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, as more generally stated by a proof of impossibility . 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 ]

Contents

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.

It is usually interpreted to mean that the graviton () in a relativistic quantum field theory cannot be a composite particle.

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Symmetries in quantum mechanics describe features of spacetime and particles which are unchanged under some transformation, in the context of quantum mechanics, relativistic quantum mechanics and quantum field theory, and with applications in the mathematical formulation of the standard model and condensed matter physics. In general, symmetry in physics, invariance, and conservation laws, are fundamentally important constraints for formulating physical theories and models. In practice, they are powerful methods for solving problems and predicting what can happen. While conservation laws do not always give the answer to the problem directly, they form the correct constraints and the first steps to solving a multitude of problems.

Higher Spin Theory or Higher Spin Gravity is a common name for field theories that contain massless fields of spin greater than two. Usually, the spectrum of such theories contains the graviton as a massless spin-two field, which explains the second name. Massless fields are gauge fields and the theories should be (almost) completely fixed by these higher spin symmetries. Higher spin theories are supposed to be consistent quantum theories and, for this reason, to give examples of quantum gravity. Most of the interest in the topic is due to the AdS/CFT correspondence where there is a number of conjectures relating higher spin theories to weakly coupled conformal field theories. It is important to note that only certain parts of these theories are known at present and not many examples have been worked out in detail except some specific toy models.

References

  1. Bub, Jeffrey (1999). Interpreting the Quantum World (revised paperback ed.). Cambridge University Press. ISBN   978-0-521-65386-2.
  2. Holevo, Alexander (2011). Probabilistic and Statistical Aspects of Quantum Theory (2nd English ed.). Pisa: Edizioni della Normale. ISBN   978-8876423758.
  3. Cowling, T.G. (1934). "The magnetic field of sunspots". Monthly Notices of the Royal Astronomical Society . 94: 39–48. Bibcode:1933MNRAS..94...39C. doi: 10.1093/mnras/94.1.39 .
  4. Haag, Rudolf (1955). "On quantum field theories" (PDF). Matematisk-fysiske Meddelelser. 29: 12.
  5. Nielsen, M.A.; Chuang, Isaac L. (1997-07-14). "Programmable quantum gate arrays". Physical Review Letters. 79 (2): 321–324. arXiv: quant-ph/9703032 . Bibcode:1997PhRvL..79..321N. doi:10.1103/PhysRevLett.79.321.