A.P. Davydov – Ph.D.(Phys.-Math.), Associate Professor, Department of Applied and Theoretical Physics,  Institute of Natural Science and Standardization of Nosov Magnitogorsk State Technical University E-mail: ap-dav@yandex.ru

T.P. Zlydneva – Ph.D.(Pedagogic), Associate Professor, Department of Applied Mathematics and Informatics,

Institute of Natural Science and Standardization of Nosov Magnitogorsk State Technical University E-mail: pmi@magtu.ru, tapazl@yandex.ru

The necessity of the concept of the photon wave function in coordinate representation from the point of view of the correct interpretation of methods for obtaining coherent non-laser radiation is substantiated. Based on the simulation of the photon wave function in the coordinate representation, the Young’s interference experiment and its equivalent experiments with single photons in the MachZehnder interferometer are explained, which can significantly reduce the inconsistency of wave-particle duality of light. It is emphasized that the photon is not an elementary particle, but is a quasi-particle of the physical vacuum, the propagation of which forms a spin wave and can formally be described by a wave function in the coordinate representation. However, the wave function of quantum objects is not a physical object, therefore such concepts as its «propagation», «separation», as well as its «collapse» are, in fact, not legitimate. This creates a challenge for the quantum theory itself, and not only the need to find an appropriate interpretation for this theory, explaining, for example, the quantum nonlocality.

1. Landau L., Peierls R. Quantenelectrodynamik im Konfigurationsraum // Zeit. F. Phys. 1930. V. 62. P. 188−198.
2. Aspect A., Grangier P., Roger G. Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A new violation of Bell's inequalities // Phys. Rev. Lett. 1982. V. 49. № 2. P. 91−94.
3. Aspect A., Dalibard J., Roger G. Experimental test of Bell's inequalities using time-varying analyzers // Phys. Rev. Lett. 1982. V. 49. № 25. P. 1804−1807.
4. Weihs G., Jennewein T., Simon C., Weinfurter H., Zeilinger A. Violation of Bell’s inequality under strict Einstein locality conditions // Phys. Rev. Lett. 1998. V. 81. P. 5039−5043.
5. Scheidl T., Ursin R., Kofler J. et al. Violation of local realism with freedom of choice // Proceedings of the National Academy of Sciences. 2010. V. 107. № 46. P. 19708−19713.
6. Merali Z. Quantum 'spookiness' passes toughest test yet // Nature. 2015. V. 525. № 7567. P. 14−15.
7. Groblacher S., Paterek T., Kaltenbaek R. An experimental test of non-local realism // Nature. 2007. V. 446. P. 871−875. doi:10.1038/nature05677.
8. Romero J., Leach J., Jack B., Barnett S.M., Padgett M.J., Franke-Arnold S. Violation of Leggett inequalities in orbital angular momentum subspaces // New Journal of Physics. 2010. V. 12. P. 123007. DOI 10.1088/1367-2630/12/12/123007.
9. Leggett A.J., Garg A. Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks? // Phys. Rev. Lett. 1985. V. 54. № 9. P. 857−860.
10. Terexovich V.E'. Sushhestvovanie kvantovy'x ob''ektov. E'ksperimental'naya proverka metafizicheskix ustanovok // Metafizika. 2017. № 1(23). S. 104−112.
11. Grangier P., Roger G., Aspect A. Experimental evidence for a photon anti-correlation effect on a beamsplitter // Europhys. Lett. 1986. V. 1. № 4. P. 173−179.
12. Jacques V., Wu E., Grosshans F., Treussart F., Grangier P., Aspect A., Roch J.-F. Experimental realization of Wheeler's delayed choice experiment // Science. 2007. V. 315. P. 966−968. doi: 10.1126/science.1136303.
13. Peruzzo A., Shadbolt P., Brunner N., Popescu S., O'Brien J.L. A quantum delayed choice experiment // Science. 2012. V. 338. № 6107. P. 634−637. DOI 10.1126/science.1226719.
14. Ma X.-S., Kofler J., Qarry A., Tetik N. et al. Quantum erasure with causally disconnected choice // Proceedings of the National Academy of Sciences. 2013. V. 110. P. 1221−1226. DOI 10.1073/pnas.1213201110.
15. Manning A.G., Khakimov R.I., Dall R.G., Truscott A.G. Wheeler's delayed-choice gedanken experiment with a single atom // Nature Physics. 2015. V. 11. P. 539−542. DOI 10.1038/nphys3343.
16. Ma X., Kofler J., Zeilinger A. Delayed-choice gedanken experiments and their realizations // Rev. Mod. Phys. 2016. V. 88. № 1. P. 015005. doi:10.1103/RevModPhys.88.015005.
17. Vedovato F., Agnesi C., Schiavon M., Dequal D. et al. Extending Wheeler’s delayed-choice experiment to space // Science Advances. 2017. V. 3. № 10. P. e1701180. doi: 10.1126/sciadv.1701180.
18. Bialynicki-Birula I. On the Wave Function of the Photon // Acta Phys. Pol. A. 1994. V. 86. P. 97−116.
19. Mandel M., Wolf E. Optical coherence and quantum optics. Cambridge: Cambridge Univ. Press. 1995.
20. Sipe J.E. Photon wave functions // Physical Review A. 1995. V. 52. P. 1875−1883.
21. Davy'dov A.P. Kvantovaya mexanika fotona // Tezisy' dokladov XXXIII nauch. konf. prepod. MGPI «NAUKA I ShKOLA». Magnitogorsk: Izd-vo MGPI. 1995. S. 206−207.
22. Bialynicki-Birula I. The Photon Wave Function // Coherence and Quantum Optics VII. (Eberly J.H., Mandel L., & Wolf E., Ed.). NY: Plenum Press. 1996. P. 313−323.
23. Bialynicki-Birula I. Photon wave function // Progress in Optics. (Wolf E., Ed.). Amsterdam: North-Holland, Elsevier. 1996. V. XXXVI. P. 248−294.
24. Hawton M. Photon wave functions in a localized coordinate space basis // Phys. Rev. A. 1999. V. 59. № 5. P. 3223−3227.
25. Davy'dov A.P. Volnovaya funkcziya fotona v koordinatnom predstavlenii // Vestnik MaGU: Periodicheskij nauchny'j zhurnal. № 5. Magnitogorsk: Izd-vo Magnitogorskogo gos. un-ta. 2004. S. 235−243.
26. Cugnon J. The photon wave function // Open Journal of Microphysics. 2011. V. 1. № 3. P. 41−52. DOI 10.4236/ojm.2011.13008.
27. Saari P. Photon localization revisited // Quantum Optics and Laser Experiments. (S. Lyagushyn, Ed.). Croatia: InTech – Open Access Publisher. 2012. P. 49−66.
28. Davy'dov A.P. Kvantovaya mexanika fotona: volnovaya funkcziya v koordinatnom predstavlenii // E'lektromagnitny'e volny' i e'lektronny'e sistemy'. 2015. T. 20. № 5. S. 43−61.
29. Davy'dov A.P., Zly'dneva T.P. O relyativistskoj invariantnosti uravneniya neprery'vnosti v kvantovoj mexanike fotona // Mezhdunar. nauchno-issledovatel'skij zhurnal. 2016. № 4 (46). Ch. 6. S. 134−137. DOI 10.18454/IRJ.2016.46.145.
30. Davy'dov A.P., Zly'dneva T.P. O volnovoj funkczii fotona v koordinatnom i impul'snom predstavleniyax // Mezhdunar. nauchnoissledovatel'skij zhurnal. 2016. № 11 (53). Ch. 4. S. 152−155. DOI 10.18454/IRJ.2016.53.104.
31. Davy'dov A.P. Volnovaya funkcziya fotona v koordinatnom predstavlenii: monografiya. Magnitogorsk: Izd-vo Magnitogorskogo gos. texn. un-ta im. G.I. Nosova. 2015. 180 s.
32. Davy'dov A.P. E'volyucziya v prostranstve i vo vremeni volnovogo paketa fotona femtosekundnogo izlucheniya s tochki zreniya kvantovoj mexaniki // Tezisy' dokl. XLIII vnutrivuz. nauch. konf. prepod. MaGU «Sovremenny'e problemy' nauki i obrazovaniya». Magnitogorsk: Izd-vo Magnitogorskogo gos. un-ta. 2005. S. 269−270.
33. Davy'dov A.P. Modelirovanie rasprostraneniya v trexmernom prostranstve volnovogo paketa fotona // Materialy' 73-j mezhdunar. nauchno-texn. konf. «Aktual'ny'e problemy' sovremennoj nauki, texniki i obrazovaniya». Magnitogorsk: Izd-vo Magnitogorskogo gos. texn. un-ta im. G.I. Nosova. 2015. T. 3. S. 133−137.
34. Davy'dov A.P., Zly'dneva T.P. Odnofotonny'j podxod k modelirovaniyu korotkoimpul'snogo lazernogo izlucheniya // Vestnik nauki i obrazovaniya Severa-Zapada Rossii. 2015. T. 1. № 4. S. 97−111.
35. Davydov A., Zlydneva T. Modeling of short-pulse laser radiation in terms of photon wave function in coordinate representation // Instrumentation engineering, electronics and telecommunications – 2015: Paper book of the International Forum IEET-2015. P. 51−63. – Izhevsk: Publishing House of Kalashnikov ISTU. 2016. 208 p. 7 MB.
36. Davydov A.P., Zlydneva T.P. The Young’s interference experiment in the light of the single-photon modeling of the laser radiation // Information Technologies in Science, Management, Social Sphere and Medicine (ITSMSSM 2016). 2016. P. 208−215. DOI 10.2991/itsmssm-16.2016.100.
37. Davy'dov A.P., Zly'dneva T.P. O snizhenii skorosti svobodny'x fotonov pri modelirovanii ix rasprostraneniya v prostranstve s pomoshh'yu volnovoj funkczii v koordinatnom predstavlenii // Trudy' XIII Mezhdunar. nauchno-texnich. konf. «APE'P – 2016». Novosibirsk. 2016. T. 8. S. 50−57.
38. Davydov A.P., Zlydneva T.P. On the reduction of free photons speed in modeling of their propagation in space by the wave function in coordinate representation // Proceedings of 13th International scientific-technical conference on actual problems of electronic instrument engineering (APEIE). Novosibirsk. 2016. V. 1. Part. 2. P. 233−240. DOI 10.1109/APEIE.2016.7806458.
39. Giovannini D., Romero J., Potoček V. et al. Spatially structured photons that travel in free space slower than the speed of light // Science. 2015. V. 347. № 6224. P. 857−860. DOI 10.1126/science.aaa3035.
40. Davy'dov A.P., Zly'dneva T.P. Ob interferenczii sveta s tochki zreniya volnovoj funkczii fotona v koordinatnom predstavlenii // Materialy' 75-j Mezhdunar. nauchno-texn. konf. «Aktual'ny'e problemy' sovremennoj nauki, texniki i obrazovaniya». Magnitogorsk: Izd-vo MGTU im. G.I. Nosova. 2017. T. 2. S. 109−112.
41. Davy'dov A.P., Zly'dneva T.P. Modelirovanie i analiz volnovoj funkczii fotona pri kvantovo-mexanicheskom ob''yasnenii opy'ta Yunga // Materialy' I Vseros. nauch. konf. «Informaczionny'e texnologii v modelirovanii i upravlenii: podxody', metody', resheniya». Tol'yatti. 2017. Ch.1. S. 66−74. URL = https://sites.google.com/view/itmutgu-2017/sb.
42. Davydov A.P., Zlydneva T.P. The Modeling of the Young's Interference Experiment in terms of Single-photon wave function in the coordinate representation // Proc. of the IV International research conf. «Information technologies in Science, Management, Social sphere and Medicine». 2017. P. 257−265. DOI 10.2991/itsmssm-17.2017.54.
43. Davydov A.P., Zlydneva T.P. Space-Time Probability Density of Detection of a Photon in Laser Beam of the Femtosecond Range // Proceedings of 14thInternational scientific-technical conference on actual problems of electronic instrument engineering (APEIE). Novosibirsk. 2018. V. 1. P. 4. P. 58−69. URL = https://cloud.mail.ru/public/4Tsd/NymmFx5wP.
44. Davy'dov A.P. O postroenii speczial'noj teorii otnositel'nosti (STO) iz simmetrii prostranstva i vremeni bez postulatov STO // E'lektromagnitny'e volny' i e'lektronny'e sistemy'. 2003. T. 8. № 1. S. 49−58.
45. Davy'dov A.P. Kurs lekczij po kvantovoj mexanike. Matematicheskij apparat kvantovoj mexaniki: Ucheb. posobie. Magnitogorsk: Izd-vo Magnitogorskogo gos. texn. un-ta im. G.I. Nosova. 2014. 188 s.
46. Davy'dov A.P. Foton kak kvazichasticza pri vozbuzhdenii spinovoj volny' v fizicheskom vakuume na plankovskix rasstoyaniyax // Tezisy' dokl. XLIV vnutrivuz. nauch. konf. prepod. MaGU «Sovremenny'e problemy' nauki i obrazovaniya». Magnitogorsk: MaGU. 2006. S. 174.
47. Davy'dov A.P. Novy'e kvantovy'e ob''ekty' kosmomikrofiziki – e'lementarny'e bessingulyarny'e cherny'e dy'ry' – kak sledstvie KE'D i OTO // Sb. nauch. trudov «Fundamental'ny'e i prikladny'e issledovaniya». Magnitogorsk: Izd-vo MGPI. 1997. S. 22−41.
48. Davy'dov A.P. Vozmozhnost' kvantovy'x bessingulyarny'x cherny'x dy'r s plankovskimi parametrami i e'kstremal'noj metrikoj v fizike i kosmologii // E'lektromagnitny'e volny' i e'lektronny'e sistemy'. 1998. T. 3. № 2. S. 67−78.
49. Davy'dov A.P.,  Logunova A.A. E'kstremal'ny'e maksimony', struktura fundamental'ny'x chasticz, KE'D, OTO i RTG // E'lektromagnitny'e volny' i e'lektronny'e sistemy'. 2001. T. 6. № 5. S. 4−13.