No-go theorem

Last updated

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 ]


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.

See also

Related Research Articles

Dirac equation Relativistic quantum mechanical wave equation

In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-12 massive particles such as electrons and quarks for which parity is a symmetry. It is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It was validated by accounting for the fine details of the hydrogen spectrum in a completely rigorous way.

T-symmetry Time reversal symmetry in physics

T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal,

The Klein–Gordon equation is a relativistic wave equation, related to the Schrödinger equation. It is second-order in space and time and manifestly Lorentz-covariant. It is a quantized version of the relativistic energy–momentum relation. Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. Its theoretical relevance is similar to that of the Dirac equation. Electromagnetic interactions can be incorporated, forming the topic of scalar electrodynamics, but because common spinless particles like the pions are unstable and also experience the strong interaction the practical utility is limited.

Wightman axioms axiomatization of quantum field theory

In physics, the Wightman axioms, named after Lars Gårding and Arthur Wightman, are an attempt at a mathematically rigorous formulation of quantum field theory. Arthur Wightman formulated the axioms in the early 1950s, but they were first published only in 1964 after Haag–Ruelle scattering theory affirmed their significance.

In quantum mechanics, the spin–statistics theorem relates the intrinsic spin of a particle to the particle statistics it obeys. In units of the reduced Planck constant ħ, all particles that move in 3 dimensions have either integer spin or half-integer spin.

Relativistic wave equations Wave equations respecting special and general relativity

In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light. In the context of quantum field theory (QFT), the equations determine the dynamics of quantum fields. The solutions to the equations, universally denoted as ψ or Ψ, are referred to as "wave functions" in the context of RQM, and "fields" in the context of QFT. The equations themselves are called "wave equations" or "field equations", because they have the mathematical form of a wave equation or are generated from a Lagrangian density and the field-theoretic Euler–Lagrange equations.

In particle and condensed matter physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. They were discovered by Yoichiro Nambu in particle physics within the context of the BCS superconductivity mechanism, and subsequently elucidated by Jeffrey Goldstone, and systematically generalized in the context of quantum field theory. In condensed matter physics such bosons are quasiparticles and are known as Anderson-Bogoliubov modes.

Higgs mechanism

In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other being fermions) would be considered massless, but measurements show that the W+, W, and Z0 bosons actually have relatively large masses of around 80 GeV/c2. The Higgs field resolves this conundrum. The simplest description of the mechanism adds a quantum field (the Higgs field) that permeates all space to the Standard Model. Below some extremely high temperature, the field causes spontaneous symmetry breaking during interactions. The breaking of symmetry triggers the Higgs mechanism, causing the bosons it interacts with to have mass. In the Standard Model, the phrase "Higgs mechanism" refers specifically to the generation of masses for the W±, and Z weak gauge bosons through electroweak symmetry breaking. The Large Hadron Collider at CERN announced results consistent with the Higgs particle on 14 March 2013, making it extremely likely that the field, or one like it, exists, and explaining how the Higgs mechanism takes place in nature.

Rudolf Haag postulated that the interaction picture does not exist in an interacting, relativistic, quantum field theory, something now commonly known as Haag’s theorem. Haag’s original proof was subsequently generalized by a number of authors, notably Hall & Wightman (1957), who reached the conclusion that a single, universal Hilbert space representation does not suffice for describing both free and interacting fields. Reed & Simon (1975) proved that a Haag-like theorem also applies to free neutral scalar fields of different masses, which implies that the interaction picture cannot exist even in the absence of interactions.

Representation theory of the Poincaré group Representation theory of an important group in physics

In mathematics, the representation theory of the Poincaré group is an example of the representation theory of a Lie group that is neither a compact group nor a semisimple group. It is fundamental in theoretical physics.

The Coleman–Mandula theorem is a no-go theorem in theoretical physics. It states that "space-time and internal symmetries cannot be combined in any but a trivial way". Since "realistic" theories contain a mass gap, the only conserved quantities, apart from the generators of the Poincaré group, must be Lorentz scalars.

In theoretical physics, the Weinberg–Witten (WW) theorem, proved by Steven Weinberg and Edward Witten, states that massless particles with spin j > 1/2 cannot carry a Lorentz-covariant current, while massless particles with spin j > 1 cannot carry a Lorentz-covariant stress-energy. The theorem is usually interpreted to mean that the graviton cannot be a composite particle in a relativistic quantum field theory.

Asım Orhan Barut was a Turkish-American theoretical physicist.

In quantum mechanics, the Pauli equation or Schrödinger–Pauli equation is the formulation of the Schrödinger equation for spin-½ particles, which takes into account the interaction of the particle's spin with an external electromagnetic field. It is the non-relativistic limit of the Dirac equation and can be used where particles are moving at speeds much less than the speed of light, so that relativistic effects can be neglected. It was formulated by Wolfgang Pauli in 1927.

Light front quantization Technique in computational quantum field theory

The light-front quantization of quantum field theories provides a useful alternative to ordinary equal-time quantization. In particular, it can lead to a relativistic description of bound systems in terms of quantum-mechanical wave functions. The quantization is based on the choice of light-front coordinates, where plays the role of time and the corresponding spatial coordinate is . Here, is the ordinary time, is one Cartesian coordinate, and is the speed of light. The other two Cartesian coordinates, and , are untouched and often called transverse or perpendicular, denoted by symbols of the type . The choice of the frame of reference where the time and -axis are defined can be left unspecified in an exactly soluble relativistic theory, but in practical calculations some choices may be more suitable than others.

In physics, relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to those comparable to the speed of light c, and can accommodate massless particles. The theory has application in high energy physics, particle physics and accelerator physics, as well as atomic physics, chemistry and condensed matter physics. Non-relativistic quantum mechanics refers to the mathematical formulation of quantum mechanics applied in the context of Galilean relativity, more specifically quantizing the equations of classical mechanics by replacing dynamical variables by operators. Relativistic quantum mechanics (RQM) is quantum mechanics applied with special relativity. Although the earlier formulations, like the Schrödinger picture and Heisenberg picture were originally formulated in a non-relativistic background, a few of them also work with special relativity.

Pauli–Lubanski pseudovector Operator in quantum field theory

In physics, the Pauli–Lubanski pseudovector is an operator defined from the momentum and angular momentum, used in the quantum-relativistic description of angular momentum. It is named after Wolfgang Pauli and Józef Lubański,

Bargmann–Wigner equations

In relativistic quantum mechanics and quantum field theory, the Bargmann–Wigner equations describe free particles of arbitrary spin j, an integer for bosons or half-integer for fermions. The solutions to the equations are wavefunctions, mathematically in the form of multi-component spinor fields.

Symmetry in quantum mechanics Properties underlying modern physics

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.


  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.