Nā nīnau hoʻohālike a me ke kūkākūkā ʻana o ka Relativity o Einstein
ʻO ke ʻano pili o Einstein kekahi o nā kumumanaʻo koʻikoʻi loa i ka physics hou, e hoʻololi ana i ke ʻano o ko kākou hoʻomaopopo ʻana i ka hakahaka a me ka manawa. Loaʻa iā ia ʻelua mau ʻāpana: ke ʻano pili kūikawā (1905) a me ke ʻano pili laulā (1915). Ma kēia ʻatikala, e kūkākūkā mākou i kekahi mau laʻana e pili ana i ke ʻano pili o Einstein a kūkākūkā iā lākou e hāʻawi i kahi ʻike hohonu.
ʻO ka Relativity Kūikawā
Pili ka relativite kūikawā i nā mea e neʻe ana i nā wikiwiki mau e hoʻokokoke ana i ka wikiwiki o ka mālamalama. ʻElua mau hopena koʻikoʻi o kēia kumumanaʻo, ʻo ia ka hoʻonui ʻana o ka manawa a me ka hoʻoemi ʻana o ka lōʻihi.
1. Hoʻonui Manawa
Inā ʻelua mau mea nānā, hoʻokahi e kū ana ma ka Honua a ʻo kekahi e neʻe ana me ka wikiwiki, e ana lākou i nā manawa like ʻole no ka hanana like.
Laʻana pilikia:
Neʻe aku kahi astronaut ma 0.8 manawa o ka wikiwiki o ka mālamalama (c) i kahi hōkū he 10 mau makahiki māmā mai ka Honua. Pehea ka lōʻihi o ka hiki ʻana o ka astronaut i ka hōkū?
Kūkākūkā:
ʻO ka mea mua, helu mākou i ka manawa i ana ʻia e kahi mea nānā ma ka Honua:
\[ t_B = \frac{d}{v} = \frac{10 \text{ makahiki māmā}}{0.8 \, c} = 12.5 \text{ makahiki} \]
No ka helu ʻana i ka manawa i ana ʻia e ka astronaut (dilation manawa), hoʻohana mākou i ke ʻano hana:
\[ t_A = t_B \sqrt{1 – \frac{v^2}{c^2}} \]
E pani i nā waiwai i ʻike ʻia:
\[ t_A = 12.5 \sqrt{1 – (0.8)^2} \]
\[ t_A = 12.5 \sqrt{1 – 0.64} \]
\[ t_A = 12.5 \sqrt{0.36} \]
\[ t_A = 12.5 \times 0.6 \]
\[ t_A = 7.5 \text{ makahiki} \]
No laila, ʻo ka manawa i ana ʻia e nā astronauts he 7.5 mau makahiki.
2. Nā ʻūmiʻi lōʻihi
Ke neʻe kahi mea i ka wikiwiki e hoʻokokoke ana i ka wikiwiki o ka mālamalama, e ʻike ʻia kona lōʻihi he pōkole i ka mea nānā kūpaʻa.
Laʻana pilikia:
Ke holo nei kahi mokulele me ka lōʻihi maoli o 10 mika ma 0.9 manawa o ka wikiwiki o ka mālamalama. Pehea ka lōʻihi o ka mokulele i kahi mea nānā ma ka Honua?
Kūkākūkā:
No ka helu ʻana i ka hoʻemi ʻana o ka lōʻihi, hoʻohana mākou i ke ʻano hana:
\[ L = L_0 \sqrt{1 – \frac{v^2}{c^2}} \]
Ma hea:
– ʻO \( L_0 \) ka lōʻihi kūpono a i ʻole ka lōʻihi maoli (10 mika),
– ʻO \( v \) ka wikiwiki o ka mokulele (0.9c).
E pani i nā waiwai i ʻike ʻia:
\[ L = 10 \sqrt{1 – (0.9)^2} \]
\[ L = 10 \sqrt{1 – 0.81} \]
\[ L = 10 \sqrt{0.19} \]
\[ L = 10 manawa 0.436 \]
\[ L = 4.36 \text{ mika} \]
No laila, ʻo ka lōʻihi o ka mokulele e like me ka poʻe nānā ma ka Honua he 4.36 mika.
ʻO ka Relativity Laulā
Kūkākūkā ka relativi laulā i ka umekaumaha, kahi e hoʻopili ʻia ai ka hakahaka a me ka manawa e ka nuipa a me ka ikehu.
3. Maka aniani umekaumaha
Hana ʻia ka lensing umekaumaha ke pelu ʻia ka mālamalama mai kahi mea mamao e ka umekaumaha o kahi mea nui e like me ka galaxy a i ʻole ka lua ʻeleʻele.
Laʻana pilikia:
Loaʻa i ka Galaxy A ka nuipaʻa e hoʻohuli i ka mālamalama mai ka quasar B, aia ma hope ona. Inā he 1.5 kekona arc ke kihi deflection, he aha ka nuipaʻa o ka galaxy A? (E hoʻohana i ke kūpaʻa umekaumaha o Newton ʻo G = 6.674 × 10 ^ -11 N (m / kg) ^ 2, ka wikiwiki o ka mālamalama c = 3 × 10 ^ 8 m / s)
Kūkākūkā:
Hiki ke hāʻawi ʻia ke kihi o ka deflection θ e ke ʻano hana:
\[ \theta = \frac{4GM}{c^2 R} \]
Ma hea:
– ʻO \( G \) ke kūpaʻa umekaumaha,
– ʻO \( M \) ka nuipa o ka galaxy,
– ʻo \( c \) ka wikiwiki o ka mālamalama,
– ʻO \( R \) ka mamao kokoke loa ma waena o ka mālamalama a me ke kikowaena o ka galaxy.
No ka mea makemake mākou e ʻimi iā M, hoʻonohonoho hou mākou i ke ʻano:
\[ M = \frac{\theta c^2 R}{4G} \]
Manaʻo ʻia ʻo R he 5 × 10 ^ 20 mika (ka mamao awelika o nā galaxies). E hoʻololi iā θ mai nā arcseconds i nā radians (1 arcsecond = 4.848 × 10 ^ -6 radians):
\[ \theta = 1.5 \times 4.848 \times 10^{-6} \, \text{radian} = 7.272 \times 10^{-6} \, \text{radian} \]
E pani i nā waiwai i ʻike ʻia:
\[ M = \frac{(7.272 \times 10^{-6}) (3 \times 10^8)^2 (5 \times 10^{20})}{4 \times 6.674 \times 10^{-11}} \]
\[ M = \frac{(7.272 \times 10^{-6}) (9 \times 10^{16}) (5 \times 10^{20})}{26.696 \times 10^{-11}} \]
\[ M = \frac{(3.2764 \times 10^{31})}{26.696 \times 10^{-11}} \]
\[ M = 1.227 \times 10^{41} \, \text{kg} \]
No laila, ʻo ke kaumaha o ka galaxy A ma kahi o 1.227 × 10 ^ 41 kilokani.
4. Ka neʻe mua ʻana o Perihelion o Mercury
Hiki i ka relativiti laulā ke wehewehe i ka precession o ka orbit o ka honua ʻo Mercury ʻaʻole hiki ke wehewehe ʻia e nā mechanics Newtonian.
Laʻana pilikia:
He aha ka nui o ka neʻe ʻana o ka perihelion o Mercury e like me ka wehewehe ʻana e ka relativity laulā? (Ka palena pilina A: 43 arcseconds i kēlā me kēia kenekulia)
Kūkākūkā:
E hoʻohana pololei i ka ʻikepili i hāʻawi ʻia:
Wahi a ke kumumanaʻo laulā o Einstein no ka relativity, ʻo ka neʻe perihelion i wehewehe ʻia o Mercury he 43 arc kekona i kēlā me kēia kenekulia, kahi e kūlike pū ana me nā hopena nānā ʻana.
Ka hopena:
Ma ka hoʻopau ʻana i kēia mau pilikia hoʻohālike a me nā kūkākūkā, hiki iā mākou ke ʻike pehea e hāʻawi ai ka relativity a Einstein i kahi ʻike hohonu o ka manawa, ka lōʻihi, a me ke koʻikoʻi. ʻAʻole wale kēia kumumanaʻo i hoʻololi i kā mākou ʻike ʻepekema o ke ao holoʻokoʻa akā he mau noi kūpono hoʻi i ka ʻenehana hou, e like me nā ʻōnaehana hoʻokele GPS, e pono ai nā hoʻoponopono relativistic e hana pololei. ʻO ke aʻo ʻana a me ka hoʻomaopopo ʻana i ka relativity a Einstein he ʻanuʻu koʻikoʻi ia i ka ʻimi hohonu ʻana i loko o ke ao paʻakikī o ka physics.
