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).