No-go theorem explained

In theoretical physics, a no-go theorem is a theorem that states that a particular situation is not physically possible. This type of theorem imposes boundaries on certain mathematical or physical possibilities via a proof of contradiction.^{[1] [2] [3]}

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 are 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^[1]
• Kochen–Specker theorem^[1]
• 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^[4]

Quantum field theory and string theory

• Weinberg–Witten theorem states that massless particles (either composite or elementary) with spin

J > \tfrac{ 1 }{ 2 } cannot carry a Lorentz-covariant current, while massless particles with spin J > 1 cannot carry a Lorentz-covariant stress-energy. It is usually interpreted to mean that the graviton 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).^{[5] [1]}
• Hegerfeldt's theorem implies that localizable free particles are incompatible with causality in relativistic quantum theory.^[1]
• 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
• 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.^[6]
• Reeh–Schlieder theorem^[1]

Proof of impossibility

See 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 that 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

External links

• • 1406.7239 . 10.1088/1367-2630/17/4/043013 . Beating no-go theorems by engineering defects in quantum spin models . 2015 . Sadhukhan . Debasis . Roy . Sudipto Singha . Rakshit . Debraj . Sen(De) . Aditi . Sen . Ujjwal . New Journal of Physics . 17 . 4 . 043013 . 2015NJPh...17d3013S .

Notes and References

1. Andrea Oldofredi. No-Go Theorems and the Foundations of Quantum Physics . . 49 . 3 . 355–370 . 2018 . 10.1007/s10838-018-9404-5 . 1904.10991 .
2. Federico Laudisa. Against the No-Go Philosophy of Quantum Mechanics . European Journal for Philosophy of Science . 4 . 1 . 1–17 . 2014 . 10.1007/s13194-013-0071-4 . 1307.3179 .
3. Radin Dardashti. No-go theorems: What are they good for? . . 4 . 1 . 47–55 . 2021-02-21 . 10.1016/j.shpsa.2021.01.005. 33965663 . 2103.03491 . 2021SHPSA..86...47D .
4. Nielsen . M.A. . Chuang . Isaac L. . 1997-07-14 . Programmable quantum gate arrays . Physical Review Letters . 79 . 2 . 321–324 . 10.1103/PhysRevLett.79.321 . quant-ph/9703032 . 1997PhRvL..79..321N . 119447939 .
5. Haag . Rudolf . 1955 . On quantum field theories . Matematisk-fysiske Meddelelser . 29 . 12 .
6. Book: Becker. K.. Becker. M.. Melanie Becker. Schwarz. J.H.. John Henry Schwarz. 2007. String Theory and M-Theory. Cambridge. Cambridge University Press. 10. 480–482. 978-0521860697.