No-go theorem
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
- 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 - it is not possible to build a fixed, general purpose quantum computer which can be programmed to perform an arbitrary quantum computation.
- Von Neumann's no hidden variables proof
Quantum field theory and string theory
- Weinberg–Witten theorem states that massless particles with spin cannot carry a Lorentz-covariant current, while massless particles with spin 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.
- 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
- 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.
- Reeh–Schlieder theorem
General relativity
- No-hair theorem, black holes are characterized only by mass, charge, and spin
Proof of impossibility