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AGOGUNA DA KE JIN TUMBATSA (TIDES) A CIKIN LOKACI KANSA

Nauyi (gravity) yana shafar tafiyar lokaci, kamar yadda ka’idar dangantaka ta gaba ɗaya (general relativity) ta bayyana. A Duniya, saurin agogo yana canzawa da kusan kaso ɗaya cikin 10¹⁶ ga kowace mita ta tsawo. Saboda haka kwatanta agoguna masu nisa da juna na iya auna bambance-bambance a cikin potential na nauyi na Duniya (gravity potential; a taƙaice, zurfin da wuri yake ciki a cikin nauyin Duniya, wanda galibi ke bin tsawon wurin) kai tsaye — wata dabara da ake kira auna tsawo ta agogo (chronometric levelling). Har zuwa yanzu, gwaje-gwaje sun yi amfani da ita ne don bambance-bambance tsayayyu, kamar tazarar tsawo tsakanin ɗakunan gwaje-gwaje biyu, inda suka kai rashin tabbas na ƴan santimita.

Siginar da kowa zai iya hasashe

Amma nauyi a Duniya ba tsayayye ba ne. Jan Wata da Rana yana canzawa a cikin yini, ƙasa mai ƙarfi ta Duniya tana sauya siffa a matsayin martani, kuma tumbatsar ruwan teku tana ɗora nauyi a kan ƙasa. Tare, waɗannan suna canza saurin agogo da har zuwa 5 × 10⁻¹⁷ a kowane wuri ɗaya, da kari (rhythms) na kusan zagaye ɗaya da biyu a kowace rana.

Abin da agoguna biyu ke kwatantawa shi ne bambanci tsakanin wuraren da suke. Tashoshin da ke nesa da juna a tsawon duniya (longitude) suna jin tumbatsar a lokuta daban-daban; tashoshin da ke nesa da juna a faɗin duniya (latitude) suna jin ta da ƙarfi daban-daban. A faɗin nahiya, tazarar tana jujjuyawa da ƴan kaso cikin 10¹⁸. Don a bi ta, kwatanta agoguna dole ya kasance da kwanciyar hankali (stability) na kusan 1 × 10⁻¹⁸ cikin ƴan sa’o’i. Agogunan haske ba su taɓa bambance irin wannan siginar da ke canzawa da lokaci ba.

Agoguna a faɗin Turai

Wata haɗin gwiwa ta masu bincike 44, tare da Sören Dörscher na Physikalisch-Technische Bundesanstalt (PTB) a Braunschweig, Jamus, da Ian Hill na National Physical Laboratory (NPL) a Teddington, Birtaniya, a matsayin marubutan da ake tuntuɓa (corresponding authors), ta yi amfani da agogunan haske na lattice (optical lattice clocks), inda ake riƙe atom na strontium ko ytterbium a cikin raga ta hasken laser. An haɗa su ta hanyar sadarwar Turai ta wayoyin fiber na haske masu daidaitaccen phase (phase-stabilised optical fibres), wadda cibiyarta ke Paris.

Nau’i-nau’i biyu na agoguna ne suka yi babban aikin, kowanne nesa da juna da kusan kilomita 800:

  • Turin da Braunschweig (kusan km 840), Maris 2025. A nan, PTB ta tura agogonta mai ɗaukuwa (transportable) PTB-Sr4 zuwa Istituto Nazionale di Ricerca Metrologica (INRiM) ta Italiya a matsayin firikwensin nesa, ta kuma kwatanta shi da agogon ɗakin gwajinta PTB-Sr3. Wuraren sun bambanta galibi a faɗin duniya (kusan 7°), don haka tumbatsar tana isa gare su da ƙarfi daban-daban.
  • Teddington da Braunschweig (kusan km 740), Maris 2023, da agogon NPL mai suna NPL-Sr1. Kusan a faɗin duniya ɗaya amma nesa da juna da 11° a tsawon duniya, waɗannan wurare suna jin tumbatsa ɗaya a lokuta daban-daban.

Samfurin tumbatsa (tide model) ya yi hasashen bambance-bambance tsakanin wuraren da suka kai 5 × 10⁻¹⁸ daga ƙololuwa zuwa ƙololuwa (peak to peak) — ƴan kaso cikin biliyan biliyan. Dukkan nau’i-nau’in biyu sun kai kwanciyar hankalin da ake buƙata, saboda kogon laser masu tsananin kwanciyar hankali (ultrastable laser cavities), har da wani mai ɗaukuwa mai tsawon santimita 20.

Kallon lokaci yana hawa da sauka

Idan aka ɗauki matsakaici a cikin sa’o’i uku, rabo (ratio) tsakanin saurin bugun agoguna biyu (mitocinsu, frequencies) a kowane nau’i ya hau ya sauka kamar tumbatsar da aka yi hasashe. Wani nazarin bakan mitoci (spectral analysis) ya ƙara fayyace shi: dukkan kwatancen biyu sun nuna ƙaƙƙarfan kari na sau biyu a rana, wanda ya kusan ɓacewa gaba ɗaya da zarar an cire hasashen — wanda ya nuna cewa girma (amplitude) da lokaci duka sun dace. Nau’in Teddington–Braunschweig ya kuma nuna kari na sau ɗaya a rana da yanayin wurarensa ke hasashe; nau’in Turin–Braunschweig, kamar yadda aka zata, bai nuna shi ba.

Wani algorithm na bin diddigi da ake kira Kalman filter, wanda zai iya aiki a kan bayanai kai tsaye (live data), sai ya auna ƙarfin siginar da aka gani idan aka kwatanta da samfurin, inda 1 ke nufin cikakken dacewa. A cikin kusan mako ɗaya kowanne, ya sami 1.42 ± 0.35 ga Turin da 1.12 ± 0.24 ga Teddington — dukkansu sun yi nesa da sifili fiye da karkacewar daidaito (standard deviations) huɗu. Kwanaki guda-guda tuni sun yi daidai da hasashen: an bambance tumbatsar cikin ƙasa da kwana ɗaya na aunawa. Idan aka haɗa da sauran nau’i-nau’in agoguna a Paris, Turin da Teddington, matsakaici mai ma’auni (weighted average) ya kai 1.00 ± 0.12.

Don tabbatarwa, ƙungiyar ta gudanar da nazari iri ɗaya a kan agoguna biyu da ke zaune gefe da gefe a Turin, inda bambancin tumbatsa ya kai kusan 10⁻²², yayin da aka gaya wa filter ɗin ya nemi tumbatsa tsakanin wurare biyu masu nisa da juna. Ya sami ƙimomi da suka dace da sifili, kamar yadda ya kamata.

Marubutan sun ƙiyasta cewa tasirin ya yi daidai da canje-canjen tsawo na kimanin santimita 10 a kowace tasha, sau ɗaya ko sau biyu a rana.

Daga tumbatsa zuwa duwatsu masu aman wuta

Ga masana ma’auni (metrologists), darasin na aiki ne: tumbatsa wani son kai (bias) ne na gaske kuma mai yiwuwar hasashe a cikin kwatanta agoguna masu nisa, kuma matsakaici a cikin wani zangon aunawa na iya bambanta da matsakaici na dogon lokaci. Dole ne a yi musu samfuri yayin da agoguna ke nufin 10⁻¹⁸ da abin da ya wuce haka.

Ga masana kimiyyar ƙasa, agogo mai ɗaukuwa ne ya fi muhimmanci. Ya yi aiki daidai da agogunan ɗakin gwaje-gwaje tsayayyu, don haka ana iya tura agoguna zuwa wuraren da aka zaɓa saboda muhimmancinsu a fannin ilimin ƙasa (geophysical), duk inda wayar fiber ta kai. Hanyoyin sadarwar agoguna za su iya kallon sannu-sannu sake rarrabuwar ruwan ƙarƙashin ƙasa, ƙanƙara, teku da iska, ko cikar ɗakin magma a ƙarƙashin dutse mai aman wuta, kuma su duba ayyukan tauraron ɗan adam na auna nauyi (satellite gravity missions), waɗanda ke ɗaukar samfur sau ɗaya a wata, da aunawa a ƙasa ta kowace rana zuwa kowane mako.

Hanyar sadarwar tana ci gaba da girma: wata sabuwar haɗi zuwa Toruń a Poland ta faɗaɗa mafi faɗin tazara ta gabas zuwa yamma daga 11° zuwa kusan 19°, kuma ana shirin haɗi zuwa Belgium da Netherlands. Ga tashoshin da ke faɗin duniya ɗaya, siginar tumbatsa ta sau biyu a rana tana kaiwa ƙololuwa idan suna nesa da juna da 90° na tsawon duniya — tazarar da haɗi masu ketare teku (transoceanic) ne kawai za su iya kaiwa. A yanzu, tumbatsa ce gwajin: canjin nauyi da kowa zai iya lissafawa tun kafin lokaci, ta yadda daga baya za a iya amincewa da agogunan kan waɗanda ba su da sauƙin hasashe.