The fundamentals of space-time: Part 2 - Andrew Pontzen and Tom Whyntie

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

Prevodilac: Miloš Milosavljević Lektor: Mile Živković

Light: it's the fastest thing in the universe,

Svetlost. To je najbrža stvar u svemiru,

but we can still measure its speed

ali ipak možemo izmeriti njenu brzinu.

if we slow down the animation,

Ako usporimo animaciju,

we can analyze light's motion using

možemo da analiziramo kretanje svetlosti

a space-time diagram,

koristeći prostorvremenski dijagram,

which takes a flipbook of animation panels,

koji koristi kinograf sa poljima za animaciju

and turns them on their side.

i okreće ih na stranu.

In this lesson, we'll add the single experimental fact

U ovoj lekciji, dodaćemo jednu eksperimentalnu činjenicu:

that whenever anyone measures just how fast light moves,

kad god neko izmeri koliko brzo se kreće svetlost,

they get the same answer:

dobija isti rezultat:

299,792,458 meters every second,

299.792.458 metara svake sekunde,

which means that when we draw light

što znači da kada nacrtamo svetlost na našem

on our space-time diagram,

prostorvremenskom dijagramu,

it's world line always has to appear at the same angle.

njena svetska linija uvek mora da se pojavi pod istim uglom.

But we saw previously that speed,

Ali prethodno smo videli da se brzina,

or equivalently world line angles,

odnosno uglovi svetske linije,

change when we look at things from

menja kad gledamo stvari

other people's perspective.

iz perspektive drugih ljudi.

To explore this contradiction,

Da bismo istražili ovu kontradikciju, pogledajmo

let's see what happens if I start moving

šta se dešava ako ja počnem da se krećem,

while I stand still and shine the laser at Tom.

dok ja i dalje stojim sa uperenim laserom ka Tomu.

First, we'll need to construct the space-time diagram.

Prvo treba da konstruišemo prostorvremenski dijagram.

Yes, that means taking all of

Da, to znači da uzmemo sva

the different panels showing the different moments in time

različita polja koja prikazuju različite

and stacking them up.

vremenske trenutke i složimo ih.

From the side, we see the world line

S ove strane, vidimo svetsku liniju

of the laser light at its correct fixed angle,

svetlosti lasera pod svojim utvrđenim ispravnim uglom,

just as before.

kao i pre.

So far, so good.

Zasad je dobro.

But that space-time diagram represents Andrew's perspective.

Ali ovaj prostorvremenski dijagram predstavlja Endruovu perspektivu.

What does it look like to me?

Kako to izgleda meni?

In the last lesson, we showed

U poslednjoj lekciji pokazali smo

how to get Tom's perspective moving all the panels

kako se Tomova perspektiva malo pomera po poljima,

along a bit until his world line is completely vertical.

dok njegova svetska linija ne postane potpuno vertikalna.

But look carefully at the light world line.

Ali pogledajte pažljivo svetsku liniju svetlosti.

The rearrangement of the panels

Preuređenje polja

means it's now tilted over too far.

znači da je sada suviše nagnuta.

I'd measure light traveling faster than Andrew would.

Ja bih izmerio veću brzinu svetlosti nego Endru.

But every experiment we've ever done,

Ali svaki eksperiment koji smo uradili,

and we've tried very hard,

a veoma smo se trudili,

says that everyone measures light to have a fixed speed.

kaže da svako uvek meri istu brzinu svetlosti.

So let's start again.

Da počnemo ispočetka.

In the 1900s, a clever chap named Albert Einstein

Početkom 20. veka, pametni momak po imenu Albert Ajnštajn

worked out how to see things properly,

smislio je kako da vidi stvari na pravi način

from Tom's point of view,

iz Tomove perspektive,

while still getting the speed of light right.

a da i dalje dobija isti rezultat brzine svetlosti.

First, we need to glue together the separate panels

Prvo treba da spojimo odvojena polja

into one solid block.

u jedan kompaktni blok.

This gives us our space-time,

Ovim dobijamo naše prostorvreme,

turning space and time into

pretvarajući prostor i vreme

one smooth, continuous material.

u ravni, homogeni materijal.

And now, here is the trick.

I evo u čemu je trik.

What you do is stretch your block of space-time

Istegnete vaš blok prostorvremena

along the light world line,

duž svetske linije svetlosti,

then squash it by the same amount,

a onda ga sabijete za istu vrednost, ali pod pravim

but at right angles to the light world line,

uglom u odnosu na svetsku liniju svetlosti

and abracadabra!

i... abrakadabra!

Tom's world line has gone vertical,

Tomova svetska linija je postala vertikalna,

so this does represent the world from his point of view,

tako da to predstavlja svet sa njegove tačke posmatranja,

but most importantly,

ali najvažnije je

the light world line has never changed its angle,

da svetska linija svetlosti uopšte nije promenila ugao

and so light will be measured by Tom

i tako će se svetlost koju meri Tom

going at the correct speed.

kretati ispravnom brzinom.

This superb trick is known as

Ovaj sjajni trik je poznat kao

a Lorentz transformation.

Lorencova transformacija.

Yeah, more than a trick.

Da, ali osim trika...

Slice up the space-time into

Podelite prostorvreme

new panels and you have

na nova polja i imaćete

the physically correct animation.

fizički ispravnu animaciju.

I'm stationary in the car,

Ja sam nepokretan u kolima,

everything else is coming past me

sve se kreće pored mene,

and the speed of light

a brzina svetlosti je

works out to be that same fixed value

ta ista utvrđena vrednost

that we know everyone measures.

koju znamo da svi mere.

On the other hand,

S druge strane,

something strange has happened.

nešto čudno se desilo.

The fence posts aren't spaced a meter apart anymore,

Razmak između stubova na ogradi nije više 1 metar,

and my mom will be worried

i moja mama će biti zabrinuta

that I look a bit thin.

što izgledam malo mršavo.

But that's not fair. Why don't I get to look thin?

Ali to nije u redu. Zašto ja ne izgledam mršavo?

I thought physics was supposed to be the same

Mislio sam da fizika treba da bude ista

for everyone.

za svakog.

Yes, no, it is, and you do.

Da... ne... jeste. Izgledaš.

All that stretching and squashing

Sve to istezanje i sabijanje

of space-time has just muddled together

prostorvremena je pomešalo

what we used to think of separately

ono što smo navikli da posmatramo odvojeno

as space and time.

kao prostor i vreme.

This particular squashing effect

Ovaj efekat sabijanja

is known as Lorentz contraction.

je poznat kao Lorencova kontrakcija.

Okay, but I still don't look thin.

Okej, ali i dalje nisam mršav.

No, yes, you do.

Ne. Da, jesi.

Now that we know better about space-time,

Sada kad znamo više o prostorvremenu,

we should redraw

trebalo bi da ponovo

what the scene looked like to me.

nacrtamo kako je ta scena izgledala meni.

To you, I appear Lorentz contracted.

Tebi, ja izgledam sabijen Lorencovom kontrakcijom.

Oh but to you, I appear Lorentz contracted.

Aha, ali tebi, ja izgledam sabijeno.

Yes.

Da.

Uh, well, at least it's fair.

Pa, barem je pravedno.

And speaking of fairness,

Kad govorimo o pravdi,

just as space gets muddled with time,

kao što se prostor meša s vremenom,

time also gets muddled with space,

vreme se takođe meša s prostorom

in an effect known as time dilation.

u efektu poznatom kao vremenska dilatacija.

No, at everyday speeds,

Pri običnim brzinama,

such as Tom's car reaches,

kao što je brzina Tomovog auta,

actually all the effects are much, much smaller

ovi efekti su mnogo manji

than we've illustrated them.

nego što smo ih prikazali.

Oh, yet, careful experiments,

Ali, pažljivi eksperimenti,

for instance watching the behavior of tiny particles

na primer posmatranje ponašanja sićušnih čestica

whizzing around the Large Hadron Collider

koje jure u Velikom hadronskom kolajderu,

confirmed that the effects are real.

potvrdili su da su efekti stvarni.

And now that space-time is

I sada, kada je

an experimentally confirmed part of reality,

potvrđeno da je prostorvreme deo realnosti,

we can get a bit more ambitious.

možemo da budemo i malo ambiciozniji.

What if we were to start playing

Šta ako počnemo da se igramo

with the material of space-time itself?

sa samim materijalom prostorvremena?

We'll find out all about that in the next animation.

Saznaćemo sve o tome u sledećoj animaciji.