Tauira o ngā Pātai Kōrero mō te Whakawhanui i te Wā
I roto i te ahupūngao, he āhuatanga whakamīharo, he mea whakamīharo hoki te ariā o te whakawhānui wā i roto i te ariā motuhake a Albert Einstein mō te whanaungatanga. Ka tukuna e tēnei ariā he tirohanga hou mō te kore e noho pūmau te wāhi me te wā, engari he whanaungatanga, e whakawhirinaki ana ki te tere me te kaha ā-papa. Ka tūhuratia e tēnei tuhinga te whakawhānui wā me te whakarato tauira.
Ngā Kaupapa Taketake o te Ariā Motuhake o te Whakawhanaungatanga
E ai ki te ariā motuhake o te whanaungatanga, he rite tonu ngā ture ahupūngao mō ngā kaimātakitaki katoa e neke ana i te rārangi tika i te tere pumau tetahi ki tetahi (ngā anga tohutoro inertia). Ko tētahi o ngā tino pānga o tēnei ariā ko te tere o te mārama i roto i te korehau he pumau, ā, kāore e whakawhirinaki ki te nekehanga o te pūtake, o te kaimātakitaki rānei.
Ko te āhua o te whakawhānui i te wā ka puta ake hei hua o ēnei whakapae e rua. E kī ana ka pōturi ake te neke o te wā mō tētahi mea e neke tata ana ki te tere o te mārama e pā ana ki tētahi kaimātakitaki tūmau.
Tātai Whakawhanui Wā
Ko te tātai i whakamahia hei tatau i te whakawhanuitanga o te wā e whai ake nei:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Kei hea:
– \(\Delta t'\) = te wā i inehia e te kaimātakitaki e neke ana e pā ana ki te kaupapa e inehia ana.
– \(\Delta t\) = te wā i inehia e te kaimātakitaki tūmau (te wā i roto i te pūnaha inertia).
– \(v\) = te tere o te mea e neke ana.
– \(c\) = te tere o te mārama i roto i te korehau (\(3 \times 10^8\) mita ia hekona).
Hei whakahōhonu ake i tō tātou māramatanga ki tēnei ariā, me titiro tātou ki ētahi tauira pātai me ō rātou matapakinga.
Tauira Pātai 1: Te Whakawhanuitanga o te Wā i runga i te Waka Ātea
Pātai:
Kei te neke tētahi waka mokowhiti i te 0.8c (80% o te tere o te mārama) e pā ana ki a Papatūānuku. Kia pēhea te roa ka pā ki tētahi kairangi i roto i te waka mokowhiti te kotahi hāora o te wā o Papatūānuku?
Kōrero:
E mōhiotia ana:
– \(v = 0.8c\)
– \(\Delta t = 1\) hāora (te wā o te whenua)
Hei kimi i te \(\Delta t'\) (te wā i pā ki te kairangi i roto i te waka mokowhiti), ka whakamahia e mātou te tātai whakawhanui wā:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Whakakapia ngā uara e mōhiotia ana:
\[ \Delta t' = \frac{1 \text{ haora}}{\sqrt{1 – (0.8)^2}} \]
\[ \Delta t' = \frac{1 \text{ haora}}{\sqrt{1 – 0.64}} \]
\[ \Delta t' = \frac{1 \text{ haora}}{\sqrt{0.36}} \]
\[ \Delta t' = \frac{1 \text{ haora}}{0.6} \]
\[ \Delta t' = \frac{1 \text{ hāora}}{0.6} \approx 1.67 \text{ hāora} \]
Nō reira, ko te wā e hiahiatia ana e te kairangi moana i roto i te waka mokowhiti hei wheako i te 1 hāora o te wā o Papatūānuku he tata ki te 1.67 hāora.
Tauira Pātai 2: Te Pānga o te Tere ki te Whakawhanuitanga o te Wā
Pātai:
Mena ko te wā e inehia ana e te kaimātakitaki i runga i te Ao (te wā pūnaha inertia) he 2 tau, ā, e 90% te tere o te mārama e tere ana te waka mokowhiti, he aha te wā e inehia ana e te pāhihi i runga i te waka mokowhiti?
Kōrero:
E mōhiotia ana:
– \(v = 0.9c\)
– \(\Delta t = 2\) tau
Hei kimi i te \(\Delta t'\) (te wā i pā ki te pāhihi i runga i te waka rererangi), ka whakamahia e mātou te tātai whakawhanui wā:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Whakakapia ngā uara e mōhiotia ana:
\[ \Delta t' = \frac{2 \text{ tau}}{\sqrt{1 – (0.9)^2}} \]
\[ \Delta t' = \frac{2 \text{ tau}}{\sqrt{1 – 0.81}} \]
\[ \Delta t' = \frac{2 \text{ tau}}{\sqrt{0.19}} \]
\[ \Delta t' = \frac{2 \text{ tau}}{0.4359} \]
\[ \Delta t' \tata ki te 4.59 \kuputuhi{ tau} \]
Nō reira, ko te wā i inehia e ngā pāhihi i roto i te waka mokowhiti he 4.59 tau pea.
Tauira Pātai 3: Te Wā ki te Wheako i ngā Whakawhiu Roa
Pātai:
Kei te neke tētahi matūriki i te tere o te 0.6c e pā ana ki te taiwhanga. Kei te ine tētahi kaimātakitaki i roto i te taiwhanga i te haurua-ora o te matūriki hei 2 maikorohekona. He aha te haurua-ora o te pūnaha matūriki kua inehia?
Kōrero:
E mōhiotia ana:
– \(v = 0.6c\)
– \(\Delta t = 2\) maikorohekona
Hei kimi i te \(\Delta t'\), whakamahia te tātai:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Whakakapia ngā uara e mōhiotia ana:
\[ \Delta t' = \frac{2 \text{ maikorohekona}}{\sqrt{1 – (0.6)^2}} \]
\[ \Delta t' = \frac{2 \text{ maikorohekona}}{\sqrt{1 – 0.36}} \]
\[ \Delta t' = \frac{2 \text{ maikorohekona}}{\sqrt{0.64}} \]
\[ \Delta t' = \frac{2 \text{ maikorohekona}}{0.8} \]
\[ \Delta t' = 2.5 \text{ maikorohekona} \]
Nō reira, ko te haurua-ora o te pūnaha matūriki i inehia he 2.5 maikirohekona.
Tātaritanga me te Whakatau
Mai i ngā tauira i runga ake nei, ka kite tātou i te hiranga o te whānui o te wā ki te mārama ehara te wā i te pūmau tuturu. Ka taea e ngā kaimātakitaki i roto i ngā āhua rerekē o te korekore te whai i ngā inenga wā rerekē mō te kaupapa kotahi.
Mā te māramatanga hohonu ake ki te whakawhanuitanga o te wā ka huaki te kuaha ki ngā auahatanga hangarau maha, tae atu ki te ao o ngā amiorangi whakatere GPS, e hiahia ana ki ngā whakatikatika whanaungatanga kia tika ai te mahi. Hei tāpiri, ka werohia e tēnei ariā ō tātou hinengaro kia mārama ki te ao me te mooni mai i tētahi tirohanga whai kiko ake, matatini ake hoki.
Nō reira, ehara i te mea he ariā noa iho te whakawhānui wā engari he whānui hoki ngā tono mahi i roto i te whanaketanga o te hangarau me te mātauranga pūtaiao mō te ao tūroa e karapoti nei i a tātou. Ko te mārama ki ēnei mātāpono he taahiraa nui i roto i tā tātou haerenga ki te mōhio ki ngā hangarau o te heke mai, me te whakautu i ngā pātai matua mō te āhua o te wāhi me te wā.
