No-go theorem

In theoretical physics, a no-go theorem is a theorem that states that a particular situation is not physically possible. Specifically, the term describes results in quantum mechanics like Bell's theorem and the Kochen–Specker theorem that constrain the permissible types of hidden variable theories which try to explain the apparent randomness of quantum mechanics as a deterministic model featuring hidden states.[1][2]

Examples

The Weinberg–Witten theorem states that massless particles (either composite or elementary) with spin j > ​¹⁄₂ cannot carry a Lorentz-covariant current, while massless particles with spin j > 1 cannot carry a Lorentz-covariant stress-energy. The theorem is usually interpreted to mean that the graviton (j = 2) cannot be a composite particle in a relativistic quantum field theory.

In quantum information theory, a no-communication theorem is a result that gives conditions under which instantaneous transfer of information between two observers is impossible.

Other examples:

• Antidynamo theorems (e.g. Cowling's theorem)
• Coleman–Mandula theorem
• Earnshaw's theorem (it states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges)
• Haag–Łopuszański–Sohnius theorem as a generalisation of the Coleman–Mandula theorem stating that "space-time and internal symmetries cannot be combined in any but a trivial way"
• Haag's theorem
• Nielsen–Ninomiya theorem
• No-broadcast theorem
• No-cloning theorem
• No-deleting theorem
• No-hiding theorem
• No-teleportation theorem
• No-programming theorem[3]

See also

• Proof of impossibility

References

1. Bub, Jeffrey (1999). Interpreting the Quantum World (revised paperback ed.). Cambridge University Press. ISBN 978-0-521-65386-2.
2. Holevo, Alexander (2011). Probabilistic and Statistical Aspects of Quantum Theory (2nd English ed.). Pisa: Edizioni della Normale. ISBN 978-8876423758.
3. Nielsen, M. A.; Chuang, Isaac L. (1997-07-14). "Programmable Quantum Gate Arrays". Physical Review Letters. 79 (2): 321–324. arXiv:quant-ph/9703032. Bibcode:1997PhRvL..79..321N. doi:10.1103/PhysRevLett.79.321.

External links

• Beating no-go theorems by engineering defects in quantum spin models (2014)