arXiv subjects

Henrique Gomes

Publications and source records attributed to Henrique Gomes.

At least 37 records · Page 2Linked to original sources

arXiv2023

On the analogies between gravitational and electromagnetic radiative energy

We give a conceptual exposition of aspects of gravitational radiation, especially in relation to energy. Our motive for doing so is that the strong analogies with electromagnetic radiation seem not to be widely enough appreciated. In particular, we reply to some recent papers in the philosophy of physics literature that seem to deny that gravitational waves carry energy. Our argument is based on two points: (i) that for both electromagnetism and gravity, in the presence of material sources, radiation is an effective concept, unambiguously emerging only in certain regimes or solutions of the theory; and (ii) similarly, energy conservation is only unambiguous in certain regimes or solutions of general relativity. Crucially, the domain of (i), in which radiation is meaningful, has a significant overlap with the domain of (ii), in which energy conservation is meaningful. Conceptually, the overlap of regimes is no coincidence: the long-standing question about the existence of gravitational waves was settled precisely by finding a consistent way to articulate their energy and momentum.

physics.hist-ph↗

arXiv2022

Same-diff? Conceptual similarities between gauge transformations and diffeomorphisms. Part I: Symmetries and isomorphisms

The following questions are germane to our understanding of gauge-(in)variant quantities and physical possibility: how are gauge transformations and spacetime diffeomorphisms understood as symmetries, in which ways are they similar, and in which are they different? To what extent are we justified in endorsing different attitudes -- nowadays called sophistication, haecceitism, and eliminativism -- towards each? This is the first of four papers taking up this question. This first paper will discuss notions of symmetries and isomorphisms that will be used in the remaining papers in the series. There are several such notions in the literature and the question of how they mesh with empirical discernibility is a delicate one; even the orthodox view that symmetries are empirically unobservable (even in principle) has recently been challenged by Belot. Focusing on local field theories, I will provide a precise definition of dynamical symmetries in terms of the space of states of the theory at hand. I will then apply the definition to Yang-Mills theories and general relativity and show that these symmetries correspond to automorphisms of `natural' geometric structures: the small diffeomorphisms of the spacetime manifold and the small fiber-preserving diffeomorphisms of a fibered space. Finally, I will show that these automorphisms can be given a passive gloss, since they correspond 1-1 to the coordinate transformations of the underlying manifolds.

physics.hist-ph↗

arXiv2022

Same-diff? Conceptual similarities between gauge transformations and diffeomorphisms. Part II: Challenges to sophistication

The following questions are germane to our understanding of gauge-(in)variant quantities and physical possibility: how are gauge transformations and spacetime diffeomorphisms understood as symmetries, in which ways are they similar, and in which are they different? To what extent are we justified in endorsing different attitudes -- nowadays called sophistication, haecceitism, and eliminativism -- towards each? This is the second of four papers taking up this question, and it is the one that most engages with the metaphysical debates surrounding our understanding of symmetry and equivalence. In this paper, I will provide two desiderata for the application of a treatment of symmetries known as `sophistication' and show that both general relativity and Yang-Mills theory satisfy these desiderata. The first desideratum for symmetries is mathematical, and was shown to hold for general relativity and Yang-Mills in the first paper: (i) that they correspond to the automorphisms of the structured base sets for the models of the two theories. Here I will extend the desideratum to more general theories. The second desideratum is mathematical-physical: (ii) that the general type of structure to which Desideratum (i) refers is axiomatizable and that this axiomatization can be phrased in terms of basic physical predicates of the theory. In the third paper in the series I will provide yet a third desideratum, to deal with an issue that goes beyond the standard debate about sophistication.

physics.hist-ph↗

arXiv2022

Why gauge? Conceptual Aspects of Gauge theories

This thesis is about conceptual aspects of gauge theories. Gauge theories lie at the heart of modern physics: in particular, they constitute the standard model of particle physics. At its simplest, the idea of gauge is that nature is best described using a descriptively redundant language; the different descriptions are said to be related by a gauge symmetry. The over-arching question the thesis aims to answer is: how can descriptive redundancy be fruitful for physics?

physics.hist-ph↗

arXiv2021

The role of representational conventions in assessing the empirical significance of symmetries

This paper explicates the direct empirical significance (DES) of symmetries in gauge theory, with comparisons to classical mechanics. Given a physical system composed of subsystems, such significance is to be awarded to physical differences of the composite system that arise from symmetries acting solely on its subsystems. So my overarching main question is: can DES be associated to the local gauge symmetries, acting solely on subsystems? In local gauge theories, any quantity with physical significance must be a gauge-invariant quantity. To attack the question of DES from this gauge-invariant angle, we require a split of the state into its physical and its representational content: a split that is relative to a representational convention, or a gauge-fixing. Using this method, we propose a rigorous definition of DES, valid for any state. This definition fills the gaps in influential previous construals of DES. In particular, Wallace's need to specialize to `generic' states is explained and dispensed with.

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arXiv2021

How to Choose a Gauge? The case of Hamiltonian Electromagnetism

We develop some ideas about gauge symmetry in the context of Maxwell's theory of electromagnetism in the Hamiltonian formalism. One great benefit of this formalism is that it pairs momentum and configurational degrees of freedom, so that a decomposition of one side into subsets can be translated into a decomposition of the other. In the case of electromagnetism, this enables us to pair degrees of freedom of the electric field with degrees of freedom of the vector potential. Another benefit is that the formalism algorithmically identifies subsets of the equations of motion that represent time-dependent symmetries. For electromagnetism, these two benefits allow us to define gauge-fixing in parallel to special decompositions of the electric field. More specifically, we apply the Helmholtz decomposition theorem to split the electric field into its Coulombic and radiative parts, and show how this gives a special role to the Coulomb gauge (i.e. div$({\bf A}) = 0$). We relate this argument to Maudlin's (2018) discussion, which advocated the Coulomb gauge.

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arXiv2021

Noether charges: the link between empirical significance of symmetries and non-separability

A fundamental tenet of gauge theory is that physical quantities should be gauge-invariant. This prompts the question: can gauge symmetries have physical significance? On one hand, the Noether theorems relate conserved charges to symmetries, endowing the latter with physical significance, though this significance is sometimes taken as indirect. But for theories in spatially finite and bounded regions, the standard Noether charges are not gauge-invariant. I here argue that gauge-\emph{variance} of charges is tied to the nature of the non-locality within gauge theories. I will flesh out these links by providing a chain of (local) implications: `local conservation laws'${\Rightarrow}$ `conserved regional charges' $\Leftrightarrow$ `non-separability' ${\Leftrightarrow}$ `direct empirical significance of symmetries'.

physics.hist-ph↗

arXiv2021

Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches

Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or whether they can be eliminated. It is also unclear whether they are merely an auxiliary tool to simplify (and possibly localize) calculations or whether they contain independent information. Therefore their status, both in physics and philosophy of physics, remains to be fully clarified. In this overview we review the current state of affairs on both the philosophy and the physics side. In particular, we focus on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance. Finally, we determine a set of yet to be answered questions to clarify the status of gauge symmetries.

physics.hist-ph↗

arXiv2021

The quasilocal degrees of freedom of Yang-Mills theory

Gauge theories possess nonlocal features that, in the presence of boundaries, inevitably lead to subtleties. We employ geometric methods rooted in the functional geometry of the phase space of Yang-Mills theories to: (1) characterize a basis for quasilocal degrees of freedom (dof) that is manifestly gauge-covariant also at the boundary; (2) tame the non-additivity of the regional symplectic forms upon the gluing of regions; and to (3) discuss gauge and global charges in both Abelian and non-Abelian theories from a geometric perspective. Naturally, our analysis leads to splitting the Yang-Mills dof into Coulombic and radiative. Coulombic dof enter the Gauss constraint and are dependent on extra boundary data (the electric flux); radiative dof are unconstrained and independent. The inevitable non-locality of this split is identified as the source of the symplectic non-additivity, i.e. of the appearance of new dof upon the gluing of regions. Remarkably, these new dof are fully determined by the regional radiative dof only. Finally, a direct link is drawn between this split and Dirac's dressed electron.

hep-th↗

arXiv2021

The Gauge Argument: A Noether Reason

Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space of possible dynamical models in such a way that forces and charges are appropriately coupled. We review the most well-known application of this kind, known as the 'gauge argument' or 'gauge principle', discuss its difficulties, and then reconstruct the gauge argument as a valid theorem in quantum theory. We then present what we take to be a better and more general gauge argument, based on Noether's second theorem in classical Lagrangian field theory, and argue that this provides a more appropriate framework for understanding how gauge symmetry helps to constrain the dynamics of physical theories.

physics.hist-ph↗

arXiv2020

Angular momentum without rotation: turbocharging relationalism

Newton's rotating bucket pours cold water on the naive relationalist by vividly illustrating how certain rotational effects, particularly those due to non-zero angular momentum, can depend on more than just relations between material bodies. Because of such effects, rotation has played a central role in the absolute-relational debate and poses a particularly difficult challenge to the relationalist. In this paper, we provide a qualified response to this challenge that significantly weakens the absolutist position. We present a theory that, contrary to orthodoxy, can account for all rotational effects without introducing, as the absolutist does, a fixed standard of rotation. Instead, our theory posits a universal SO(3) charge that plays the role of angular momentum and couples to inter-particle relations via terms commonly seen in standard gauge theories such as electromagnetism and the Standard Model of particle physics. Our theory makes use of an enriched form of relationalism: it adds an SO(3) structure to the traditional relational description. Our construction is made possible by the modern tools of gauge theory, which reveal a simple relational law describing rotational effects. In this way, we can save the phenomena of Newtonian mechanics using conserved charges and relationalism. In a second paper, we will further explore the ontological and explanatory implications of the theory developed here.

physics.hist-ph↗

arXiv2020

Geometrodynamics as Functionalism about Time

We review three broadly geometrodynamical---and in part, Machian or relational---projects, from the perspective of spacetime functionalism. We show how all three are examples of functionalist reduction of the type that was advocated by D. Lewis, and nowadays goes by the label 'the Canberra Plan'. The projects are: (1) the recovery of geometrodynamics by Hojman et al. (1976); (2) the programme of Schuller and collaborators (Schuller 2011; Dull, Schuller et al. 2018) to deduce a metric from the physics of matter fields; (3) the deduction of the ADM Hamiltonian by Gomes and Shyam (2016). We end by drawing a positive corollary about shape dynamics: namely, it has a good rationale for the Hamiltonian it postulates.

physics.hist-ph↗

arXiv2020

Holism as the significance of gauge symmetries

Not all symmetries are on a par. For instance, within Newtonian mechanics, we seem to have a good grasp on the empirical significance of boosts, by applying it to subsystems. This is exemplified by the thought experiment known as Galileo's ship: the inertial state of motion of a ship is immaterial to how events unfold in the cabin, but is registered in the values of relational quantities such as the distance and velocity of the ship relative to the shore. But the significance of gauge symmetries seems less clear. For example, can gauge transformations in Yang-Mills theory---taken as mere descriptive redundancy---exhibit a similar relational empirical significance as the boosts of Galileo's ship? This question has been debated in the last fifteen years in philosophy of physics. I will argue that the answer is `yes', but only for a finite subset of gauge transformations, and under special conditions. Under those conditions, we can mathematically identify empirical significance with a failure of supervenience: the state of the Universe is not uniquely determined by the intrinsic state of its isolated subsystems. Empirical significance is therefore encoded in those relations between subsystems that stand apart from their intrinsic states.

physics.hist-ph↗

arXiv2020

Large gauge transformations, gauge invariance, and the QCD $θ_{\text{YM}}$-term

The eliminative view of gauge degrees of freedom -- the view that they arise solely from descriptive redundancy and are therefore eliminable from the theory -- is a lively topic of debate in the philosophy of physics. Recent work attempts to leverage properties of the QCD $θ_{\text{YM}}$-term to provide a novel argument against the eliminative view. The argument is based on the claim that the QCD $θ_{\text{YM}}$-term changes under "large" gauge transformations. Here we review geometrical propositions about fiber bundles that unequivocally falsify these claims: the $θ_{\text{ YM}}$-term encodes topological features of the fiber bundle used to represent gauge degrees of freedom, but it is fully gauge-invariant. Nonetheless, within the essentially classical viewpoint pursued here, the physical role of the $θ_{\text{YM}}$-term shows the physical importance of bundle topology (or superpositions thereof) and thus weighs against (a naive) eliminativism.

physics.hist-ph↗

arXiv2019

Notes on a few quasilocal properties of Yang-Mills theory

Gauge theories possess non-local features that, in the presence of boundaries, inevitably lead to subtleties. In this article, we continue our study of a unified solution based on a geometric tool operating on field-space: a connection form. We specialize to the $D+1$ formulation of Yang-Mills theories on configuration space, and we precisely characterize the gluing of the Yang-Mills field across regions. In the $D+1$ formalism, the connection-form splits the electric degrees of freedom into their pure-radiative and Coulombic components, rendering the latter as conjugate to the pure-gauge part of the gauge potential. Regarding gluing, we obtain a characterization for topologically simple regions through closed formulas. These formulas exploit the properties of a generalized Dirichlet-to-Neumann operator defined at the gluing surface; through them, we find only the radiative components and the local charges are relevant for gluing. Finally, we study the gluing into topologically non-trivial regions in 1+1 dimensions. We find that in this case, the regional radiative modes do not fully determine the global radiative mode (Aharonov-Bohm phases). For the global mode takes a new contribution from the kernel of the gluing formula, a kernel which is associated to non-trivial cohomological cycles. In no circumstances do we find a need for postulating new local degrees of freedom at boundaries. $\text{The partial results of these notes have been completed and substantially clarified in a more recent, comprehensive article from October 2019. (titled: "The quasilocal degrees of freedom of Yang-Mills theory").}$

hep-th↗

arXiv2019

A unified geometric framework for boundary charges and dressings: non-Abelian theory and matter

Boundaries in gauge theories are a delicate issue. Arbitrary boundary choices enter the calculation of charges via Noether's second theorem, obstructing the assignment of unambiguous physical charges to local gauge symmetries. Replacing the arbitrary boundary choice with new degrees of freedom suggests itself. But, concretely, such boundary degrees of freedom are spurious---i.e. they are not part of the original field content of the theory---and have to disappear upon gluing. How should we fit them into what we know about field-theory? We resolve these issues in a unified and geometric manner, by introducing a connection 1-form, $\varpi$, in the field-space of Yang-Mills theory. Using this geometric tool, a modified version of symplectic geometry---here called `horizontal'---is possible. Independently of boundary conditions, this formalism bestows to each region a physical notion of charge: the horizontal Noether charge. The horizontal gauge charges always vanish, while global charges still arise for reducible configurations characterized by global symmetries. The field-content itself is used as a reference frame to distinguish `gauge' and `physical'; no new degrees of freedom, such as group-valued edge modes, are required. Different choices of reference fields give different $\varpi$'s, which are cousins of gauge-fixing like the Higgs-unitary and Coulomb gauges. But the formalism extends well beyond gauge-fixings, for instance by avoiding the Gribov problem. For one choice of $\varpi$, would-be Goldstone modes arising from the condensation of matter degrees of freedom play precisely the role of the known group-valued edge modes, but here they arise as preferred coordinates in field space, rather than new fields. For another choice, in the Abelian case, $\varpi$ recovers the Dirac dressing of the electron.

hep-th↗

arXiv2019

Gauging the Boundary in Field-space

Local gauge theories are in a complicated relationship with boundaries. Whereas fixing the gauge can often shave off unwanted redundancies, the coupling of different bounded regions requires the use of gauge-variant elements. Therefore, coupling is inimical to gauge-fixing, as usually understood. This sort of reasoning has led some to declare the coupling of subsystems to be the raison d'être of gauge. Indeed, while gauge-fixing is entirely unproblematic for a single region without boundary, it introduces arbitrary boundary conditions on the gauge degrees of freedom themselves -- these conditions lack a physical interpretation when they are not functionals of the original fields. Such arbitrary boundary choices creep into the calculation of charges through Noether's second theorem, muddling the assignment of physical charges to local gauge symmetries. The confusion brewn by gauge at boundaries is well-known, and must be contended with both conceptually and technically. Here I explicate the problems mentioned above and illustrate a possible resolution: in a recent series of papers the notion of a connection-form was put forward and implemented in the field-space of gauge theories. Using this tool, a modified version of symplectic geometry -- called `horizontal' -- is possible. Independently of boundary conditions, this formalism bestows to each region a physically salient, relational notion of charge: the horizontal Noether charge. Meanwhile, as required, the connection-form mediates a peaceful composition of regions, one compatible with the attribution of horizontal Noether charges to each region.

physics.hist-ph↗

arXiv2018

Timeless configuration space and the emergence of classical behavior

The inherent difficulty in talking about quantum decoherence in the context of quantum cosmology is that decoherence requires subsystems, and cosmology is the study of the whole Universe. Consistent histories gave a possible answer to this conundrum, by phrasing decoherence as loss of interference between alternative histories of closed systems. When one can apply Boolean logic to a set of histories, it is deemed 'consistent'. However, the vast majority of the sets of histories that are merely consistent are blatantly nonclassical in other respects, and further constraints than just consistency need to be invoked. In this paper, I attempt to give an alternative answer to the issues faced by consistent histories, by exploring a timeless interpretation of quantum mechanics of closed systems. This is done solely in terms of path integrals in non-relativistic, timeless, configuration space. What prompts a fresh look at such foundational problems in this context is the advent of multiple gravitational models in which Lorentz symmetry is not fundamental, but only emergent. And what allows this approach to overcome previous barriers to a timeless, conditional probabilities interpretation of quantum mechanics is the new notion of records -- made possible by an inherent asymmetry of configuration space. I outline and explore consequences of this approach for foundational issues of quantum mechanics, such as the natural emergence of the Born rule, conservation of probabilities, and the Sleeping Beauty paradox.

quant-ph↗