Do dispositions and propensities have a role in the

philosophy of QM?

Mauro DoratoDept. of Philosophy

University of Rome 3dorato@uniroma3.it

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 Relational

ii) Dispositional 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

1.2The 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 non-dispositional, 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 non-local 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 non-local 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)

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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?