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.

  • Bell's Palsy

    • However, if no specific cause can be identified, the condition is known as Bell's palsy.
    • Bell's palsy is defined as an idiopathic unilateral facial nerve paralysis, usually self-limiting.
    • Bell's palsy affects each individual differently.
    • Even without any treatment, Bell's palsy tends to carry a good prognosis.
    • Describe the condition of Bell's palsy and its effects on the face

  • Facial (VII) Nerve

    • Lower motor neuron lesions can result in a cranial nerve VII palsy (Bell's palsy is the idiopathic form of facial nerve palsy), manifested as both upper and lower facial weakness on the same side of the lesion.
    • A person attempting to show his teeth and raise his eyebrows with Bell's palsy on his right side (left side of the image).

  • Trigonometry and Complex Numbers: De Moivre's Theorem

  • Probability Histograms and the Normal Curve

    • Approximately normal distributions occur in many situations, as explained by the central limit theorem.
    • If you were to construct a probability histogram of these events with many trials, the histogram would appear to be bell-shaped.
    • If the graph is approximately bell-shaped and symmetric about the mean, you can usually assume normality.
    • Notice that the histogram is not bell-shaped, indicating that the distribution is not normal.
    • The histogram looks somewhat bell-shaped, indicating normality.

  • Introduction

    • In this chapter, you will study means and the Central Limit Theorem.
    • The Central Limit Theorem (CLT for short) is one of the most powerful and useful ideas in all of statistics.
    • The second alternative says that if we again collect samples of size n that are "large enough," calculate the sum of each sample and create a histogram, then the resulting histogram will again tend to have a normal bell-shape.
    • You have just demonstrated the Central Limit Theorem (CLT).
    • The Central Limit Theorem tells you that as you increase the number of dice, the sample means tend toward a normal distribution (the sampling distribution).

  • The Gauss Model

    • One reason for their popularity is the central limit theorem, which states that, under mild conditions, the mean of a large number of random variables independently drawn from the same distribution is distributed approximately normally, irrespective of the form of the original distribution.
    • The Gaussian distribution is sometimes informally called the bell curve.
    • However, there are many other distributions that are bell-shaped (such as Cauchy's, Student's, and logistic).
    • The terms Gaussian function and Gaussian bell curve are also ambiguous since they sometimes refer to multiples of the normal distribution whose integral is not 1; that is, for arbitrary positive constants $a$, $b$ and $c$.
    • Explain the importance of the Gauss model in terms of the central limit theorem.

  • Stokes' Theorem

    • Stokes' theorem relates the integral of the curl of a vector field over a surface to the line integral of the field around the boundary.
    • The generalized Stokes' theorem is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.
    • The Kelvin–Stokes theorem, also known as the curl theorem, is a theorem in vector calculus on $R^3$.
    • The Kelvin–Stokes theorem is a special case of the "generalized Stokes' theorem."
    • As we have seen in our previous atom on gradient theorem, this simply means:

  • The Inventions of the Telephone and Electricity

    • Alexander Graham Bell is commonly credited as the inventor of the first practical telephone.
    • Bell's telephone transmitter (microphone) consisted of a double electromagnet, in front of which a membrane, stretched on a ring, carried an oblong piece of soft iron cemented to its middle.
    • The first long-distance telephone call was made on August 10, 1876, by Bell from the family homestead in Brantford, Ontario, to his assistant located in Paris, Ontario, some 10 miles away.
    • In June 1876, Bell exhibited a telephone prototype at the Centennial Exhibition in Philadelphia.
    • Bell's telephone was the first apparatus to transmit human speech via machine.