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Álvaro Mozota Frauca

Publications and source records attributed to Álvaro Mozota Frauca.

14 recordsLinked to original sources
arXiv2026

Gauge and Metaphysics of Spacetime

Some authors have argued that spacetime in general relativity should be given a radically different interpretation from the ones given to spacetime in other theories in virtue of it being a gauge theory. In this article I review this sort of argument and argue against this view. That is, I argue that spacetime in general relativity can be understood analogously to spacetime in other models and that the argument from the diffeomorphism invariance of the theory misapplies the concepts of gauge theory to a context in which they are of limited application.

physics.hist-ph↗
arXiv2026

The Dynamics of Quantum Gravity: the Missing Piece in the Spacetime Emergentist Account

Quantum gravity suggests that spacetime may not be fundamental, and it has been argued that we can understand a theory without a fundamental spacetime if we are able to claim that spacetime `emerges' from some non-spatiotemporal entities. In this sense, strategies like functionalism have been deployed to claim that this emergence is possible and plausible, both in principle and in practice for current approaches to quantum gravity. In this article I argue that this analysis is incomplete, as it tends to overlook the way the dynamics of these theories is `quantum' in a way that differs from standard quantum theory. The challenge for the emergentist (and for the quantum gravity theorist) is to give an interpretation not only to the kinematical and classical aspects of these theories, but to the dynamical and quantum ones, and to show how the spacetime roles can be fulfilled, if possible at all. Therefore, I argue that some current approaches to quantum gravity seem to fail to provide meaningful theories, that spacetime functionalism is of no help, and that the position of the spacetime emergentists is weakened, as they lack any example of a successful reduction of spacetime to some truly quantum non-spatiotemporal stuff.

physics.hist-ph↗
arXiv2026

Diffeomorphism-Invariant Quantities in Phase Space: More than Correlations

A popular view in the foundations of diffeomorphism-invariant theories is that their physical content is encoded in correlations or `observables': a set of phase space functions that have vanishing Poisson brackets with the constraints related to diffeomorphisms. In this article I study the phase space structure of models with a temporal diffeomorphism invariance and prove a series of formal results that challenge this view in a few ways. First, I show how this view is not applicable to all the phase space trajectories of every diffeomorphism-invariant theory. Second, I show how correlations can be proved to be invariant only in a way that generalizes the standard definition of invariance and in a way that does not provide smooth phase space functions. Third, I prove that spatiotemporal relations are also invariant. Fourth, I prove that spatiotemporal structures are indispensable for defining the invariant content of diffeomorphism-invariant models. Finally, I comment that these results are expected to be generalizable for models invariant under $d$-dimensional diffeomorphisms, which represents a challenge for some views in the foundations of general relativity and quantum gravity.

gr-qc↗
arXiv2026

The Limitations of the Notion of `Observable' in Diffeomorphism-Invariant Models

The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with this symmetry and building quantum versions of them. In this article I distinguish between two senses of gauge transformation: local and global, and I argue that the notion of observable appears more naturally in the local sense of gauge transformation. Then, I argue that diffeomorphism invariance can be understood as a gauge symmetry only from a global point of view, and hence, that the concept of observable applies only in a restricted manner. This has the consequence that some popular claims in the literature, such as the claim that the physical content of diffeomorphism-invariant models is encoded in correlations, are unfounded.

physics.hist-ph↗
arXiv2026

Does Quantum Cosmology Predict the Age of the Universe?

The problem of time of quantum gravity has been argued to make canonical approaches unsatisfactory. In this article I study how it affects quantum cosmology and reach the same conclusion. The advantage of studying the cosmological case is that its simplicity makes the discussion much clearer and less technical. The classical models I will be concerned with describe how two degrees of freedom, the scale factor and a scalar field, evolve with respect to a time variable. After quantizing the model, this time variable just disappears, and I argue that this is problematic. Indeed, this variable in the classical model allowed us to make claims like `the universe is 13.8 billion years old' and I will argue that these claims are physically meaningful predictions that are lost in quantum cosmology. I will analyze some of the relational positions in the quantum gravity and quantum cosmology literature that tend to deny the physical meaning of time variables and I will argue against them for the case of classical cosmology. I conclude that the age of the universe is a physical prediction of classical cosmological models, that it is missing from quantum cosmology, and that this should make us suspect that there is something wrong with this sort of approach.

physics.hist-ph↗
arXiv2025

Against Radical Relationalism: in Defense of the Ordinal Structure of Time

Some authors in the quantum gravity community endorse, explicitly or implicitly, a radical relationalist view of time which states that the ordinal structure of time is not needed even in our classical theories, especially in general relativity. In this article I analyze this position and the arguments supporting it, and I argue that there are some serious concerns with some of the radical relationalists' arguments which make it an unattractive position. In this sense, I conclude that the chrono-ordinal structures of our theories play important theoretical and explanatory roles and that they can be taken to be part of the empirical content of our theories.

physics.hist-ph↗
arXiv2025

Quantum Cosmology and the Age of the Universe

In this article I study how the problem of time of canonical approaches to quantum gravity affects the simple minisuperspace models used in quantum cosmology. I follow some authors who have argued that this issue makes the quantization of general relativity problematic to conclude that the same applies in the case of quantum cosmology. In particular, I argue that temporal structures are lost in quantization and that this is a problem, as they encode part of the empirical content of classical cosmology, such as the age of the universe.

gr-qc↗
arXiv2024

The problem of time for non-deparametrizable models and quantum gravity

In this article I introduce a distinction between two types of reparametrization invariant models and I argue that while both suffer from a problem of time at the time of applying canonical quantization methods to quantize them, its severity depends greatly on the type of model. Deparametrizable models are models that have time as a configuration or phase space variable and this makes it the case that the problem of time can be solved. In the case of non-deparametrizable models, we cannot find time in the configuration or phase space of the model, and hence the techniques that allow solving the problem in the deparametrizable case do not apply. This seems to signal that the canonical quantization techniques fail to give a satisfactory quantization of non-deparametrizable models. As I argue that general relativity is non-deparametrizable, this implies that the canonical quantization of this theory may fail to provide a successful theory of quantum gravity.

gr-qc↗
arXiv2024

GPS Observables in Newtonian Spacetime or Why We Do Not Need 'Physical' Coordinate Systems

Some authors have defended the claim that one needs to be able to define 'physical coordinate systems' and 'observables' in order to make sense of general relativity. Moreover, in Rovelli (Physical Review D, 65(4), 044017 2002), Rovelli proposes a way of implementing these ideas by making use of a system of satellites that allows defining a set of 'physical coordinates', the GPS coordinates. In this article I oppose these views in four ways. First, I defend an alternative way of understanding general relativity which implies that we have a perfectly fine interpretation of the models of the theory even in the absence of 'physical coordinate systems'. Second, I analyze and challenge the motivations behind the 'observable' view. Third, I analyze Rovelli's proposal and I conclude that it does not allow extracting any physical information from our models that wasn't available before. Fourth, I draw an analogy between general relativistic spacetimes and Newtonian spacetimes, which allows me to argue that as 'physical observables' are not needed in Newtonian spacetime, then neither are they in general relativity. In this sense, I conclude that the 'observable' view of general relativity is unmotivated.

physics.hist-ph↗
arXiv2024

In Which Sense Can We Say That First-Class Constraints Generate Gauge Transformations?

In this paper, I consider a recent controversy about whether first-class constraints generate gauge transformations in the case of electromagnetism. I argue that there is a notion of gauge transformation, the extended notion, which is different from the original gauge transformation of electromagnetism, but at the same time not trivial, which allows the making of that claim. I further argue that one can expect that this claim can be extended to more general theories, and that Dirac's conjecture may be true for some physically reasonable theories and only in this sense of gauge transformation. Finally, I argue that the extended notion of gauge transformation seems unnatural from the point of view of classical theories, but that it nicely fits with the way quantum versions of gauge theories are constructed.

physics.hist-ph↗
arXiv2024

Foundational Issues in Group Field Theory

In this paper I offer an introduction to group field theory (GFT) and to some of the issues affecting the foundations of this approach to quantum gravity. I first introduce covariant GFT as the theory that one obtains by interpreting the amplitudes of certain spin foam models as Feynman amplitudes in a perturbative expansion. However, I argue that it is unclear that this definition of GFTs amounts to something beyond a computational rule for finding these transition amplitudes and that GFT doesn't seem able to offer any new insight into the foundations of quantum gravity. Then, I move to another formulation of GFT which I call canonical GFT and which uses the standard structures of quantum mechanics. This formulation is of extended use in cosmological applications of GFT, but I argue that it is only heuristically connected with the covariant version and spin foam models. Moreover, I argue that this approach is affected by a version of the problem of time which raises worries about its viability. Therefore, I conclude that there are serious concerns about the justification and interpretation of GFT in either version of it.

gr-qc↗
arXiv2024

Time is Order

In this paper I argue that the fundamental aspect of our notion of time is that it defines an order relation, be it a total order relation between configurations of the world or just a partial order relation between events. This position is in contrast with a relationalist view popular in the quantum gravity literature, according to which it is just correlations between physical quantities that we observe and which capture every aspect of temporality in the world, at least according to general relativity. I argue that the view of time as defining an order relation is perfectly compatible with the way general relativity is applied, while the relationalist view has to face some challenges. This debate is important not only from the perspective of the metaphysics of space and time and of how to interpret our physical theories, but also for the development and understanding of theories of quantum gravity.

physics.hist-ph↗
arXiv2024

Geometrogenesis in GFT: An Analysis

In this paper I introduce the idea of geometrogenesis as suggested in the group field theory literature and I offer a criticism of it. Geometrogenesis in the context of GFT is the idea that what we observe as the big bang is nothing else but a phase transition from a non-geometric phase of the universe to a geometric one which is the one we live in and the one to which the spacetime concepts apply. GFT offers the machinery to speak about geometric and non-geometric phases, but I argue that there are serious conceptual issues that threaten the viability of the idea. Some of these issues are directly related to the foundations of GFT and are concerned with the fact that it isn't clear what GFT amounts to and how to understand it. The other main source of trouble has to do with geometrogenesis itself and its conceptual underpinnings as it is unclear whether it requires the addition of an extra temporal or quasitemporal dimension which is unwanted and problematic.

physics.hist-ph↗
arXiv2016

How to Measure the Quantum Measure

The histories-based framework of Quantum Measure Theory assigns a generalized probability or measure $μ(E)$ to every (suitably regular) set $E$ of histories. Even though $μ(E)$ cannot in general be interpreted as the expectation value of a selfadjoint operator (or POVM), we describe an arrangement which makes it possible to determine $μ(E)$ experimentally for any desired $E$. Taking, for simplicity, the system in question to be a particle passing through a series of Stern-Gerlach devices or beam-splitters, we show how to couple a set of ancillas to it, and then to perform on them a suitable unitary transformation followed by a final measurement, such that the probability of a final outcome of "yes" is related to $μ(E)$ by a known factor of proportionality. Finally, we discuss in what sense a positive outcome of the final measurement should count as a minimally disturbing verification that the microscopic event $E$ actually happened.

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