Background independence: Lessons for further decades of dispute

Teitel, Trevor

doi:10.1016/j.shpsb.2018.10.001

Cited by 4 publications

(6 citation statements)

References 56 publications

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“…where M is a differentiable (3+1)-manifold, η ab , is a fixed Lorentzian metric field 9 , and φ : M → R is a dynamical real scalar field. By contrast, a theory's dynamically possible models (DPMs), are the subset of the KPMs which obey the theory's dynamical equations.…”

Section: A Klein Gordon Equationmentioning

confidence: 99%

“…It is important to distinguish two kinds of symmetry [5] (spacetime 8 The name SR1 is picked to follow the notation set in [1]. 9 It's important to note the difference between ηµν and η ab . Any tensor object with greek indices (e.g., ηµν ) is to be understood as the components of a certain tensor in a particular coordinate system.…”

Section: Klein Gordon -Symmetriesmentioning

confidence: 99%

“…Let us now use this generally covariant formulation to help us understand this theory's background structure. As mentioned in the introduction, there is ongoing debate [1,2,[6][7][8][9][10] about what exactly should and should not count as background structure. However, it is widely agreed that any fixed field ought to count as background structure.…”

Section: Klein Gordon -Background Structurementioning

confidence: 99%

“…There can be other sorts of background structure in our theories than those which are declared upfront as fixed fields. There is a wide literature attempting to find a way of systematically identifying these hidden background structures [1,2,[6][7][8][9][10].…”

Section: Grmentioning

confidence: 99%

“…It is now widely believed that the key conceptual shift which sets GR apart from its predecessors is not its general covariance as Einstein thought but rather its background independence, i.e., its complete lack of background structure. This consensus, however, is largely only verbal as there is still substantial debate about what exactly should and should not count as background structure [1,2,[6][7][8][9][10]. The central goal in this debate is to find a relatively simple notion of background structure such that all intuitively GR-like spacetime theories lack background structure while all intuitively GR-unlike spacetime theories (e.g., special relativity, Newtonian gravity, etc.)…”

Section: Introductionmentioning

confidence: 99%

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A Discrete Analog of General Covariance -- Part 1: Could the world be fundamentally set on a lattice?

Grimmer¹

2022

Preprint

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A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a theory's substantive content from its merely representational artifacts. It is an indispensable tool for a modern understanding of spacetime theories, especially regarding their background structures and symmetry. Motivated by quantum gravity, one may wish to extend these notions to quantum spacetime theories (whatever those are). Relatedly, one might want to extend these notions to discrete spacetime theories (i.e., lattice theories). This paper delivers such an extension with surprising consequences.One's first intuition regarding discrete spacetime theories may be that they introduce a great deal of fixed background structure (i.e., a lattice) and thereby limit our theory's possible symmetries down to those which preserve this fixed structure (i.e., only certain discrete symmetries). By so restricting symmetries, lattice structures appear to be both theory-distinguishing and fundamentally "baked-into" our discrete spacetime theories. However, as I will discuss, all of these intuitions are doubly wrong and overhasty. Discrete spacetime theories can and do have continuous translation and rotation symmetries. Moreover, the exact same theory can be given a wide variety of lattice structures and can even be described with no lattice at all. As my discrete analog of general covariance will reveal: lattice structure is rather less like a fixed background structure or part of an underlying manifold and rather more like a coordinate system, i.e., merely a representational artifact. Ultimately, I show that the lattice structure supposedly underlying any discrete "lattice" theory has the same level of physical import as coordinates do, i.e., none at all. Thus, the world cannot be "fundamentally set on a square lattice" (or any other lattice) any more than it could be "fundamentally set in a certain coordinate system". Like coordinate systems, lattice structures are just not the sort of thing that can be fundamental; they are both thoroughly representational. Spacetime cannot be discrete (even when it might be representable as such).

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Section: A Klein Gordon Equationmentioning

confidence: 99%

Section: Klein Gordon -Symmetriesmentioning

confidence: 99%

Section: Klein Gordon -Background Structurementioning

confidence: 99%

Section: Grmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Discrete Analog of General Covariance -- Part 1: Could the world be fundamentally set on a lattice?

Grimmer¹

2022

Preprint

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Geometrical Constructivism and Modal Relationalism: Further Aspects of the Dynamical/Geometrical Debate

Read

2020

International Studies in the Philosophy of Science

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I draw together some recent literature on the debate between dynamical versus geometrical approaches to spacetime theories, in order to argue that (i) there exist defensible versions of the geometrical approach; (ii) these versions of the geometrical approach can provide constructive explanations (in the sense of Einstein) of dynamical effects; (iii) light can be shed upon different relationalist views about spacetime which have been articulated in the context of this debate by appeal to the distinction between modal versus non-modal relationalism.

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Holes in Spacetime: Some Neglected Essentials

Teitel¹

2019

The Journal of Philosophy

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The hole argument purports to show that all spacetime theories of a certain form are indeterministic, including General Relativity. The argument has sparked an industry of searching for a metaphysics of spacetime with the right modal implications to rescue determinism. In this paper, I first argue that certain prominent replies to the hole argument—namely, those that appeal to an essentialist doctrine about spacetime—fail to deliver the requisite modal implications. My argument involves showing that threats to determinism like the hole argument are more general than has heretofore been recognized. I then propose a novel essentialist doctrine about spacetime that successfully rescues determinism, what I call sufficiency metric essentialism. However, I ultimately argue that this doctrine is independently problematic, and teaches us that no essentialist doctrine about spacetime can succeed. I close by suggesting some lessons for future work on spacetime and the metaphysics of physics more broadly, and also drawing some morals for contemporary metaphysics, in particular about whether essence can be used to articulate a precise structuralist doctrine, and the relationship between essence and modality.

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Background independence: Lessons for further decades of dispute

Cited by 4 publications

References 56 publications

A Discrete Analog of General Covariance -- Part 1: Could the world be fundamentally set on a lattice?

A Discrete Analog of General Covariance -- Part 1: Could the world be fundamentally set on a lattice?

Geometrical Constructivism and Modal Relationalism: Further Aspects of the Dynamical/Geometrical Debate

Holes in Spacetime: Some Neglected Essentials

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