Epr (Einstein, Podolsky, Rosen) Paradox
The EPR paradox was proposed by physicists Albert Einstein, Boris Podolsky, and Nathan Rosen (EPR) in a 1935 Physical Review article titled "Can Quantum Mechanical Description of Physical RealityBe Considered Complete?" The EPR paradox was intended to demonstrate the inadequacy of the prevailing interpretation of quantum mechanics, specifically in regard to the relationships between distant particles predicted by quantum nonlocality. The paradox argues for incompleteness or hidden variables in the quantum mechanical description of nature.
One of the foundations of quantum theory is the uncertainty principle that places limits on the accuracy of measurements on the atomic scale. According to the uncertainty principle, it is impossible to measure two complementary variables such as the momentum and the position of a particle with exact precision. Likewise, the components of a particle's spin cannot be all known simultaneously.
If, for example, two particles have some correlated property, such as momentum, spin, or polarization state, such that they have opposite values of that property (in the case of spin this could result from a spin 0 particle decaying into two spin 1/2 particles (one with +1/2 spin the other with -1/2 spin). The particles, designated A and B, are then allowed to travel a long distance from each other in order to rule out the possibility of an exchange or signal traveling between them during the course of later measurements. A measurement performed on A to determine its z component spin, would fix A's z component spin at the expense of uncertainty in other quantum properties. According to EPR, if particle B were separated from A by light years of distance, according to special relativity theory (wherein faster-than-light travel is not possible), the measurement of A cannot instantly affect the measurement of B.
The paradox is established because the particles are also bound by the law of conservation of angular momentum. Thus if the measurement on A finds its z component spin to be +1/2, then the z component of B's spin must, at that instant be -1/2 (i.e., if they together originally had zero spin, then their spins must still add up to zero). We could now choose to measure some other component of the spin of particle B. If a measurement of the x component is performed, then since the z component is already known through the correlation of the spins, the result is that we know values for both the x and z components of the spin simultaneously. This extra information would contradict the limitations of the uncertainty principle.
One of the motivations of the EPR experiment was the desire of the proponents to demonstrate the existence of "objective reality"; that is, that a physical system contains more information than is specified by the Schrödinger equation, which gives probabilities for finding a particle in a given state but does not simultaneously define all of the physical parameters of the system. According to the EPR proponents, a system has at all times real values for momentum, position, spin, and all other parameters regardless of whether they are measured or not, a belief Einstein summed up in his remark that "God does not play dice." Their explanation of the fact that the EPR experiment provides more information about a system than is strictly allowed by the uncertainty principle is that the information was there all along, and that all of the components of spin were defined from the beginning of the experiment. Theories of this sort are sometimes referred to as hidden-variable theories, because they suggest that there may be parameters that completely define the state of a particle or system, but that are not necessarily accessible to experiment due to the fact that measurement disturbs the system. Such theories were countered in 1964 by Bell's theorem, which placed restrictions on the types of hidden-variable theories that could reproduce the results of quantum mechanics.
Subsequent tests, such as the French physicist Alain Aspect experiment in 1982, have verified Bell's theorem and unfavorably resolved the EPR paradox against its proponents. By studying quantum properties of paired photons shot away from each other, Aspect demonstrated that the only way a hidden-variable theory can be valid is if the principle of locality is abandoned and it is assumed that the two particles, A and B, can interact instantaneously no matter how far separated they are. As this would violate the speed-of-light velocity limit of special relativity, it casts severe doubt on the validity of the concept of objective reality at the atomic level.
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