Mafunso ndi Zitsanzo za Ubale wa Einstein
Kugwirizana kwa Einstein ndi chimodzi mwa ziphunzitso zofunika kwambiri mu sayansi ya masiku ano, zomwe zimasintha momwe timamvetsetsera malo ndi nthawi. Chili ndi magawo awiri: ubale wapadera (1905) ndi ubale wamba (1915). M'nkhaniyi, tikambirana zitsanzo zingapo zokhudzana ndi ubale wa Einstein ndikuzikambirana kuti timvetsetse bwino.
Ubale Wapadera
Kugwirizana kwapadera kumakhudza zinthu zomwe zimayenda pa liwiro losasinthasintha lomwe likuyandikira liwiro la kuwala. Zotsatira ziwiri zazikulu za chiphunzitsochi ndi kukulitsa nthawi ndi kupindika kwa kutalika.
1. Kutambasula kwa Nthawi
Ngati pali owonera awiri, mmodzi wosaima padziko lapansi ndi wina woyenda mofulumira kwambiri, adzayesa nthawi zosiyana za chochitika chomwecho.
Chitsanzo cha mavuto:
Woyenda mumlengalenga amayenda ndi liwiro la kuwala ka 0.8 kuposa liwiro la kuwala (c) kupita ku nyenyezi yomwe ili pa zaka 10 za kuwala kuchokera ku Dziko Lapansi. Kodi woyenda mumlengalenga amatenga nthawi yayitali bwanji kuti akafike ku nyenyeziyo?
Kukambirana:
Choyamba, timawerengera nthawi yomwe wowonera padziko lapansi amayesa:
\[ t_B = \frac{d}{v} = \frac{10 \text{ light years}}{0.8 \, c} = 12.5 \text{ years} \]
Kuti tiwerengere nthawi yomwe woyendetsa ndege amayesa (kukulitsa nthawi), timagwiritsa ntchito njira iyi:
\[ t_A = t_B \sqrt{1 – \frac{v^2}{c^2}} \]
M'malo mwa mfundo zodziwika bwino:
\[t_A = 12.5 \sqrt{1 – (0.8)^2} \]
\[t_A = 12.5 \sqrt{1 – 0.64} \]
\[t_A = 12.5 \sqrt{0.36} \]
\[t_A = 12.5 \nthawi 0.6 \]
\[t_A = 7.5 \lemba{zaka} \]
Kotero, nthawi yomwe oyenda mumlengalenga anayeza inali zaka 7.5.
2. Kupindika Kwautali
Chinthu chikayenda pa liwiro loyandikira liwiro la kuwala, kutalika kwake kudzaoneka kochepa kwa wowonera wosasuntha.
Chitsanzo cha mavuto:
Chombo chapamlengalenga chokhala ndi kutalika kwenikweni kwa mamita 10 chikuyenda pa liwiro la kuwala ndi 0.9 nthawi. Kodi chombocho chingakhale chautali bwanji kwa wowonera padziko lapansi?
Kukambirana:
Kuti tiwerenge kutalika kwa kufupika, timagwiritsa ntchito fomula iyi:
\[ L = L_0 \sqrt{1 – \frac{v^2}{c^2}} \]
Kumene:
– \( L_0 \) ndi kutalika koyenera kapena kutalika kwenikweni (mamita 10),
– \( v \) ndi liwiro la ndege (0.9c).
M'malo mwa mfundo zodziwika bwino:
\[ L = 10 \sqrt{1 – (0.9)^2} \]
\[ L = 10 \sqrt{1 - 0.81} \]
\[ L = 10 \sqrt{0.19} \]
\[L = 10 \nthawi 0.436 \]
\[ L = 4.36 \malemba{mita} \]
Kotero, kutalika kwa ndegeyo malinga ndi owonera padziko lapansi ndi mamita 4.36.
Kugwirizana Kwathunthu
Kugwirizana kwa zinthu kumakambirana za mphamvu yokoka, komwe malo ndi nthawi zimakhudzidwa ndi kulemera ndi mphamvu.
3. Magalasi Okoka Mphamvu
Kuyang'ana kwa mphamvu yokoka kumachitika pamene kuwala kochokera ku chinthu chakutali kumapindika ndi mphamvu yokoka ya chinthu chachikulu monga mlalang'amba kapena dzenje lakuda.
Chitsanzo cha mavuto:
Galaxy A ili ndi kulemera kokwanira kuti ichotse kuwala kuchokera ku quasar B, yomwe ili kumbuyo kwake. Ngati ngodya ya deflection ndi 1.5 arc seconds, kodi kulemera kwa galaxy A ndi kotani? (Gwiritsani ntchito mphamvu yokoka ya Newton G = 6.674×10^-11 N(m/kg)^2, liwiro la kuwala c = 3×10^8 m/s)
Kukambirana:
Ngodya ya deflection θ ingaperekedwe ndi fomula iyi:
\[ \theta = \frac{4GM}{c^2 R} \]
Kumene:
– \( G \) ndi mphamvu yokoka,
– \( M \) ndi kulemera kwa mlalang'amba,
– \( c \) ndi liwiro la kuwala,
– \( R \) ndiye mtunda wapafupi kwambiri pakati pa kuwala ndi pakati pa mlalang'amba.
Popeza tikufuna kupeza M, tasinthanso fomula iyi:
\[ M = \frac{\theta c^2 R}{4G} \]
Tiyerekeze kuti R ndi 5×10^20 metres (mtunda wapakati wa milalang'amba). Sinthani θ kuchokera ku arcseconds kupita ku radians (1 arcsecond = 4.848×10^-6 radians):
\[ \theta = 1.5 \nthawi 4.848 \nthawi 10^{-6} \, \text{radian} = 7.272 \nthawi 10^{-6} \, \text{radian} \]
M'malo mwa mfundo zodziwika bwino:
\[ M = \frac{(7.272 \nthawi 10^{-6}) (3 \nthawi 10^8)^2 (5 \nthawi 10^{20})}{4 \nthawi 6.674 \nthawi 10^{-11}} \]
\[ M = \frac{(7.272 \times 10^{-6}) (9 \times 10^{16}) (5 \times 10^{20})}{26.696 \times 10^{-11}} \]
\[ M = \frac{(3.2764 \times 10^{31})}{26.696 \times 10^{-11}} \]
\[ M = 1.227 \nthawi 10^{41} \, \malemba{kg} \]
Kotero, kulemera kwa mlalang'amba A ndi pafupifupi 1.227×10^41 kilogalamu.
4. Kuchuluka kwa Mercury mu Perihelion
Kugwirizana kwa dziko lonse kungafotokozenso za kuyendayenda kwa dziko la Mercury komwe sikungathe kufotokozedwa ndi makina a Newtonian.
Chitsanzo cha mavuto:
Kodi kukula kwa kusintha kwa Mercury's perihelion ndi kotani monga momwe tafotokozera ndi general relativity? (Chiwerengero cha ubale A: 43 arcseconds per century)
Kukambirana:
Gwiritsani ntchito deta yomwe yaperekedwa mwachindunji:
Malinga ndi chiphunzitso cha Einstein cha relativity, kusintha kwa perihelion kwa Mercury komwe kwafotokozedwa ndi masekondi 43 a arc pa zana, komwe kukugwirizananso ndi zotsatira za kuwona.
Pomaliza:
Mwa kumaliza zitsanzo ndi zokambiranazi, titha kuwona momwe ubale wa Einstein umathandizira kumvetsetsa bwino nthawi, kutalika, ndi mphamvu yokoka. Chiphunzitsochi sichinangosintha momwe timaonera chilengedwe chonse mwasayansi komanso chili ndi ntchito zothandiza muukadaulo wamakono, monga machitidwe oyendera GPS, omwe amafunikira kusintha kwa ubale kuti agwire ntchito molondola. Kuphunzira ndi kumvetsetsa ubale wa Einstein ndi gawo lofunikira pakufufuza mozama dziko lovuta la sayansi.
