Einstein-Podolsky-Rosen paradox

This bizarre prediction, known as the Einstein-Podolsky-Rosen paradox, has been verified many times in the laboratory. The most famous version involves two electrons manipulated into a mixed state with combined spin of 0, The electrons are separated in space before the spin of one (and only one) electron is measured, say, in a Stern-Gerlach machine. If that electron is found to be spin up, then by conservation of spin angular momentum, the other electron must be spin down, and vice versa. This holds true even if the ratio of the distance between the measurements to the time between the measurements is greater than the speed of light. See the discussion in Townsend [To, Sections 5,4 and 5,5] and the references therein. 

In this section we have presented a mathematical foundation for entanglement of quantum systems. This foundation lies behind most modern discussions of quantum computing, as well as the Einstein-Podolsky-Rosen paradox. 

Exercise 11.4 Can you exploit the Einstein-Podolsky-Rosen paradox to send information faster than the speed of light ... 

A. Kyprianidis and J. P. Vigier, Action-at-a-distance The mystery of Einstein-Podolsky-Rosen correlations, in F. Selleri (Ed.), Quantum Mechanics versus Local Realism The Einstein-Podolsky—Rosen Paradox, ISBN 0-30-642739-7, Plenum, New York, 1988, p. 273. 

N. Cufaro-Petroni, A. Garuccio, F. Selleri, and J. P. Vigier, On a contradiction between the classical (idealized) quantum theory of measurement and the conservation of the square of the total angular momentum in Einstein-Podolsky-Rosen paradox, C. R. Acad. Sci., Ser. B (Sciences Physiques), 290(6), 111-114 (1980). 

N. Cufaro-Petroni and J. P. Vigier, Causal superluminal interpretation of the Einstein-Podolsky-Rosen paradox, Lett. Nuovo Cimento 26(5) (Ser. 2), 149-154 (1979). 

Cramer, J.G. (1980) Generalized absorber theory and the Einstein-Podolsky-Rosen paradox, Phys. Rev.D, 1980 (22) 362-376. 

It turned out that in the Bohr-Einstein controversy, Bohr was right. The Einstein-Podolsky-Rosen paradox resulted (in agreement with Bohr s view) in the concept of entangled states. These states have been used experimentally teleport a photon state without violating the Heisenberg uncertainty principle. Also, the entangled states stand behind the idea of quantum computing with a superposition (qubit) of two states a 0) + b l) instead of 0) and 1) as information states. 

In the case that a particle with spin 0 decays into two electrons, observing the spin of one electron determines the spin of the second electron. Since this indicates that information transmits faster than light, it violates the relativistic theory Einstein-Podolsky-Rosen paradox) (Einstein et al. 1935). Bohr could not provide a counterargument to this. Later, this paradox was resolved by Bell s inequality, which limits the correlation of subsequent measurements of particles that have interacted and then separated on the local hidden-variable theory (Bell 1964), and Aspect s experiment, which proves the violation of this inequality (Aspect et al. 1982). 

J.S. Bell, On the Einstein-Podolsky-Rosen paradox. Physics 1 (1964) 195. 

---