Norton's Dome
Norton's Dome is a thought experiment by John D. Norton, Professor at the University of Pittsburgh , Center for Philosophy of Science. It is used to indicate a constellation whose system of differential equations, according to classical mechanics, has not only one unambiguous solution, but two, and is thus intended to provide an example of indeterminism or against determinism .
The background is Laplace 's assumption that all systems of classical mechanics can be described by systems of differential equations that have only one solution and are thus uniquely determined.
Norton goes to from an idealized experiment with a friction on a dome (engl. Dome ) slipping point-like mass from which rests at the start of the experiment at the apex of the dome. The shape of the dome is cleverly chosen so that the function for the force that acts on the mass point is not Lipschitz continuous at the apex . However, according to Picard-Lindelöf's theorem, this is a prerequisite for the differential equation formed to describe the motion to be uniquely solved. This results in two solutions: on the one hand, the mass can remain on the vertex indefinitely, but on the other hand, surprisingly, it can also slide off the dome spontaneously and at an unpredictable time in any direction.
Norton's thought experiment is intended to show that spontaneous, uncaused events can arise on the macroscopic level of classical mechanics without having to deal with quantum mechanics and its fluctuations .
It joins a large number of examples that were created with the same intention, but until then assume an infinite number of steps, of mass particles, infinite mass density or other infinite requirements and are therefore located as "super tasks" in the area outside of classical mechanics . Earman and Norton provide an overview.
The problem published by Norton in 2003 under the title `` Causation as Folk Science '' has sparked lively discussions about the extent to which it actually meets the conditions of Newtonian mechanics and to what extent it supports or refutes indeterminism or determinism. Major objections relate to the violation of Lipschitz continuity or the principle of physical symmetry , see an impermissible idealization, or classify it as "unphysical" for other reasons. In 2008 Norton responded with another publication in which he responded to some objections, which in turn led to counter-arguments. Samuel C. Fletcher summarizes these in a section " Attempts to Demolish the Dome ". Charlotte Werndl provides another, extensive analysis.
Web links
- John Norton's website on the problem
Individual evidence
- ^ John Earman, John Norton: Infinite pains: the trouble with supertasks . In: Adam Morton, Stephen P. Stich (eds.), Benacerraf and His Critics. Blackwell . 1996, p. 231-261 ( pitt.edu [PDF]).
- ^ Norton, John D .: Causation as Folk Science . Philosopher's Imprint, Vol. 3, No. 4, 2003 ( handle.net ).
- ^ Norton, John D .: The Dome: An Unexpectedly Simple Failure of Determinism . Philosophy of Science, Vol. 75, No. 5, 2008 ( lse.ac.uk [PDF]).
- ^ Samuel C. Fletcher: What Counts as a Newtonian System? The View from Norton's Dome. European Journal for Philosophy of Science 2.3: 275-297, 2012 ( jamesowenweatherall.com [PDF]).
- ^ Werndl, C .: Determinism and Indeterminism . In: P. Humphreys (ed), Oxford Handbook for the Philosophy of Science . Oxford University Press, 2015 ( pitt.edu [PDF]).