*Hanoch Gutfreund and Jürgen Renn*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691174631
- eISBN:
- 9781400888689
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691174631.003.0017
- Subject:
- Physics, History of Physics

This chapter shows that in the limit of weak fields and low velocities, the equation of the geodesic line reduces to Newton's equation of motion. It proceeds to derive the gravitational field ...
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This chapter shows that in the limit of weak fields and low velocities, the equation of the geodesic line reduces to Newton's equation of motion. It proceeds to derive the gravitational field equation. Next, the chapter uses the gravitational field equation to derive the three effects that served as the first tests of the theory: the bending of light by the gravitational field of the sun, the shift to the red of spectral lines emitted by atoms in a gravitational field (gravitational redshift), and the motion of the perihelion of planet Mercury. After a short remark about expressing Maxwell's equations of the electromagnetic field, the chapter turns to the “so-called cosmological problem.” Its main theme is the defense of Mach's principle, which states that all inertial phenomena, namely the fictitious forces arising in accelerated reference frames, are caused by all the masses in the universe.Less

This chapter shows that in the limit of weak fields and low velocities, the equation of the geodesic line reduces to Newton's equation of motion. It proceeds to derive the gravitational field equation. Next, the chapter uses the gravitational field equation to derive the three effects that served as the first tests of the theory: the bending of light by the gravitational field of the sun, the shift to the red of spectral lines emitted by atoms in a gravitational field (gravitational redshift), and the motion of the perihelion of planet Mercury. After a short remark about expressing Maxwell's equations of the electromagnetic field, the chapter turns to the “so-called cosmological problem.” Its main theme is the defense of Mach's principle, which states that all inertial phenomena, namely the fictitious forces arising in accelerated reference frames, are caused by all the masses in the universe.

*Flavio Mercati*

- Published in print:
- 2018
- Published Online:
- April 2018
- ISBN:
- 9780198789475
- eISBN:
- 9780191831294
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198789475.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

Shape Dynamics is a new theory of gravity that is based on fewer and more fundamental first principles than General Relativity. The most important feature of this theory is the replacement of ...
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Shape Dynamics is a new theory of gravity that is based on fewer and more fundamental first principles than General Relativity. The most important feature of this theory is the replacement of relativity of simultaneity with a more tractable gauge symmetry, namely invariance under spatial conformal transformations. This book contains both a quick introduction for readers curious about Shape Dynamics and a detailed walk-through of the historical and conceptual motivations for the theory, its logical development from first principles and an in-depth description of its present status. The book is sufficiently self-contained for an undergrad student with some basic background in General Relativity and Lagrangian/Hamiltonian mechanics. It is intended both as a reference text for students approaching the subject and as a review for researchers interested in the theory.Less

Shape Dynamics is a new theory of gravity that is based on fewer and more fundamental first principles than General Relativity. The most important feature of this theory is the replacement of relativity of simultaneity with a more tractable gauge symmetry, namely invariance under spatial conformal transformations. This book contains both a quick introduction for readers curious about Shape Dynamics and a detailed walk-through of the historical and conceptual motivations for the theory, its logical development from first principles and an in-depth description of its present status. The book is sufficiently self-contained for an undergrad student with some basic background in General Relativity and Lagrangian/Hamiltonian mechanics. It is intended both as a reference text for students approaching the subject and as a review for researchers interested in the theory.

*Flavio Mercati*

- Published in print:
- 2018
- Published Online:
- April 2018
- ISBN:
- 9780198789475
- eISBN:
- 9780191831294
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198789475.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

This chapter describes the fundamental problem at the core of Newton’s dynamics: the definition of inertia. This is provided by an absolute structure in Newtonian mechanics, but, as Leibniz and later ...
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This chapter describes the fundamental problem at the core of Newton’s dynamics: the definition of inertia. This is provided by an absolute structure in Newtonian mechanics, but, as Leibniz and later Mach argued, it should be dynamically determined. This is the core of Newton’s famous ‘bucket experiment’. Assuming this law as a postulate, without first defining the notions of ‘rest’, ‘uniform motion’ and ‘right (or straight) line’, is inconsistent. In a universe that is, in Barbour’s words, like ‘bees swarming in nothing’, how is one to talk about rest/uniform motion/straight lines? With respect to what? The problem is that of establishing a notion of equilocality: in an everchanging universe, what does it mean for an object to be at the same place at dierent times?Less

This chapter describes the fundamental problem at the core of Newton’s dynamics: the definition of inertia. This is provided by an absolute structure in Newtonian mechanics, but, as Leibniz and later Mach argued, it should be dynamically determined. This is the core of Newton’s famous ‘bucket experiment’. Assuming this law as a postulate, without first defining the notions of ‘rest’, ‘uniform motion’ and ‘right (or straight) line’, is inconsistent. In a universe that is, in Barbour’s words, like ‘bees swarming in nothing’, how is one to talk about rest/uniform motion/straight lines? With respect to what? The problem is that of establishing a notion of equilocality: in an everchanging universe, what does it mean for an object to be at the same place at dierent times?