Democratic principle

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In the context of General Relativity, the democratic principle allows quick, order-of-magnitude calculations for the strength of gravitomagnetic effects such as frame-dragging. While the principle is fairly intuitive, it does not have a rigorous mathematical definition.

John Wheeler (1990) on the practical application of Mach's principle to experiment (pp.232-233):

"It is not necessary to enter into the mathematics of the theory to state its simple consequence ... Each mass has an "inertia-contributing" power, a voting power, equal to its mass, there, divided by the distance from there to here. "

According to the general principle of relativity, rotation is a relative property, and a state of motion that a satellite senses as being "absolutely non-rotating" is a local state, dictated partly by the relative rotation of the background stars, but also partly by the rotation of the body that the satellite orbits. Applying the democratic principle, we can calculate the influence of these two rotations on the satellite by calculating the relative contributions of these two collections of massenergy to the background gravitational field strength at the satellite's location, and then weighting their contributions on the satellite's "sense of rotation" accordingly.

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Isaac Newton's rotating bucket argument was designed to demonstrate that true rotational motion cannot be defined as the relative rotation of the body with respect to the immediately surrounding bodies. It is one of five arguments from the "properties, causes, and effects" of "true motion and rest" that support his contention that, in general, true motion and rest cannot be defined as special instances of motion or rest relative to other bodies, but instead can be defined only by reference to absolute space. Alternatively, these experiments provide an operational definition of what is meant by "absolute rotation", and do not pretend to address the question of "rotation relative to what?" General relativity dispenses with absolute space and with physics whose cause is external to the system, with the concept of geodesics of spacetime.

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General relativity, also known as the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.

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In physics, spacetime is any mathematical model which fuses the three dimensions of space and the one dimension of time into a single four-dimensional manifold. The fabric of space-time is a conceptual model combining the three dimensions of space with the fourth dimension of time. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur.

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In theoretical physics, particularly in discussions of gravitation theories, Mach's principle is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The purpose of the hypothesis was to attempt to explain how rotating objects maintain a frame of reference, such as gyroscopes and spinning celestial bodies. The idea is that the existence of absolute rotation is determined by the large-scale distribution of matter, as exemplified by this anecdote:

You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don't move?

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Absolute space and time Theoretical foundation of Newtonian mechanics

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Isaac Newton's rotating spheres argument attempts to demonstrate that true rotational motion can be defined by observing the tension in the string joining two identical spheres. The basis of the argument is that all observers make two observations: the tension in the string joining the bodies and the rate of rotation of the spheres. Only for the truly non-rotating observer will the tension in the string be explained using only the observed rate of rotation. For all other observers a "correction" is required that accounts for the tension calculated being different from the one expected using the observed rate of rotation. It is one of five arguments from the "properties, causes, and effects" of true motion and rest that support his contention that, in general, true motion and rest cannot be defined as special instances of motion or rest relative to other bodies, but instead can be defined only by reference to absolute space. Alternatively, these experiments provide an operational definition of what is meant by "absolute rotation", and do not pretend to address the question of "rotation relative to what?" General relativity dispenses with absolute space and with physics whose cause is external to the system, with the concept of geodesics of spacetime.

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In physics, the concept of absolute rotation—rotation independent of any external reference—is a topic of debate about relativity, cosmology, and the nature of physical laws.

Frame-dragging Effect of general relativity

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Criticism of the theory of relativity of Albert Einstein was mainly expressed in the early years after its publication in the early twentieth century, on scientific, pseudoscientific, philosophical, or ideological bases. Though some of these criticisms had the support of reputable scientists, Einstein's theory of relativity is now accepted by the scientific community.

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