He Whakamārama mō te Ariā Whakawhanaungatanga a Einstein
Nā ngā ariā a Albert Einstein mō te whanaungatanga, arā, te Ariā Motuhake o te Whakawhanaungatanga (1905) me te Ariā Whānui o te Whakawhanaungatanga (1915), i huri te māramatanga o te wāhi, te wā, me te kaha ā-papatipu. Ko ēnei ariā he pou o te ahupūngao hou, e awe ana i ngā momo mara mai i te ao tūroa ki te miihini irahiko. I roto i tēnei tuhinga, ka tūhuratia ngā kaupapa matua o ēnei ariā, ō rātou pānga, me ō rātou whakamanatanga whakamātautau.
### Ariā Motuhake o te Whakawhanaungatanga
Ko te Ariā Motuhake o Einstein mō te Whakawhanaungatanga e pā ana ki ngā mea e neke ana i ngā tere pumau—ngā anga tohutoro korekore. E rua ngā poutū e whakatūria ana:
1. Te Mātāpono o te Whakawhanaungatanga: He rite tonu ngā ture ahupūngao i roto i ngā anga tohutoro korekore katoa. Ko te tikanga tēnei kāore e taea e tētahi whakamātautau te wehewehe i tētahi anga korekore i tētahi atu.
2. Te Pūmautanga o te Tere o te Mārama: He pūmau te tere o te mārama i roto i te korehau mō ngā kaimātakitaki katoa, ahakoa te nekehanga whanaunga, te nekehanga rānei o te pūtake mārama.
Nā tēnei anga i hua mai ai ētahi whakatau hou:
#### Whakawhanuitanga o te Wā
Ko tētahi o ngā putanga tino whakamiharo ko te whakawhanuitanga o te wā. E ai ki te Whakawhanuitanga Motuhake, he whanaungatanga te haere o te wā, ā, e whakawhirinaki ana ki te tere o te kaimātakitaki. Ka pōturi ake te karaka e neke ana i te karaka tūmau. I roto i te pāngarau, ko te tātai whakawhanuitanga o te wā ko:
\[ \Delta t' = \Delta t / \sqrt{1 – v^2/c^2} \]
I konei, ko \( \Delta t' \) te wā i inehia e te kaimātakitaki e neke ana, ko \( \Delta t \) te wā i inehia e te kaimātakitaki tūmau, ko \( v \) te tere o te kaimātakitaki e neke ana, ā, ko \( c \) te tere o te mārama.
#### Te Whakaitinga o te Roa
E matapaetia ana hoki e te ariā te whakapoto roa: ka poto ake te nekehanga o ngā mea i te ahunga o tā rātou nekehanga. Ko te whakapoto e homai ana e:
\[ L' = L \sqrt{1 – v^2/c^2} \]
Ko \( L' \) te roa e inehia ana e te kaimātakitaki e neke ana, ā, ko \( L \) te roa i roto i te anga okiokinga o te mea.
#### Te Whakawhanaungatanga o te Whai Wā Kotahi
Kāore te ōritetanga i te tino tūturu i roto i te Whakawhanaungatanga Motuhake. Ko ngā kaupapa e kitea ana he ōritetanga ki tētahi kaimātakitaki, kāore pea i te pērā ki tētahi atu i roto i te nekehanga ōrite. Ka whakararuraru tēnei i tō tātou māramatanga tawhito mō te "ināianei" ao whānui.
#### Taurite Papatipu-Pūngao
I ahu mai te whārite rongonui a Einstein \( E = mc^2 \) i te Ariā Motuhake o te Whakawhanaungatanga, e kī ana he mea whakawhitiwhiti te papatipu me te pūngao. Ahakoa he iti noa te papatipu ka taea te huri hei nui rawa te pūngao, he tirohanga nui tēnei mō te ahupūngao karihi.
### Te Ariā Whānui o te Whakawhanaungatanga
Ka whakawhānuihia e te Whānuitanga Whānuitanga te Whānuitanga Motuhake ki te whakauru i te kaha ā-papatipu me te whakaterenga. I mua i a Einstein, i māramahia te kaha ā-papatipu mā te ture a Newton mō te kaha ā-papatipu whānui, e whakaatu ana i a ia hei kaha i waenganui i ngā papatipu. I whakaarohia anō e Einstein te kaha ā-papatipu ehara i te mea he kaha engari ko te piko o te wāhi-wā i puta mai i te papatipu me te pūngao.
#### Te Āwhiowhio o te Wāhi-ā-Rohe
I roto i te Whānuitanga Whānui, ka puta he piko i roto i te papanga wā-ā-whā ngā mea nunui. Ka neke ngā mea i ngā ara piko i roto i tēnei wā-ā-whā, e kiia ana he kukume ā-papa. He kupu whakarite ngāwari ko tētahi pōro taumaha e whakatakotoria ana ki runga i tētahi pepa rapa, ka piko ai te pepa. Ka whai noa ngā pōro iti e takahurihia ana i ngā ara piko ki te pōro taumaha.
Ko te whārite matua e whakahaere ana i tēnei piko ko te Whārite Marae a Einstein:
\[ R_{\mu \nu} – \frac{1}{2} R g_{\mu \nu} + \Lambda g_{\mu \nu} = \frac{8 \pi G}{c^4} T_{\mu \nu} \]
I konei, ko \( R_{\mu \nu} \) te tensor piko Ricci, ko \( R \) te piko tauine, ko \( g_{\mu \nu} \) te tensor ine, ko \( \Lambda \) te pūmau aorangi, ko \( G \) te pūmau ā-papatipu, ā, ko \( T_{\mu \nu} \) te tensor pūngao-aukati.
#### Ngā Pānga o te Whakawhanaungatanga Whānui
1. Te Whakawhanuitanga o te Wā i te Āhuatanga o te Papatūānuku: Ka pōturi ake te haere o te wā i roto i ngā āputa kaha ake o te āputa. I whakaūtia tēnei e te whakamātautau Pound-Rebka (1959) ā, he mea nui mō te tika o te GPS, me whai whakaaro ki ngā rerekētanga wā i puta mai i te āputa o te Papatūānuku.
2. Te Piko o te Mārama: Ka pā te mārama ki te taha o tētahi mea nui mā te whai i tētahi ara piko. I kitea tuatahitia tēnei i te wā o te korōtanga o te rā i te tau 1919 e Arthur Eddington, hei whakaū i te ariā.
3. Ngā Ngaru Ā-Toi: E matapaetia ana e te Whānuitanga Whānui ngā ngaru i roto i te wā-ā-wāhi i puta mai i te whakaterenga o ngā mea nunui, pērā i te hanumitanga o ngā pōro pango. I kitea tuatahitia ēnei ngaru e LIGO i te tau 2015, ā, i huaki ai he matapihi tirotiro hou ki te ao whānui.
4. Ngā Pū Pango: Mā ngā otinga ki ngā whārite o te mara ka matapaetia ngā rohe e hangaia ai e te piko ā-wāhi-wā he pae tawhiti e kore ai e taea te mawhiti atu i tua atu, e mōhiotia ana ko ngā pū pango. Ko ngā taunakitanga tirotiro, pērā i te pae tawhiti i tangohia e te Event Horizon Telescope i te tau 2019, e tautoko ana i tō rātou noho.
### Manatoko Whakamātautau
Kua whakamatautauria rawatia ngā ariā a Einstein, ā, kua whakaūtia hoki mā roto i ngā whakamātautau me ngā kitenga maha:
– Te Whakawhanuitanga o te Wā: Kua whakaūtia mā roto i ngā roanga ora o ngā matūriki i roto i ngā whakatere me ngā inenga karaka atomika tika i roto i ngā waka rererangi me ngā amiorangi.
– Te Piko o te Mārama: Ka kitea pinepinetia i te wā o ngā porowhita o te rā, mā te arotahi ā-papa, te wāhi e piko ai te mārama mai i ngā whetū tawhiti huri noa i ngā tupuni nunui.
– Te Huringa Whero o te Āhua-papa: I manatokohia mā te mātakitaki i te nekehanga o te auau mārama mai i ngā whetū, mā roto hoki i ngā whakamātautau tika pēnei i te Gravity Probe A.
### Whakamutunga
Nā ngā ariā whanaungatanga a Einstein i tino whakarerekē tō tātou māramatanga ki te ao whānui. Nā te Whakawhanaungatanga Motuhake i whakahou te wā me te wāhi, i whakatū ai i tō rāua hononga me te rerekētanga ki te nekehanga. I whakaurua mai e ia te ōritetanga papatipu-pūngao, he mea nui ki ngā tauhohenga karihi me te ahupūngao matūriki. I whakakapia e te Whakawhanaungatanga Whānui te ariā ā-papatipu a Newton, i whakamārama i te ā-papatipu hei piko ā-wāhi-wā, me te matapae i ngā āhuatanga pēnei i ngā ngaru ā-papatipu me ngā pōro pango, i whakaūtia e te arorangi me te ao tūroa o ēnei rā.
E hipa ana ngā mahi a Einstein i ngā ariā pūtaiao; i hurihia te rapunga whakaaro, i akiaki i te tangata kia whakaaroaro anō ki ngā ariā o te ao tūroa me te hanganga o te ao tūroa. Kei te mau tonu tōna taonga tuku iho i roto i ngā rangahau tonu e tūhura ana i ngā hohonutanga o te ao tūroa, mai i te kaha ā-papatipu ki ngā tauira ao tūroa, e akiakihia ana e ngā mātāpono i whakaaroarohia e ia i te rautau kua pahure.
