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Moscow University Physics Bulletin

The “Paradox” of Karl Popper and Its Connection with the Heisenberg Uncertainty Principle and Quantum Ghost Images

Aleksandr V. Belinsky

Published Sep 1, 2018• 10 citations
Publisher

Abstract

Abstract An experiment to verify the adequacy of the Heisenberg uncertainty principle, as proposed by Karl Popper and implemented in practice, is considered. As in the Einstein–Podolsky–Rosen paradox, the quantum properties of an entangled pair of elementary particles are used. In this case, a ghost image of a narrow slit is actually formed. The results of the experiment, at first glance, support a violation of the uncertainty principle. However, analysis of the spatial resolution of the slit ghost image shows that this is not correct. A more correct description of diffraction in the case of spatially limited light beams, gives no violation of the uncertainty principle. The results can be also used to estimate the extreme quality of diffraction limited ghost images.

DOI
10.3103/s0027134918050053

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Abstract An experiment to verify the adequacy of the Heisenberg uncertainty principle, as proposed by Karl Popper and implemented in practice, is considered. As in the Einstein–Podolsky–Rosen paradox, the quantum properties of an entangled pair of elementary particles are used. In this case, a ghost image of a narrow slit is actually formed. The results of the experiment, at first glance, support a violation of the uncertainty principle. However, analysis of the spatial resolution of the slit ghost image shows that this is not correct. A more correct description of diffraction in the case of spatially limited light beams, gives no violation of the uncertainty principle. The results can be also used to estimate the extreme quality of diffraction limited ghost images.
Abstract In an effort to challenge the Copenhagen interpretation of quantum mechanics, Karl Popper proposed an experiment involving spatially separated entangled particles. In this experiment, one of the particles passes through a very narrow slit, and thereby its position becomes well-defined. This particle therefore diffracts into a large divergence angle; this effect can be understood as a consequence of the Heisenberg uncertainty principle. Popper further argued that its entangled partner would become comparably localized in position, and that, according to his understanding of the Copenhagen interpretation of quantum mechanics, the ‘mere knowledge’ of the position of this particle would cause it also to diffract into a large divergence angle. Popper recognized that such behavior could violate the principle of causality in that the slit could be removed and the partner particle would be expected to respond instantaneously. Popper thus concluded that it was most likely the case that, in an actual experiment, the partner photon would not undergo increased diffractive spreading and thus that the Copenhagen interpretation is incorrect. Here, we report and analyze the results of an implementation of Popper’s proposal. We find that the partner beam does not undergo increased diffractive spreading. Our work helps to clarify the issues raised in Popper’s proposal, and it provides further insight into the nature of entanglement and its relation to the uncertainty principle as applied to correlated particles.
One of the most surprising consequences of quantum mechanics is the entanglement of two or more distant particles. Even though there are still open questions regarding some fundamental issues related to entangled systems, quantum entanglement has started to play important roles in practical applications. Quantum imaging is one of the hot topics. Quantum imaging has many interesting features which are useful for different applications. For example, quantum imaging can be nonlocal, which is useful for secure two-dimensional information transfer. Quantum imaging can reach a much higher spatial resolution compared with classical imaging, even beyond the diffraction limit. This is useful for lithography and other microsystems fabrication technology. The super-resolution does not represent a violation of the uncertainty principle, it is just a quantum multi-particle phenomenon. Can quantum imaging be simulated classically? This question is closely related to the concerns of Einstein-Podolsky-Rosen of 1935. An attempted answer is given based on the analysis of a recent experiment of biphoton imaging-interference/diffraction.
An entangled pair of photons (1 and 2) are emitted to opposite directions. A narrow slit is placed in the path of photon 1 to provide precise knowledge of its position on the yyy axis and this also determines the precise yyy position of its twin, photon 2, due to quantum entanglement. Is photon 2 going to experience a greater uncertainty in momentum, i.e., a greater Δpy\Delta p_{y}Δpy​, due to the precise knowledge of its position yyy? The experimental data shows $\Delta y\Delta p_{y}<\hbar $ for photon 2. Can this recent realization of the historical thought experiment of Karl Popper signal a violation of the uncertainty principle?
An entangled pair of photon 1 and 2 are emitted in opposite directions along the positive and negative x -axis. A narrow slit is placed in the path of photon 1 which provides precise knowledge about its position along the y -axis and because of the quantum entanglement this in turn provides precise knowledge of the position y of its twin, photon 2. Does photon 2 experience a greater uncertainty in its momentum, i.e., a greater Δ p y , due to the precise knowledge of its position y ? This is the historical thought experiment of Sir Karl Popper which was aimed to undermine the Copenhagen interpretation in favor of a realistic viewpoint of quantum mechanics. Thispaper reports an experimental realization of the Popper’s experiment. One may not agree with Popper’s position on quantum mechanics; however, it calls for a correct understanding and interpretation of the experimental results. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Abstract One of the most surprising consequences of quantum mechanics is the entanglement of two or more distant particles. The “ghost” image experiment demonstrated the astonishing nonlocal behavior of an entangled photon pair. Even though we still have question in regard to fundamental issues of the entangled quantum systems, quantum entanglement has started to play important roles in practical applications. Quantum lithography is one of the hot topics. We have demonstrated a prove‐of‐principle quantum lithography experiment recently. The experimental results have beaten the classical diffraction limit by a factor of two. This is a quantum mechanical two‐photon phenomenon but not a violation of the uncertainty principle.
Quantum ghost diffraction harnesses quantum correlations to record diffraction or interference features using photons that have never interacted with the diffractive element. By designing an optical system in which the diffraction pattern can be produced by double slits of variable width either through a conventional diffraction scheme or a ghost diffraction scheme, we can explore the transition between the case where ghost diffraction behaves as conventional diffraction and the case where it does not. For conventional diffraction the angular extent increases as the scale of the diffracting object is reduced. By contrast, we show that no matter how small the scale of the diffracting object, the angular extent of the ghost diffraction is limited (by the transverse extent of the spatial correlations between beams). Our study is an experimental realisation of Popper's thought experiment on the validity of the Copenhagen interpretation of quantum mechanics. We discuss the implication of our results in this context and explain that it is compatible with, but not proof of, the Copenhagen interpretation.