Bell's theorem

Bell's theorem is the most famous legacy of the late John Bell. It is famous for drawing an important line in the sand between quantum mechanics (QM) and the world as we know it intuitively. It is simple and elegant, and at the same time touches upon many of the fundamental philosophical issues that relate to modern physics. In it simplest form, Bell's theorem states:

Related Topics:
John Bell - Quantum mechanics

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No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.

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This theorem has even been called "the most profound in science" (Stapp, 1975). Bell's seminal 1965 paper was entitled "On the Einstein Podolsky Rosen paradox". He showed that the assumption of local realism - that particle attributes have definite values independent of the act of observation and that physical effects have a finite propagation speed - leads to a requirement for certain types of phenomena which is not present in quantum mechanics. This requirement is called "Bell's inequality". Similar inequalities have subsequently been derived by different authors which are collectively termed "Bell inequalities". They all make the same assumptions about local realism -- that a quantum-level object has a well defined state which accounts for all its measurable properties and that distant objects do not exchange information faster than the speed of light. These well defined properties are often called hidden variables.

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The inequalities concern measurements made by remotely located observers (often called Alice and Bob) on entangled pairs of particles that have interacted and then separated. Assuming hidden variables, they lead to strict limits on the possible values of the correlation of subsequent measurements that can be obtained from the particle pairs. Bell discovered that these limits are outside the predictions of quantum mechanics in special cases. Quantum mechanics does not assume the existence of hidden variables associated with individual particles, and so the inequalities do not apply to it. The QM predicted correlation is due to quantum entanglement of the pair, with the idea that their state is not determined until the point at which a measurement is made on one or the other. This idea is fully in accordance with the Heisenberg uncertainty principle, one of the most fundamental concepts in quantum mechanics.

Related Topics:
Alice and Bob - Entangled - Heisenberg uncertainty principle

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If one accepts Bell's theorem: either quantum mechanics is wrong, or local realism is wrong. They cannot both be correct. So which is right? To answer that scientifically, experiments needed to be performed. It took many years and many improvements in technology to get the answer.

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Bell test experiments to date overwhelmingly show that the inequalities of Bell's theorem are violated. This provides empirical evidence against local realism and demonstrating that some of the "spooky action at a distance" suggested by the famous Einstein Podolsky Rosen (EPR) thought experiment do in fact occur. They are also taken as positive evidence in favor of QM. The principle of special relativity is saved by the no-communication theorem, which proves that it is impossible for Alice to communicate information to Bob (or vice versa) faster than the speed of light.

Related Topics:
Bell test experiments - EPR - No-communication theorem

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John Bell's papers examined both John von Neumann's 1932 proof of the incompatibility of hidden variables with QM and Albert Einstein and his colleagues' seminal 1935 paper on the subject.

Related Topics:
John von Neumann - Albert Einstein

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