Laʻana o nā nīnau kūkākūkā o ka hoʻonui manawa
I loko o ke ʻano physics, he mea hoihoi a hoihoi ka manaʻo o ka hoʻonui ʻana i ka manawa i loko o ke kumumanaʻo kūikawā o Albert Einstein no ka relativity. Hāʻawi kēia kumumanaʻo i kahi kuanaʻike hou i ke ʻano o ka hakahaka a me ka manawa ʻaʻole he mau mea paʻa akā he pilina, e hilinaʻi ana i ka wikiwiki a me ke koʻikoʻi. E ʻimi kikoʻī kēia ʻatikala i ka hoʻonui ʻana i ka manawa a hāʻawi i nā laʻana.
Nā Kumu o ke Kumumanaʻo Kūikawā o ka Relativity
ʻŌlelo ke kumumanaʻo kūikawā o ka relativity ua like nā kānāwai o ka physics no nā mea nānā a pau e neʻe ana ma kahi laina pololei ma ka wikiwiki mau me ka pili ʻana kekahi i kekahi (nā kiʻi inertial o ka kuhikuhi). ʻO kekahi o nā hopena nui o kēia kumumanaʻo, ʻo ia ka wikiwiki o ka mālamalama i loko o kahi hakahaka he mau a ʻaʻole ia e hilinaʻi i ka neʻe ʻana o ke kumu a i ʻole ka mea nānā.
ʻO ka hanana o ka hoʻonui ʻana o ka manawa e kū mai ana ma muli o kēia mau postulate ʻelua. Ua ʻōlelo ʻia e neʻe mālie ka manawa no kahi mea e neʻe kokoke ana i ka wikiwiki o ka mālamalama e pili ana i kahi mea nānā paʻa.
Formula Hoʻonui Manawa
ʻO ke ʻano i hoʻohana ʻia no ka helu ʻana i ka dilation manawa penei:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Ma hea:
– \(\Delta t'\) = ka manawa i ana ʻia e kahi mea nānā e neʻe ana e pili ana i ka hanana e ana ʻia ana.
– \(\Delta t\) = ka manawa i ana ʻia e kahi mea nānā paʻa (manawa i loko o kahi ʻōnaehana inertial).
– \(v\) = ka wikiwiki o ka mea e neʻe ana.
– \(c\) = ka wikiwiki o ka mālamalama i loko o kahi hakahaka (\(3 \times 10^8\) mika i kekona).
I mea e hoʻoikaika ai i ko kākou ʻike i kēia manaʻo, e nānā kākou i kekahi mau nīnau hoʻohālike a me kā lākou mau kūkākūkā ʻana.
Laʻana Nīnau 1: Hoʻonui Manawa ma luna o kahi Mokulele
Nīnau:
Ke neʻe nei kahi mokulele ma 0.8c (80% o ka wikiwiki o ka mālamalama) e pili ana i ka Honua. Pehea ka lōʻihi o ka manawa e ʻike ai kahi astronaut i loko o ka mokulele i hoʻokahi hola o ka manawa Honua?
Kūkākūkā:
Ua ʻike ʻia:
– \(v = 0.8c\)
– \(\Delta t = 1\) hola (manawa honua)
No ka loaʻa ʻana o \(\Delta t'\) (ka manawa i ʻike ʻia e ka astronaut ma ka mokulele), hoʻohana mākou i ke ʻano hoʻonui manawa:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
E pani i nā waiwai i ʻike ʻia:
\[ \Delta t' = \frac{1 \text{ hola}}{\sqrt{1 – (0.8)^2}} \]
\[ \Delta t' = \frac{1 \text{ hola}}{\sqrt{1 – 0.64}} \]
\[ \Delta t' = \frac{1 \text{ hola}}{\sqrt{0.36}} \]
\[ \Delta t' = \frac{1 \text{ hola}}{0.6} \]
\[ \Delta t' = \frac{1 \text{ hola}}{0.6} \approx 1.67 \text{ hola} \]
No laila, ʻo ka manawa e pono ai no kahi astronaut i loko o kahi mokulele e ʻike ai i 1 hola o ka manawa Honua ma kahi o 1.67 mau hola.
Laʻana Nīnau 2: Ka Hopena o ka wikiwiki ma ka hoʻonui ʻana i ka manawa
Nīnau:
Inā ʻelua mau makahiki ka manawa i ana ʻia e kahi mea nānā ma ka Honua (manawa ʻōnaehana inertial), a ke neʻe nei kahi moku lewa ma 90% o ka wikiwiki o ka mālamalama, he aha ka manawa i ana ʻia e kahi mea holo ma luna o ka moku lewa?
Kūkākūkā:
Ua ʻike ʻia:
– \(v = 0.9c\)
– \(\Delta t = 2\) mau makahiki
No ka loaʻa ʻana o \(\Delta t'\) (ka manawa i ʻike ʻia e ka mea holo ma ka mokulele), hoʻohana mākou i ke ʻano hoʻonui manawa:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
E pani i nā waiwai i ʻike ʻia:
\[ \Delta t' = \frac{2 \text{ makahiki}}{\sqrt{1 – (0.9)^2}} \]
\[ \Delta t' = \frac{2 \text{ makahiki}}{\sqrt{1 – 0.81}} \]
\[ \Delta t' = \frac{2 \text{ makahiki}}{\sqrt{0.19}} \]
\[ \Delta t' = \frac{2 \text{ makahiki}}{0.4359} \]
\[ \Delta t' \approx 4.59 \text{ makahiki} \]
No laila, ʻo ka manawa i ana ʻia e nā ohua ma ka mokulele ma kahi o 4.59 mau makahiki.
Laʻana Nīnau 3: Ka Manawa e ʻIke ai i nā ʻŌpū Lōʻihi
Nīnau:
Ke neʻe nei kekahi ʻāpana ma ka wikiwiki o 0.6c e pili ana i ka hale hana. Ke ana nei kekahi mea nānā ma ka hale hana i ka hapalua ola o ka ʻāpana ma ke ʻano he 2 microseconds. He aha ka hapalua ola o ka ʻōnaehana ʻāpana i ana ʻia?
Kūkākūkā:
Ua ʻike ʻia:
– \(v = 0.6c\)
– \(\Delta t = 2\) mau mikrosekona
No ka loaʻa ʻana o \(\Delta t'\), e hoʻohana i ke ʻano hana:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
E pani i nā waiwai i ʻike ʻia:
\[ \Delta t' = \frac{2 \text{ microseconds}}{\sqrt{1 – (0.6)^2}} \]
\[ \Delta t' = \frac{2 \text{ microseconds}}{\sqrt{1 – 0.36}} \]
\[ \Delta t' = \frac{2 \text{ microseconds}}{\sqrt{0.64}} \]
\[ \Delta t' = \frac{2 \text{ microseconds}}{0.8} \]
\[ \Delta t' = 2.5 \text{ microseconds} \]
No laila, ʻo ka hapalua ola o ka ʻōnaehana ʻāpana i ana ʻia he 2.5 microseconds.
Ka Nānā ʻana a me ka Hopena
Mai nā hiʻohiʻona ma luna, hiki iā mākou ke ʻike pehea e pāʻani ai ka hoʻonui ʻana o ka manawa i kahi kuleana koʻikoʻi i ka hoʻomaopopo ʻana ʻaʻole he mau paʻa loa ka manawa. Hiki i nā mea nānā ma nā kūlana inertial like ʻole ke loaʻa nā ana manawa like ʻole no ka hanana like.
ʻO ka ʻike hohonu ʻana i ka hoʻonui ʻana o ka manawa e wehe i ka puka i nā hana hou he nui, me ke kahua o nā satelite hoʻokele GPS, e pono ai nā hoʻoponopono relativistic no ka hana pololei. Eia kekahi, hoʻokūkū kēia manaʻo i ko mākou manaʻo e hoʻomaopopo i ke ao holoʻokoʻa a me ka ʻoiaʻiʻo mai kahi kuanaʻike waiwai a paʻakikī hoʻi.
No laila, ʻaʻole wale ka hoʻonui ʻana o ka manawa he manaʻo kumumanaʻo akā he mau noi kūpono ākea hoʻi i ka hoʻomohala ʻana i ka ʻenehana a me ka ʻike ʻepekema e pili ana i ke ao holoʻokoʻa a puni mākou. ʻO ka hoʻomaopopo ʻana i kēia mau loina he ʻanuʻu koʻikoʻi ia i kā mākou huakaʻi i ka hoʻokele ʻana i nā ʻenehana e hiki mai ana a me ka pane ʻana i nā nīnau kumu e pili ana i ke ʻano o ka lewa a me ka manawa.
