Objects or Events?: Towards an Ontology for Quantum Field Theory

Andreas Bartels
1999 Philosophy of Science  
The recent work of P. Teller and S. Auyang in the philosophy of Quantum Field Theory (QFT) has stimulated the search for the fundamental entities of that theory. In QFT, the classical notion of a particle collapses. The theory does not only forbid classical, i.e. spatiotemporally identifiable particles, but it makes particles of the same type conceptually indistinguishable. Teller and Auyang have suggested competing ersatz-ontologies which could account for the (loss of the particles(: Field
more » ... articles(: Field quanta vs. Field events. However, both ontologies suffer from serious defects. While quanta lack numerical identity, spatiotemporal localizability, and independence from basis-representations, events -if understood as concrete measurement events -are related to the theory only statistically. I propose an alternative solution: The entities of QFT are events of the type (Quantum system S is in quantum state ((. The latter are not point events, but Davidsonian events, i.e. they can be identified by their location inside the causal net of the world. 1.Preface In recent analytical work on ontology, ontological problems raised by modern physics are mentioned casually at most. This corresponds to a widespread neglect of analytic ontology by people studying the ontological consequences that follow from physics theories, e.g., from Quantum Field Theory. In this paper I shall argue that, despite the spirit of mutual disregard of ontology and physics, exchange of ideas between those fields can be beneficial. Some of the moves in the development of pure ontological conceptions do seem to address the ontological problems that arise in physics theories. Ontological conceptions, such as the ones developed by P. Strawson 1959 , W.V.O. Quine 1960 , D.M. Armstrong 1989 , and D. Davidson 1969 interpreted as (responding( to problems of ontology discussed in the recent work on QFT by P. Teller 1995 and S. Auyang 1995. The emergence of increasingly abstract types of objects in the physics domain, seems to coincide with the replacement of spatiotemporal localizability as the essence of identity -as it appears in P. Strawson´s conception of particulars -by W.V.O. Quine´s logical criterion of identity. This criterion allows for fundamental entities other than objects in space and time, and thereby opens the door for spatiotemporally non-localizable entities like quantum (particles(. If we reject, however, space and time as supplying the primary criterion of identity, the problem immediately arises of how to account for cases in which theories employ entities that cannot be distinguished by means of their theoretical predicates, as it is the case for quantum (particles(. In this case, Quine recommends to turn to the Universals relative to which these entities are indistinguishable. This means, however, in the case of Quantum physics that types of quantum states have to count as the physical entities and this is in conflict with the intuition that physics theories deal with concrete physical systems. According to D.M. Armstrong, the things we deal with in ordinary discourse and in scientific theories are states of affairs, i.e. instantiations of Universals. Since quanta are indistinguishable entities, i.e. they cannot be distinguished independently of their being different instantiations of the same excitation mode, this idea fits the quanta-interpretation of QFT, as advocated by P. Teller. In contrast to the quanta-interpretation of P. Teller, S. Auyang thinks that spatiotemporal identity proves to be the only form of identity applying to concrete things (Teller´s quanta, according to Auyang, do not only suffer from being indistinguishable, but also from the fact that quanta-representations of physical states are basis-dependent). In the domain of QFT, however, spatiotemporally identifiable classical objects do not exist. It is not objects, but concrete physical events that make up the quantum field. Unfortunately, it turns out to be inappropriate to identify the entities of QFT with Auyang´s events, because what Auyang means by (events( are either the events of measurement which are related to the theory merely by statistical relations, or they are general descriptions of a type of events (e.g. the presence of a number of a certain sort of quanta). In the latter case, however, they are not concrete physical entities. There remains, however, another solution. This is to take the fundamental entities of QFT to be events, without identifying them by their spatiotemporal location. Instead these events can Quine´s treatment of scientific ontology has favoured the admission of abstract objects as perfectly acceptable existents. The distinction between concrete and abstract objects, according to Quine´s view, reflects a philosophical superstition with regard to the supposed naturalness of a particular language which Quine hopes to reveal as the result of familiarity. The second important move in ontology, compared to the more empiristic ontological thinking of Strawson, is Quine´s awareness of the consequences following from the occurence of indistinguishable objects in scientific theories. Where indistinguishable objects occur, it seems to be legitimate, according to Quine, to take the universals, with respect to which the objects are indistinguishable, to be the objects of discourse. Such realism with respect to Universals (even if the commitment is merely a formal one, as in Quine´s case) is objectionable, Armstrong says. According to realism, as understood by Armstrong, two indistinguishable objects are objects that are built up by the same set of Universals, and therefore actually appear to be one rather than two. Therefore, realism, according to Armstrong, reduces the problem of indistinguishable objects to triviality. Armstrong´s alternative conception is a revitalization of (universalia in rebus(: What one has here, are neither distinct particulars, distinguished from each other by their respective primitive thisness, nor universals existing independently of their instances, but states of affairs that instantiate Universals (Armstrong 1989, p.95). Yet, how can the objection which Armstrong raises against realism be avoided ? Should not states of affairs instantiating the same bundle of Universals count as one state of affairs ? According to Armstrong, qualitatively identical states of affairs can be bundled up in different ways from a certain set of Universals (Armstrong 1989, p.93) and thereby be different things. But which ever interpretation the clause (in different ways( may receive in various domains of discourse, there are no (different ways( in which two quanta can be instantiations of the same quantum state. There can be two of them despite the fact that they cannot be distinguished by any theoretical or experimental means. It is now time to explain what the theoretical requirements are for choosing a quanta-interpretation of QFT. What does it mean that quanta are indistinguishable and what are the problems of their interpretation ? quantum system. The transition to another basis representation changes the sort of quanta involved. Even if electrons and photons are not numerable, they are still countable. Since any eigen-state of a system can be characterized by a set of occupation numbers n 1 , n 2 ,... , quanta are countable particulars with well defined physical characteristics, which can be used as building blocks for the specification of the state of any quantum system. Therefore, they seem to provide an ideal ersatz-ontology replacing the classical particles. 3 There is one major problem with the proposed replacement of particles by quanta: How can the quanta-interpretation be reconciled with the existence of superpositions of exact number states which are in fact states with an indefinite number of quanta ? The Fock space does not just include the different eigen-states characterized by definite occupation numbers, but also superpositions of those eigen-states which represent states with an indefinite number of quanta. How can a physical system, characterized by an indefinite-number state relative to the chosen basis, be interpreted as some composition of quanta ? According to Teller 1995, an acceptable interpretation of such states can be achieved, if one takes superpositions to be (propensities to reveal one of the superimposed properties under the right (measurement( conditions( (Teller 1995, p.32). An indefinite-number state is the presence of a property which reveals itself in measurements in the form of the occurence of exact numbers of quanta, according to the probability measures given by the superposition. The acceptance of this proposal depends in the first place on the general acceptance of propensity-interpretations of superpositions in general. Even if this general acceptance is taken for granted, there is a more specific reason for rejection: The property specifying probabilities for the manifestation of certain collections of quanta cannot itself be a property of some definite collection. Thus, what is that property a property of ? According to Teller, we can dissolve this difficulty, if we declare the indefinite-number state to be not a state of something independently existing, but rather a property that is exemplified by different types of quanta -the definite-number collections of quanta which appear in measurements (cf. Teller 1995, p.105). 3 Cf. French/Redhead 1988 (p.238): (there are strong arguments for regarding the (quantized excitation( view of quantum particles as the correct one(. I find this answer unconvincing. It is not the claim that a property is specified by propensities which is problematic here; neither is it the fact that the entities realizing this property through their occurence cannot be said to be the bearers of the property. The real problem is, in my view, that a statement according to which a quantum system has a property of that kind is explicated by recourse to entities the occurence of which cannot be predicted by the theory. The occurences of quanta, by which a superposition state is realized, are single measurement events, and the theory -according to our current knowledge -is not able to account for single measurement events. The ontology for QFT should not be built upon a type of entities the presence or absence of which is not a consequence of the theory. The fact that superposition states can only be assigned to the quantum system itself very much favours an interpretation according to which events of the type (quantum system S is in quantum state (( are the building blocks of QFT-ontology. Neither classical particles nor ephemeral quanta seem to provide a reasonable ontological basis for QFT. Since classical particles are spatiotemporal individuals, but are not allowed by the theory, whereas quanta are allowed by the theory, but are no spatiotemporal individuals, the search should focus on things that fulfill both conditions. The latter are what Auyang 1995 calls the events that make up the quantum field. 3.The Event Interpretation and its Problems The Fock space description of quantum systems can be developed by introducing the so-called lowering and raising operators. These operators, corresponding to some basis, carry a vector describing a definite number of quanta into a vector describing one fewer (or one more) quantum. If one chooses the position basis, the raising operator, ( ( (x), associated with each space-time point takes the vector representing any state to a new state with one additional quantum located at x. The quantum field is just this association of an operator with each of the space-time points. Applied to concrete quantum states, (, the field operator, ((x, t), at space-time point, (x, t), determines expectation values (((((x, t)((( , e.g. the expectation value for an exact momentum state occuring at the point, (x, t). Thus, the quantum field does not supply us directly with specific values of physical quantities -this is what distinguishes it from a classical, e.g. the classical electromagnetic field; 1 instead it is (something that charts the spatiotemporal relations of any of a large set of possible field configurations ( (Teller 1995, p.103). 4 According to Teller, the idea that QFT is a genuine field theory essentially stems from its historical genesis (Teller 1995, p.69f.). Starting with a classical physical field, ((x, t), we can, by Fourier expansion, arrive at a formal description of the field in the form of classical harmonic oscillators, a(k, t), satisfying the classical oscillator equation (k is a coefficient of the Fourier expansion). Those oscillators, a, (and their complex conjugates, a ( ) can then be interpreted as the raising and lowering operators, a and a ( , relative to a momentum basis (where k is interpreted as momentum). The classical field description can then be replaced by the operator-valued field description (field quantization) of the form ( ( (x, t) = ( d 3 k a(k, t) e ikx . (Field quantization( presents the classical field in a way in which the Fock space formalism can be applied. The corresponding Fock space is defined by vectors which are specified by occupation numbers for the various field excitations (field modes). Thus, even if we start from the quantization of the classical electromagnetic field, there is good reason to think of the Fock space formalism with its occupation-number states as the core of the theory. The (fieldtheoretic( description of QFT does not prevent us to think of quanta as the objects of the theory. It is exactly her focus on (field quantization( that governs Auyang´s treatment of QFT. A field, ((t, x), Auyang claims, is (a dynamical variable for a continuous system whose points are indexed by the parameters t and x ( (Auyang 1995, p.48). Quantum fields are obtained by replacing the classical field variable by operators obeying certain commutator relations (Auyang 1995, p.50). Quantum fields, according to Auyang, (constitute the basic ontology of the world( (Auyang 1995, p.50). Whereas spatiotemporally extended fields make up the primary stuff of the world, field quanta are portions of excitations by which a field may be characterized under cartain circumstances (when interaction can be ignored). Why are field quanta not the entities of QFT ? According to Auyang, the prima facie which Davidson claims that it exists between the events we refer to in ordinary speech and some states of affairs by which we represent such events (Davidson 1980, p.164f.). According to Davidson, events are the pieces of reality which can be represented by means of different states of affairs, depending on the focus we choose to characterize the event. For instance, we may choose to characterize events by means of the causal consequences they have. The pouring of a dose of arsenic into a glass of water may be represented by the state of affairs that is expressed by the sentence (John kills Agatha by poisoning(. Likewise, some occupation number state expresses a state of affairs representing the event that quantum system S is in quantum state (, relative to a chosen basis. Quanta are, according to this view, not the building blocks of quantum reality, but they are (conceptual) building blocks used to construct representations of quantum reality. The stuff of which quantum reality is made is neither quanta nor point events, but Davidsonian events.
doi:10.1086/392723 fatcat:na7vshium5dgrmhcdz7q2naege