The fundamentals of space-time: Part 1 - Andrew Pontzen and Tom Whyntie

Osnove prostorvremena: Prvi deo - Endru Poncen (Andrew Pontzen) i Tom Vajnti (Tom Whyntie)

Prevodilac: Miloš Milosavljević Lektor: Mile Živković

Space: it's where things happen.

Prostor je: ono gde se nešto dešava.

Time: it's when things happen.

Vreme je: ono kada se nešto dešava.

We can measure where things are

Možemo izmeriti gde se nešto nalazi

and when things take place,

i kada se nešto dešava,

but in modern physics,

ali u modernoj fizici

we realize when and where

vidimo da su "kada" i "gde"

are actually part of the same question.

u stvari delovi jednog istog pitanja.

Because when it comes to understanding the universe,

Jer kad se radi o razumevanju svemira,

we need to replace three-dimensional space plus time

treba da zamenimo trodimenzionalni prostor plus vreme

with a single concept:

jednim pojmom:

four-dimensional space-time.

četvorodimenzionalnim prostorvremenom.

We'll explore and explain space-time

Istražićemo i objasniti prostorvreme

in this series of animations.

u ovom nizu animacija.

Animations?

Animacija?

Yeah.

Da.

Well, we're not very animated are we?

Pa, nismo baš animirani, zar ne?

Sure we are! Look, I can go from here to here.

Naravno da jesmo. Vidi, mogu da odem odavde dovde.

Whoa! How'd you get from here to there?

Kako si stigao odavde do tamo?

How fast did you go?

Koliko brzo si išao?

Did you run? Walk?

Jesi li trčao? Hodao?

Did you even go in a straight line?

Jesi li uopšte išao pravolinijski?

Ah! To answer that, you'll need to make our cartoon physics

Da bih na to odgovorio, moramo da napravimo našu animiranu fiziku

look more like physics physics.

da izgleda više kao prava fizika.

You'll need more panels.

Trebaće vam više sličica.

More panels, please!

Još sličica molim!

Okay, in each panel, Andrew's in a slightly different place.

Dobro. Na svakoj sličici, Endru je na malo drugačijem mestu.

So I can see each one records

Tako da ja vidim da svaka pokazuje

where Andrew is at a different time.

gde je Endru u različitom trenutku.

That's great. But it would be easier to see

To je odlično. Ali, bilo bi lakše videti šta se dešava

what's going on if we could cut out

kad bismo isekli

all the hundreds of panels and stack them up

sve te stotine sličica i složili ih

like a flip book.

kao kineograf.

Right, now let's flip through the book

Tako, a sada da ga izlistamo

so that we can see one panel after another

da bismo videli sličice jednu za drugom

getting through 24 in every second.

kako prolaze, 24 u sekundi.

See! I told you it was an animation.

Vidite! Rekao sam vam da je to animacija.

Now you can see me walking along.

Sada možete da me vidite kako hodam.

Drawing all those panels and putting them into a flip book

Crtanje svih ovih sličica i njihovo slaganje u kineograf

is just one way of recording the way I'm moving.

samo je jedan način prikazivanja toga kako se krećem.

It's how animation, or even movies, work.

Tako animacije, ili čak i filmovi, funkcionišu.

As it turns out, at my walking speed,

Kako vidimo, brzinom kojom ja hodam,

it takes two seconds to get past each fence post,

potrebno je dve sekunde da prođem svaki stubić ograde,

and they're spaced four meters apart.

a razmak između njih je 4 metra.

So we can calculate my velocity --

Tako da možemo izračunati da je moja brzina -

how fast I'm moving through space - -

koliko brzo se krećem kroz prostor -

is two meters per second.

dva metra u sekundi.

But I could've worked that out from the panels

Ali do toga sam mogao da dođem pomoću sličica

without flipping through them.

bez njihovog listanja.

From the edge of the flip book,

Gledajući kineograf odozgo

you can see all of the copies of the fence posts

možete videti sve primerke stubića

and all of the copies of Andrew

i sve primerke Endrua,

and he's in a slightly different place in each one.

a on je na svakom od njih na malo drugačijem mestu.

Now we can predict everything that will happen to Andrew

Možemo predvideti sve što će se desiti Endruu

when we flip through 24 pages every second,

ako okrećemo 24 stranice svake sekunde,

including his speed of motion,

uključujući i njegovu brzinu kretanja,

just by looking.

samo posmatranjem.

No need to flip through at all.

Ne moramo uopšte da okrećemo strane.

The edge of this flip book

Pogled odozgo na ovaj kineograf

is known as a space-time diagram

je poznat kao prostorvremenski dijagram

of Andrew's journey through, you guessed it,

Endruovog putovanja kroz, pogodili ste,

space and time.

prostor i vreme.

We call the line that represents Andrew's journey

Liniju koja predstavlja Endruov put nazivamo

his world line.

njegovom svetskom linijom.

If i jog instead of walking,

Ako trčim umesto da hodam,

I might be able to get past a fence post every second.

možda ću prolaziti pored stubića za 1 sekundu.

He's not very athletic.

On nije baš sportski tip.

Anyway, when we look at this new flip book from the edge,

Svejedno, ako posmatramo odozgo ovaj novi kineograf,

we can do the same analysis as before.

možemo da uradimo istu analizu kao malopre.

The world line for Andrew jogging

Svetska linija Endrua koji džogira

is more tilted over

je nakrivljenija

than the world line for Andrew walking.

nego svetska linija Endrua kad hoda.

We can tell he's going twice as fast as before

Možemo da vidimo da se kreće dvaput brže

without flipping the panels.

bez listanja sličica.

But here's the clever bit.

Ali evo domišljatog dela.

In physics, it's always good to view things from other perspectives.

U fizici je uvek dobro pogledati stvari iz drugih perspektiva.

After all, the laws of physics

Ipak, fizički zakoni

should be the same for everyone

treba da budu isti za svakoga

or no one will obey them.

ili ih niko neće poštovati.

So let's rethink our cartoon

Da razmotrimo onda ponovo naš crtać

and have the camera follow Andrew jogging along

i stavimo kameru da prati Endrua kako džogira

as the fence posts approach and pass behind him.

dok prolazi stubiće ograde.

Still viewing it as a flip book of panels,

Gedajući ga još uvek kao kineograf,

we don't need to redraw anything.

ne moramo ništa ponovo da crtamo.

We simply move all of the cutout frames slightly

Samo malo pomerimo sve sličice zajedno

until Andrew's tilted world line

dok Endruova iskošena svetska linija

becomes completely vertical.

ne postane potpuno vertikalna.

To see why, let's flip it.

Da bismo videli zašto, hajde da izlistamo.

Yes, now I'm stationery, just jogging on the spot,

Da, sad sam u jednom mestu, samo trčim na tački

in the center of the panel.

u centru sličice.

On the edge of the flip book,

Gledajući kineograf odozgo,

my world line was going straight upwards.

moja svetska linija je išla pravo nagore.

The fence posts are coming past me.

Stubići prolaze pored mene.

It's now their world lines that are tilted.

Sada su njihove svetske linije iskošene.

This rearrangement of the panels is known as a

Ovo preuređivanje sličica je poznato kao

Galilean transformation,

Galilejeva transformacija

and it lets us analyze physics from someeone else's perspective.

i dopušta nam da analiziramo fiziku iz tuđe perspektive.

In this case, mine.

U ovom slučaju - moje.

After all, it's always good to see things from other points of view,

Uvek je dobro videti stvari iz perspektive drugih,

especially when the viewers are moving

naročito kad se posmatrači kreću

at different speeds.

različitim brzinama.

So long as the speeds aren't too high.

Sve dok brzine ne postanu suviše velike.

If you're a cosmic ray moving at the speed of light,

Ako ste kosmički zrak koji se kreće brzinom svetlosti,

our flip book of your point of view falls apart.

naš kineograf vaše tačke posmatranja se raspada.

To stop that from happening,

Da bismo to sprečili,

we'll have to glue panels together.

moramo da slepimo sličice.

Instead of a stack of separate panels,

Umesto hrpe odvojenih sličica,

we'll need a solid block of space-time,

trebaće nam homogen blok prostorvremena,

which we'll come to in the next animation.

do čega ćemo doći u sledećoj animaciji.