Mehlala ea Lipotso tse Buisanang ka Tšusumetso ea Kamano ea Einstein
Likhopolo tsa Einstein tsa kamano, ho kenyeletsoa le likhopolo tsa hae tse ikhethang le tse akaretsang tsa kamano, li fetotse kutloisiso ea rona ea sebaka, nako le matla a khoheli. Le hoja Einstein a qalile ho hlahisa likhopolo tsena mathoasong a lekholo la bo20 la lilemo, tšusumetso ea tsona saenseng le theknolojing ea sejoale-joale e bile kholo. Sehlooho sena se tla hlahloba mehlala e 'maloa ea mathata a hlahlobang tšusumetso e kholo ea kamano ea Einstein maemong a fapaneng le ho bontša kamoo khopolo ena e fetotseng mokhoa oa rona oa saense kateng.
Mohlala oa Potso ea 1: Katoloso ea Nako le Leeto la Sebaka
Potso:
Sefofa-sepakapaka se etela naleli e bolelele ba dilemo tse 4 tsa lesedi ho tloha Lefatsheng ka lebelo la lesedi le fetang la lesedi ka makgetlo a 0,8 (0,8c). Sefofa-sepakapaka se nahana hore leeto le tla nka nako e kae?
Puisano:
Ho utloisisa ketsahalo ea ho atoloha ha nako, re sebelisa mokhoa oa motheo oa kamano e khethehileng:
\[t' = \frac{t}{\gamma} \]
moo \( \gamma \) e leng ntlha ya Lorentz e fanweng ke:
\[ \gamma = \frac{1}{\sqrt{1 – \left(\frac{v}{c}\right)^2}} \]
Mona, \( v = 0,8c \) le \( c \) ke lebelo la lesedi. Ebe,
\[ \gamma = \frac{1}{\sqrt{1 – (0,8)^2}} = \frac{1}{\sqrt{1 – 0,64}} = \frac{1}{\sqrt{0,36}} = \frac{1}{0,6} \hoo e ka bang 1,667 \]
Haeba sebaka sa naleli e le lilemo tse 4 tsa leseli 'me mofofisi oa linaleli a tsamaea ka lebelo la 0,8c, nako e bonoang ke moshebelli Lefatšeng (t) ke:
\[ t = \frac{Distance}{Lebelo} = \frac{4 \text{light years}}{0,8c} = 5 \text{years} \]
Leha ho le jwalo, nako eo setsebi sa dinaledi (t') se e fumanang ke:
\[ t' = \frac{t}{\gamma} = \frac{5 \mongolo{dilemo}}{1,667} \hoo e ka bang 3 \mongolo{dilemo} \]
Kahoo, ho ea ka bo-rasaense ba linaleli, leeto lena le nkile lilemo tse ka bang 3 feela, leha ho le joalo ho ea ka pono ea Lefatše le nkile lilemo tse 5.
Mohlala oa Potso ea 2: Ho Khutsufala ha Bolelele le Tlhokomelo ea Liteko
Potso:
Sefofa-sebakeng se bolelele ba limithara tse 100 se lekanngoa ha se phomotse ha se bapisoa le Lefatše. Haeba sefofa-sebakeng se tsamaea ka lebelo la 0,6c ha se bapisoa le moshebelli ea lefatšeng, se bonahala se le bolelele bo bokae ho moshebelli ea lefatšeng?
Puisano:
Ho honyela ha bolelele ke phello e 'ngoe ea ho itšetleha ka maemo e hlalositsoeng ke ho itšetleha ka maemo ho khethehileng, e hlalositsoeng ke:
\[ L = L_0 \sqrt{1 – \left(\frac{v}{c}\right)^2} \]
moo \( L_0 \) e leng bolelele ba ntho e phomotseng, \( v \) ke lebelo le amanang, mme \( L \) ke bolelele ba ntho e amanang le lebelo le amanang. Bakeng sa sefofane:
\[ L_0 = 100 \mongolo{dimithara}, \; v = 0,6c, \mongolo{ ebe} \]
\[ L = L_0 \sqrt{1 – \left(\frac{v}{c}\right)^2} = 100 \sqrt{1 – (0,6)^2} = 100 \sqrt{1 – 0,36} = 100 \sqrt{0,64} = 100 \makgetlo a 0,8 = 80 \mongolo{methara} \]
Kahoo, bolelele ba sefofane ho ea ka bashebelli ba Lefatšeng ke limithara tse 80.
Mohlala Potso ea 3: Matla a khoheli le Khopolo-taba ea Kamano e Akaretsang ho GPS
Potso:
Lisathelaete tsa GPS li potoloha Lefatše bophahamong ba 20.200 km ka holim'a bokaholimo ba Lefatše ka lebelo la hoo e ka bang 3,874 km/s. U sebelisa kakaretso ea kamano, bala tokiso ea nako eo lisathelaete tsa GPS li hlokang ho e etsa letsatsi le letsatsi ho ikarabella bakeng sa litlamorao tsa matla a khoheli a Lefatše.
Puisano:
Li-satellite tsa GPS li tlameha ho fetola nako ea tsona bakeng sa litlamorao tse peli tse kholo: ho atoloha ha nako ka lebaka la lebelo le phahameng (relativity e khethehileng) le ho atoloha ha nako ka lebaka la matla a khoheli (relativity e akaretsang). Leha ho le joalo, re tla tsepamisa maikutlo holim'a phello ea matla a khoheli mona:
Ha ho sebelisoa khopolo-taba ea kakaretso ea kamano, nako e tla feta butle haholo tšimong e matla ea matla a khoheli. Foromo ea matla a khoheli a bonahalang a tsoa kakaretsong ea kamano ke:
\[ t_g = t_0 \left( 1 – \frac{2GM}{Rc^2} \right) \]
moo \( R \) e leng sebaka ho tloha bohareng ba matla a khoheli, \( G \) ke ntho e sa fetoheng ya matla a khoheli, \( M \) ke boima ba Lefatshe, \( c \) ke lebelo la lesedi, mme \( t_0 \) ke nako ya moshebelli ya 'emeng' hodima lefatshe.
E fanoe:
– Boima ba Lefatše, \( M \hoo e ka bang 5,972 \makhetlo a 10^{24} \mongolo{ kg} \)
– Radius ea Lefatše, \( R_{\text{surface}} \hoo e ka bang 6.371 \times 10^6 \text{m} \)
– Bophahamo ba sathelaete, \( H = 20.200 \makgetlo a 10^3 \mongolo{m} \)
– Kahoo sebaka ho tloha bohareng ba Lefatše ho ea sathelaeteng, \( R = R_{\text{surface}} + H \approx 26.571 \times 10^6 \text{m} \)
Phapang ea nako ka letsatsi pakeng tsa sathelaete le bokaholimo ba Lefatše, ho nahanoa feela ka matla a khoheli:
\[ \Delta t_g \approx \frac{2GM}{c^2} \left( \frac{1}{R_{\text{surface}}} – \frac{1}{R} \right) \]
Ho e nkela sebaka:
\[ \Delta t_g \approx \frac{2 \times 6,67408 \times 10^{-11} \text{ m}^3 \text{ kg}^{-1} \text{ s}^{-2} \times 5,972 \times 10^{24} \text{ kg}}{(3 \times 10^8 \text{ m/s})^2} \left( \frac{1}{6,371 \times 10^6 \text{ m}} – \frac{1}{26,571 \times 10^6 \text{ m}} \right) \]
Kamora ho bala, sephetho sena se lekana le tokiso ea nako ea letsatsi le letsatsi bakeng sa li-satellite tsa GPS, e leng nako e ka bang 7 microseconds e liehang ho feta nako ea bokaholimo ba Lefatše. Ka hona, li-satellite tsa GPS li hloka ho ikarabella bakeng sa phello ena ho boloka ho nepahala.
Tšusumetso e Khōlō Theknolojing le Kutloisisong ea Bokahohle
Mehlala ena e hlakisa hore kamano ea Einstein ha se khopolo-taba ea 'mele feela empa hape e na le lits'ebetso tse pharaletseng tse sebetsang. Ho tloha katoloso ea nako leetong la sepakapaka ho ea ho khutsufatso ea bolelele le tokiso ea nako theknolojing ea GPS, kamano ea Einstein e bile le tšusumetso e kholo.
Dintlha tse ntjha mafapheng a fapaneng a theknoloji, saense, esita le filosofi di bontsha tshusumetso ya kgopolo ena. Ho amana ho nolofaditse ho batlisisa sebaka ka botebo, ntshetsopele ya theknoloji e tswetseng pele ya puisano, le kutlwisiso e ntjha ya cosmology le masoba a matsho.
Qetellong, khopolo-taba ea Einstein ea kamano e ntse e le karolo ea bohlokoa ea thuto ea fisiks ea sejoale-joale 'me e ntse e tsoela pele ho ba mohloli oa pululelo le lipatlisiso bakeng sa bo-rasaense lefatšeng ka bophara.
