CORE Metadata, citation and similar papers at core.ac.uk Provided by CERN Document Server Experimental realization of Popper's Experiment: Violation of the Uncertainty Principle? Yoon-Ho Kim∗ and Yanhua Shihy Department of Physics University of Maryland, Baltimore County Baltimore, Maryland 21250, U.S.A. (Revised 19 October 1999, to appear in Foundations of Physics) from EPR’s gedankenexperiment, the physics community An entangled pair of photons (1 and 2) are emitted to remained ignorant of Popper’s experiment. opposite directions. A narrow slit is placed in the path of In this paper we wish to report a recent realization photon 1 to provide the precise knowledge of its position on of Popper’s thought experiment. Indeed, it is astonish- the -axis and this also determines the precise -position of y y ing to see that the experimental results agree with Pop- its twin, photon 2, due to quantum entanglement. Is photon 2 per’s prediction. Through quantum entanglement one going to experience a greater uncertainty in momentum, that may learn the precise knowledge of a photon’s position is, a greater ∆p because of the precise knowledge of its posi- y and would therefore expect a greater uncertainty in its tion y? The experimental data show ∆y∆py <hfor photon 2. Can this recent realization of the thought experiment of momentum under the usual Copenhagen interpretation Karl Popper signal a violation of the uncertainty principle? of the uncertainty relations. However, the measurement shows that the momentum does not experience a corre- sponding increase of uncertainty. Is this a violation of the uncertainty principle? As a matter of fact, one should not be surprised with the experimental result and should not consider this ques- I. INTRODUCTION tion as a new challenge. Similar results have been demon- strated in EPR type of experiments and the same ques- Uncertainty, one of the basic principles of quantum me- tion has been asked in EPR’s 1935 paper [2]. In the past chanics, distinguishes the world of quantum phenomena decades, we have been worrying about problems concern- from the realm of classical physics. Quantum mechani- ing causality, locality, and reality more than the “crux” cally, one can never expect to measure both the precise of the EPR paradox itself: the uncertainty principle. position and momentum of a particle at the same time. It is prohibited. We say that the quantum observables “position” and “momentum” are “complementary” be- II. POPPER'S EXPERIMENT cause the precise knowledge of the position (momentum) implies that all possible outcomes of measuring the mo- Similar to the EPR’s gedankenexperiment, Popper’s ex- mentum (position) are equally probable. periment is also based on the feature of two-particle en- Karl Popper, being a “metaphysical realist”, however tanglement. Quantum mechanics allows the entangled took a different point of view. In his opinion, the quan- EPR-type state, a state in which if the position or mo- tum formalism could and should be interpreted realisti- mentum of particle 1 is known the corresponding ob- cally: a particle must have precise position and momen- servable of its twin, particle 2, is then 100% determined tum, which shares the same view as Einstein. In this re- [2]. Popper’s original thought experiment is schemati- gard he invented a thought experiment in the early 1930’s cally shown in Fig. 1. A point source S, positronium as which aimed to support the realistic interpretation of Popper suggests, is placed at the center of the experimen- quantum mechanics and undermine the Copenhagen or- tal arrangement from which entangled pairs of particles thodoxy [1]. What Popper intends to show in his thought 1 and 2 are emitted in opposite directions along the re- experiment is that a particle can have both precise posi- spective positive and negative x-axes towards two screens tion and momentum at the same time through the corre- A and B. There are slits on both screens parallel to the lation measurement of an entangled two-particle system. y-axis and the slits may be adjusted by varying their This bears striking similarity to what EPR gedanken- widths ∆y. Beyond the slits on each side stand an array experiment of 1935 seeks to conclude [2]. But different of Geiger counters for the coincidence measurements of the particle pairs as shown in the figure. The entangled pair could be emitted to any direction in 4π solid angles from the point source. However, if particle 1 is detected ∗Email: [email protected] in a certain direction then particle 2 is known to be in the †Email: [email protected] opposite direction due to the momentum conservation of the quantum pair. 1 First, let us imagine the case in which slits A and B are width of its “diffraction pattern” at a certain distance adjusted both very narrowly. In this circumstance, coun- from “screen” B. This is obtained by recording coinci- ters should come into play which are higher up and lower dences between detectors D1 and D2 while scanning de- down as viewed from the slits. The firing of these coun- tector D2 along its y-axis which is behind “screen” B at a ters is indicative of the greater ∆py due to the smaller ∆y certain distance. Instead of a battery of Geiger counters, for each particle. There seems to be no disagreement in in our experiment only two photon counting detectors D1 this situation between both the Copenhagen school and and D2 placed behind the respective slits A and B are Popper and both sides can provide a reasonable explana- used for the coincidence detection. Both D1 and D2 are tion according to their own philosophical beliefs. driven by step motors and so can be scanned along their Next, suppose we keep the slit at A very narrow and y-axes. ∆y∆py of “photon 2” is then readily calculated leave the slit at B wide open. The main purpose of and compared with h [6]. the narrow slit A is to provide the precise knowledge The use of a “point source” in the original proposal has of the position y of particle 1 and this subsequently de- been much criticized and considered as the fundamen- termines the precise position of its twin (particle 2) on tal mistake Popper made [7] [8]. The major objection is side B through quantum entanglement. Now, asks Pop- that a point source can never produce a pair of entangled per, in the absence of the physical interaction with an particles which preserves two-particle momentum conser- actual slit, does particle 2 experience a greater uncer- vation. However, notice that a “point source” is not a tainty in ∆py due to the precise knowledge of its position? necessary requirement for Popper’s experiment. What is Based on his “statistical-scatter” theory, Popper provides required is the position entanglement of the two-particle a straightforward prediction: particle 2 must not experi- system: if the position of particle 1 is precisely known, ence a greater ∆py unless a real physical narrow slit B is the position of particle 2 is also 100% determined. So applied. However, if Popper’s conjecture is correct, this one can learn the precise knowledge of a particle’s posi- would imply the product of ∆y and ∆py of particle 2 tion through quantum entanglement. Quantum mechan- could be smaller than h (∆y∆py <h). This may pose a ics does allow the position entanglement for an entangled serious difficulty for the Copenhagen camp and perhaps system (EPR state) and there are certain practical mech- for many of us. On the other hand, if particle 2 going anisms, such as that the “ghost-image” effect shown in to the right does scatter like its twin which has passed our experiment, that can be used for its realization. though slit A, even though slit B is wide open, we are The schematic experimental setup is shown in Fig.4 then confronted with an apparent action-at-a-distance! with detailed indications of the various distances. A CW Argon ion laser line of λp = 351:1nm is used to pump a 3mm long beta barium borate (BBO) crystal III. REALIZATION OF POPPER'S EXPERIMENT for type-II SPDC [10] to generate an orthogonally polar- ized signal-idler photon pair. The laser beam is about We have realized Popper’s experiment with the use of 3mm in diameter with a diffraction limited divergence. the entangled two-photon source of spontaneous para- It is important not to focus the pump beam so that the metric down conversion (SPDC) [3] [4]. In order to phase-matching condition, ks + ki = kp, is well rein- clearly demonstrate all aspects of the historical and mod- forced in the SPDC process [4], where kj (j = s; i; p) ern experimental concerns in a practical manner, Pop- is the wavevectors of the signal (s), idler (i), and pump per’s original design is slightly modified as shown in (p) respectively. The collinear signal-idler beams, with Fig. 2. The two-photon source is a CW Argon ion λs = λi = 702:2nm =2λp are separated from the pump laser pumped SPDC which provides a two-photon entan- beam by a fused quartz dispersion prism, and then split gled state that preserves momentum conservation for the by a polarization beam splitter PBS. The signal beam signal-idler photon pair in the SPDC process. By taking (“photon 1”) passes through the converging lens LS with advantage of the nature of entanglement of the signal- a 500mm focal length and a 25mm diameter. A 0:16mm idler pair (also labeled “photon 1” and “photon 2”) one slit is placed at location A which is 1000mm (= 2f)be- could make a “ghost image” of slit A at “screen” B, see hind the lens LS.