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Moscow University Physics Bulletin

On the Violation of Causality in Quantum Experiments

Aleksandr V. Belinsky

Published May 1, 2018• 2 citations
Publisher

Abstract

Four experimental situations are analyzed from the viewpoint of fulfilling the causality principle: instantaneous collapse of the quantum state vector of a system of entangled particles, a quantum eraser, the quantum Zeno paradox, and light transformation by a nonlinear beam splitter. The last is a planar interface of two transparent dielectrics, at least one of which possesses Kerr nonlinearity, that is, its refractive index depends on the intensity of radiation that penetrates it. It has been shown that the causality principle in the first two cases can be violated only in the sense of the instantaneousness of the manifestation of the effect with respect to the cause. For a nonlinear beam splitter, in addition to the directly opposite predictions given by the quantum and classical theories of its description for the behavior of phase fluctuations of the radiation transformed by the splitter, the causality principle is violated in the most general sense: the effect of the following event on the previous one. The quantum Zeno paradox occupies an intermediate position of democratic involvement of the cause and effect in the general cascade of two subsequent events, i.e., the first event can prevent the second event, just as the second event can prevent the first one.

DOI
10.3103/s0027134918030037

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Four experimental situations are analyzed from the viewpoint of fulfilling the causality principle: instantaneous collapse of the quantum state vector of a system of entangled particles, a quantum eraser, the quantum Zeno paradox, and light transformation by a nonlinear beam splitter. The last is a planar interface of two transparent dielectrics, at least one of which possesses Kerr nonlinearity, that is, its refractive index depends on the intensity of radiation that penetrates it. It has been shown that the causality principle in the first two cases can be violated only in the sense of the instantaneousness of the manifestation of the effect with respect to the cause. For a nonlinear beam splitter, in addition to the directly opposite predictions given by the quantum and classical theories of its description for the behavior of phase fluctuations of the radiation transformed by the splitter, the causality principle is violated in the most general sense: the effect of the following event on the previous one. The quantum Zeno paradox occupies an intermediate position of democratic involvement of the cause and effect in the general cascade of two subsequent events, i.e., the first event can prevent the second event, just as the second event can prevent the first one.
The transformation of light by a nonlinear beamsplitter is considered. The beamsplitter is formed by a plane interface between two transparent dielectrics, at least one of which has a Kerr nonlinearity; i.e., its refractive index depends on the intensity of the penetrating radiation. It is shown that the interpretation of the result of calculation of quantum fields at the outputs from such a beamsplitter indicates a violation of the principle of causality in the sense that a subsequent event affects the previous one.
This is a review of a very interesting (in the authors' view) phenomenon — the operation of a nonlinear light beam splitter. The beam splitter is a flat interface between two transparent dielectrics, at least one of which exhibits Kerr nonlinearity, i.e., its refractive index depends on the transmitted radiation intensity. Interestingly, quantum and classical theories make directly opposite predictions about the phase fluctuations of the output radiation of this device. In classical theory, the phases remain unchanged; in quantum theory, the phases fluctuate in accordance with the amplitude–phase uncertainty relation. The origin of this difference is established at the fundamental level. A further remarkable point about this quantum paradox is that not only is the source beam split in two but one can also create conditions where the two split parts are respectively dominated by amplitude noise and phase noise, thus allowing the selection of photon fluctuations. Results of original studies are summarized and further developed.
A nonlinear beam splitter is shown to be an interesting object of investigation for the following reasons. First, the classical and quantum theories of its description give directly opposite behaviors of the phase fluctuations: according to the classical theory, the phase is unchanged; according to the quantum theory, the phase fluctuations increase or decrease, depending on the suppression or growth of amplitude fluctuations. The fundamental cause of these differences has been established. Second, the quantum fluctuations of the input mode can be separated into the amplitude and phase ones, so that the predominantly phase fluctuations are directed into one output mode, say, the reflected one, while the amplitude fluctuations are directed into the other (transmitted) mode.
Demonstrations of quantum entanglement which confirm the violation of Bell's inequality indicate that under certain conditions action at a distance is possible. This consequence seems to contradict the relativistic principle of causality, which asserts that an effect never precedes its cause, in any reference frame. By analyzing a numerical example of Bell's experiment with entangled pairs of photons, we show how observers in two inertial reference frames can disagree about the causality relation between two events. One observer claims that event 1 is the cause of event 2, while the other claims that event 1 is the result of event 2. The solution we suggest to the paradox is that in entangled systems, one can find pairs of "entangled events" which have symmetrical causality relations. Each of the events can serve as a cause or as an effect, depending on the frame of reference in which they are observed.
Demonstrations of quantum entanglement (QE), which confirm the violation of Bell’s inequality, indicate that under certain conditions action at a distance is possible. This consequence seems to contradict the relativistic principle of causality, which asserts that an effect never precedes its cause, in any reference frame. By analyzing a numerical example of Bell’s experiment with entangled pairs of photons, we show how observers in two inertial reference frames can disagree about the causality relation between two events. One observer claims that event 1 is the cause of event 2, while the other claims that event 1 is the result of event 2. The solution we suggest to the paradox is that in entangled systems, one can find pairs of “entangled events” which have symmetrical causality relations. Each of the events can serve as a cause or as an effect, depending on the frame of reference in which they are observed.
It has been found that a nonlinear beam splitter is an interesting object for investigation for the following reasons. First, the classical and quantum descriptions of this object give opposite results for the behavior of phase fluctuations: according to the classical theory, the phase remains unchanged, whereas the quantum theory predicts that phase fluctuations increase or decrease in correlation with a decrease or increase in amplitude fluctuations. Second, quantum fluctuations of the input mode can be separated into amplitude and phase fluctuations, so that phase fluctuations are directed predominantly into one output mode, say the reflected mode, whereas amplitude fluctuations are directed predominantly into the other (transmitted) mode.