No-go theorem

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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.

• The no-communication theorem in quantum information theory gives conditions under which instantaneous transfer of information between two observers is impossible.
• Antidynamo theorems is a general category of theorems that restrict the type of magnetic fields that can be produced by dynamo action.
  • Cowling's theorem states that an axisymmetric magnetic field cannot be maintained through a self-sustaining dynamo action by an axially symmetric current.^[3]
• 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.
• 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.
• Haag's theorem states that the interaction picture does not exist in an interacting, relativistic, quantum field theory (QFT).^[4]
• Nielsen–Ninomiya theorem limits when it is possible to formulate a chiral lattice theory for fermions.
• No-broadcast theorem
• No-cloning theorem
• Quantum no-deleting theorem
• No-hiding theorem
• No-teleportation theorem
• No-programming theorem^[5]
• 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.

• PBR theorem

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 in the fact that the first one is strictly based on logical consequences, instead the last one require also an experimental part^[clarify].

See also[]

• Proof of impossibility
• Arrow's impossibility theorem

References[]

External links[]

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