{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:07:18Z","timestamp":1760148438298,"version":"build-2065373602"},"reference-count":71,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T00:00:00Z","timestamp":1682899200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Higher Education of the Russian Federation","award":["075-15-2022-311"],"award-info":[{"award-number":["075-15-2022-311"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>It is known that the fundamental Lifshitz theory, which is based on the first principles of thermal quantum field theory, experiences difficulties when compared with precise measurements of the Casimir force. We analyzed the nonconventional fit of the response functions of many materials along the imaginary frequency axis to the empirical model of \u201cmodified\u201d oscillators, which was recently proposed in the literature. According to our results, this model is unacceptable because at high frequencies it leads to the asymptotic behavior of the response functions, which is in contradiction with that following from the fundamental physical principles. We calculated the Casimir interaction in the configurations of several precise experiments using the Lifshitz theory and the response functions to the quantized electromagnetic field expressed in terms of modified oscillators and demonstrated that the obtained results are excluded by the measurement data. This invalidated a claim made in the literature that the Casimir\u2013van der Waals forces calculated using these response functions are in remarkable agreement with the experimental values. Possible reasons for a disagreement between experiment and theory are discussed, and the way to improve the situation is indicated.<\/jats:p>","DOI":"10.3390\/sym15051011","type":"journal-article","created":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T12:02:31Z","timestamp":1682942551000},"page":"1011","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Comparison of the Lifshitz Theory Using the Nonconventional Fit of Response Functions with Precise Measurements of the Casimir Force"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0495-5907","authenticated-orcid":false,"given":"Galina L.","family":"Klimchitskaya","sequence":"first","affiliation":[{"name":"Central Astronomical Observatory at Pulkovo of the Russian Academy of Sciences, 196140 Saint Petersburg, Russia"},{"name":"Peter the Great Saint Petersburg Polytechnic University, 195251 Saint Petersburg, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8560-998X","authenticated-orcid":false,"given":"Vladimir M.","family":"Mostepanenko","sequence":"additional","affiliation":[{"name":"Central Astronomical Observatory at Pulkovo of the Russian Academy of Sciences, 196140 Saint Petersburg, Russia"},{"name":"Peter the Great Saint Petersburg Polytechnic University, 195251 Saint Petersburg, Russia"},{"name":"Kazan Federal University, 420008 Kazan, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,1]]},"reference":[{"unstructured":"Mahanty, J., and Ninham, B.W. (1976). Dispersion Forces, Academic Press.","key":"ref_1"},{"doi-asserted-by":"crossref","unstructured":"Milonni, P.W. (1994). The Quantum Vacuum. An Introduction to Quantum Electrodynamics, Academic Press.","key":"ref_2","DOI":"10.1016\/B978-0-08-057149-2.50014-X"},{"doi-asserted-by":"crossref","unstructured":"Mostepanenko, V.M., and Trunov, N.N. (1997). The Casimir Effect and Its Applications, Clarendon Press.","key":"ref_3","DOI":"10.1093\/oso\/9780198539988.001.0001"},{"doi-asserted-by":"crossref","unstructured":"Milton, K.A. (2001). The Casimir Effect: Physical Manifestations of Zero-Point Energy, World Scientific.","key":"ref_4","DOI":"10.1142\/4505"},{"doi-asserted-by":"crossref","unstructured":"Parsegian, V.A. (2005). Van der Waals Forces: A Handbook for Biologists, Chemists, Engineers, and Physicists, Cambridge University Press.","key":"ref_5","DOI":"10.1017\/CBO9780511614606"},{"doi-asserted-by":"crossref","unstructured":"Buhmann, S.Y. (2012). Disperson Forces, Springer. Volumes 1 and 2.","key":"ref_6","DOI":"10.1007\/978-3-642-32466-6_1"},{"unstructured":"Langbein, D. (2013). Theory of Van der Waals Attraction, Springer.","key":"ref_7"},{"unstructured":"Bordag, M., Klimchitskaya, G.L., Mohideen, U., and Mostepanenko, V.M. (2015). Advances in the Casimir Effect, Oxford University Press.","key":"ref_8"},{"doi-asserted-by":"crossref","unstructured":"Sernelius, B.E. (2018). Fundamentals of van der Waals and Casimir Interactions, Springer.","key":"ref_9","DOI":"10.1007\/978-3-319-99831-2"},{"unstructured":"Lifshitz, E.M., and Hamermesh, M. (1992). Perspectives in Theoretical Physics, Newnes.","key":"ref_10"},{"unstructured":"Lifshitz, E.M., and Pitaevskii, L.P. (1980). Statistical Physics, Pergamon. Pt II.","key":"ref_11"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1827","DOI":"10.1103\/RevModPhys.81.1827","article-title":"The Casimir force between real materials: Experiment and theory","volume":"81","author":"Klimchitskaya","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1038\/nphoton.2011.39","article-title":"The Casimir effect in microstructured geometries","volume":"5","author":"Rodrigues","year":"2011","journal-title":"Nat. Photon."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1142\/S0217979211057736","article-title":"Control of the Casimir force using semiconductor test bodies","volume":"25","author":"Klimchitskaya","year":"2011","journal-title":"Int. J. Mod. Phys. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"045003","DOI":"10.1103\/RevModPhys.88.045003","article-title":"Materials perspective on Casimir and van der Waals interactions","volume":"88","author":"Woods","year":"2016","journal-title":"Rev. Mod. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"033402","DOI":"10.1103\/PhysRevB.63.033402","article-title":"Stiction, adhesion, and the Casimir effect in micromechanical systems","volume":"63","author":"Buks","year":"2001","journal-title":"Phys. Rev. B"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1209\/epl\/i2001-00298-x","article-title":"Metastability and the Casimir effect in micromechanical systems","volume":"54","author":"Buks","year":"2001","journal-title":"Europhys. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1941","DOI":"10.1126\/science.1057984","article-title":"Quantum mechanical actuation of microelectromechanical system by the Casimir effect","volume":"291","author":"Chan","year":"2001","journal-title":"Science"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"211801","DOI":"10.1103\/PhysRevLett.87.211801","article-title":"Nonlinear Micromechanical Casimir Oscillator","volume":"87","author":"Chan","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"263106","DOI":"10.1063\/1.2152835","article-title":"Scaling of micro- and nanodevices actuated by the Casimir force","volume":"87","author":"Barcenas","year":"2005","journal-title":"Appl. Phys. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"053512","DOI":"10.1063\/1.2472651","article-title":"Contact angle influence on the pull-in voltage of microswitches in the presence of capillary and quantum vacuum effects","volume":"101","author":"Palasantzas","year":"2007","journal-title":"J. Appl. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"063548","DOI":"10.1063\/1.2711409","article-title":"Pull-in voltage of microswitch rough plates in the presence of electromagnetic and acoustic Casimir forces","volume":"101","author":"Palasantzas","year":"2007","journal-title":"J. Appl. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1140\/epjb\/e2013-40779-5","article-title":"Geometry and charge carrier induced stability in Casimir actuated nanodevices","volume":"86","year":"2013","journal-title":"Eur. Phys. J. B"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"125413","DOI":"10.1103\/PhysRevB.87.125413","article-title":"Significance of the Casimir force and surface roughness for actuation dynamics of MEMS","volume":"87","author":"Broer","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"165423","DOI":"10.1103\/PhysRevB.88.165423","article-title":"Sensitivity of micromechanical actuation on amorphous to crystalline phase transformations under the influence of Casimir forces","volume":"88","author":"Sedighi","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1845","DOI":"10.1038\/ncomms2842","article-title":"Casimir forces on a silicon micromechanical chip","volume":"4","author":"Zou","year":"2013","journal-title":"Nat. Commun."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"054016","DOI":"10.1103\/PhysRevApplied.4.054016","article-title":"Nonlinear Actuation Dynamics of Driven Casimir Oscillators with Rough Surfaces","volume":"4","author":"Broer","year":"2013","journal-title":"Phys. Rev. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"27102","DOI":"10.1038\/srep27102","article-title":"Casimir switch: Steering optical transparancy with vacuum forces","volume":"6","author":"Liu","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"104501","DOI":"10.1063\/1.4993672","article-title":"Optical switching of a graphene mechanical switch using the Casimir effect","volume":"122","author":"Inui","year":"2017","journal-title":"J. Appl. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"014010","DOI":"10.1103\/PhysRevApplied.10.014010","article-title":"Demonstration of the Optical Chopper Driven by the Casimir Force","volume":"10","author":"Klimchitskaya","year":"2018","journal-title":"Phys. Rev. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3640","DOI":"10.1039\/C7CS00817A","article-title":"Solid-state electrical applications of protein and peptide based nanomaterials","volume":"47","author":"Panda","year":"2018","journal-title":"Chem. Soc. Rev."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"245421","DOI":"10.1103\/PhysRevB.103.245421","article-title":"Casimir pressure in peptide films on metallic substrates: Change of sign via graphene coating","volume":"103","author":"Klimchitskaya","year":"2021","journal-title":"Phys. Rev. B"},{"doi-asserted-by":"crossref","unstructured":"Klimchitskaya, G.L., Mostepanenko, V.M., and Tsybin, O.Y. (2022). Attractive and Repulsive Fluctuation Induced Pressure in Peptide Films Deposited on Semiconductor Substrates. Symmetry, 14.","key":"ref_33","DOI":"10.3390\/sym14102196"},{"doi-asserted-by":"crossref","unstructured":"Mostepanenko, V.M. (2021). Casimir Puzzle and Conundrum: Discovery and Search for Resolution. Universe, 7.","key":"ref_34","DOI":"10.3390\/universe7040084"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2241002","DOI":"10.1142\/S0217751X22410020","article-title":"Current status of the problem of thermal Casimir force","volume":"37","author":"Klimchitskaya","year":"2022","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"eabg2272","DOI":"10.1126\/sciadv.abg2272","article-title":"Self-consistent dielectric functions of materials: Toward accurate computation of Casimir\u2013van der Waals forces","volume":"7","author":"Aboutalebi","year":"2021","journal-title":"Sci. Adv."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1038\/2241197a0","article-title":"Application of the Lifshitz theory to the calculation of van der Waals forces across thin lipid films","volume":"224","author":"Parsegian","year":"1969","journal-title":"Nature"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1016\/S0006-3495(70)86326-3","article-title":"Van der Waals forces: Special characteristics in lipid-water systems and a general method of calculation based on the Lifshitz theory","volume":"10","author":"Ninham","year":"1970","journal-title":"Biophys. J."},{"key":"ref_39","first-page":"125","article-title":"Hamaker constant of inorganic materials","volume":"70","year":"1979","journal-title":"Adv. Coll. Interface Sci."},{"doi-asserted-by":"crossref","unstructured":"Landau, L.D., Lifshitz, E.M., and Pitaevskii, L.P. (1984). Electrodynamics of Continuous Media, Pergamon.","key":"ref_40","DOI":"10.1016\/B978-0-08-030275-1.50007-2"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0001-8686(80)80006-6","article-title":"The calculation of Hamaker constant from Lifshitz theory with application to wetting phenomena","volume":"14","author":"Hough","year":"1980","journal-title":"Adv. Coll. Interface Sci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"052109","DOI":"10.1103\/PhysRevA.62.052109","article-title":"Precise measurement of the Casimir force using gold surfaces","volume":"62","author":"Harris","year":"2000","journal-title":"Phys. Rev. A"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"075412","DOI":"10.1103\/PhysRevB.77.075412","article-title":"Influence of random roughness on the Casimir force at small separations","volume":"77","author":"Palasantzas","year":"2008","journal-title":"Phys. Rev. B"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"022117","DOI":"10.1103\/PhysRevA.69.022117","article-title":"Theory confronts experiment in the Casimir force measurements: Quantification of errors and precision","volume":"69","author":"Chen","year":"2004","journal-title":"Phys. Rev. A"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1088\/1751-8113\/40\/17\/F04","article-title":"Kramers\u2013Kronig relations for plasma-like permittivities and the Casimir force","volume":"40","author":"Klimchitskaya","year":"2007","journal-title":"J. Phys. A: Math. Theor."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"105031","DOI":"10.1103\/PhysRevD.84.105031","article-title":"Proximity force approximation for the Casimir energy as a derivative expansion","volume":"84","author":"Fosco","year":"2011","journal-title":"Phys. Rev. D"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"50001","DOI":"10.1209\/0295-5075\/97\/50001","article-title":"Casimir forces beyond the proximity force approximation","volume":"97","author":"Bimonte","year":"2012","journal-title":"Europhys. Lett."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"074110","DOI":"10.1063\/1.3686903","article-title":"Material dependence of Casimir force: Gradient expansion beyond proximity","volume":"100","author":"Bimonte","year":"2012","journal-title":"Appl. Phys. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"045019","DOI":"10.1103\/PhysRevD.88.045019","article-title":"Material dependence of Casimir interaction between a sphere and a plate: First analytic correction beyond proximity force approximation","volume":"88","author":"Teo","year":"2013","journal-title":"Phys. Rev. D"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"20002","DOI":"10.1209\/0295-5075\/118\/20002","article-title":"Going beyond PFA: A precise formula for the sphere-plate Casimir force","volume":"118","author":"Bimonte","year":"2017","journal-title":"Europhys. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"043901","DOI":"10.1103\/PhysRevLett.119.043901","article-title":"Plasma versus Drude Modeling of the Casimir Force: Beyond the Proximity Force Approximation","volume":"119","author":"Hartmann","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"062504","DOI":"10.1103\/PhysRevA.97.062504","article-title":"Proximity force approximation and specular reflection: Application of the WKB limit of Mie scattering to the Casimir effect","volume":"97","author":"Spreng","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"114003","DOI":"10.1088\/1402-4896\/aae34e","article-title":"Advancing numerics for the Casimir effect to experimentally relevant asect ratios","volume":"93","author":"Hartmann","year":"2018","journal-title":"Phys. Scr."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"012115","DOI":"10.1103\/PhysRevA.72.012115","article-title":"Casimir effect with rough metallic mirrors","volume":"72","author":"Lambrecht","year":"2005","journal-title":"Phys. Rev. A"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"077101","DOI":"10.1103\/PhysRevD.75.077101","article-title":"Tests of new physics from precise measurements of the Casimir pressure between two gold-coated plates","volume":"75","author":"Decca","year":"2007","journal-title":"Phys. Rev. D"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1140\/epjc\/s10052-007-0346-z","article-title":"Novel constraints on light elementary particles and extra-dimensional physics from the Casimir effect","volume":"51","author":"Decca","year":"2007","journal-title":"Eur. Phys. J. C"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"165443","DOI":"10.1103\/PhysRevB.85.165443","article-title":"Gradient of the Casimir force between Au surfaces of a sphere and a plate measured using an atomic force microscope in a frequency-shift technique","volume":"85","author":"Chang","year":"2012","journal-title":"Phys. Rev. B"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"137401","DOI":"10.1103\/PhysRevLett.110.137401","article-title":"Demonstration of the Casimir Force between Ferromagnetic Surfaces of a Ni-Coated Sphere and a Ni-Coated Plate","volume":"110","author":"Banishev","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"155410","DOI":"10.1103\/PhysRevB.88.155410","article-title":"Casimir interaction between two magnetic metals in comparison with nonmagnetic test bodies","volume":"88","author":"Banishev","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"104101","DOI":"10.1103\/PhysRevB.81.104101","article-title":"Thermal Casimir interaction between two magnetodielectric plates","volume":"81","author":"Geyer","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"184434","DOI":"10.1103\/PhysRevB.93.184434","article-title":"Isoelectronic determination of the thermal Casimir force","volume":"93","author":"Bimonte","year":"2016","journal-title":"Phys. Rev. B"},{"unstructured":"Palik, E.D. (1985). Handbook of Optical Constants of Solids, Academic Press.","key":"ref_62"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"035338","DOI":"10.1103\/PhysRevB.76.035338","article-title":"Control of the Casimir force by the modification of dielectric properties with light","volume":"76","author":"Chen","year":"2007","journal-title":"Phys. Rev. B"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"312002","DOI":"10.1088\/1751-8113\/41\/31\/312002","article-title":"Conductivity of dielectric and thermal atom-wall interaction","volume":"41","author":"Klimchitskaya","year":"2008","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"090403","DOI":"10.1103\/PhysRevLett.107.090403","article-title":"Reduction of the Casimir Force from Indium Tin Oxide Film by UV Treatment","volume":"107","author":"Chang","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"045436","DOI":"10.1103\/PhysRevB.85.045436","article-title":"Modifying the Casimir force between indium tin oxide film and Au sphere","volume":"85","author":"Banishev","year":"2012","journal-title":"Phys. Rev. B"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"042109","DOI":"10.1103\/PhysRevA.83.042109","article-title":"Making precise predictions of the Casimir force between metallic plates via a weighted Kramers\u2013Kronig transform","volume":"83","author":"Bimonte","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"66001","DOI":"10.1209\/0295-5075\/ac8c69","article-title":"Probing the response of metals to low-frequency s-polarized evanescent waves","volume":"139","author":"Klimchitskaya","year":"2022","journal-title":"Europhys. Lett."},{"doi-asserted-by":"crossref","unstructured":"Klimchitskaya, G.L., Mostepanenko, V.M., and Svetovoy, V.B. (2022). Experimentum crusis for electromagnetic response of metals to evanescent waves and the Casimir puzzle. Universe, 8.","key":"ref_69","DOI":"10.3390\/universe8110574"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"900","DOI":"10.1140\/epjc\/s10052-020-08465-y","article-title":"An alternative response to the off-shell quantum fluctuations: A step forward in resolution of the Casimir puzzle","volume":"80","author":"Klimchitskaya","year":"2020","journal-title":"Eur. Phys. J. C"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"012805","DOI":"10.1103\/PhysRevA.105.012805","article-title":"Theory-experiment comparison for the Casimir force between metallic test bodies: A spatially nonlocal dielectric response","volume":"105","author":"Klimchitskaya","year":"2022","journal-title":"Phys. Rev. A"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/5\/1011\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:27:51Z","timestamp":1760124471000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/5\/1011"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,1]]},"references-count":71,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["sym15051011"],"URL":"https:\/\/doi.org\/10.3390\/sym15051011","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,5,1]]}}}