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.
REFERENCES
W. Heisenberg, Z. Phys. 43, 172 (1927).
A. V. Belinsky and V. B. Lapshin, Uch. Zap. Fiz. Fak. Mosk. Gos. Univ., No. 4, 164001 (2016).
A. V. Belinsky and V. B. Lapshin, Phys.-Usp. 60, 325 (2017).
A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
D. N. Klyshko, JETP Lett. 6, 23 (1967).
S. L. Akhmanov, V. V. Fadeev, R. V. Khokhlov, and O. N. Chunaev, JETP Lett. 6, 85 (1967).
D. N. Klyshko, A. N. Penin, and B. F. Polkovnikov, JETP Lett. 11, 5 (1970).
A. S. Chirkin, M. Yu. Saigin, and I. V. Shutov, J. Russ. Laser Res. 29, 336 (2008).
A. V. Belinskii and D. N. Klyshko, J. Exp. Theor. Phys. 78, 259 (1994).
D. N. Klyshko, J. Exp. Theor. Phys. 67, 1131 (1988).
Quantum Imaging, Ed. by M. I. Kolobov (Springer, New York, 2007).
K. Popper, Naturwissenschaften 22, 807 (1934).
K. Popper, Quantum Theory and the Schism in Physics, Ed. by W.W. Bartley III (Rowan and Littlefield, 1982).
Y. H. Kim and Y. Shih, Found. Phys. 29, 12 (1999).
A. Sudbery, Philos. Sci. 52, 170 (1985).
T. Qureshi, Am. J. Phys. 73, 511 (2005).
A. J. Short, Found. Phys. Lett. 14, 275 (2001).
T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Ru-bin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. A 53, 2804 (1996).
A. V. Belinsky, Vestn. Mosk. Univ., Ser. 3: Fiz. Astron., No. 3, 34 (1999).
E. V. Kovlakov, I. B. Bobrov, S. S. Straupe, and S. P. Kulik, Phys. Rev. Lett. 118, 030503 (2017).
S. B. Gurevich, V. V. Konstantinov, V. K. Sokolov, and D. F. Chernykh, Holographic Techniques of Data Transmission and Processing (Sov. Radio, Moscow, 1978).
S. A. Rodionov, Basic Optics (GITMO, St. Petersburg, 2000).
E. Kennard, Z. Phys. 44, 326 (1927).
H. Weyl, Gruppentheorie und Quantenmechanik (Hirzel, Leipzig, 1928).
E. Schrödinger, Phys.-Math. Kl. 14, 296 (1930).
H. P. Robertson, Phys. Rev. 34, 163 (1929).
L. A. Rozema, A. Darabi, D. H. Mahler, et al., Phys. Rev. Lett. 109, 100404 (2012).
M. Ozawa, Phys. Rev. A 67, 042105 (2003).
A. P. Lund and H. M. Wiseman, New J. Phys. 12, 093011 (2010).
R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, London, 1963), Vol. 1.
A. V. Belinsky and D. N. Klyshko, Laser Phys. 6, 1082 (1996).
A. V. Belinskii, Phys.-Usp. 46, 877 (2003).
A. V. Belinsky, Quantum Measurements (BINOM, Moscow, 2015).
A. Peres and D. R. Termo, Rev. Mod. Phys. 76, 93 (2004).
ACKNOWLEDGMENTS
I am grateful to D.N. Puhov for his help. This work was carried out with the support of the Russian Foundation for Basic Research (grant no. 18-01-00598).
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Translated by N. Petrov
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Belinsky, A.V. The “Paradox” of Karl Popper and Its Connection with the Heisenberg Uncertainty Principle and Quantum Ghost Images. Moscow Univ. Phys. 73, 447–456 (2018). https://doi.org/10.3103/S0027134918050053
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DOI: https://doi.org/10.3103/S0027134918050053