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. This type of theorem imposes boundaries on certain mathematical or physical possibilities via a proof by 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]
• Von Neumann's no hidden variables proof

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).^[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]

General relativity

• No-hair theorem, black holes are characterized only by mass, charge, and spin

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 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