Anti-knot
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An anti-knot is defined as a mathematical knot. An anti-knot would be a knot on a rope that cancels out the corresponding knot when the two are made to meet along the rope. Anti-knots do not exist, which it is easy to prove:
Proof 1.
A configuration containing a knot and an anti-knot is indistinquishable from a line with no knot at all. The only knot K with an antiknot is thus the unknot K = 0 (the perfect line).
Proof 2.
- The mathematical knot energy of a line with no knot at all is equal to zero.
- The knot energy of any knot can be shown to be greater than zero.
- As the knot energies of knot and anti-knot are both greater than zero, the sum would be greater than zero, in contradiction to the zero knot energy of the unknotted line, which both knots would build up per definition of the anti-knot.
Highly speculative physical theories, trying to describe elementary particles as knots and their anti-particles as anti-knots, are thereby proven false.
Literature
- Ian Stewart Finding the energy to solve a knotty problem New Scientist 06 March 1993
- Tzihong Chiueh Integrability and Topology of Three-Dimensional Vector Fields Chinese Journal of Physics Vol. 35, No. 1 Feb 1997 4-12
- R.H. Crowell, R.H. Fox Introduction to Knot Theory Ginn & Co. New York 1963
See also
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