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Norton’s dome is intriguing; other departures from determinism in classical physics include “space invaders”: in some many-particle systems a particle can devel
by leephillips 6y ago
Norton’s dome is intriguing; other departures from determinism in classical physics include “space invaders”: in some many-particle systems a particle can develop an infinite velocity, which sends it “out of world”; then time reversibility means it can enter the world unpredictably. I mention both of these in an article about unsolved problems in classical physics: http://arstechnica.com/science/2014/08/the-never-ending-conundrums-of-classical-physics/ http://arstechnica.com/science/2014/08/the-never-ending-conu...
- twic 6y ago> Take a simple bottle of milk like the ones pictured here, with a cylindrical section below a tapering segment. Those bottles are rectangular!
- leephillips 6y agoThey are rectangular cylinders. The shape works for the problem under discussion.
- wodenokoto 6y agoI thought you where making up words, saying “rectangular cylinder”, but apparently it’s a thing: https://www.quora.com/Geometry-What-is-a-rectangular-cylinder https://www.quora.com/Geometry-What-is-a-rectangular-cylinde...
- leephillips 6y agoA cylinder can have any cross section.
- martincmartin 6y agoDoesn't conservation of energy preclude this? If all particles start with finite energy, and only finite energy is added to the system, won't the total energy stay finite? Or are you assuming an infinite potential somewhere, e.g. gravity from a point "planet"?
- leephillips 6y agoThe examples I know of all involve gravitational or similar potentials, so there is unbounded negative energy available from 1/r. But you can still get singularities without collisions: Xia, Annals of Math. 135 411–468 (1992).
- selimthegrim 6y agoNorton doesn't understand the principle of virtual work and should go back and read D'Alembert and Lanczos.
- jayd16 6y ago>which sends it “out of world” Wouldn't any system have to include this "out of world" particle? Doesn't its inclusion mean "the world" simply grows at that infinite rate?
- cozzyd 6y agoAt least a few of these seem to be cases where the concept of a point particle breaks down. There are similar problems in E&M at caustics that are solved by remembering that E&M waves have non-zero wavelength.