Mach's principle

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The Mach principle is one of Ernst Mach called physical principle with which he one the reasons for the existence of absolute space by Isaac Newton in the criticized bucket experiment. According to Mach's principle, one cannot speak of a movement of a body in relation to an absolute space , but only of movements in relation to all other bodies in the universe. In particular, this concerns the definition of inertial systems and the effect of inertial forces . The principle played a role in the development of the general theory of relativity by Albert Einstein , according to which the curvature of space-time is only determined by the matter and energy in it.

The statement of Mach's principle is difficult to formulate exactly and in the literature a large number of different versions of Mach's principle are listed, some of which differ significantly.

Newton's Bucket Experiment and Mach's Critique

Parabolic shape of the interface between two immiscible liquids that have been set in rotation under the action of vertical gravitational force

Newton in particular represented the existence of absolute space and an absolute time and justified them in his Philosophiae Naturalis Principia Mathematica of 1687 (Book I, Scholium) with the bucket experiment. One can therefore always prove whether the water in a bucket rotates around its axis of rotation relative to an absolute space, since in this case the surface of the water forms a paraboloid of rotation due to the centrifugal forces , regardless of whether the bucket itself rotates with it or not.

Mach's objection to this thought experiment is that Newton does not take into account the influence of the rest of the matter in the universe on water. Newton's experiment would only matter in an otherwise empty universe. In the real universe, in which matter is present, instead of a rotation relative to an absolute space, as Newton claims, only a rotation relative to the other celestial bodies is important for the experiment:

“Newton's experiment with the rotating water vessel only teaches that the relative rotation of the water against the walls of the vessel does not arouse any noticeable centrifugal forces, but that they are awakened by the relative rotation against the mass of the earth and the other celestial bodies. Nobody can say how the experiment would go if the vessel walls became thicker and more massive, finally several miles thick. There is only one attempt, and we have to bring it into harmony with the other facts known to us, but not with our arbitrary poems. "

For example, the centrifugal force would remain the same when the earth moves around the sun, when the earth and the sun are at rest and the masses of the universe rotate around the sun-earth system.

With a similar consideration, George Berkeley (De Motu 1721) criticized Newton's definition of motion in relation to an absolute space.

The brothers Immanuel Friedlaender and Benedict Friedlaender investigated the influence of rotating masses as part of a modification of Newton's theory . A test to determine the effect of the rotating earth on a rapidly rotating top was carried out by August Föppl in 1904.

Mach's principle and the general theory of relativity

The principle was named by Albert Einstein in 1918 after Ernst Mach, who represented it in 1883 in his book The Mechanics in Their Development . Mach's principle was one of the ideas that guided Einstein in developing general relativity . However, it later proved to be incompatible with some concrete formulations of Mach's principle. So in 1949 Kurt Gödel constructed a solution of the equations of the GTR with a rotating universe that blatantly violated Mach's principle ( Gödel universe ), but it was not realistic and made time travel possible. In 1962 Ozsvath and Engelbert Schücking gave a finite version of the Gödel universe, in which no time travel is possible and which violates Mach's principle.

It is questionable whether other formulations of Mach's principle are compatible with the theory of relativity.

One motive for the development of the Brans Dicke theory was to explicitly incorporate Mach's principle through the introduction of an additional scalar field to the metric tensor.

Albert Einstein saw a realization of Mach's principle in the Lense-Thirring effect of 1918, which is controversial.

literature

Web links

Individual evidence

  1. ↑ See for example Julian B. Barbour, Herbert Pfister (Ed.): Mach's Principle. From Newton's Bucket to Quantum Gravity. Birkhäuser, 1995, ISBN 0-8176-3823-7 (English) or the listing in Hermann Bondi, Joseph Samuel: The Lense-Thirring Effect and Mach's Principle (PDF; 101 kB), 1996, doi: 10.1016 / S0375-9601 ( 97) 00117-5 (English).
  2. ^ Isaac Newton, Principia, editor Florian Cajori, University of California Press 1934, p. 10
  3. ^ Ernst Mach: The mechanics in their development , FA Brockhaus, Leipzig 1883, p. 216/217 (quotation in original spelling ).
  4. ↑ a b Eckhard Rebhan: Theory of Relativity and Cosmology (=  Theoretical Physics ). Springer, Berlin / Heidelberg 2012, ISBN 978-3-8274-2314-6 , pp. 179–182 ( limited preview in Google Book search).
  5. ^ Friedlaender, Absolute or relative movement?, Berlin 1896, digitized
  6. ^ Herbert Pfister, On the history of the so-called Lense-Thirring effect, General Relativity and Gravitation, Volume 39, 2007, pp. 1735-1748
  7. ^ Nahin, Times Machines, Springer 1999, p. 84
  8. ↑ Einstein was significantly involved in deriving it and calculated a corresponding effect in the previous theories of his GTR. See Herbert Pfister, On the history of the so-called Lense-Thirring effect, General Relativity and Gravitation, Volume 39, 2007, pp. 1735-1748