
however, takes place with the act of registration,
because it is the discontinuous change of our knowledge
in the instant of registration that has its image in the
discontinuous
change
of
the
probability
function”.(Heisenberg 1958, p.54)]
Getting a bit more precise about
dispositions in QM
1) Dispositionalism = contextualism
If the value revealed by the measurement
interaction causally depends, at least in part,
on the interaction, we have a kind of
contextualism and therefore dispositions
(Clifton and Pagonis 1995, p. 283)
2) Dispositions as selected by a particular kind
of measurement (Suarez 2004)
Summarizing the 2) part
• A QM property is categorically possessed if
(and only if) the state it corresponds to is an
eigenstate of the observable. Otherwise it is
dispositional
• Example: a quantum entity in a singlet state
has a disposition to manifest a certain spin in
a given direction, depending on the
orientation of the Stern-Gerlach apparatus
3) Dispositions in dynamical reduction
models: “flashy GRW”
• microsystems have an irreducible probabilistic
disposition to localize in a region of space
given by a diameter of  = 10-5 cm, once every
100 million years (the frequency f suggested in
the original GRW-model is 10-16 sec -1).
• In a cubic centimer, there are more than 107
flashes
“Flashy” GRW
[...] the GRW jumps are well localized in
ordinary space. Indeed each is centered
on a particular spacetime point (x, t). So
we can propose these events as the basis
of the “local beables” of the theory. These
are the mathematical counterparts in the
theory to real events at definite places
and times in the real world [(as distinct
from the many purely mathematical
constructions that occur in the working out of
physical theories, as distinct from things
which may be real but not localized, and
distinct from the “observables” of other
formulations of quantum mechanics, for
which we have no use here).] A piece of
matter then is a galaxy of such events.
[Bell, 1987, 205]
GRW and matter density collapse:
a theory of a field in spacetime
Some details (from A.G.T.Z.)
1. Q is the position operator,  the collapse operator defined for any point
x in space, the center of the collapse, and the constant of localization
2 The system evolves unitarily from T0 until a random time T1, distributed a
la Poisson with rate Nf, where f is the frequency given above and N the number of
particles. At T1 the wave function is multiplied by the previous gaussian operator,
.
I1 is chosen at random from 1…..N. The center of collapse is also chosen
randomly, with probability distribution, given by
Then the process is iterated for time T2 when another collapse occurs
Tumulka’s relativistic version of GRW
• The wavefunction provides conditional
probability measures over the flashes”…
“what we are left with is just the set of
flashes and a rule (which depends on initial
wavefunction) for calculating the probability
for the next flash … to occur at a particular
location given a particular set of other
flashes” (Maudlin 2006)
• This rule is a way to encode real,
measurable dispositions (propensities)]
Explanation as unification
• The localizations explain the definiteness of the
macroworld, in the sense that they allow a
unification of the micro and the macro-world,
characterized by a unique dynamics: QM is a
universal theory, governed by Schroedinger’s
eq.
• The theory is exact in the sense of Bell, as it tells
us precisely how often and where the
localization occurs.
• The propensity to localize is a measurable
disposition ascribable to microentities, but its
manifestation is an event taking place in
spacetime, i.e., the flash.
Why GRW dispositions are
explanatory
• Despite their irreducibility to a categorical basis, the
irreducibly probabilistic dispositions of quantum
entities to localize are endowed with explanatory
power, as they explain why Schrödinger’s cat is
either dead or alive, or better, why the cat is dead
and alive “for a split second”.
• Since they are “spontaneous”, they are uncaused
• The new clinamena (propensities to localize)
generate “the local beables of the theory”, out of
which spacetime is construed. Therefore they are
metaphysically prior to the localization events, and,
contrary to A.G.T.Z, are “metaphysically primitive”
What do we gain by introducing
dispositions in “flashy GRW?”
• We do not consider the manifestation of the
disposition (i.e., the flash itself) as explanatorily
ultimate, but leave the room open for a future
grounding of the disposition to localize. GRW is
a phenomenological theory
• We do not take into our ontology the
configuration space, as Albert does, in order to
make sense of the reality of the wave function (a
similar point has been advocated by Suarez for
Bohm’s ontology with the field)
Single case propensities or chances?
• I prefer propensities applied to single
cases, since it would make sense to talk
about the disposition to collapse even for
an electron universe
• For arguments to the contrary, see Friggs,
Hoefer, (SHPMP, 1997)
4) Dispositions in no-collapse views
• Bohr
• Many worlds/Rovelli’s relationism
• Bohm (reducible)
• Selective interpretation (Suarez)
4.1 Bohr and two readings of his thought
1)It is meaningless to talk about the properties of a quantum
system before measurement and independently of a classical
apparatus: the latter provides the “transcendental conditions”
for any meaningful talk about quantum phenomena, even if
needed only to ascribe them intrinsic dispositions…
2) A system in a superposed state possesses irreducible,
objective dispositions to reveal certain properties, which are
independent of the kind of measurement we perform upon it.
Despite the fact that Bohr did not talk explicitly about them,
only dispositions can make sense of his motto contraria sunt
complementa:
Are these two equally plausible reading of Bohr’s thought?
B.’s nonseparability pushes toward 1)
• Contextualism of “phenomena” for Bohr refers to
the nonseparability of classical apparatuses and the
behavior and properties revealed by micro-systems,
exactly as in relativity one cannot separate space
from time without chosing an inertial frame. But
contextualism implies a relational view of
disposition, which must be rejected
• In favour of 1, Bohr might have added that the
definiteness of properties of M is a necessary
condition to attribute even a disposition to the entity
before the measurement interaction. If M has no
position, it has no property at all involving position,
not even a dispositional one!
Complementarity pushes toward 2
• According to Bohr two properties are complementary if
and only if they are mutually exclusive and jointly
exhaustive (see Murdoch 1987). We say that they are
mutually exclusive because, from the point of view of the
classical language, they can be attributed to the same
system at the same time only via a contradiction. In fact,
complementary properties cannot be simultaneously
revealed by the same experiment, given that any
apparatus obeys classical physics.
• On the other hand, if we refer to a quantum system
before measurement, the complementary properties
must be regarded as jointly exhaustive, because any
attempt at attributing a not-yet measured system only
one of the two properties would yield an incomplete
description: an electron is neither a particle nor a wave,
but has dispositional features belonging to both
concepts.
Conclusion on Bohr
• it is not absurd to attribute to an entity realist like Bohr the
view that microsystems have real tendencies to display
well-defined measurement values in a given experimental
context, that somehow “extract” some “latent aspect” or
some information from a mind-independent entity.
• However, attributing a micro-system M a “real disposition”
to show a certain definite value in a measurement context
does not explain or add much in the context of his
philosophy, as it just amounts to saying that if we measure
M we get a definite result.
• All the problems of Bohr’s philosophy remain intact
4.2 Dispositions in many worlds?
|Universe > = j i | World-i >, |i |2 = 1
• |World > = |object1 > |object2 > |object3 >…
• A single world is a totality of objects possessing
a definite, classical state (chairs, tables, people
have a definite position), while the universe is in
a gigantic superposition of mutually incompatible
worlds (orthogonal states). Therefore the
universe is really in an indefinite state
Relationism and brain-centered
categorical properties in MW
• Since the whole universe is in a global state of
superposition, we could as well conclude that, relative to
the quantum state of the universe, the properties of the
universe are really indefinite, and definiteness is a
perspectival, relational matter, depending on worlds, or
branches (contexts)
• That the dispositional reading of MW is not so implausible
can be gathered also by the notion of a centered-world put
forward by Saunders (1995): only perceived states are
definite, and non-perceived ones are really superposed.
Reality in itself is entangled, and has the ungrounded
disposition to correlate to our brain states in such a way
that we perceive the world as having definite properties.
Rovelli’s relationalism
• It is meaningless to attribute an intrinsic,
absolute property to a non-correlated system,
since “S has q” is true only for S and may not be
true for S’
• To the extent that “a variable (of a system S) can
have a well-determined value q for one observer
(instrument) (O) and at the same time fail to
have a determined value for another observer
(O’)”, no sense can be made of any nondispositional, categorically possessed property
• But this view is hardly explanatory: it has no
proposal as to how where and when the
correlations occur
4.3 Bohm’s determinism
The i’s particle’s velocity depends on the
positions of the other particles in a nonlocal way
• Bohm’s dispositional properties (i.e., spin in a
given direction) are fully reducible to
positions and context
• Attributing particles intrinsic dispositions to
influence each other trajectories in a nonlocal fashion does not make the theory more
acceptable, because of the non-local nature
of the interaction
4.4 Selective interpretations
• «A selection is an interaction designed to
test a particular disposition (Fine’s “aspect”)
of a quantum system. Among the
dispositional properties I include those
responsible for values of position,
momentum, spin and angular momentum.
In a selection, the pointer position interacts
only with the property of the system that is
under test» (Suarez, BJPS, 2004, 232)
Selections and measurements
• M. note that, according to the standard
view of measurement, a measurement is
not a selection, since it is an interaction of
the apparatus with all the properties
(dispositional properties) of the quantum
system, while here we are dealing with just
one, W(O)
Representing a dispositional property
In order to represent a given dispositional property
(spin along x, or W(x)), we can exploit the fact that
“for every property of a quantum system originally in
a superposition there is a mixed state which is
probabilistically equivalent (for that property) to the
superposition” (Suarez BJPS, 2004, p.242)




1
1
 
 upx 1 downx 2  
 downx
2
2


1
1
W ( x)  Pup ,down   Pdown ,up 
2
2
1
upx
2
Here we suppose that the pointer position
interacts with only one property of the systems,
represented by W(O), with O being a particular
observable. W(O) is not the full state of the
system, but simply the state corresponding to its
property O.
This implies that the initial state of the system is
a non-ignorance interpretable, proper mixture
over the eigenstates of O
Some comments
• How does a selection of a disposition occur, namely is
the selection a physical process?
• If it isn’t a physical process, then selections look like a
merely formal trick
• If it is, we need to know more about it, in terms of a more
precise description (GRW). Selections are a provisional
account of measurement interactions (lack of
explanatory power)
• Isn’t the selection wiew according too much weight to the
notion of measurement anyway?
• in certain measurements, we test more than one
property at a time (in Stern-Gerlach we test two
dispositions, position and spin direction)
• The possibility of replacing superpositions by mixtures
before the measurement process is not understandable
only in terms of dispositions
Conclusion
• Unlike the situation in GRW, attributing a
micro-system M a “real disposition” to
show a certain definite value in a
measurement context amounts to saying
that if we measure M we get a definite
result. Where is the explanatory power?