Single stone synchronization

In the theory of relativity , the Einstein synchronization (also Poincaré-Einstein synchronization ) is a convention for the synchronization of clocks in different places.

Einstein's Convention

According to Albert Einstein's definition (1905), a light signal is sent from clock 1 to clock 2 at the time, whereupon a light signal is sent back immediately, for example by a mirror, that it reaches clock 1 at the time . The one-stone synchronization now consists in setting clock 2 so that it is the time of reflection . While the constancy of the speed of light on a closed path is one of the postulates of the special theory of relativity (in contrast to Poincaré without the assumption of an ether), the one-stone synchronization also adds the speed of light for "one direction" . ${\ displaystyle \ tau _ {1}}$ ${\ displaystyle \ tau _ {2}}$ ${\ displaystyle (\ tau _ {1} + \ tau _ {2}) / 2}$ ${\ displaystyle c}$

Many different approaches achieve the same synchronization as a result, for example sending a light signal halfway between clock 1 and clock 2 or the "slow" transport of a third clock from clock 1 to clock 2, at the limit of vanishing speed.

In a publication from 1917 Einstein presented a definition according to which it can be decided whether pairs of indications of clocks resting against each other were simultaneous or not, whereby this definition neither requires a specific parameterization of displays of one or the other clock, nor the term Speed or even considerations regarding the "disappearance" of different speed values from zero. Using this definition of simultaneity, clocks are simply considered to run synchronously if the pairs of their displays, which were measured as being at the same time, also looked the same. ${\ displaystyle \ tau}$

But only in inertial systems does this synchronization appear so natural that it is easy to forget that it is just a convention. In the general case, e.g. B. in a rotating reference system , the non-transitivity of the synchronization comes into play. If clock 1 and clock 2 are not synchronized directly but rather via a chain from other clocks, the result depends on the route selected. The synchronization along the circumference of a rotating disk results in a time jump to the output clock, which depends on the direction of rotation . This comes into play with the Sagnac interferometer and the Ehrenfest paradox . In the Global Positioning System to this effect must be considered.

The first fundamental discussion of conventionality comes from Hans Reichenbach . Most attempts to refute conventionality are deemed to have failed. The outstanding exception is Malament's argument that the symmetry of the causal connection ( temporality ) implies the one- stone synchronization . Since he published this argument in 1977, there has been a steady stream of both negative and approving work.

History: Poincaré

As early as 1898, Henri Poincaré emphasized that for the simplest possible formulation of the laws of nature it would be advantageous to assume the speed of light as constant in all directions. Also, the definition of the simultaneity of events in different places is merely a convention aimed at simplicity.

The Lorentz ether theory based on legend, he defined 1900, the synchronization of clocks as follows: two clocks A and B send each other each a light signal. Since all observers can assume, due to the validity of the relativity principle , to rest in the ether , they assume the constancy of the speed of light in all directions. Therefore, for a correct synchronization of the clocks, they will only consider the runtime of the signals and coordinate their observations with one another.

In 1904 Poincaré expanded this example as follows: If clock A shows the time 0, it sends a signal to B. Similarly, if clock B shows 0, it sends a signal to A. If both clocks show the same time t when the signals arrive, the clocks are by definition synchronous.

swell

↑ A. Einstein: On the electrodynamics of moving bodies . In: Annals of Physics . tape 17 , 1905, pp. 891–921 ( physik.uni-augsburg.de [PDF]).
↑ A. Einstein: About the special and general theory of relativity . Springer, Berlin / Heidelberg / New York 2001, ISBN 3-540-42452-0 , pp. 14-19 , §8-9 ( Text Archive - Internet Archive ). See English translation: Relativity: The Special and General Theory. ( Wikisource )
↑ D. Dieks: Becoming, relativity and locality. In: The Ontology of Spacetime. ( philsci-archive.pitt.edu )
^ Neil Ashby: Relativity in the Global Positioning System. In: Living Rev. Relativity. 6, 2003 ( livingreviews.org ).
^ Henri Poincaré: The measure of time . In: The Value of Science . BG Teubner, Leipzig 1906, chap. 2, p. 26–43 ( Wikisource - French: La mesure du temps . 1898. Translated by Emilie Weber).
^ Henri Poincaré: La théorie de Lorentz et le principe de réaction . In: Archives néerlandaises des sciences exactes et naturelles . tape 5 , 1900, pp. 252–278 ( Wikisource or archive.org - German translation).
^ Henri Poincaré: The present state and the future of mathematical physics . In: The Value of Science . BG Teubner, Leipzig 1906, chap. 7–9, pp. 129–159 ( Wikisource or Textarchiv - Internet Archive - French: L'état actuel et l'avenir de la physique mathématique . 1904. Translated by Emilie Weber).

literature

Books

Hans Reichenbach : Axiomatics of the relativistic space-time theory. 1924- (reprinted by Vieweg 1965)
Hans Reichenbach: The philosophical meaning of the theory of relativity- In: Works. Vol. 3, Vieweg 1979, ISBN 3-528-08363-8 .
HP Robertson : Postulates versus Observation in the Special Theory of Relativity. In: Reviews of Modern Physics. 1949.
Peter Galison : Einstein's clocks, Poincaré's cards. Working on the order of time . Fischer, Frankfurt 2003, ISBN 3-10-024430-3 .
Dennis Dieks (Ed.): The Ontology of Spacetime. Elsevier, 2006, ISBN 0-444-52768-0 .

Journal articles on Malament's argument

D. Malament: Causal Theories of Time and the Conventionality of Simultaniety. In: Noûs. 11, 1977, pp. 293-300.
A. Grünbaum : David Malament and the Conventionality of Simultaneity: A Reply. ( philsci-archive.pitt.edu ).
S. Sarkar, J. Stachel: Did Malament Prove the Non-Conventionality of Simultaneity in the Special Theory of Relativity? In: Philosophy of Science. Volume 66, No. 2.
R. Rynasiewicz: Definition, Convention, and Simultaneity: Malament's Result and Its Alleged Refutation by Sarkar and Stachel. In: Philosophy of Science. Volume 68, No. 3, Supplement, ( philsci-archive.pitt.edu ).
Hanoch Ben-Yami: Causality and Temporal Order in Special Relativity. In: British Jnl. for the Philosophy of Sci. Volume 57, No. 3, pp. 459-479. ( abstract ).

Web links

Conventionality of Simultaneity in the Stanford Encyclopedia of Philosophy

[1] A. Einstein: On the electrodynamics of moving bodies . In: Annals of Physics . tape 17 , 1905, pp. 891–921 ( physik.uni-augsburg.de [PDF]).

[2] A. Einstein: About the special and general theory of relativity . Springer, Berlin / Heidelberg / New York 2001, ISBN 3-540-42452-0 , pp. 14-19 , §8-9 ( Text Archive - Internet Archive ). See English translation: Relativity: The Special and General Theory. ( Wikisource )

[3] D. Dieks: Becoming, relativity and locality. In: The Ontology of Spacetime. ( philsci-archive.pitt.edu )

[4] Neil Ashby: Relativity in the Global Positioning System. In: Living Rev. Relativity. 6, 2003 ( livingreviews.org ).

[5] Henri Poincaré: The measure of time . In: The Value of Science . BG Teubner, Leipzig 1906, chap. 2, p. 26–43 ( Wikisource - French: La mesure du temps . 1898. Translated by Emilie Weber).

[6] Henri Poincaré: La théorie de Lorentz et le principe de réaction . In: Archives néerlandaises des sciences exactes et naturelles . tape 5 , 1900, pp. 252–278 ( Wikisource or archive.org - German translation).

[7] Henri Poincaré: The present state and the future of mathematical physics . In: The Value of Science . BG Teubner, Leipzig 1906, chap. 7–9, pp. 129–159 ( Wikisource or Textarchiv - Internet Archive - French: L'état actuel et l'avenir de la physique mathématique . 1904. Translated by Emilie Weber).