Ajụjụ Ihe Nlereanya Na-atụle Mmetụta nke Mmekọrịta Einstein
Echiche Einstein banyere mmekọrịta, gụnyere ozizi pụrụ iche na nke izugbe ya banyere mmekọrịta, agbanweela nghọta anyị banyere oghere, oge, na ike ndọda. Ọ bụ ezie na Einstein bu ụzọ webata echiche ndị a na mmalite narị afọ nke 20, mmetụta ha na sayensị na teknụzụ nke oge a dị oke ukwuu. Isiokwu a ga-enyocha ọtụtụ nsogbu ihe atụ ndị na-enyocha mmetụta dị ukwuu nke mmekọrịta Einstein n'ọtụtụ ọnọdụ ma gosipụta otu ozizi a si agbanwe echiche sayensị anyị.
Ajụjụ Ihe atụ nke 1: Mgbasa Oge na Njem Eluigwe
Ajụjụ:
Onye na-aga mbara igwe na-aga kpakpando afọ ìhè anọ site n'ụwa na ọsọ ìhè okpukpu 0,8 (0,8c). Ogologo oge ole ka onye na-aga eluigwe na ala chere na njem ahụ ga-ewe?
Azịza:
Iji ghọta ihe na-eme ka oge gbasaa, anyị na-eji usoro bụ isi nke mmekọrịta pụrụ iche:
\[t' = \frac{t}{\gamma} \]
ebe \( \gamma \) bụ ihe Lorentz nke enyere site na:
\[ \gamma = \frac{1}{\sqrt{1 – \left(\frac{v}{c}\right)^2}} \]
N'ebe a, \( v = 0,8c \) na \( c \) bụ ọsọ nke ìhè. Mgbe ahụ,
\[ \gamma = \frac{1}{\sqrt{1 – (0,8)^2}} = \frac{1}{\sqrt{1 – 0,64}} = \frac{1}{\sqrt{0,36}} = \frac{1}{0,6} \ihe dị ka 1,667 \]
Ọ bụrụ na anya nke kpakpando ahụ bụ afọ ìhè anọ, onye na-aga mbara igwe ahụ na-agagharịkwa n'ọsọ nke 0,8c, oge onye na-ekiri ihe na-eme n'ụwa (t) hụrụ bụ:
\[ t = \frac{Ogologo} {Ọsọ} = \frac{4 \text{afọ ọkụ}}{0,8c} = 5 \text{afọ} \]
Agbanyeghị, oge onye na-aga mbara igwe (t') nwere bụ:
\[ t' = \frac{t}{\gamma} = \frac{5 \text{ afọ}}{1,667} \ihe dị ka 3 \text{ afọ} \]
Ya mere, dịka ndị na-aga mbara igwe si kwuo, njem ahụ were naanị ihe dị ka afọ atọ, ọ bụ ezie na site n'echiche ụwa, o were afọ ise.
Ajụjụ Ihe Nlereanya nke 2: Mkpụkọ Ogologo na Nleba Anya Nnwale
Ajụjụ:
A tụrụ ụgbọ elu mbara igwe mita 100 n'ogologo ma e jiri ya tụnyere ụwa. Ọ bụrụ na ụgbọ elu mbara igwe ahụ na-agagharị n'ọsọ nke 0,6c ma e jiri ya tụnyere onye na-ekiri ihe n'ụwa, ogologo oge ole ka ọ dị onye na-ekiri ihe n'ụwa?
Azịza:
Mkpụkọ ogologo bụ mmetụta ọzọ gbasara mmekọrịta site na njikọ pụrụ iche, nke egosipụtara site na:
\[ L = L_0 \sqrt{1 – \left(\frac{v}{c}\right)^2} \]
ebe \( L_0 \) bụ ogologo ihe ahụ mgbe ọ na-ezu ike, \( v \) bụ ọsọ mmekọrịta, na \( L \) bụ ogologo ihe ahụ n'ọsọ mmekọrịta. Maka ụgbọelu ahụ:
\[ L_0 = 100 \ederede{ mita}, \; v = 0,6c, \ederede{ mgbe ahụ} \]
\[ L = L_0 \sqrt{1 – \left(\frac{v}{c}\right)^2} = 100 \sqrt{1 – (0,6)^2} = 100 \sqrt{1 – 0,36} = 100 \sqrt{0,64} = 100 \ugboro 0,8 = 80 \text{mita} \]
Ya mere, dịka ndị na-ekiri ihe na-eme n'ụwa si kwuo, ogologo nke ụgbọelu ahụ bụ mita iri asatọ.
Ajụjụ Ihe Nlereanya nke 3: Ike ndọda na Echiche nke Njiko Izugbe na GPS
Ajụjụ:
Satellite GPS na-agbagharị Ụwa n'ebe dị elu nke kilomita 20.200 n'elu ụwa na ọsọ nke ihe dị ka kilomita 3,874 n'otu awa. Jiri relativity izugbe gbakọọ oge satellite GPS kwesịrị ime kwa ụbọchị iji tụlee mmetụta nke ike ndọda ụwa.
Azịza:
Satellite GPS ga-agbanwe oge ha maka mmetụta abụọ bụ isi: mgbasa oge n'ihi oke ọsọ (njikọ pụrụ iche) na mgbasa oge n'ihi oke ike ndọda (njikọ izugbe). Agbanyeghị, anyị ga-elekwasị anya na mmetụta nke ike ndọda ebe a:
Site n'iji ozizi nke njiko ihe n'ozuzu, oge ga-agafe nwayọ nwayọ n'ọhịa ike ndọda siri ike. Usoro maka njiko ihe doro anya site na njiko ihe n'ozuzu bụ:
\[ t_g = t_0 \ekpe( 1 – \frac{2GM}{Rc^2} \nri) \]
ebe \(R \) bụ anya site na etiti ndọda ike, \(G \) bụ ihe ndọda ike, \(M \) bụ oke nke Ụwa, \(c \) bụ ọsọ nke ìhè, na \(t_0 \) bụ oge nke onye na-ekiri ihe 'na-eguzo' n'elu ụwa.
E nyere:
– Ibu nke Ụwa, \( M \ihe dị ka 5,972 \ugboro 10^{24} \text{ kg} \)
– radius nke ụwa, \( R_{\text{surface}} \ihe dịka 6.371 \times 10^6 \text{ m} \)
– Ogologo satịlaịtị, \( H = 20.200 \ugboro 10^3 \ederede{ m} \)
– Ya mere, anya dị site n'etiti ụwa ruo na satịlaịtị, \( R = R_{\text{surface}} + H \approx 26.571 \times 10^6 \text{ m} \)
Oge dị iche n'etiti satịlaịtị na elu ụwa kwa ụbọchị, ma e jiri naanị ike ndọda mee ihe:
\[ \Delta t_g \approx \frac{2GM}{c^2} \left( \frac{1}{R_{\text{surface}}} – \frac{1}{R} \right) \]
Ịdochi ya:
\[ \Delta t_g \approx \frac{2 \times 6,67408 \times 10^{-11} \text{ m}^3 \text{ kg}^{-1} \text{ s}^{-2} \times 5,972 \times 10^{24} \text{ kg}}{(3 \times 10^8 \text{ m/s})^2} \left( \frac{1}{6,371 \times 10^6 \text{ m}} – \frac{1}{26,571 \times 10^6 \text{ m}} \right) \]
Mgbe agbakọchara ya, nsonaazụ a na-adaba na mmezi oge kwa ụbọchị maka satịlaịtị GPS, nke dị ihe dị ka maịkroskond asaa nwayọ karịa oge elu ụwa. Ya mere, satịlaịtị GPS kwesịrị ịtụle mmetụta a iji nọgide na-enwe izi ezi.
Mmetụta Dị Ukwuu Na Teknụzụ na Nghọta nke Eluigwe na Ala
Ihe atụ ndị a na-eme ka o doo anya na mmekọrịta Einstein abụghị naanị ozizi anụ ahụ nkịtị kamakwa o nwekwara ọtụtụ ojiji bara uru. Site na mgbasa oge na njem mbara igwe ruo na mkpụkọ ogologo na mmezi oge na teknụzụ GPS, mmekọrịta Einstein emeela nnukwu mmetụta.
Mmepụta ihe ọhụrụ n'ọtụtụ ngalaba teknụzụ, sayensị, na ọbụna nkà ihe ọmụma na-egosi mmetụta nke ozizi ahụ. Relativity emeela ka inyocha mbara igwe dị omimi, mmepe nke teknụzụ nkwukọrịta ka mma, na nghọta ọhụrụ nke cosmology na oghere ojii.
N'ikpeazụ, ozizi Einstein nke ikwurịta okwu ka bụ akụkụ dị mkpa nke ọmụmụ ihe gbasara fizik nke oge a ma nọgide na-abụ isi iyi nke mkpali na nchọpụta maka ndị ọkà mmụta sayensị n'ụwa niile.
