No-go theorem

Not to be confused with No-ghost 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][failed verification – see discussion]}

Instances of no-go theorems

Full descriptions of the no-go theorems named below are given in other articles linked to their names. A few of them are broad, general categories under which several theorems fall. Other names are broad and general-sounding but only refer to a single theorem.

Classical electrodynamics

• Antidynamo theorems is a general category of theorems that restrict the type of magnetic fields that can be produced by dynamo action.
• Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges.

Non-relativistic quantum Mechanics and quantum information

• Bell's theorem
• Kochen–Specker theorem
• PBR theorem
• No-hiding theorem
• No-cloning theorem
• Quantum no-deleting theorem
• No-teleportation theorem
• No-broadcast theorem
• The no-communication theorem in quantum information theory gives conditions under which instantaneous transfer of information between two observers is impossible.
• No-programming theorem^[3]

Quantum field theory and string theory

• Weinberg–Witten theorem states that massless particles (either composite or elementary) with spin ${\displaystyle \;J>{\tfrac {1}{2}}\;}$  cannot carry a Lorentz-covariant current, while massless particles with spin ${\displaystyle \;J>1\;}$  cannot carry a Lorentz-covariant stress-energy. It is usually interpreted to mean that the graviton (${\displaystyle \;J=2\;}$ ) in a relativistic quantum field theory cannot be a composite particle.
• Nielsen–Ninomiya theorem limits when it is possible to formulate a chiral lattice theory for fermions.
• Haag's theorem states that the interaction picture does not exist in an interacting, relativistic, quantum field theory (QFT).^[4]
• Hegerfeldt's theorem implies that localizable free particles are incompatible with causality in relativistic quantum theory.
• Coleman–Mandula theorem states that "space-time and internal symmetries cannot be combined in any but a trivial way".
• Haag–Łopuszański–Sohnius theorem is a generalisation of the Coleman–Mandula theorem.
• Goddard–Thorn theorem or the no-ghost theorem,
• Maldacena–Nunez no-go theorem: any compactification of type IIB string theory on an internal compact space with no brane sources will necessarily have a trivial warp factor and trivial fluxes.^[5]

Proof of impossibility

Main article: Proof of impossibility

In mathematics there is the concept of proof of impossibility referring to problems impossible to solve. The difference between this impossibility and that of the no-go theorems is: a proof of impossibility states a category of logical proposition that may never be true; a no-go theorem instead presents a sequence of events that may never occur.

See also

• Arrow's impossibility theorem

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. S2CID 119447939.
4. Haag, Rudolf (1955). "On quantum field theories" (PDF). Matematisk-fysiske Meddelelser. 29: 12.
5. Becker, K.; Becker, M.; Schwarz, J.H. (2007). "10". String Theory and M-Theory. Cambridge: Cambridge University Press. p. 480-482. ISBN 978-0521860697.

External links

•   Quotations related to No-go theorem at Wikiquote
• Beating no-go theorems by engineering defects in quantum spin models (2014)