Bell's theorem

(noun)

A no-go theorem famous for drawing an important line in the sand between quantum mechanics (QM) and the world as we know it classically. In its simplest form, Bell's theorem states: No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.

Related Terms

Examples of Bell's theorem in the following topics:

  • Philosophical Implications

    • John Bell showed by Bell's theorem that this "EPR" paradox led to experimentally testable differences between quantum mechanics and local realistic theories.

  • Introduction to The Sampling Theorem

    • The last equation is known as the Sampling Theorem.
    • The sampling theorem is due to Harry Nyquist, a researcher at Bell Labs in New Jersey.
    • In a 1928 paper Nyquist laid the foundations for the sampling of continuous signals and set forth the sampling theorem.
    • A generation after Nyquist's pioneering work Claude Shannon, also at Bell Labs, laid the broad foundations of modern communication theory and signal processing.
    • Shannon's A Mathematical Theory of Communication published in 1948 in the Bell System Technical Journal, is one of the profoundly influential scientific works of the 20th century.

  • Examples

    • Here is a result which is a special case of a more general theorem telling us how the Fourier transform scales.
    • Here $a$ is a parameter which corresponds to the width of the bell-shaped curve.

  • Kinetic Energy and Work-Energy Theorem

    • The work-energy theorem states that the work done by all forces acting on a particle equals the change in the particle's kinetic energy.
    • The principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle.
    • This relationship is generalized in the work-energy theorem.

  • Gravitational Attraction of Spherical Bodies: A Uniform Sphere

    • The Shell Theorem states that a spherically symmetric object affects other objects as if all of its mass were concentrated at its center.
    • That is, a mass $m$ within a spherically symmetric shell of mass $M$, will feel no net force (Statement 2 of Shell Theorem).
    • We can use the results and corollaries of the Shell Theorem to analyze this case.
    • This diagram outlines the geometry considered when proving The Shell Theorem.
    • (Note: The proof of the theorem is not presented here.

  • Convergence Theorems

  • A.2 Parseval's Theorem

  • Some Basic Theorems for the Fourier Transform

    • And finally, we have the convolution theorem.
    • The convolution theorem is one of the most important in time series analysis.
    • The convolution theorem is worth proving.

  • Gauss's Law

    • Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.
    • The law can be expressed mathematically using vector calculus in integral form and differential form, both are equivalent since they are related by the divergence theorem, also called Gauss's theorem.

  • Spaces Associated with a linear system Ax = y