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No-go theorem

No-go theorem is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand No-go theorem rather than just read about it. In short: 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.

Key takeaways

  • No-go theorem belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect No-go theorem to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of No-go theorem from memory before moving on to harder problems.

Reference excerpt

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 No-broadcast theorem No-cloning theorem No-communication theorem in quantum information theory gives conditions under which instantaneous transfer of information between two observers is impossible. No-deleting theorem No-hiding theorem 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. No-teleportation theorem PBR theorem Von Neumann's no hidden variables proof

Quantum field theory and string theory Coleman–Mandula theorem states that "space-time and internal symmetries cannot be combined in any but a trivial way". Goddard–Thorn theorem (no-ghost theorem) Haag–Łopuszański–Sohnius theorem is a generalisation of the Coleman–Mandula theorem. Haag's theorem states that the interaction picture does not exist in an interacting, relativistic, quantum field theory (QFT). Hegerfeldt's theorem implies that localizable free particles are incompatible with causality in relativistic quantum theory. Maldacena–Núñez 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. Nielsen–Ninomiya theorem limits when it is possible to formulate a chiral lattice theory for fermions. Reeh–Schlieder theorem Weinberg–Witten theorem states that massless particles (either composite or elementary) with spin J > 1 2 {\displaystyle \;J>{\tfrac {1}{2}}\;} cannot carry a Lorentz-covariant current, while massless particles with spin J > 1 {\displaystyle \;J>1\;} cannot carry a Lorentz-covariant stress-energy. It is usually interpreted to mean that the graviton ( J = 2 {\displaystyle \;J=2\;} ) in a relativistic quantum field theory cannot be a composite particle.

Relativity and cosmology No-hair theorem, black holes are characterized only by mass, charge, and spin No-interaction theorem states that interactions cannot exist in finite system of particles in special relativity, unless fields are introduced Weinberg's no-go theorem (see cosmological constant problem).

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

References

External links Quotations related to No-go theorem at Wikiquote Sadhukhan, Debasis; Roy, Sudipto Singha; Rakshit, Debraj; Sen(De), Aditi; Sen, Ujjwal (2015). "Beating no-go theorems by engineering defects in quantum spin models". New Journal of Physics. 17 (4) 043013. arXiv:1406.7239. Bibcode:2015NJPh...17d3013S. doi:10.1088/1367-2630/17/4/043013.

Worked examples

Example 1 — a first encounter with No-go theorem

Start with the simplest possible case. Write down what No-go theorem claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to No-go theorem before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about No-go theorem ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of No-go theorem

In research
No-go theorem appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses No-go theorem in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
No-go theorem is common in secondary-school and first-year university syllabi. It links to neighbouring topics No-go theorems, Quantum field theory, Supersymmetry, so understanding it makes those chapters shorter.
In everyday life
Look for No-go theorem outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study No-go theorem in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what No-go theorem means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain No-go theorem out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is No-go theorem in simple terms?

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.

Why does No-go theorem matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study No-go theorem?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on No-go theorem.

Tags

  • No-go theorems
  • Quantum field theory
  • Supersymmetry

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