Mibvunzo yeMienzaniso neKukurukurirana kweEinstein's Relativity
Kuwirirana kwaEinstein ndeimwe yedzidziso dzakakosha mufizikisi yemazuva ano, ichichinja manzwisisiro atinoita nzvimbo nenguva. Ine zvikamu zviviri: special relativity (1905) uye general relativity (1915). Muchinyorwa chino, tichakurukura mienzaniso yakati wandei inosanganisira wirirano yaEinstein uye tichakurukura nezvayo kuti tinzwisise zvakadzama.
Kuwirirana Kwakakosha
Special relativity inobata zvinhu zvinofamba nekumhanya kwakafanana zvichiswedera pakumhanya kwechiedza. Migumisiro miviri mikuru yedzidziso iyi kuwedzera nguva uye kudzikira kwehurefu.
1. Kuwedzerwa Kwenguva
Kana paine vacherechedzi vaviri, mumwe akamira pasi pano uye mumwe achifamba nekumhanya kukuru, vanoyera nguva dzakasiyana dzechiitiko chimwe chete.
Muenzaniso wematambudziko:
Mutyairi wendege anofamba nekumhanya kwechiedza ka0.8 (c) akananga kunyeredzi iri kure nepasi pemakore gumi echiedza. Mutyairi wendege anotora nguva yakareba sei kuti asvike kunyeredzi?
Kukurukurirana:
Kutanga, tinoverenga nguva inoyerwa nemucherechedzi ari panyika:
\[ t_B = \frac{d}{v} = \frac{10 \text{ light years}}{0.8 \, c} = 12.5 \text{ years} \]
Kuti tiverenge nguva inoyerwa nemuchadenga (kuwedzera nguva), tinoshandisa fomura iyi:
\[ t_A = t_B \sqrt{1 – \frac{v^2}{c^2}} \]
Tsiva tsika dzinozivikanwa:
\[t_A = 12.5 \sqrt{1 – (0.8)^2} \]
\[t_A = 12.5 \sqrt{1 – 0.64} \]
\[t_A = 12.5 \sqrt{0.36} \]
\[t_A = 12.5 \kawa 0.6 \]
\[t_A = 7.5 \chinyorwa{makore} \]
Saka, nguva yakayerwa nevatyairi vendege yaive makore 7.5.
2. Kusungana Kurefu
Kana chinhu chichifamba nekumhanya kuri pedyo nekumhanya kwechiedza, kureba kwacho kuchaonekwa kupfupi kune munhu asingamiri.
Muenzaniso wematambudziko:
Chikepe chemuchadenga chine hurefu hwemamita gumi chaihwo chinofamba nekumhanya kwechiedza ka0.9 kanopfuura kumhanya kwechiedza. Chikepe chemuchadenga chingave chakareba sei kune muoni ari panyika?
Kukurukurirana:
Kuti tiverenge kureba kwekudzikira kwehurefu, tinoshandisa fomura:
\[ L = L_0 \sqrt{1 – \frac{v^2}{c^2}} \]
Di mana:
– \( L_0 \) ndiyo urefu hwakakodzera kana kuti urefu chaihwo (mamita gumi),
– \( v \) ndiyo kumhanya kwendege (0.9c).
Tsiva tsika dzinozivikanwa:
\[ L = 10 \sqrt{1 - (0.9)^2} \]
\[ L = 10 \sqrt{1 - 0.81} \]
\[ L = 10 \sqrt{0.19} \]
\[L = 10 \kawa 0.436 \]
\[ L = 4.36 \mashoko{ mamita} \]
Saka, kureba kwendege iyi, sekureva kwevacherechedzi vari paNyika, i4.36 metres.
Kuwirirana Kwakazara
Kuwirirana kwakajairika kunotaura nezvesimba rinokwevera pasi, uko nzvimbo nenguva zvinopesvedzerwa nehuremu nesimba.
3. Lenzi yegiravhiti
Kuona magirazi emudenga kunoitika kana chiedza chinobva kuchinhu chiri kure chikakombamiswa negiravhiti yechinhu chikuru chakadai segorofu kana gomba dema.
Muenzaniso wematambudziko:
Galaxy A ine huremu hwakakwana hwekudzora chiedza kubva kuquasar B, iyo iri shure kwayo. Kana kona yekutsauka iri 1.5 arc seconds, huremu hwegalaxy A chii? (Shandisai gravitational constant yaNewton G = 6.674×10^-11 N(m/kg)^2, kumhanya kwechiedza c = 3×10^8 m/s)
Kukurukurirana:
Kona yekutsauka θ inogona kupihwa nefomura:
\[ \theta = \frac{4GM}{c^2 R} \]
Di mana:
– \( G \) ndiyo simba rinokwevera pasi,
– \( M \) huremu hweboka renyeredzi,
– \( c \) ndiko kumhanya kwechiedza,
– \( R \) ndiyo daro riri pedyo pakati pechiedza nepakati pegorozi.
Sezvo tichida kuwana M, tinorongazve fomura:
\[ M = \frac{\theta c^2 R}{4G} \]
Ngatitii R i5×10^20 metres (avhareji yedaro remagalaxies). Shandura θ kubva kuma arcseconds kuenda kuma radians (1 arcsecond = 4.848×10^-6 radians):
\[ \theta = 1.5 \nguva 4.848 \nguva 10^{-6} \, \text{radian} = 7.272 \nguva 10^{-6} \, \text{radian} \]
Tsiva tsika dzinozivikanwa:
\[ M = \frac{(7.272 \kawa 10^{-6}) (3 \kawa 10^8)^2 (5 \kawa 10^{20})}{4 \kawa 6.674 \kawa 10^{-11}} \]
\[ M = \frac{(7.272 \kawa 10^{-6}) (9 \kawa 10^{16}) (5 \kawa 10^{20})}{26.696 \kawa 10^{-11}} \]
\[ M = \frac{(3.2764 \times 10^{31})}{26.696 \times 10^{-11}} \]
\[ M = 1.227 \kawa 10^{41} \, \text{kg} \]
Saka, huremu hwegiraxy A hunosvika 1.227×10^41 kg.
4. Kuenderera mberi kweMercury muPerihelion
Kuwirirana kwakajairika kunogonawo kutsanangura kuenderera mberi kwekufamba kwepasi reMercury uko kusingatsanangurike neNewtonian mechanics.
Muenzaniso wematambudziko:
Chii chiri kukura kwekuchinja kweperihelion kweMercury sezvinotsanangurwa ne general relativity? (Relation parameter A: 43 arcseconds per century)
Kukurukurirana:
Shandisa data rakapihwa zvakananga:
Zvinoenderana nedzidziso yaEinstein ye relativity, kutsanangurwa kwe perihelion shift yeMercury i43 arc seconds per century, izvo zvinoenderanawo nemhedzisiro yekucherechedza.
Mhedziso:
Nekupedzisa mienzaniso iyi yezvinetso nehurukuro, tinogona kuona kuti wirirano yaEinstein inopa sei kunzwisisa kwakadzama kwenguva, kureba, uye simba rinokwevera pasi. Dzidziso iyi haina kungochinja maonero edu esainzi pamusoro pezvinhu zvose asi inewo mashandisirwo anoshanda mu tekinoroji yemazuva ano, senge masisitimu ekufamba neGPS, ayo anoda kugadziriswa kwewirirano kuti ashande nemazvo. Kudzidza nekunzwisisa wirirano yaEinstein idanho rakakosha mukuongorora zvakadzama munyika yakaoma yefizikisi.
