The main goal of our research is to investigate some fundamental questions about the nature of space and time, such as “are space and time fundamental elements of reality?” and “do space and time possess an intimate quantum nature, as matter seems to have?”. In order to find a plausible answer to these questions, we rely on science, and thus we look at what modern physics has to say about that.

We already know from Einstein’s general theory of relativity that gravity is deeply linked to space and time, to the point that spatial and temporal phenomena, such as for example the ticking of a clock, are not only influenced by, but are by themselves a manifestation of the gravitational field. Now, if we assume that gravity is a field, just like the electro-magnetic one, then it is very likely that, if we look at it very closely, it will show the strange behavior typical of quantum systems. But, if gravity and space and time are one and the same thing, then the above reasoning entails that space and time behave at short scales as quantum entities. According to the most promising programs for straightforwardly quantizing the gravitational field of general relativity, this is in fact the case.

All the theoretical implementations of quantum general relativity so far agree to some extent in delivering a short-scale picture of physical space as a quantum superposition of structures with very weak (or even absent) spatial connotations -being them either field magnitudes or atoms in a literal sense. This fact renders entirely mysterious how classical space can emerge from a quantum “foam” of different and mutually exclusive arrangements of parts that might even lack any spatiality. Another open problem in quantum general relativity is that many quantization procedures lead to a static, timeless equation governing the behavior of the fundamental elements of the theory (whatever they are). This might hint at the fact that, at the fundamental level, time simply does not exists or, less radically, that temporal degrees of freedom are either hidden inside the formalism or were cut away from the quantum formalism due to a mistaken quantization procedure.

The
project will first analyze in depth the issue of elaborating an
account of what a superposition of quantum-gravitational “bits”
really amounts to. With this respect, an approach towards quantum
physics known as *primitive ontology* will be adopted. The main
tenet of this approach, which dates back to the French physicist
Louis de Broglie, is that some of the features that contribute to the
“fuziness” of quantum systems are not in fact real, but
just a consequence of an incomplete description of these systems.
What quantum physics lacks, in fact, is an ontological bedrock made
of “stuff” with a well-defined position at each time. Once
a dynamical law that describes the behavior of this primitive
ontology is provided, the resulting theory is capable of recovering
the same empirical predictions of standard quantum theory.

It is then
clear that, by showing that the primitive ontology approach can be
safely adopted also in quantum general relativity, the problem of the
superpositions of quantum-gravitational structures would be avoided.
However, the problem is now shifted to provide a coherent account of
structures that, obviously, are not in space and time. The project
will attempt to solve this issue by resorting to a metaphysical
stance known as *ontic structural realism*. This position holds
that the fundamental entities are, structures, that is, networks of
objects that stand in some physical relation. The important point is
that, in a structural realist framework, objects do not need to be
individuated with respect to their position in space but, rather, it
is sufficient to specify their “position” in the relational
structure. The research will provide a thorough characterization of
what an arrangement of quantum-gravitational bits is by elaborating a
metaphysical account of notions such as “object”,
“relation”, and “structure”, which is able to
accommodate these concepts in a context where there is no external
space and time that can confer a straightforward meaning upon them.
The research will also investigate how these *self-subsisting*
*structures* evolve dynamically in a way such that the emergence
of our everyday space and time can be explained.

Elaborating a physical description of
the dynamical evolution of self-subsisting structures would face the
second problem mentioned above, namely, the lack of a clear
characterization of time-like degrees of freedom that comes whenever
we try to quantize the dynamics of general relativity. To this
extent, we will try a different route, and consider the theoretical
tools provided by *shape dynamics*. This theory is, in a certain
approximation, empirically equivalent to general relativity, yet
different from this latter theory in that shape dynamics admits a
definite time-like direction for the dynamical evolution. This
theoretical framework might be favorable to a primitive ontology
approach to quantum gravity because such a built-in dynamical
“scaffolding” can be exploited to describe the evolution of
self-subsisting structures in terms of ever-changing dynamical
stages.

Asking how
space and time look at the quantum scale is a legitimate and, indeed,
intriguing question for physicists, philosophers, and anybody
interested in the ultimate nature of reality. The *prima facie*
picture delivered by quantum gravity of a fundamental reality being
basically “spacetimeless” represents a radical departure
from the intuitive, manifest image of the world we are accustomed to,
which then pushes us to clarify and sharpen this picture in order to
explain how our everyday conception of space and time can be
recovered from the rather different image of the world provided by
modern physics.