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 by contradiction.
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 Kochen–Specker theorem No-broadcast theorem No-cloning theorem No-communication theorem in quantum information theory gives conditions under which instantaneous transfer of information between two observers is impossible. No-deleting theorem No-hiding theorem No-programming theorem - it is not possible to build a fixed, general purpose quantum computer which can be programmed to perform an arbitrary quantum computation. No-teleportation theorem PBR theorem Von Neumann's no hidden variables proof
Quantum field theory and string theory Coleman–Mandula theorem states that "space-time and internal symmetries cannot be combined in any but a trivial way". Goddard–Thorn theorem (no-ghost theorem) Haag–Łopuszański–Sohnius theorem is a generalisation of the Coleman–Mandula theorem. Haag's theorem states that the interaction picture does not exist in an interacting, relativistic, quantum field theory (QFT). Hegerfeldt's theorem implies that localizable free particles are incompatible with causality in relativistic quantum theory. Maldacena–Núñez 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. Nielsen–Ninomiya theorem limits when it is possible to formulate a chiral lattice theory for fermions. Reeh–Schlieder theorem Weinberg–Witten theorem states that massless particles (either composite or elementary) with spin J > 1 2 {\displaystyle \;J>{\tfrac {1}{2}}\;} cannot carry a Lorentz-covariant current, while massless particles with spin J > 1 {\displaystyle \;J>1\;} cannot carry a Lorentz-covariant stress-energy. It is usually interpreted to mean that the graviton ( J = 2 {\displaystyle \;J=2\;} ) in a relativistic quantum field theory cannot be a composite particle.
Relativity and cosmology No-hair theorem, black holes are characterized only by mass, charge, and spin No-interaction theorem states that interactions cannot exist in finite system of particles in special relativity, unless fields are introduced Weinberg's no-go theorem (see cosmological constant problem).
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
References
External links Quotations related to No-go theorem at Wikiquote Sadhukhan, Debasis; Roy, Sudipto Singha; Rakshit, Debraj; Sen(De), Aditi; Sen, Ujjwal (2015). "Beating no-go theorems by engineering defects in quantum spin models". New Journal of Physics. 17 (4) 043013. arXiv:1406.7239. Bibcode:2015NJPh...17d3013S. doi:10.1088/1367-2630/17/4/043013.
