Isibonelo Semibuzo Yengxoxo Yokwelulwa Kwesikhathi
Ku-physics, umqondo wokwanda kwesikhathi uyinto ethakazelisayo nethakazelisayo ngaphakathi kombono okhethekile ka-Albert Einstein wokuhlobana kwezinto. Lo mbono unikeza umbono omusha wokuthi isikhala nesikhathi akuzona izinto eziphelele kodwa zihlobene kanjani, kuncike esivinini nasemgudwini wamandla adonsela phansi. Lesi sihloko sizohlola ukwanda kwesikhathi ngokuningiliziwe futhi sinikeze izibonelo zezinkinga.
Izisekelo Zombono Okhethekile Wokuhlobana
Ithiyori ekhethekile yokuhlobana ithi imithetho yefiziksi iyafana kubo bonke ababukeli abahamba emgqeni oqondile ngesivinini esingaguquki maqondana nomunye nomunye (amafreyimu angenawo amandla okubhekisela). Enye yemiphumela eyinhloko yale thiyori ukuthi ijubane lokukhanya endaweni engenamuntu lihlala njalo futhi alixhomekile ekunyakazeni komthombo noma kombonisi.
Isenzakalo sokwanda kwesikhathi sivela ngenxa yalezi zimo ezimbili. Sithi isikhathi sizohamba kancane kakhulu ngento ehamba eduze kwesivinini sokukhanya uma kuqhathaniswa nomqapheli omile.
Ifomula Yokwandisa Isikhathi
Ifomula esetshenziswa ukubala ukwandiswa kwesikhathi yilena elandelayo:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Di mana:
– \(\Delta t'\) = isikhathi esilinganiswa ngumqapheli ohambayo maqondana nesenzakalo esilinganiswayo.
– \(\Delta t\) = isikhathi esilinganiswa ngumqapheli omile (isikhathi ohlelweni olungenalo i-inertial).
– \(v\) = isivinini sento ehambayo.
– \(c\) = isivinini sokukhanya endaweni engenalutho (\(3 \izikhathi ezingu-10^8\) amamitha ngomzuzwana).
Ukuze sijulise ukuqonda kwethu lo mqondo, ake sibheke eminye imibuzo eyisibonelo kanye nezingxoxo zayo.
Isibonelo Umbuzo 1: Ukwelulwa Kwesikhathi Emkhathini
Umbuzo:
Indizamkhathi ihamba ngo-0.8c (80% wejubane lokukhanya) uma kuqhathaniswa noMhlaba. Kuzothatha isikhathi esingakanani ukuthi usomkhathi ongaphakathi kwendizamkhathi azizwe ihora elilodwa lesikhathi soMhlaba?
Ingxoxo:
Kuyaziwa:
– \(v = 0.8c\)
– \(\Delta t = 1\) amahora (isikhathi somhlaba)
Ukuze sithole isikhathi esibonwa yi-astronaut emkhathini), sisebenzisa ifomula yokwandiswa kwesikhathi:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Faka amanani aziwayo esikhundleni sawo:
\[ \Delta t' = \frac{1 \text{ hour}}{\sqrt{1 – (0.8)^2}} \]
\[ \Delta t' = \frac{1 \text{ hour}}{\sqrt{1 – 0.64}} \]
\[ \Delta t' = \frac{1 \text{ hour}}{\sqrt{0.36}} \]
\[ \Delta t' = \frac{1 \text{ hour}}{0.6} \]
\[ \Delta t' = \frac{1 \text{ hours}}{0.6} \cishe kube ngu-1.67 \text{ hours} \]
Ngakho-ke, isikhathi esidingwa yi-astronaut esemkhathini ukuze abhekane nehora eli-1 lesikhathi soMhlaba cishe singamahora ayi-1.67.
Isibonelo Umbuzo 2: Umphumela Wejubane Ekukhulisweni Kwesikhathi
Umbuzo:
Uma isikhathi esilinganiswa ngumqapheli eMhlabeni (isikhathi sesistimu ye-inertial) siyiminyaka emi-2, futhi umkhumbi-mkhathi uhamba ngesivinini sokukhanya esingu-90%, yisiphi isikhathi esilinganiswa ngumgibeli osemkhumbi-mkhathi?
Ingxoxo:
Kuyaziwa:
– \(v = 0.9c\)
– \(\Delta t = 2\) iminyaka
Ukuze sithole isikhathi esibonwa ngumgibeli endizeni, sisebenzisa ifomula yokwandisa isikhathi:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Faka amanani aziwayo esikhundleni sawo:
\[ \Delta t' = \frac{2 \text{ years}}{\sqrt{1 – (0.9)^2}} \]
\[ \Delta t' = \frac{2 \text{years}}{\sqrt{1 – 0.81}} \]
\[ \Delta t' = \frac{2 \text{years}}{\sqrt{0.19}} \]
\[ \Delta t' = \frac{2 \text{years}}{0.4359} \]
\[ \Delta t' \cishe 4.59 \umbhalo{ iminyaka} \]
Ngakho-ke, isikhathi esilinganiswa ngabagibeli abasemkhathini cishe siyiminyaka engu-4.59.
Isibonelo Umbuzo 3: Isikhathi Sokubona Ukuncishiswa Okude
Umbuzo:
Inhlayiya ihamba ngesivinini esingu-0.6c uma kuqhathaniswa nelebhu. Umqapheli elabhorethri ulinganisa isigamu sokuphila kwenhlayiya njengemizuzwana emi-2. Iyini isigamu sokuphila esilinganisiwe sesimiso sezinhlayiya?
Ingxoxo:
Kuyaziwa:
– \(v = 0.6c\)
– \(\Delta t = 2\) amasekhondi amancane
Ukuze uthole \(\Delta t'\), sebenzisa ifomula:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Faka amanani aziwayo esikhundleni sawo:
\[ \Delta t' = \frac{2 \text{ microseconds}}{\sqrt{1 – (0.6)^2}} \]
\[ \Delta t' = \frac{2 \text{ microseconds}}{\sqrt{1 – 0.36}} \]
\[ \Delta t' = \frac{2 \text{ microseconds}}{\sqrt{0.64}} \]
\[ \Delta t' = \frac{2 \text{ microseconds}}{0.8} \]
\[ \Delta t' = 2.5 \text{ microseconds} \]
Ngakho-ke, isigamu sokuphila esilinganisiwe sohlelo lwezinhlayiya singama-microsecond angu-2.5.
Ukuhlaziywa kanye nesiphetho
Kusukela ezibonelweni ezingenhla, singabona ukuthi ukwanda kwesikhathi kudlala indima ebalulekile ekuqondeni ukuthi isikhathi asiyona into engaguquki ngokuphelele. Ababukeli ezimweni ezahlukene ze-inertia bangaba nezilinganiso zesikhathi ezihlukene zesenzakalo esifanayo.
Ukuqonda okujulile kokwelulwa kwesikhathi kuvula ithuba lokuthola izinto ezintsha eziningi zobuchwepheshe, okuhlanganisa nomkhakha wamasathelayithi okuzulazula nge-GPS, adinga ukulungiswa okuhlobene ukuze kusebenze kahle. Ngaphezu kwalokho, lo mqondo uphonsela izingqondo zethu inselele yokuqonda indawo yonke kanye neqiniso ngombono ocebile noyinkimbinkimbi.
Ngakho-ke, ukwanda kwesikhathi akuyona nje umqondo wemfundiso kodwa futhi kunezindlela eziningi ezisebenzayo ekuthuthukisweni kobuchwepheshe nolwazi lwesayensi mayelana nendawo yonke esizungezile. Ukuqonda lezi zimiso kuyisinyathelo esibalulekile ohambweni lwethu lokuqonda ubuchwepheshe besikhathi esizayo nokuphendula imibuzo eyisisekelo mayelana nohlobo lwesikhala nesikhathi.
