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Fortschritte der Physik

Experimental Realization of Popper's Experiment – Violation of The Uncertainty Principle?

Yanhua H. Shih, Yoon-Ho Kim

Published May 1, 2000• 3 citations

Abstract

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 $y$ axis and this also determines the precise $y$ 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 $\Delta p_{y}$, due to the precise knowledge of its position $y$? 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?

DOI: 10.1002/(sici)1521-3978(200005)48:5/7<463::aid-prop463>3.3.co;2-b

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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

y

axis and this also determines the precise

y

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

\Delta p_{y}

, due to the precise knowledge of its position

y

? 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 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

y

axis and this also determines the precise

y

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

Δp_{y}

, due to the precise knowledge of its position

y

? The experimental data shows $ΔyΔp_{y}

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.

Summary form only given. In early 1930's, Karl Popper, a metaphysical realist, proposed a thought experiment to support his realistic interpretation of quantum mechanics, which shared the same goal of the EPR gedankenexperiment. Based on the same EPR two-particle entangled state, Popper asked: if the precise position of particle 2 is known due to the precise measurement of the position for its entangled twin particle 1, does particle 2 experience a greater uncertainty in its momentum? This question has been ignored for many years. One may not like Popper's philosophy of quantum mechanics; however, his question is closely related to an important problem in recent hot applications: what one can predict for the remaining parts of an entangled state if one of the subsystems is measured alone? We have realized Popper's experiment with the use of entangled two-photon source of spontaneous parametric down conversion. We conclude from this experiment: in an entangled two-particle system, the precise knowledge of the position of a particle, which is determined by the two-particle entanglement, does not necessarily produce an uncertainty in its momentum.

Uncertainty, being perhaps the most basic principle of quantum mechanics, distinguishes the world of quantum phenomena from the realm of classical physics. Quantum entanglement, being perhaps the most surprising consequence of quantum mechanics, on the other hand apparently suggests paradoxes relating to or violations of the quantum mechanical uncertainty principle in some experimental situations. Popper's thought experiment is an example. We wish to report a recent realization of Popper's experiment. The experimental data show that there appears to be a violation of the uncertainty principle. This is, however as we shall argue in this paper, only an illusion provided that we take the teachings of quantum mechanics seriously.

The realization of Karl Popper's experiment by Shih and Kim (published 1999) produced the result that Popper hoped for: no ``action at a distance'' on one photon of an entangled pair when a measurement is made on the other photon. This experimental result is interpretable in local realistic terms: each photon has a definite position and transverse momentum most of the time; the position measurement on one photon (localization in a slit) disturbs the transverse momentum of that photon in a non-predictable way in accordance with the uncertainty principle; however, there is no effect on the other photon (the photon that is not in a slit) no action at a distance. The position measurement (localization within a slit) of the one photon destroys the coherence (entanglement) between the photons; i.e. decoherence occurs. This can be understood physically as an electromagnetic interaction between the photon in the slit and the electrons of the atoms in the surface of the solid that forms the slit.

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.