Papers by Alvaro Mozota Frauca
Foundations of physics, May 20, 2024
In this paper I offer an introduction to group field theory (GFT) and to some of the issues affec... more 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.
arXiv (Cornell University), Jul 21, 2023
In this paper I introduce the idea of geometrogenesis as suggested in the group field theory lite... more 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 nongeometric 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.
arXiv (Cornell University), Jun 26, 2023
In this paper I argue that the fundamental aspect of our notion of time is that it defines an ord... more 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.
General Relativity and Gravitation, 2023
In this paper I raise a worry about the most extended resolutions of the problem of time of canon... more In this paper I raise a worry about the most extended resolutions of the problem of time of canonical quantizations of general relativity. The reason for this is that these resolutions are based on analogies with deparametrizable models for which the problem can be solved, while I argue in this paper that there are good reasons for doubting about these resolutions when the theory is not deparametrizable, which is the case of general relativity. I introduce an example of a non-deparametrizable model, a double harmonic oscillator system expressed by its Jacobi action, and argue that the problem of time for this model is not solvable, in the sense that its canonical quantization doesn't lead to the quantum theory of two harmonic oscillators and the standard resolutions of the problem of time don't work for this case. I argue that as general relativity is strongly analogous to this model, one should take seriously the view that the canonical quantization of general relativity doesn't lead to a meaningful quantum theory. Finally, I comment that this has an impact on the foundations of different approaches to quantum gravity.
International Journal of Theoretical Physics, 2017
The histories-based framework of Quantum Measure Theory assigns a generalized probability or meas... more 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.
Geometrogenesis in GFT: An Analysis
Philosophy of Physics
General Relativity and Gravitation
In this paper I raise a worry about the most extended resolutions of the problem of time of canon... more In this paper I raise a worry about the most extended resolutions of the problem of time of canonical quantizations of general relativity. The reason for this is that these resolutions are based on analogies with deparametrizable models for which the problem can be solved, while I argue in this paper that there are good reasons for doubting about these resolutions when the theory is not deparametrizable, which is the case of general relativity. I introduce an example of a non-deparametrizable model, a double harmonic oscillator system expressed by its Jacobi action, and argue that the problem of time for this model is not solvable, in the sense that its canonical quantization doesn’t lead to the quantum theory of two harmonic oscillators and the standard resolutions of the problem of time don’t work for this case. I argue that as general relativity is strongly analogous to this model, one should take seriously the view that the canonical quantization of general relativity doesn’t le...
International Journal of Theoretical Physics, 2017
The histories-based framework of Quantum Measure Theory assigns a generalized probability or meas... more 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.
articles by Alvaro Mozota Frauca
How to Measure the Quantum Measure
The histories-based framework of Quantum Measure Theory assigns a generalized probability or meas... more The histories-based framework of Quantum Measure Theory assigns a generalized probability or measure $\mu$(E) to every (suitably regular) set E of histories. Even though $\mu$(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 $\mu$(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 $\mu$(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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Papers by Alvaro Mozota Frauca
articles by Alvaro Mozota Frauca