Misali na Tambayoyin Tattaunawa Game da Faɗaɗa Lokaci
A fannin kimiyyar lissafi, manufar faɗaɗa lokaci wani abu ne mai ban sha'awa da ban sha'awa a cikin ka'idar dangantakar Albert Einstein ta musamman. Wannan ka'idar tana ba da sabon hangen nesa kan yadda sarari da lokaci ba halittu ne masu cikakken tsari ba amma suna da alaƙa, sun dogara ne akan gudu da nauyi. Wannan kasidar za ta bincika faɗaɗa lokaci dalla-dalla kuma ta ba da misalai.
Tushen Ka'idar Dangantaka ta Musamman
Ka'idar musamman ta dangantaka ta bayyana cewa dokokin kimiyyar lissafi iri ɗaya ne ga duk masu lura da ke tafiya a layi madaidaiciya a cikin saurin da ya dace da juna (tsarin tunani mara motsi). Ɗaya daga cikin manyan abubuwan da wannan ka'idar ke nufi shi ne cewa saurin haske a cikin sarari yana da daidaito kuma baya dogara da motsin tushen ko mai lura.
Al'amarin faɗaɗa lokaci yana tasowa ne sakamakon waɗannan zato guda biyu. Yana nuna cewa lokaci zai yi tafiya a hankali ga abu da ke tafiya kusa da saurin haske idan aka kwatanta da mai lura da ke tsaye.
Tsarin Faɗaɗa Lokaci
Tsarin da ake amfani da shi don ƙididdige faɗaɗa lokaci shine kamar haka:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Ina:
– \(\Delta t'\) = lokacin da aka auna ta hanyar mai lura da abin da ya faru dangane da abin da aka auna.
– \(\Delta t\) = lokaci da aka auna ta hanyar mai lura da wuri (lokaci a cikin tsarin inertial).
– \(v\) = saurin abin da ke motsi.
– \(c\) = saurin haske a cikin injin tsabtace iska (\(sau 3 10^8\) mita a kowace daƙiƙa).
Domin zurfafa fahimtarmu game da wannan ra'ayi, bari mu duba wasu misalai na tambayoyi da tattaunawarsu.
Misali Tambaya ta 1: Faɗaɗa Lokaci a Jirgin Sama
Tambaya:
Wani jirgin sama yana tafiya a 0.8c (kashi 80% na saurin haske) idan aka kwatanta da Duniya. Tsawon wane lokaci ne wani ɗan sama jannati a cikin jirgin zai yi amfani da awa 1 na lokacin Duniya?
Tattaunawa:
An sani:
– \(v = 0.8c\)
– \(\Delta t = 1\) sa'o'i (lokacin duniya)
Domin nemo \(\Delta t'\) (lokacin da ɗan sama jannatin ya fuskanta a cikin jirgin sama), muna amfani da dabarar faɗaɗa lokaci:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Maye gurbin dabi'un da aka sani:
\[ \Delta t' = \frac{1 \text{ awa}}{\sqrt{1 – (0.8)^2}} \]
\[ \Delta t' = \frac{1 \text{ awa}}{\sqrt{1 – 0.64}} \]
\[ \Delta t' = \frac{1 \text{ hour}}{\sqrt{0.36}} \]
\[ \Delta t' = \frac{1 \text{ awa}}{0.6} \]
\[ \Delta t' = \frac{1 \text{ hours}}{0.6} \approx 1.67 \text{ hours} \]
Don haka, lokacin da ɗan sama jannati a cikin jirgin sama ke buƙata don ya fuskanci awa 1 na lokacin Duniya shine kimanin awanni 1.67.
Misali Tambaya ta 2: Tasirin Sauri akan Faɗaɗa Lokaci
Tambaya:
Idan lokacin da mai lura a Duniya ya auna (lokacin tsarin inertial) shekaru 2 ne, kuma jirgin sama yana tafiya da kashi 90% na saurin haske, menene lokacin da fasinja a cikin jirgin sama ke aunawa?
Tattaunawa:
An sani:
– \(v = 0.9c\)
– \(\Delta t = 2\) shekaru
Domin nemo \(\Delta t'\) (lokacin da fasinja ya fuskanta a cikin jirgin sama), muna amfani da dabarar faɗaɗa lokaci:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Maye gurbin dabi'un da aka sani:
\[ \Delta t' = \frac{2 \text{ shekaru}}{\sqrt{1 – (0.9)^2}} \]
\[ \Delta t' = \frac{2 \text{ shekaru}}{\sqrt{1 – 0.81}} \]
\[ \Delta t' = \frac{2 \text{ shekaru}}{\sqrt{0.19}} \]
\[ \Delta t' = \frac{2 \text{ shekaru}}{0.4359} \]
\[ \Delta t' \kimanin 4.59 \text{ shekaru} \]
Don haka, lokacin da fasinjojin da ke cikin jirgin sama ke aunawa yana da kimanin shekaru 4.59.
Misali Tambaya ta 3: Lokaci Don Jin Doguwar Nakuda
Tambaya:
Kwayar cuta tana tafiya a gudun 0.6c idan aka kwatanta da dakin gwaje-gwaje. Mai lura a dakin gwaje-gwaje yana auna rabin rayuwar ƙwayar cuta a matsayin microseconds 2. Menene rabin rayuwar ƙwayar cuta da aka auna na tsarin ƙwayar cuta?
Tattaunawa:
An sani:
– \(v = 0.6c\)
– \(\Delta t = 2\) ƙananan daƙiƙa
Domin nemo \(\Delta t'\), yi amfani da dabarar:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Maye gurbin dabi'un da aka sani:
\[ \Delta t' = \frac{2 \text{ microseconds}}{\sqrt{1 – (0.6)^2}} \]
\[ \Delta t' = \frac{2 \text{ microseconds}}{\sqrt{1 – 0.36}} \]
\[ \Delta t' = \frac{2 \text{ microseconds}}{\sqrt{0.64}} \]
\[ \Delta t' = \frac{2 \text{ microseconds}}{0.8} \]
\[ \Delta t' = 2.5 \text{ microseconds} \]
Saboda haka, rabin rayuwar da aka auna na tsarin barbashi shine microseconds 2.5.
Bincike da Kammalawa
Daga misalan da ke sama, za mu iya ganin yadda faɗaɗa lokaci ke taka muhimmiyar rawa wajen fahimtar cewa lokaci ba cikakken tsari ba ne. Masu lura a yanayi daban-daban na rashin tabbas na iya samun ma'aunin lokaci daban-daban don wannan lamari.
Fahimtar zurfafa fahimtar faɗaɗa lokaci yana buɗe ƙofa ga sabbin fasahohi da yawa, gami da a fannin tauraron ɗan adam na kewaya GPS, waɗanda ke buƙatar gyare-gyare masu alaƙa don aiki daidai. Bugu da ƙari, wannan ra'ayi yana ƙalubalantar tunaninmu don fahimtar sararin samaniya da gaskiya daga hangen nesa mai wadata da rikitarwa.
Saboda haka, faɗaɗa lokaci ba wai kawai ra'ayi ne na nazari ba, har ma yana da fa'idodi masu yawa a cikin haɓaka fasaha da ilimin kimiyya game da sararin samaniya da ke kewaye da mu. Fahimtar waɗannan ƙa'idodi muhimmin mataki ne a tafiyarmu ta ƙwarewa a fasahar zamani da kuma amsa tambayoyi masu mahimmanci game da yanayin sararin samaniya da lokaci.
