Plate trick

In mathematics and physics, the plate trick, also known as Dirac's string trick (after Paul Dirac, who introduced and popularized it),[1][2] the belt trick, or the Balinese cup trick (it appears in the Balinese candle dance), is any of several demonstrations of the idea that rotating an object with strings attached to it by 360 degrees does not return the system to its original state, while a second rotation of 360 degrees, a total rotation of 720 degrees, does.[3] Mathematically, it is a demonstration of the theorem that SU(2) (which double-covers SO(3)) is simply connected. To say that SU(2) double-covers SO(3) essentially means that the unit quaternions represent the group of rotations twice over.[3] A detailed, intuitive, yet semi-formal articulation can be found in the article on tangloids.

  1. ^ Staley, Mark (2010-01-12). "Understanding Quaternions and the Dirac Belt Trick". arXiv:1001.1778 [physics.pop-ph].
  2. ^ Schiller, Christoph (2021-01-13). "Testing a conjecture on the origin of the standard model". The European Physical Journal Plus. 136 (1): 79. doi:10.1140/epjp/s13360-020-01046-8. ISSN 2190-5444.
  3. ^ a b Staley, Mark (May 2010). "Understanding Quaternions and the Dirac Belt Trick". European Journal of Physics. 31 (3): 467–478. arXiv:1001.1778. Bibcode:2010EJPh...31..467S. doi:10.1088/0143-0807/31/3/004. S2CID 118533499.