Norton's dome

Norton's dome is a thought experiment that models an apparently non-deterministic system within the bounds of Newtonian mechanics. It was devised by John D. Norton and first discussed in his paper "Causation as Folk Science".[1][2]

The model consists of an idealized particle initially sitting motionless at the apex of an idealized radially symmetrical frictionless dome described by the equation

h={\frac {2}{3g}}r^{\frac {3}{2}},

where h is the vertical displacement from the top of the dome to a point on the dome, r is the geodesic distance from the centre of the dome to that point (in other words, a radial coordinate r is "inscribed" on the surface),[3] and g the acceleration due to gravity.[4]

Norton shows that there are two classes of mathematical solutions to the model of the system under Newtonian physics. In the first, the particle stays sitting at the top of the dome forever. In the second, the particle sits at the top of the dome, and then after an artbitrary period of time starts to slide from the central point down the dome. The apparent paradox in this second case is that this would seem to occur for no discernible reason, and without any radial force being exerted on it by any other entity, apparently contrary to both physical intuition and normal intuitive concepts of cause and effect, yet the motion is still entirely consistent with the mathematics of Newton's laws of motion.

Norton's dome problem can be regarded as a problem in physics, mathematics, or philosophy.[5][6][7] It poses interesting philosophical questions about the concepts of causality, determinism, and probability theory.

While many criticisms have been made of Norton's thought experiment, such as it being a violation of the principle of Lipschitz continuity, or in violation of the principles of physical symmetry, or that it is somehow in some other way "unphysical", there is no consensus among its critics as to why they regard it as invalid.

See also

References

  1. ↑ Norton, John D. (November 2003). "Causation as Folk Science". Philosopher's Imprint 3 (4): 1–22. hdl:2027/spo.3521354.0003.004. C0 control character in |id= at position 74 (help)
  2. ↑ Laraudogoitia, Jon Pérez (2013). "On Norton’s dome". Synthese 190 (14): 2925–2941. doi:10.1007/s11229-012-0105-z.
  3. ↑ John Norton's webpage for the Norton dome problem
  4. ↑ Stanford Encyclopedia of Philosophy Causal Determinism
  5. ↑ Reutlinger, Alexander (2013). A Theory of Causation in the Social and Biological Sciences. Palgrave Macmillan. p. 109. ISBN 9781137281043.
  6. ↑ Wilson, M. (2009). "Determinism and the Mystery of the Missing Physics". The British Journal for the Philosophy of Science 60 (1): 173–193. doi:10.1093/bjps/axn052.
  7. ↑ Fletcher, Samuel Craig (2011). "What counts as a Newtonian system? The view from Norton’s dome". European Journal for Philosophy of Science 2 (3): 275–297. doi:10.1007/s13194-011-0040-8.

External links

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