Arch and scaffold: How Einstein found his field equations

Janssen, Michel; Renn, Jürgen

doi:10.1063/pt.3.2979

Cited by 27 publications

(6 citation statements)

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“…Hence, they satisfy h T = 0 and ∂ i h T ij = 0. As scalar, vector and tensor cosmological perturbations decouple from each other at linear order, we can consider the line element ds 2 = a 2 (η)[−dη 2 + (δ ij + h T ij )dx i dx j ] (H. 35) and study the ij component of Einstein's equations. In order to do so we can directly take the traceless and transverse part of equation (H.16).…”

Section: H6 Gravitational Waves In Bd-λcdm Cosmologymentioning

confidence: 99%

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Brans–Dicke Gravity with a Cosmological Constant Smoothes Out ΛCDM Tensions

Peracaula

Gómez-Valent

Pérez

et al. 2019

ApJL

127

138

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We analyze Brans-Dicke gravity with a cosmological constant, Λ, and cold dark matter (BD-ΛCDM for short) in the light of the latest cosmological observations on distant supernovae, Hubble rate measurements at different redshifts, baryonic acoustic oscillations, large scale structure formation data, gravitational weak-lensing and the cosmic microwave background under full Planck 2015 CMB likelihood. Our analysis includes both the background and perturbations equations. We find that BD-ΛCDM is observationally favored as compared to the concordance ΛCDM model, which is traditionally defined within General Relativity (GR). In particular, some well-known persisting tensions of the ΛCDM with the data, such as the excess in the mass fluctuation amplitude σ 8 and specially the acute H 0 -tension with the local measurements, essentially disappear in this context. Furthermore, viewed from the GR standpoint, BD-ΛCDM cosmology mimics quintessence at 3σ c.l. near our time.

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Section: H6 Gravitational Waves In Bd-λcdm Cosmologymentioning

confidence: 99%

“…We do not pretend to present an exhaustive nor chronological overview of the history of GR and field equations here. For a historical approach, see[34,35].…”

mentioning

confidence: 99%

Brans–Dicke Gravity with a Cosmological Constant Smoothes Out ΛCDM Tensions

Peracaula

Gómez-Valent

Pérez

et al. 2019

ApJL

127

138

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“…Einstein and Besso aimed to calculate deviations γ μν from Minkowski's values δ μν (δ μν = 1 for μ = ν and δ μν = 0 for μ = ν) so that g μν = −δ μν + γ μν . 18 Thus, 15 This is the so-called Ricci tensor; see eg., Janssen and Renn (2015a) for a recent account of Einstein's path toward field equations. 16 Equation 5 corresponds to the so-called 'harmonic coordinate condition'.…”

Section: From the Besso-einstein Argument To The §12 Argumentmentioning

confidence: 99%

Nothing but coincidences: the point-coincidence and Einstein’s struggle with the meaning of coordinates in physics

Giovanelli

2021

Euro Jnl Phil Sci

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In his 1916 review paper on general relativity, Einstein made the often-quoted oracular remark that all physical measurements amount to a determination of coincidences, like the coincidence of a pointer with a mark on a scale. This argument, which was meant to express the requirement of general covariance, immediately gained great resonance. Philosophers such as Schlick found that it expressed the novelty of general relativity, but the mathematician Kretschmann deemed it as trivial and valid in all spacetime theories. With the relevant exception of the physicists of Leiden (Ehrenfest, Lorentz, de Sitter, and Nordström), who were in epistolary contact with Einstein, the motivations behind the point-coincidence remark were not fully understood. Only at the turn of the 1960s did Bergmann (Einstein's former assistant in Princeton) start to use the term 'coincidence' in a way that was much closer to Einstein's intentions. In the 1980s, Stachel, projecting Bergmann's analysis onto his historical work on Einstein's correspondence, was able to show that what he started to call 'the point-coincidence argument' was nothing but Einstein's answer to the infamous 'hole argument'. The latter has enjoyed enormous popularity in the following decades, reshaping the philosophical debate on spacetime theories. The point-coincidence argument did not receive comparable attention. By reconstructing the history of the argument and its reception, this paper argues that this disparity of treatment is not justified. This paper will also show that the notion that only coincidences are observable in physics marks every critical step of Einstein's struggle with the meaning of coordinates in physics.

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“…e.g. Brighouse (1994); Butterfield (1989); Hoefer (1996); Weatherall (2018), and many more), it has been claimed that, ever since Einstein's own discussion of the hole argument (see Earman & Norton (1987); Janssen & Renn (2015) for a description), sophistication is, in effect if not in name, how the majority of theoretical physicists see isomorphic models: as reported by e.g. (Wald, 1984, p. 438), (O'Neill, 1983, p. 5), (Hawking & Ellis, 1975, p. 68).…”

Section: Morals Of This Thesismentioning

confidence: 99%

Why gauge? Conceptual Aspects of Gauge theories

Gomes¹

2022

Preprint

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This thesis is the result of my own work and includes nothing which is the outcome of work done in collaboration except as declared in the preface and specified in the text.It is not substantially the same as any work that has already been submitted before for any degree or other qualification except as declared in the preface and specified in the text.• Chapters 2 and 3 are partly based on H. Gomes, "Same-Diff ?: Part I: Conceptual similarities (and one difference) between gauge transformations and diffeomorphisms," and H. Gomes, "Same-Diff ?: Part II: A compendium of similarities between gauge transformations and diffeomorphisms (2021, unpublished);• Chapter 4 is based on my contributions to: H. Gomes, J. Butterfield, and B. Roberts, "The Gauge Argument: A Noether Reason ", Forthcoming in 'The Physics and Philosophy of Noether's Theorems', Cambridge University Press, (2021);• Chapter 5 is based on joint work: H. Gomes and J. Butterfield: "How to Choose a Gauge?The case of Hamiltonian Electromagnetism ", (2021, unpublished);• Chapter 6 is partly based on H. Gomes, "Holism as the empirical significance of symmetries", European Journal of the Philosophy of Science (2020); H. Gomes, "Noether charges: the link between empirical significance of symmetries and non-separability", Forthcoming in 'The Physics and Philosophy of Noether's Theorems', Cambridge University Press, (2021); H. Gomes, "Gauging the Boundary in Field-space", Studies in the History and Philosophy of Science, (2019); and H. Gomes, "The role of representational conventions in assessing the empirical significance of symmetries", (2020, unpublished). AcknowledgementsI would like to thank:• The Cambridge International Trust, for the complete funding of the studies that have led to this thesis.• My supervisor and personal hero, Jeremy Butterfield, who patiently guided me through this transition. His generosity of spirit is only comparable to his encyclopedic knowledge of the field; all I can say is that I tried my best to learn on both accounts.• My co-supervisor, Hasok Chang, for ushering me into the wonderful topic of philosophy of science; and Gordon Belot, Jim Weatherall, Aldo Riello, and Bryan Roberts, for many interesting and helpful conversations on the topic of gauge.

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Arch and scaffold: How Einstein found his field equations

Abstract: In his later years, Einstein often claimed that he had obtained the field equations of general relativity by choosing the mathematically most natural candidate. His writings during the period in which he developed general relativity tell a different story.

Cited by 27 publications

References 5 publications

Brans–Dicke Gravity with a Cosmological Constant Smoothes Out ΛCDM Tensions

Brans–Dicke Gravity with a Cosmological Constant Smoothes Out ΛCDM Tensions

Nothing but coincidences: the point-coincidence and Einstein’s struggle with the meaning of coordinates in physics

Why gauge? Conceptual Aspects of Gauge theories

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