SAMFURIN MAƁOYIN MAƁALLAI NA SCHRÖDINGER DA BA A WALLAFA BA, AN SAME SHI A VIENNA

Idan ka jefa tsabar kuɗi mai adalci, akwai yiwuwar kashi hamsin cikin ɗari cewa za ta faɗi da kai. A kimiyyar lissafi ta gargajiya, wannan yiwuwar tana nuna jahilci ne kawai: ƙarfin jefawar, juriyar iska da sauransu ne ke yanke sakamakon, kuma idan duk suna hannunka jefawar za ta zama abar hasashe. Injiniyar kwantum (quantum mechanics) ta bambanta. Tsarinta yawanci yana hasashen yiwuwa ne kawai. Tun farko, wasu masana kimiyyar lissafi sun yi mamaki ko ba ta cika ba — ko ƙarin maɓoyin maɓallai (hidden variables) za su iya dawo da hoto na ƙaddara-tabbatacciya a ƙarƙashinta.

A 1932, John von Neumann ya wallafa abin da aka ɗauka sosai a matsayin hujja cewa hakan ba zai yiwu ba. Grete Hermann ta gano matsaloli game da gamammiyarsa tun 1935, amma sukar ta kusan ba a lura da ita ba. An gane iyakokin hujjar sosai ne kawai bayan ka’idar maɓoyin maɓallai ta ƙaddara-tabbatacciya ta David Bohm a 1952 da sukar John Bell a 1966. A tsakani, a cewar Flavio Del Santo na Jami’ar Geneva da Jami’ar Constructor a Bremen, neman samfurorin maɓoyin maɓallai ya kusan ɓacewa fiye da shekaru goma.

Photon da ba zai iya sani ba

Tambayar ta dawo a tsakiyar yaƙi. A ranar 18 ga Mayu 1943, masanin lissafi kuma masanin kimiyyar lissafi Edmund Taylor Whittaker ya gabatar da lacca a London yana iƙirarin cewa injiniyar kwantum ta karya “ɗaurin tilas”. A ranar 3 ga Janairu 1944, Satyendra Nath Bose ya faɗi kusan haka a Delhi: “Shekaru hamsin da suka wuce imani da sanadi da ƙaddara ya kasance cikakke. A yau masana kimiyyar lissafi sun sami ilimi amma sun rasa imaninsu.”

Whittaker ya ƙara wata hujja mai sauƙi. Photon da aka polarize yana wucewa ta polarizer da yiwuwar cos²φ, inda φ shi ne kusurwar da ke tsakanin polarization ɗinsa da polarizer: wannan ita ce dokar Malus. A ɗauka cewa kowane photon yana ɗauke da ɓoyayyen bit ɗaya, 0 don “wucewa” 1 kuma don “toshewa”. Ga photon N, N cos²φ daga cikinsu dole su ɗauki 0. Amma za ka iya juya polarizer yayin da photon ɗin suke cikin tafiya. Bit ɗinsu ba za su iya canzawa ba, don haka adadin da ke wucewa ma ba zai iya canzawa ba — amma dokar Malus ta ce dole ya canza. Maɓoyin maɓallai, Whittaker ya kammala, ba su yiwuwa.

Martani goma sha ɗaya, da na goma sha biyu

Hujjar ta tayar da muhawara a cikin Nature: gudummawa goma sha ɗaya cikin kusan shekara ɗaya, goma a wannan mujallar ɗaya kuma a cikin Proceedings of the Physical Society. Masanin gwaji Gilbert West ya ƙi yarda cewa “akwai da yawa waɗanda, da sanin yadda zato ke iya ɓoyewa cikin sauƙi a cikin aikin nazari, suke ƙin a buge su da lissafi.” Sannan ya faɗi muhimmin abu: Whittaker ya nuna ne kawai cewa sanadi yana gazawa idan duk ɓoyayyun ma’aunai na photon ne; lu’ulu’un polarizer yana da nasa. Masanin lissafi Henry Piaggio ya rufe musayar a Maris 1945 da sulhu, yana ambato Bertrand Russell: babu dalili tabbatacce na cikakkiyar ƙaddara-tabbatacciya, amma babu dalili a kanta ma.

Abin da babu wanda ya sani har zuwa yanzu shi ne cewa akwai martani na goma sha biyu. Yana nan a matsayin daftarin rubutun hannu mara kwanan wata mai taken “Collapse of Determinism” a cikin Ma’ajiyar Erwin Schrödinger ta Babban Ɗakin Karatu na Kimiyyar Lissafi na Austria, a Jami’ar Vienna. Yana ambaton muhawarar har zuwa wata wasiƙa ta 25 ga Nuwamba 1944, don haka an rubuta shi bayan haka. Del Santo ya wallafa cikakken rubutunsa na farko da nazarinsa.

’Yan layuka da suka ceci ƙaddara-tabbatacciya

“Ni ma wannan ƙarshe ya ba ni mamaki,” Schrödinger ya rubuta. “Domin rashin hankalin da aka samo a fili yana fitowa ne daga zaton sauƙaƙawa na ƙimomin ma’auni biyu kawai masu rabuwa.”

Gyaransa: ba kowane photon wata ɓoyayyiyar lamba ta gaske λ tsakanin 0 da 1, a bazu daidai, kuma bari photon ya wuce idan λ ≥ sin²φ. Kason photon ɗin da ke wucewa sai ya zama daidai cos²φ — dokar Malus, tare da kowane sakamako an ƙayyade shi tun da wuri ta lambar photon da kusurwar polarizer. Don magance polarizer na biyu, Schrödinger ya ƙara sabuntawa ta ƙaddara-tabbatacciya: lambar photon da ya wuce tana zama λ′ = (λ − sin²φ)/cos²φ, wanda ke sake bazar da waɗanda suka tsira daidai a kan 0 zuwa 1. Del Santo ya nuna cewa polarizer na biyu a kusurwa φ′ sai ya bar kason cos²(φ′ − φ) nasu ya wuce, kamar yadda injiniyar kwantum ta yi hasashe. Schrödinger kuma ya ba da ƙa’idar photon da aka mayar (reflected): “Ba na ganin wani saɓani a cikin ɗaukar waɗannan canje-canje.”

Del Santo ya ƙara wani abu da ya bayyana ya kuɓuce wa kowa a cikin muhawarar, har da Whittaker da Schrödinger: babu wani abu na kwantum musamman game da bit ɗaya ya yi kaɗan. Tsabar kuɗi ma tana buƙatar fiye da bit ɗaya idan za ka iya motsa ƙasa yayin da take sama.

Mai ƙaddara-tabbatacciya wanda ba shi ba

Sauran rubutun ya koma ga falsafa. “Shaidar gwaji + fitar da ma’ana ba za su taɓa tabbatar da cewa ko ra’ayin ƙaddara-tabbatacciya ko na rashin ƙaddara ba zai yiwu ba,” Schrödinger ya rubuta, kuma “roƙo mafi ƙarfi a goyon bayan rashin ƙaddara ya girmi injiniyar kwantum.”

Ga Del Santo, saboda haka samfurin hujja ce ta ka’ida (proof of principle), ba sauya ra’ayi ba. Tun farkon shekarun 1920, ƙarƙashin tasirin Franz Exner, Schrödinger ya riƙe cewa “dokokin Yanayi suna da halin ƙididdiga gaba ɗaya” kuma ya kira ƙaddara-tabbatacciya “son zuciya na falsafa”.

Me ya sa bai taɓa aika shi ba? Heinrich Pelzer ya wallafa amsoshin maɓoyin maɓallai ga Whittaker a Mayu 1944, waɗanda aka ambata a muhawarar Nature a Janairu 1945. Sigarsa ta adadi, a cikin wani ɗan gajeren rubutu da aka ƙara a lokacin gyaran bugu, daidai take da ta Schrödinger ga polarizer ɗaya, ko da yake ba tare da bayyananniyar ƙa’idar sabuntawa ga kowane photon ba. Del Santo yana nuna cewa Schrödinger, da ya ji labarinta, wataƙila ya ɗauka cewa an riga an faɗi abin.

Tarihin da ya biyo baya ma yana cikin takardar. Bohm ya farfaɗo da maɓoyin maɓallai a 1952; a 1964 Bell ya nuna cewa samfurorin maɓoyin maɓallai na gida (local) suna yin hasashe da za a iya gwadawa, kuma tun daga lokacin gwaje-gwaje sun kawar da wannan rukuni. Einstein, Schrödinger da Bohm — sunaye uku da aka fi ɗauka a matsayin zakarun ƙaddara-tabbatacciya — duka sun gina irin waɗannan samfurorin a wani lokaci. Babu ɗaya daga cikinsu, Del Santo ya yi jayayya, da ya kasance mai ƙaddara-tabbatacciya kawai.