The Development of Machian Themes in the Twentieth Century

2006 ◽  
Author(s):  
Julian Barbour
Keyword(s):  
Twentieth Century ◽  
General Relativity ◽  
Quantum Gravity ◽  
Space Time ◽  
Field Theories ◽  
Absolute Space ◽  
Rates Of Change ◽  
Space And Time

This chapter charts the complicated legacy of Mach's critique of absolute space and time. In 1902, Poincaré achieved a clear formulation of what a truly Machian mechanics should accomplish: it should permit a unique prediction of future motion on the basis of just the relative separations of bodies, and these separations' rates of change. However, this work made no impact on Einstein, despite his admiration for Mach. The discussion explains how several independent ideas that dominated Einstein's thinking about space, time and matter led him to a quite different interpretation (or misinterpretation) of Mach. This chapter also argues that, despite the misinterpretation, general relativity is perfectly Machian (in a sense that is the analogue for field theories of Poincaré's criterion), and that this shows general relativity to be ‘timeless’ in a certain sense, which is suggestive of quantum gravity.

Related to Relativity

2019 ◽  
pp. 265-284
Author(s):  
Steven J. Osterlind
Keyword(s):  
Twentieth Century ◽  
General Relativity ◽  
Special Relativity ◽  
Golden Age ◽  
Albert Einstein ◽  
Space Time ◽  
Theory Of Relativity ◽  
Scientific Exploration ◽  
Richard Burton ◽  
Time Continuum

This chapter provides the context for the early twentieth-century events contributing to quantification. It was the golden age of scientific exploration, with explorers like David Livingstone, Sir Richard Burton, and Sir Ernest Shackleton, and intellectual pursuits, such as Hilbert’s set of unsolved problems in mathematics. However, most of the chapter is devoted to discussing the last major influencer of quantification: Albert Einstein. His life and accomplishments, including his theory of relativity, make up the final milestone on our road to quantification. The chapter describes his time in Bern, especially in 1905, when he published several famous papers, most particularly his law of special relativity, and later, in 1915, when he expanded it to his theory of general relativity. The chapter also provides a layperson’s description of the space–time continuum. Women of major scientific accomplishments are mentioned, including Madame Currie and the mathematician Maryam Mirzakhani.

On the general correspondence between field theories and the theories of direct interparticle action

1968 ◽  
Vol 64 (4) ◽  
pp. 1071-1079 ◽  
Author(s):  
J. V. Narlikar
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Riemannian Space ◽  
Arbitrary Spin ◽  
Space Time ◽  
Field Theories ◽  
Classical Electrodynamics ◽  
General Correspondence ◽  
General Conditions

AbstractIt is well known that classical electrodynamics can be described both as a field theory and as a theory of direct interparticle action. In the present paper it is shown that, provided certain general conditions are satisfied, fields of arbitrary spin have their counterparts in ‘direct particle fields’. This correspondence between the two formalisms is established in the Riemannian space-time used for general relativity.

scholarly journals TOPOLOGICAL GRAVITY LOCALIZATION ON A δ-FUNCTION LIKE BRANE

2007 ◽  
Vol 22 (38) ◽  
pp. 2939-2946
Author(s):  
M. O. TAHIM ◽  
C. A. S. ALMEIDA
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Topological Field Theories ◽  
Extra Dimension ◽  
Discrete Symmetry ◽  
Field Theories ◽  
Topological Field ◽  
Topological Gravity ◽  
Classical Gravity ◽  
Gravity Localization

In the celebrated Plebanski formalism of topological gravity, the constraints connecting topological field theories and gravity are imposed in spacetimes with trivial topology. In the braneworld context there are two distinct regions of the spacetime, namely, the bulk and the braneworld volume. In this work we show how to construct topological classical gravity in a scenario containing one extra dimension and a δ-function like three-brane which naturally emerges from a spontaneously broken discrete symmetry. Starting from a D = 5 theory we obtain the action for General Relativity in the Palatini form in the bulk as well as in the braneworld volume. This result is important for future insights about quantum gravity on brane scenarios.

scholarly journals On the emergence of the structure of physics

2018 ◽  
Vol 376 (2118) ◽  
pp. 20170231 ◽  
Author(s):  
S. Majid
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Recent Work ◽  
Space Time ◽  
Quantum Space ◽  
Conceptual Level ◽  
Theme Issue ◽  
Self Duality ◽  
Born Reciprocity

We consider Hilbert’s problem of the axioms of physics at a qualitative or conceptual level. This is more pressing than ever as we seek to understand how both general relativity and quantum theory could emerge from some deeper theory of quantum gravity, and in this regard I have previously proposed a principle of self-duality or quantum Born reciprocity as a key structure. Here, I outline some of my recent work around the idea of quantum space–time as motivated by this non-standard philosophy, including a new toy model of gravity on a space–time consisting of four points forming a square. This article is part of the theme issue ‘Hilbert’s sixth problem’.

scholarly journals SYMMETRIES, SINGULARITIES AND THE DE-EMERGENCE OF SPACE

2008 ◽  
Vol 17 (03n04) ◽  
pp. 525-531 ◽  
Author(s):  
THIBAULT DAMOUR ◽  
HERMANN NICOLAI
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Recent Work ◽  
Lie Algebras ◽  
Planck Scale ◽  
Space Time ◽  
Moody Algebra ◽  
Type Analysis ◽  
Infinite Dimensional ◽  
Background Independence

Recent work has revealed intriguing connections between a Belinsky–Khalatnikov–Lifshitz-type analysis of spacelike singularities in general relativity and certain infinite-dimensional Lie algebras, particularly the "maximally extended" hyperbolic Kac–Moody algebra E10. In this essay we argue that these results may lead to an entirely new understanding of the (quantum) nature of space(–time) at the Planck scale, and hence — via an effective "de-emergence" of space near the singularity — to a novel mechanism for achieving background independence in quantum gravity.

scholarly journals Quantum gravity as a metaphysical problem

2017 ◽  
Vol 1 (5) ◽  
pp. 163-170
Author(s):  
Ilja Schmelzer
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Einstein Equations ◽  
Absolute Space ◽  
Quantum Theories ◽  
Approximation Techniques ◽  
Metaphysical Problem ◽  
Space And Time ◽  
Important Argument

The problem with quantum gravity is usually presented as if it would be difficult to construct even a single quantum theory of relativistic gravity. This is shown to be wrong. A straightforward approach using standard, well-studied methods allows to construct mathematically well-defined quantum theories which give, in a certain classical limit, the Einstein equations of GR: GR may be transformed into a field theory on a fixed background by breaking diffeomorphism symmetry using harmonic coordinates. The resulting field theory may be regularized using standard lattice approximation techniques. The result is a well-defined canonical theory with a finite number of degrees of freedom, which can be quantized without problems in a canonical way. Why such a straightforward way to quantize gravity is simply ignored? We identify missing explanation of relativistic symmetry as an important argument, and propose a solution. evaluate possible explanations why this simple possibility to construct a theory of quantum gravity is ignored. While a lot of different metaphysical and sociological reasons play a role, we identify as a main point a preference of the scientific community for the relational philosophy behind the spacetime interpretation of GR, in opposition to the Newtonian concept of absolute space and time (substantivalism). We conclude that the quantization of gravity is not a problem of physics, but a metaphysical problem. It is a problem of the relational philosophy of space and time in the tradition of Descartes and Leibniz, which is the base of the spacetime interpretation of GR, because this philosophy is incompatible with the known examples of theories of quantum gravity.

The Lens of Gravity

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Twentieth Century ◽  
General Relativity ◽  
General Theory ◽  
Solar Eclipse ◽  
History Of Physics ◽  
Space Time ◽  
Paradigm Shifts ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
History Of

This chapter describes how gravity provided the backdrop for one of the most important paradigm shifts in the history of physics. Prior to Albert Einstein’s general theory of relativity, trajectories were paths described by geometry. After the theory of general relativity, trajectories are paths caused by geometry. This chapter explains how Einstein arrived at his theory of gravity, relying on the space-time geometry of Hermann Minkowski, whose work he had originally harshly criticized. The confirmation of Einstein’s theory was one of the dramatic high points in twentieth-century history of physics when Arthur Eddington journeyed to an island off the coast of Africa to observe stellar deflections during a solar eclipse. If Galileo was the first rock star of physics, then Einstein was the first worldwide rock star of science.

scholarly journals Theory of quantum gravity beyond Einstein and space-time dynamics with quantum inflation

2015 ◽  
Vol 30 (28n29) ◽  
pp. 1545002 ◽  
Author(s):  
Yue-Liang Wu
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Minkowski Space ◽  
Gauge Field ◽  
Gravitational Force ◽  
Proper Time ◽  
Space Time ◽  
Coordinate Space ◽  
Gauge Symmetries ◽  
Minkowski Space Time

In this talk, I present a theory of quantum gravity beyond Einstein. The theory is established based on spinnic and scaling gauge symmetries by treating the gravitational force on the same footing as the electroweak and strong forces. A bi-frame space-time is initiated to describe the laws of nature. One frame space-time is a globally flat coordinate Minkowski space-time that acts as an inertial reference frame for the motions of fields, the other is a locally flat non-coordinate Gravifield space-time that functions as an interaction representation frame for the degrees of freedom of fields. The Gravifield is sided on both the globally flat coordinate space-time and locally flat non-coordinate space-time and characterizes the gravitational force. Instead of the principle of general coordinate invariance in Einstein theory of general relativity, some underlying principles with the postulates of coordinate independence and gauge invariance are motivated to establish the theory of quantum gravity. When transmuting the Gravifield basis into the coordinate basis in Minkowski space-time, it enables us to obtain equations of motion for all quantum fields and derive basic conservation laws for all symmetries. The gravity equation is found to be governed by the total energy–momentum tensor defined in the flat Minkowski space-time. When the spinnic and scaling gauge symmetries are broken down to a background structure that possesses the global Lorentz and scaling symmetries, we arrive at a Lorentz invariant and conformally flat background Gravifield space-time that is characterized by a cosmic vector with a non-zero cosmological mass scale. We also obtain the massless graviton and massive spinnon. The resulting universe is in general not isotropic in terms of conformal proper time and turns out to be inflationary in light of cosmic proper time. The conformal size of the universe has a singular at the cosmological horizon to which the cosmic proper time must be infinitely large. We show a mechanism for quantum inflation caused by the quantum loop contributions. The Gravifield behaves as a Goldstone-like field that transmutes the local spinnic gauge symmetry into the global Lorentz symmetry, which makes the spinnic gauge field becomes a hidden gauge field. As a consequence, the bosonic gravitational interactions can be described by the Goldstone-like Gravimetric field and space-time gauge field. The Einstein theory of general relativity is expected to be an effective low energy theory. Two types of gravity equation are resulted, one is the extension to Einstein’s equation of general relativity, and the other is a new type of gravitational equation that characterizes the spinnon dynamics.

scholarly journals Space–Time Physics in Background-Independent Theories of Quantum Gravity

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 251
Author(s):  
Martin Bojowald
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Riemannian Geometry ◽  
Loop Quantum Gravity ◽  
Space Time ◽  
Time Analysis ◽  
Complete Space ◽  
Background Independence ◽  
Starting Point

Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine not only the dynamics of space–time but also its geometry, which may have equally important implications for claims of potential physical observations. One of the leading candidates for background-independent quantum gravity is loop quantum gravity. By combining and interpreting several recent results, it is shown here how the canonical nature of this theory makes it possible to perform a complete space–time analysis in various models that have been proposed in this setting. In spite of the background-independent starting point, all these models turned out to be non-geometrical and even inconsistent to varying degrees, unless strong modifications of Riemannian geometry are taken into account. This outcome leads to several implications for potential observations as well as lessons for other background-independent approaches.

scholarly journals Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle

2021 ◽  
Author(s):  
David Escors ◽  
Grazyna Kochan
Keyword(s):  
Mathematical Model ◽  
General Relativity ◽  
Black Hole ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Zero Point ◽  
Space Time ◽  
Planck Length ◽  
Exclusion Zone ◽  
Curvature Perturbation

General relativity is a theory for gravitation based on Riemannian geometry, difficult to compatibilize with quantum mechanics. This is evident in relativistic problems in which quantum effects cannot be discarded. For example in quantum gravity, gravitation of zero-point energy or events close to a black hole singularity. Here, we set up a mathematical model to select general relativity geodesics according to compatibility with the uncertainty principle. To achieve this, we derived a geometric expression of the uncertainty principle (GeUP). This formulation identified proper space-time length with Planck length by a geodesic-derived scalar. GeUP imposed a minimum allowed value for the interval of proper space-time which depended on the particular space-time geometry. GeUP forced the introduction of a “zero-point” curvature perturbation over flat Minkowski space, caused exclusively by quantum uncertainty but not to gravitation. When applied to the Schwarzschild metric and choosing radial-dependent geodesics, our mathematical model identified a particle exclusion zone close to the singularity, similar to calculations by loop quantum gravity. For a 2 black hole merger, this exclusion zone was shown to have a radius that cannot go below a value proportional to the energy/mass of the incoming black hole multiplied by Planck length.

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