Final Report Summary - METFUNDPHYS (Metaphysics of identity, properties, and relations in fundamental physics)
This project belongs to the category of philosophical reflections on the new concepts and theories developed in fundamental physical sciences. It is an unquestionable truism that modern physics advances our knowledge of the inner workings of the universe at a record-breaking speed. These scientific advancements are made not only in terms of the amount of new data and facts gathered, but most importantly in terms of new and often dramatic insights into what the world looks like at the fundamental level. The main motivation behind the current project is the desire to analyze some of the consequences of the contemporary physical theories of matter with respect to the broader questions concerning the nature of the external world (those questions are traditionally categorized as ontological, or metaphysical). More specifically, the main goal is to derive useful and novel lessons regarding the ontological categories with which we tend to describe reality, such as the categories of identity, objects, individuality, discernibility, properties and relations, from the mathematical principles of quantum theory (including non-relativistic quantum mechanics and relativistic quantum field theory). With respect to this ambitious goal, the project has achieved a host of interesting and interconnected results that can push the boundary of scientifically-informed philosophical investigations.
The starting point of the research conducted under the current project was a preparatory work on a comprehensive logical and philosophical framework within which it would be possible to express various philosophical intuitions concerning the concept of the discernibility of objects and its connections with numerical identity and distinctness. Several independent grades of discernibility have been distinguished, and their mutual logical relations determined. In addition to that two philosophical roles of the concept of discernibility have been spelled out, and arguments have been presented to the effect that only a handful of the available grades of discernibility can fulfil these roles.
The notion of discernibility plays a crucial role in the interpretation of the metaphysical consequences of the quantum theory of many particles. Given the symmetrization postulate, it is often argued that quantum particles of the same type are indiscernible by their properties or relations, and thus the Leibnizian Principle of the Identity of Indiscernibles is violated. In response to this challenge some philosophers point out that there is a grade of discernibility, known as weak, which can be proven to discern all fermions and even bosons of the same type. We argue, on the other hand, that weak discernibility cannot properly individuate objects because, first and foremost, it does not offer any means to make reference to one object rather than the other. On top of that, all the relations of weak discernibility used in the context of quantum mechanics have one fatal flaw: they namely make inevitable reference to the concept of numerical identity (distinctness), and thus are inappropriate for fulfilling the second task discernibility should perform, i.e. grounding the facts of distinctness in qualitative facts.
On the other hand, it is well known that the absolute indiscernibility thesis regarding particles of the same type follows only if we assume that reference to individual particles is made through the use of labels in the labeled tensor product formalism. However, there is an alternative approach to the problem of the individuation of particles that uses quantum properties to individuate them. These properties are formalized with the help of appropriate symmetric projection operators. One of the important results of the project is a precisification of the conception of quantum properties satisfying the postulate of permutation invariance, and a proof that indeed fermions and bosons may be discerned by such properties. The discernibility claim can also be supported independently by the label-less Fock space formalism, which is a more general way to describe states of many particles typically used in quantum field theory. However, there are several unintuitive and troubling consequences of the unorthodox property-based approach to quantum individuation that have to be addressed. For instance, we have to accept that compositions of identical fermions can be separated into an infinity of distinct subsystems, or that they possess a multitude of incompatible (non-commuting) properties. Several strategies of how to deal with this problem have been considered, of which the preferred one is based on selecting position as the privileged way of identifying subsystems within a composite system.
On the philosophical side of the project particular attention has been paid to the influential doctrine of Ontic Structural Realism (OSR) and its claim of the fundamentality of relational structure. In this project we have proposed to interpret OSR not as a claim about the identity of the elements of a structure in the actual world, but rather as a thesis regarding the way objects are identified in counterfactual scenarios (across possible worlds). This new interpretation of OSR is closely related to essentialism and anti-haecceitism. These positions and their consequences for the ontological interpretation of the symmetries of physical theories have been thoroughly evaluated. In addition, a new notion of a symmetry of relational structures, which is more in line with the metaphysical assumptions of structuralism and anti-haecceitism, has been put forward and analyzed.
Another result of the project that deserves mention here is an analysis of perfect correlations in quantum entangled systems done in terms of counterfactually interpreted causality. Three causal models explaining the correlations between space-like separated systems have been developed, and their non-standard features (such as circularity or frame-dependence) have been evaluated. It is argued that the correlations cannot be explained non-causally by reference to the extrinsic character of properties in entangled systems. The final phase of the project also included investigations into some ontological interpretations of quantum field theory (QFT), with an emphasis on numerous problems afflicting the particle interpretation of QFT. Some new arguments have been developed showing the untenability of the popular interpretation of field quanta (quanta of excitation) as independent, particle-like entities.
The results described above can impact the field of philosophical reflection on physics in many different ways. The development of essentialist structuralism has the potential to move the ontological debate on structures in a new direction, avoiding some of the well-known pitfalls of the traditional OSR. New insights into the problem of discernibility in the context of quantum mechanics should likewise influence future debates in this area of philosophy (this impact is already visible in the growing number of citations of the publications written under the project). On a more general level the project contributes positively to the mutual cooperation between physicists and philosophers, emphasizing the need for and the benefits of interdisciplinary studies. The dissemination activities in the form of presentations and popular lectures should also influence the general public outside of the community of scholars and inform them about deeper philosophical and ontological aspects of modern scientific theories.
The starting point of the research conducted under the current project was a preparatory work on a comprehensive logical and philosophical framework within which it would be possible to express various philosophical intuitions concerning the concept of the discernibility of objects and its connections with numerical identity and distinctness. Several independent grades of discernibility have been distinguished, and their mutual logical relations determined. In addition to that two philosophical roles of the concept of discernibility have been spelled out, and arguments have been presented to the effect that only a handful of the available grades of discernibility can fulfil these roles.
The notion of discernibility plays a crucial role in the interpretation of the metaphysical consequences of the quantum theory of many particles. Given the symmetrization postulate, it is often argued that quantum particles of the same type are indiscernible by their properties or relations, and thus the Leibnizian Principle of the Identity of Indiscernibles is violated. In response to this challenge some philosophers point out that there is a grade of discernibility, known as weak, which can be proven to discern all fermions and even bosons of the same type. We argue, on the other hand, that weak discernibility cannot properly individuate objects because, first and foremost, it does not offer any means to make reference to one object rather than the other. On top of that, all the relations of weak discernibility used in the context of quantum mechanics have one fatal flaw: they namely make inevitable reference to the concept of numerical identity (distinctness), and thus are inappropriate for fulfilling the second task discernibility should perform, i.e. grounding the facts of distinctness in qualitative facts.
On the other hand, it is well known that the absolute indiscernibility thesis regarding particles of the same type follows only if we assume that reference to individual particles is made through the use of labels in the labeled tensor product formalism. However, there is an alternative approach to the problem of the individuation of particles that uses quantum properties to individuate them. These properties are formalized with the help of appropriate symmetric projection operators. One of the important results of the project is a precisification of the conception of quantum properties satisfying the postulate of permutation invariance, and a proof that indeed fermions and bosons may be discerned by such properties. The discernibility claim can also be supported independently by the label-less Fock space formalism, which is a more general way to describe states of many particles typically used in quantum field theory. However, there are several unintuitive and troubling consequences of the unorthodox property-based approach to quantum individuation that have to be addressed. For instance, we have to accept that compositions of identical fermions can be separated into an infinity of distinct subsystems, or that they possess a multitude of incompatible (non-commuting) properties. Several strategies of how to deal with this problem have been considered, of which the preferred one is based on selecting position as the privileged way of identifying subsystems within a composite system.
On the philosophical side of the project particular attention has been paid to the influential doctrine of Ontic Structural Realism (OSR) and its claim of the fundamentality of relational structure. In this project we have proposed to interpret OSR not as a claim about the identity of the elements of a structure in the actual world, but rather as a thesis regarding the way objects are identified in counterfactual scenarios (across possible worlds). This new interpretation of OSR is closely related to essentialism and anti-haecceitism. These positions and their consequences for the ontological interpretation of the symmetries of physical theories have been thoroughly evaluated. In addition, a new notion of a symmetry of relational structures, which is more in line with the metaphysical assumptions of structuralism and anti-haecceitism, has been put forward and analyzed.
Another result of the project that deserves mention here is an analysis of perfect correlations in quantum entangled systems done in terms of counterfactually interpreted causality. Three causal models explaining the correlations between space-like separated systems have been developed, and their non-standard features (such as circularity or frame-dependence) have been evaluated. It is argued that the correlations cannot be explained non-causally by reference to the extrinsic character of properties in entangled systems. The final phase of the project also included investigations into some ontological interpretations of quantum field theory (QFT), with an emphasis on numerous problems afflicting the particle interpretation of QFT. Some new arguments have been developed showing the untenability of the popular interpretation of field quanta (quanta of excitation) as independent, particle-like entities.
The results described above can impact the field of philosophical reflection on physics in many different ways. The development of essentialist structuralism has the potential to move the ontological debate on structures in a new direction, avoiding some of the well-known pitfalls of the traditional OSR. New insights into the problem of discernibility in the context of quantum mechanics should likewise influence future debates in this area of philosophy (this impact is already visible in the growing number of citations of the publications written under the project). On a more general level the project contributes positively to the mutual cooperation between physicists and philosophers, emphasizing the need for and the benefits of interdisciplinary studies. The dissemination activities in the form of presentations and popular lectures should also influence the general public outside of the community of scholars and inform them about deeper philosophical and ontological aspects of modern scientific theories.