Einstein–Podolsky–Rosen paradox
The Einstein–Podolsky–Rosen (EPR) paradox is a thought experiment proposed by physicists Albert Einstein, Boris Podolsky and Nathan Rosen, which argues that the description of physical reality provided by quantum mechanics is incomplete.They argued that no action taken on the first particle could instantaneously affect the other, since this would involve information being transmitted faster than light, which is impossible according to the theory of relativity.Einstein, Podolsky, and Rosen therefore concluded that quantum theory does not provide a complete description of reality.[2] The term "Einstein–Podolsky–Rosen paradox" or "EPR" arose from a paper written in 1934 after Einstein joined the Institute for Advanced Study, having fled the rise of Nazi Germany.As Manjit Kumar writes, "EPR argued that they had proved that ... [particle] B can have simultaneously exact values of position and momentum.The EPR paper says: "We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.They postulate that these elements of reality are, in modern terminology, local, in the sense that each belongs to a certain point in spacetime.Each element may, again in modern terminology, only be influenced by events that are located in the backward light cone of its point in spacetime (i.e. in the past).Einstein later expressed to Erwin Schrödinger that, "it did not come out as well as I had originally wanted; rather, the essential thing was, so to speak, smothered by the formalism.[9] Shortly before the EPR paper appeared in the Physical Review, The New York Times ran a news story about it, under the headline "Einstein Attacks Quantum Theory".[10] The story, which quoted Podolsky, irritated Einstein, who wrote to the Times, "Any information upon which the article 'Einstein Attacks Quantum Theory' in your issue of May 4 is based was given to you without authority."[11]: 189 The Times story also sought out comment from physicist Edward Condon, who said, "Of course, a great deal of the argument hinges on just what meaning is to be attached to the word 'reality' in physics."[11]: 190 The publication of the paper prompted a response by Niels Bohr, which he published in the same journal (Physical Review), in the same year, using the same title.Bohr concluded that EPR's "arguments do not justify their conclusion that the quantum description turns out to be essentially incomplete."[13] Einstein struggled unsuccessfully for the rest of his life to find a theory that could better comply with his idea of locality.It seems as if information has propagated (faster than light) from Alice's apparatus to make Bob's positron assume a definite spin in the appropriate axis.On the other hand, David Bohm had recently developed the first successful hidden-variable theory, but it had a grossly nonlocal character.[23][24] Bell set out to investigate whether it was indeed possible to solve the nonlocality problem with hidden variables, and found out that first, the correlations shown in both EPR's and Bohm's versions of the paradox could indeed be explained in a local way with hidden variables, and second, that the correlations shown in his own variant of the paradox couldn't be explained by any local hidden-variable theory.To understand the first result, consider the following toy hidden-variable theory introduced later by J.J. Sakurai:[25]: 239–240 in it, quantum spin-singlet states emitted by the source are actually approximate descriptions for "true" physical states possessing definite values for the z-spin and x-spin.Bell showed, however, that such models can only reproduce the singlet correlations when Alice and Bob make measurements on the same axis or on perpendicular axes.As soon as other angles between their axes are allowed, local hidden-variable theories become unable to reproduce the quantum mechanical correlations.The present view of the situation is that quantum mechanics flatly contradicts Einstein's philosophical postulate that any acceptable physical theory must fulfill "local realism".[27][28] Inspired by Schrödinger's treatment of the EPR paradox back in 1935,[29][30] Howard M. Wiseman et al. formalised it in 2007 as the phenomenon of quantum steering.EPR describe the principle of locality as asserting that physical processes occurring at one place should have no immediate effect on the elements of reality at another location.[20]: 427–428 [32] Causality is preserved because there is no way for Alice to transmit messages (i.e., information) to Bob by manipulating her measurement axis.Furthermore, Bob is able to perform his measurement only once: there is a fundamental property of quantum mechanics, the no-cloning theorem, which makes it impossible for him to make an arbitrary number of copies of the electron he receives, perform a spin measurement on each, and look at the statistical distribution of the results.Neither the EPR paradox nor any quantum experiment demonstrates that superluminal signaling is possible; however, the principle of locality appeals powerfully to physical intuition, and Einstein, Podolsky and Rosen were unwilling to abandon it.[34] Bohm's variant of the EPR paradox can be expressed mathematically using the quantum mechanical formulation of spin.The operators corresponding to the spin along the x, y, and z direction, denoted Sx, Sy, and Sz respectively, can be represented using the Pauli matrices:[25]: 9The right hand side of the equations show that the measurement of Sx on Bob's positron will return, in both cases, +x or −x with probability 1/2 each.
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