The Project in Detail

The main goal of the project is to provide qualitative and quantitative answers to the question regarding the nature of space and time, and the origin of the “quantumness” of the world. The goal will be achieved by investigating the possibility of constructing a novel and ontologically clear theoretical approach to quantum gravity. The project is thus aimed at giving a substantial contribution to the philosophy and foundations of physics.

The research for a theory of quantum gravity, that is, a theoretical framework that unifies the physical description of quantum and gravitational phenomena, is one of the most long-lived enterprises in modern physics. The term gravitational quanta was used for the first time by Léon Rosenfeld in 1930, but today -almost 90 years later- there is still no well-established physical theory of quantum gravity. Nonetheless, the need for such a theory is evident: quantum theory breaks with classical mechanics in describing the states of material systems as being subject to superpositions and entanglement, the latter being independent of spatiotemporal distance, thus giving rise to non-local correlations between measurement outcomes. General relativity, on the other hand, breaks with pre-relativistic theories of spacetime in being background independent: spacetime is itself a dynamical entity instead of being a inert “arena” where the evolution of physical systems takes place. In interpreting scientific theories, philosophers seek traits that are stable, that is, that will be retained throughout theory change in physics. Against the background of their clear empirical confirmation, it seems that both quantum non-locality and background independence are such traits.

The taxonomy of possible approaches to the problem of quantum gravity is huge, complex and controversial. However, two main strands can be roughly recognized. The first one seeks to find a unification of all the fundamental interactions known in nature by enlarging the Standard Model of particle physics: (super)string theories are the most notable variant of this type of approach, usually dubbed covariant. The other type of approaches focuses on elaborating a formulation of general relativity suitable of being quantized using a physically well-defined procedure originally put forward by Paul Dirac in the 1960’s. In this case, the aim is to find a theory of quantum general relativity, without seeking any unification. This is the case for the canonical quantum gravity program, whose best worked out theory so far is loop quantum gravity. Given that the project is primarily concerned with the nature of space and time, rather than with issues about the extension of the Standard Model, it will focus on the problem of finding a quantum description of general relativistic physics.

There are two striking features that broadly characterize the theories falling in the scope of the canonical program. The first is that quantum-gravitational states are taken to represent purely spatial, as opposed to spatiotemporal, physical degrees of freedom. This fact seems at odds with the spirit of relativistic physics, according to which there are no objective facts that are purely spatial or temporal. Even if we accept that a theory of quantum gravity faithful to the canonical approach should acknowledge an ontological primacy of space over time, still such a theory, being a quantum theory, would describe short-scale space as a quantum superposition of quantum-gravitational states. It is then not clear how a classical, smooth three-dimensional space -let alone classical spacetime- is supposed to emerge from such a “probabilistic cloud” of states (to borrow an expression used by Carlo Rovelli). This illustrates the fact that, in canonical quantum gravity, there is no clear ontology of spacetime.

The second feature of the canonical approach is that the equation that describes the dynamical evolution of these states -the Wheeler-DeWitt equation- does not involve any time, be it a physical or just a mathematical parameter. This feature carries a huge number of implications, most notably the consequence that the notion of temporal development seems to be cut off from the physical picture. The issue is compelling and bears a deep significance both for physicists and for philosophers. Indeed, in a timeless universe, the ticking of a clock would have no physical meaning, while in fact clocks are a vital part of the experimental apparatuses used by physicists. Also, this frozen picture would be at odds with the temporal passage that we experience in everyday life.

These huge conceptual problems in the physics and the metaphysics of canonical quantum gravity are the project’s rationale for challenging this theoretical program, while still acknowledging the need for a quantum treatment of general relativistic physics as a vital condition for gaining a clear insight into the fundamental nature of space, time, and the quantum realm.

The project’s starting point is to elaborate a novel variant of the so-called primitive ontology approach to quantum physics. The primitive ontology approach has so far been successfully applied to non-relativistic quantum mechanics, and consists in postulating an ontology of material “stuff” (being it particles, matter fields, or material events) localized in space and time -what the physicist John Bell called local beables– and then supplying a non-local law for its dynamical development. The important point is that primitive ontology theories account for the “quantumness” of the world just in terms of the behavior of the fundamental elements of the ontology, thus relegating the talk of quantum operators, superpositions, wave-function collapses, and the like to a mere descriptive role deprived of any ontological import. Hence, theories such as the de Broglie-Bohm theory and the GRW theory are able to recover the empirical predictions of standard quantum mechanics while being ontologically clear in that they do not concern obscure and ill-defined concepts -such as that of probabilistic clouds of states- but the well-defined notion of dynamical development in time of material stuff occupying space.

Translating this approach to quantum gravity, however, would represent a radical -and, so far, mostly unexplored- extension of the original ideas, to the point of ending up with an entirely new approach. In fact, constructing a physically interesting primitive ontology theory in this context amounts first of all to postulating a primitive ontology that is strictly speaking neither material nor spatiotemporal, because it is supposed to constitute some sort of ontological ground floor that supports the emergence of classical spacetime inhabited by matter. Secondly, the beables postulated in a gravitational context are not “local” in the sense adopted in the standard approach. Indeed, what is “local” in local beables à la Bell consists in being localized in a background space at a given time, contra the requirement of background independence of general relativistic physics. Finally, the dynamical development of the primitive ontology in this context cannot be evaluated against the background of a fixed universal time.

In order to work out such a non-standard version of the primitive ontology framework, two shifts in paradigm are required. The first shift involves the underlying physics, and consists in challenging the dominant view that a quantum theory of the gravitational field has to start from general relativity. Instead, a new theoretical framework will be considered, namely, shape dynamics. Shape dynamics is a theory of gravity that (locally) is empirically indistinguishable from general relativity, yet structurally different from it in that shape dynamics admits a privileged parametrization of the dynamical evolution. Such a dynamical ordering structure is exactly what a primitive ontology theory needs, because this structure would be enough to ground an objective time-like ordering of the beables’ configurations that accounts for the unfolding of the dynamics. Note, however, that shape dynamics does not presuppose neither space nor time as fundamental ingredients of reality. Instead, the formal machinery on which it is based -the so-called best-matching procedure- presupposes a commitment to a peculiar form of Leibnizian/Machian relationalism according to which space comes from a relational ordering of the basic elements of the ontology (spatial or kinematic relationalism) and time is an abstraction from the ordering of kinematic configurations (temporal or dynamic relationalism.

The project will capitalize on the very favorable structural features of shape dynamics by carefully investigating the philosophical and technical morals that the shape dynamics framework suggests with respect to the primitive ontology approach, such as those regarding what kind of primitive ontology is best suited for quantum shape dynamics (e.g., discrete or field-like? Totally non-spatiotemporal, or at least with some spatial features?) and what kind of equations of motion best describe the behavior of such ontology against the dynamical “canvas” of shape dynamics (e.g., determinist or stochastic? first-order or second-order with respect to the privileged parameter?).

The second shift involves the metaphysics, and consists in developing appropriate conceptual tools for the analysis of an appropriate ontology and ideology for a primitive ontology theory based on shape dynamics. It is in fact obvious that such a metaphysical analysis cannot be carried out by using standard notions like “object”, “relation”, “property”, “supervenience”, as far as these concepts are implemented with the help of pre-existing notions of space and time. The paradigmatic example is given by the requirement of physical existence itself. In standard metaphysics, it is quite uncontroversial that physical objects have to be located somewhere at a certain time, otherwise it would be impossible to distinguish them from, e.g., abstract objects like numbers. This requirement cannot for sure be consistently applied to fundamental objects in quantum shape dynamics since these objects are not located in spacetime. Instead, a new account of background independent self-subsisting structures has to be adopted, which employs non-standard metaphysical notions.

In a nutshell, these structures are networks of fundamental elements of the ontology. These primitive elements are individuated solely in virtue of a fundamental kinematic relation -which replaces standard spatial relations- in which they enter as relata; in turn different kinematic configurations of objects would be individuated with respect to a fundamental dynamic relation -which replaces standard temporal relations and constitutes the metaphysical basis underlying the notions of time and change. In this sense, such a primitive ontology would be part of a self-subsisting structure weaved up by these two world-building relations. Consequently, it will be maintained that ontic structural realism is the best-suited metaphysical framework to be adopted in this context, since this framework makes it is easy to show that the fundamental objects in the ontology are individuated solely by the relations they stand in, without any need for intrinsic identities or individuation with respect to an external embedding spacetime.

The project will deliver an extensive conceptual analysis aimed at showing what it is that makes self-subsisting structures physical despite their not being material and not being embedded in an external spacetime. With this respect, the project will try a novel route, and will cast the analysis of self-subsisting structures in terms of non-standard dependence relations. This analysis will exploit the so-called structural equation modeling framework. This framework has recently gained some popularity among metaphysicians because it provides a unified methodology for the analysis of both causal and metaphysical dependencies. The project will highlight how the structural equation modeling framework admits mixed chains of dependence (i.e. neither strictly causal, nor metaphysical), and will argue for the existence of a novel class of dependence relations that are half-way between causation and grounding. The kinematic and dynamic relations will be then analyzed and characterized under the light of this non-standard analytical framework.

The project will also provide a conceptual and technical description of how a primitive ontology theory based on shape dynamics and complying with the metaphysical framework sketched above would look like. With this respect, the project will take advantage of the best-matching framework as a device to construct a totally relational dynamics. Best-matching will hence be used to implement a theory of motion of the primitive ontology describe above over a properly constructed relational space, in fact called shape space. The condition that such a theory (the base theory) has to fulfill in order to be considered physically interesting is that, in the appropriate approximation, it becomes a general relativistic theory coupled with a standard non-local theory of material local beables (the target theory).