Imibuzo Yesibonelo kanye Nengxoxo Ngokuhlobana Kuka-Einstein
Ukuhlobana kuka-Einstein kungenye yezinkolelo-mbono eziyisisekelo kakhulu kwifiziksi yanamuhla, okushintsha indlela esiqonda ngayo isikhala nesikhathi. Kuqukethe izingxenye ezimbili: ukuhlobana okukhethekile (1905) kanye nokuhlobana okujwayelekile (1915). Kulesi sihloko, sizoxoxa ngezibonelo eziningana zezinkinga ezihilela ukuhlobana kuka-Einstein kanye nezixazululo zazo ukuze sinikeze ukuqonda okujulile.
Ubudlelwano Obukhethekile
Ubudlelwano obukhethekile buphathelene nezinto ezihamba ngesivinini esingaguquki ezisondela esivinini sokukhanya. Imiphumela emibili ebalulekile yalo mbono ukwanda kwesikhathi kanye nokuncipha kobude.
1. Ukwelulwa Kwesikhathi
Uma kukhona ababukeli ababili, oyedwa omile eMhlabeni nomunye ohamba ngesivinini esikhulu, bazolinganisa izikhathi ezahlukene zesenzakalo esifanayo.
Isibonelo sezinkinga:
I-astronaut ihamba ngesivinini sokukhanya esiphindwe izikhathi ezingu-0.8 (c) iya enkanyezini eqhele ngeminyaka yokukhanya eyi-10 ukusuka eMhlabeni. Kuthatha isikhathi esingakanani i-astronaut ukufika enkanyezini?
Ingxoxo:
Okokuqala, sibala isikhathi esilinganiswa ngumqapheli eMhlabeni:
\[ t_B = \frac{d}{v} = \frac{10 \text{ light years}}{0.8 \, c} = 12.5 \text{ years} \]
Ukuze sibale isikhathi esilinganiswe yi-astronaut (ukwanda kwesikhathi), sisebenzisa ifomula:
\[ t_A = t_B \sqrt{1 – \frac{v^2}{c^2}} \]
Faka amanani aziwayo esikhundleni sawo:
\[t_A = 12.5 \sqrt{1 – (0.8)^2} \]
\[t_A = 12.5 \sqrt{1 – 0.64} \]
\[t_A = 12.5 \sqrt{0.36} \]
\[t_A = 12.5 \izikhathi 0.6 \]
\[t_A = 7.5 \umbhalo{iminyaka} \]
Ngakho-ke, isikhathi esilinganiswe osomkhathi sasiyiminyaka engu-7.5.
2. Ukufinyela Okude
Uma into ihamba ngesivinini esisondela esivivinyweni sokukhanya, ubude bayo buzobonakala bufushane kumbukeli omile.
Isibonelo sezinkinga:
Indizamkhathi enobude bangempela bamamitha ayi-10 ihamba ngesivinini sokukhanya esiphindwe izikhathi ezingu-0.9. Indizamkhathi ingaba isikhathi esingakanani kumbukeli eMhlabeni?
Ingxoxo:
Ukuze sibale ubude bokufinyela, sisebenzisa ifomula:
\[ L = L_0 \sqrt{1 – \frac{v^2}{c^2}} \]
Di mana:
– \( L_0 \) ubude obufanele noma ubude bangempela (amamitha ayi-10),
– \( v \) ijubane lendiza (0.9c).
Faka amanani aziwayo esikhundleni sawo:
\[ L = 10 \sqrt{1 – (0.9)^2} \]
\[ L = 10 \sqrt{1 – 0.81} \]
\[ L = 10 \sqrt{0.19} \]
\[L = 10 \izikhathi 0.436 \]
\[ L = 4.36 \umbhalo{ amamitha} \]
Ngakho-ke, ubude bendiza ngokusho kwababukeli eMhlabeni bungamamitha angu-4.36.
Ubudlelwano Okuvamile
Ukuhlobana okuvamile kuxoxa ngamandla adonsela phansi, lapho isikhala nesikhathi kuthonywa khona ubukhulu namandla.
3. Ilensi Yokudonsa Amandla
Ukubona i-gravitational lensing kwenzeka lapho ukukhanya okuvela entweni ekude kugoba ngenxa yamandla adonsela phansi ento enkulu njenge-galaxy noma umgodi omnyama.
Isibonelo sezinkinga:
I-Galaxy A inesisindo esanele sokususa ukukhanya ku-quasar B, engemuva kwayo. Uma i-engeli yokuphambuka ingu-1.5 arc seconds, iyini isisindo somthala A? (Sebenzisa i-Newton's gravitational constant G = 6.674×10^-11 N(m/kg)^2, isivinini sokukhanya c = 3×10^8 m/s)
Ingxoxo:
I-engeli yokuphambuka θ inganikezwa ngefomula:
\[ \theta = \frac{4GM}{c^2 R} \]
Di mana:
– \( G \) kuyinto engaguquki,
– \( M \) isisindo somthala,
– \( c \) ijubane lokukhanya,
– \( R \) ibanga eliseduze kakhulu phakathi kokukhanya kanye nesikhungo somthala.
Njengoba sifuna ukuthola u-M, sihlela kabusha ifomula:
\[ M = \frac{\theta c^2 R}{4G} \]
Ake sithi u-R ungamamitha angu-5×10^20 (ibanga elimaphakathi lemithala). Guqula u-θ kusuka kumasekhondi e-arc ube ama-radian (isekhondi elilodwa = ama-radian angu-4.848×10^-6):
\[ \theta = 1.5 \izikhathi 4.848 \izikhathi 10^{-6} \, \umbhalo{radian} = 7.272 \izikhathi 10^{-6} \, \umbhalo{radian} \]
Faka amanani aziwayo esikhundleni sawo:
\[ M = \frac{(7.272 \izikhathi 10^{-6}) (3 \izikhathi 10^8)^2 (5 \izikhathi 10^{20})}{4 \izikhathi 6.674 \izikhathi 10^{-11}} \]
\[ M = \frac{(7.272 \times 10^{-6}) (9 \times 10^{16}) (5 \times 10^{20})}{26.696 \times 10^{-11}} \]
\[ M = \frac{(3.2764 \times 10^{31})}{26.696 \times 10^{-11}} \]
\[ M = 1.227 \izikhathi 10^{41} \, \umbhalo{kg} \]
Ngakho-ke, isisindo somthala A singamakhilogremu angu-1.227×10^41.
4. Ukuqala kwe-Perihelion kwe-Mercury
Ukuhlobana okuvamile kungachaza nokulandelana komjikelezo weplanethi iMercury okungenakuchazwa ngobuchwepheshe beNewtonian.
Isibonelo sezinkinga:
Ubukhulu bokushintsha kwe-perihelion kaMercury njengoba kuchazwa yi-general relativity? (Ipharamitha yobudlelwano A: amasekhondi angu-43 ngekhulu)
Ingxoxo:
Sebenzisa idatha enikeziwe ngqo:
Ngokusho kombono ka-Einstein jikelele wokuhlobana kwezinto, ukushintsha kwe-perihelion kweMercury okuchazwe kungamasekhondi angu-43 e-arc ngekhulu leminyaka, okuhambisana nemiphumela yokubuka.
I-Kesimpulan:
Ngokuqedela lezi zinkinga nezingxoxo zezibonelo, singabona ukuthi ubudlelwano buka-Einstein bunikeza kanjani ukuqonda okujulile kwesikhathi, ubude, kanye namandla adonsela phansi. Lo mbono awuzange uguqule umbono wethu wesayensi ngendawo yonke kuphela kodwa futhi unezinhlelo ezisebenzayo kwezobuchwepheshe besimanje, njengezinhlelo zokuzulazula ze-GPS, ezidinga ukulungiswa kobudlelwano ukuze zisebenze ngokunembile. Ukufunda nokuqonda ubudlelwano buka-Einstein kuyisinyathelo esibalulekile ekujuleni ezweni eliyinkimbinkimbi le-physics.
