
Thai: 
เราได้สำรวจ
อะไรไปมากด้วยการทดลองการความคิด
โดยผมลอยอยู่ในอวกาศ
ผมอยู่ที่ศูนย์กลางกรอบอ้างอิงของผม
ตรงที่เวลาเท่ากับ 0
ในกรอบอ้างอิงของผม
เพื่อนคนหนึ่งเดินทาง
ด้วยยานอวกาศผ่านผมไป
ด้วยความเร็ว v
ผมจะบอกว่าขนาดเท่ากับ v
และมันเดินทางในทิศบวก x
เราจะสนใจ
เราสนใจ
แค่มิติ x เพื่อให้ง่าย
และเราได้คิดถึงการหลอมรวมสเปซ
กับเวลาในกรอบอ้างอิงของผม
เทียบกับกรอบอ้างอิงของเธอ
ปริศนาที่เราเจอ
ในวิดีโอที่แล้วคือว่า เราจะจัดการ
ให้อัตราเร็วแสง
เท่าเดิมเสมอ
สำหรับทุกกรอบอ้างอิงได้อย่างไร?
เพื่อจัดการเรื่องนี้ เราต้อง
สร้างแนวคิดเรื่องสเปซเวลาขึ้นมา
ผมควรพูดเร็วกว่านี้ สเปซเวลา
สเปซเวลา ขอผมเขียนนะ spacetime
ครั้งแรกที่ผมได้ยินคนพูดว่าสเปซเวลา
ผมคิดว่าคนเขาพูดถึง

Bulgarian: 
Вече успяхме
да проучим
много неща с нашия
малък мисловен експеримент,
при който се нося
в Космоса.
Аз съм в центъра на
моята отправна система
и точно при
време равно на 0
в отправната ми система
един приятел идва в космически кораб,
който ме подминава
със скорост v,
ще кажа, че големината е v,
и това се движи
в положителна посока х.
Ще се фокусираме –
и се фокусирахме –
просто върху измерение х,
за да опростим нещата.
И мислихме за съгласуването
на Космос и време
в отправната си система
в сравнение с нейната
отправна система.
Главоблъсканицата,
пред която бях изправен в предишни видеа,
е как да съгласуваме това,
че скоростта на светлината
винаги ще е същата
във всяка отправна система.
И за да ги съгласуваме,
трябваше да изнамерим
идеята за пространство-времето.
Трябва да го кажа още по-бързо –
пространство-време.
Нека го запиша –
пространство-време.
И първият път, когато чух
за пространство-времето,
предположих, че хората
говореха просто

English: 
- [Voiceover] So we've
already been able to explore
a lot with our little thought experiment
where I am floating in space.
I'm at the center of
my frame of reference,
and right at time equals zero
in my frame of reference,
a friend comes in a
spaceship passing me by
with a velocity v,
I'll say the magnitude is v,
and it's going in the
positive x direction.
We're just going to focus,
and we have been focusing,
just on the x dimension for simplicity.
And we've thought about reconciling space
and time in my frame of reference
relative to her frame of reference.
The conundrum that we've faced
in previous videos is how do we reconcile
that the speed of light is always
going to be the same in
every frame of reference?
And to reconcile them, we
had to essentially come
up with the idea of spacetime.
I should say it even faster, spacetime.
Spacetime, let me write it out, spacetime.
And the first time I
heard about spacetime,
I assumed that people were just talking

Korean: 
지금까지 우리는 사고 실험을 통해
우주 공간의 한 점의 상황에 대해
살펴 볼 수 있었습니다
제가 제 기준으로 중심이 되고,
시간이 0초일 때,
제 기준계로
우주선에 타고 있는 친구가
속도 v로 저를 지나칩니다
속도의 크기를 v라고 두고,
양의 x축 방향으로 이동한다고 합시다
우리는 지금까지
그리고 앞으로도,
간단함을 위해 x축 차원만 고려합니다
우리는 서로 다른 기준틀의
시간과 공간 간의
관계를 생각하였습니다
우리가 이전의 동영상에서
부딫힌 난제는 빛의 속도가 일정하개
어떻게 두 기준틀을
조정할 수 있는지입니다
두 기준틀을 조정하기 위해서는
시공간이라는 아이디어를 떠올려야 합니다
시간과 공간이라고 하지 않고, 
붙여서 시공간이라고 부르겠습니다
시공간이라고 합쳐서 적겠습니다
제가 처음에 시공간에 대해 들었을 때에는
사람들이 그저

Korean: 
시간과 공간을 서로 독립된 것으로 생각하고
그 위에 자신의 점을 찍는 것이라고 생각했습니다
그러나 시공간이라고 함은,
둘이 합쳐진 하나의 연속체를 의미하는 것이고,
시간과 공간은 시공간에서의
서로 다른 방향에 불과합니다
이것을 시공간 말고도,
다른 이름으로
불러도 그렇게 큰
상관은 없습니다
그러나 중요한 것은 이것은 시공간이고,
시간과 공간이 합쳐진 연속체의 개념이라는 것입니다
시공간을 표현하려고 할 때,
빛의 속력이 절대적으로 일정하기 위해서는
시간과 공간이
기존에 생각하였던 대로
서로 독립적이지 않고
절대적이지 않음을 알 수 있습니다
우리는 이 민코우스키 공간의
다이어그램을 각각의
기준틀에 대하여 그렸습니다
이 시공간 다이어그램의
제 기준틀은
흰색으로 그려져 있고,
제 친구의 기준틀은
다이어그램 안에서
파란색으로 나타나 있습니다
이 두 축, x축과 x'축
사이에 형성된 각,

English: 
about space and time as independent things
and just plotting your
point in space and time.
But when people talk about spacetime,
they're really talking about
this continuum of one thing,
and we're just talking
about different directions
in spacetime.
They could have called
this something else.
They could have called this spime,
or tace, or stace,
or a lot of different things.
But this is spacetime,
and it's this idea that
it's this continuum.
And when we started to
make spacetime diagrams,
we realized in order
for the speed of light
to be absolute, that time and space
weren't as independent of each other
as we thought, and they
weren't as absolute
as we thought.
And we constructed these Minkowsky
spacetime diagrams for each
of our frames of reference.
So my frame of reference,
the spacetime diagram,
is here in white,
and for my friend's frame of reference,
her spacetime diagram is here
in this blue color.
The angle formed between these axes,
between the x and the x prime axis

Thai: 
สเปซกับเวลาเป็นสิ่งที่แยกจากกัน
เวลาพลอตจุดในสเปซกับเวลา
แต่เวลาคนเขาพูดถึงสเปซเวลา
เขากำลังหมายถึงสิ่งที่เป็นหนึ่งเดียว
และเราแค่พูดถึงทิศต่างๆ ของ
สเปซเวลา
เราเรียกมันเป็นอย่างอื่นก็ได้
เขาจะเรียกมันว่า spime
หรือ tace หรือ stace ก็ได้
ตั้งชื่อได้หลายอย่างเลย
แต่ spacetime นี้
มันคือแนวคิดที่ว่า มันเป็นปริมาณต่อเนื่อง
และเมื่อเราเริ่มสร้างแผนภาพสเปซเวลา
เรารู้ว่าเพื่อให้อัตราเร็วแสง
เป็นปริมาณสัมบูรณ์ เวลากับสเปซ
ต้องไม่อิสระจากกันอย่างที่เรา
เคยคิด และพวกมันไม่ใช่ปริมาณสัมบูรณ์
อย่างที่เคยคิด
และเราได้สร้างแผนภาพสเปซเวลา
มินคอฟสกีให้
กรอบอ้างอิงของเราแต่ละอัน
กรอบอ้างอิงของผม
แผนภาพสเปซเวลา
ตรงนี้สีขาว
และกรอบอ้างอิงของเพื่อนผม
แผนภาพสเปซเวลาของเธออยู่ตรงนี้
วาดด้วยสีฟ้า
มุมที่ทำระหว่างแกนเหล่านี้
ระหว่างแกน x กับแกน x ไพรม์

Bulgarian: 
за пространството и времето
като независими неща
и просто поставяме на графиката
точката в пространството и времето.
Но когато хората говорят
за пространство-времето,
те говорят за този континуум
от едно нещо
и просто говорим за
различни посоки
в пространство-времето.
Можеха да го нарекат
и по друг начин.
Можеха да го нарекат
коме или врекос, или косвре,
или много различни неща.
Но това е
пространство-времето
и е тази идея,
че то е континуум.
И когато започнахме да правим
пространствено-времеви диаграми,
осъзнахме, че за да може скоростта
на светлината да е абсолютна,
времето и пространството
не са независими една от друга,
както си мислехме,
и не са толкова абсолютни,
колкото си мислехме.
И създадохме тези
пространствено-времеви
диаграми на Минковски
за всяка от нашите отправни системи.
Отправната ми система,
пространствено-времевата
диаграма
е тук в бяло,
а за отправната система
на приятелката ми,
нейната пространствено-времева
диаграма
е в този син цвят.
Ъгълът, образуван
между тези оси,
между оста х
и оста х'

Thai: 
และแกน ct กับ ct ไพรม์
มุมอัลฟานี่ตรงนี้
มุมนี้จะขึ้นอยู่กับ
ความเร็วสัมพัทธ์ของเธอ
ในกรอบอ้างอิงของผม
ถ้าความเร็วของเธอเป็น v
หรือขนาดความเร็วของเธอเป็น v
ในกรอบอ้างอิงของผม
มุมนี้ที่เราเห็น
จะเป็นอินเวอร์สแทนเจนต์
หรืออาร์กแทนเจนต์ของอัตราส่วน
ระหว่างความเร็วสัมพัทธ์ของเธอ
กับอัตราเร็วแสง
ค่านี้จะเท่ากับอินเวอร์สแทนเจนต์
ของ v ส่วน c
ยิ่งเธอเร็วเท่าไหร่
สองตัวนี้จะเริ่มบีบหากันมากขึ้น
และถ้าเธอเข้าหาอัตราเร็วแสง
มุมทั้งสองจะเข้าใกล้ 45 องศา
และเริ่มซ้อนกัน
ถ้าเขาเดินทางเข้าใกล้
อัตราเร็วแสงจริงๆ
มันน่าสนใจอยู่แล้ว
แนวคิดที่ว่าสเปซกับเวลาไม่ได้
อิสระจากกัน มันต่อเนื่องกัน
เรียกว่าสเปซเวลา 
แต่พวกคุณบางคนอาจบอกว่า

Bulgarian: 
и ct и оста ct',
този ъгъл алфа тук,
това ще зависи от
нейната сравнителна скорост
в моята отправна система.
Ако нейната скорост е v,
или големината
на нейната скорост е v,
в моята отправна система,
този ъгъл, както вече видяхме,
ще е обратно пропорционалният
тангенс,
или арктангенсът,
на съотношението
между нейната
сравнителна скорост
и големината на скоростта
на светлината.
Това ще е равно на обратно пропорционалния
тангенс на v върху с.
Колкото по-бързо
се движи тя,
тези две неща ще започнат
да се сближават,
и ако някак тя се доближи до
скоростта на светлината,
и двете ще доближат
ъгъл от 45 градуса
и ще започнат
да съвпадат,
ако тя успее да се доближат
до скоростта на светлината.
И това вече е интересно –
тази идея, че пространството
и времето не са толкова независими,
че всичко това е континуум,
наречен пространство-време,
но някои от вас
вероятно казаха:

Korean: 
그리고 ct축과 ct'축 사이의
각 알파는
제 기준틀과의 상대 속도에
영향을 받는 값입니다
만약 상대 속도가 v라면,
또는 속도의 크기가 v라면,
제 기준틀에서 보았을 때
이 각은
광속과 상대 속도의 비율의
탄젠트의 역함수,
또는 arctan의
값이 됩니다
따라서 이것은 v/c의
탄젠트 역함수의 값입니다
따라서 더 빠르게 움직일수록
이 두 선은 더욱 가까워지게 되고,
만약 빛의 속도에 접근하게 되면
두 각은 45도에 가까워지게 되고
광속에 가까워지면서
두 직선이
서로 만나기 시작합니다
시간과 공간이 분리되어 있지 않고,
시공간이라는 하나의 연속체라는
아이디어는 매우 흥미롭습니다
그러나 여러분들 중

English: 
and the ct and the ct prime axis,
this angle alpha here,
this is going to be dependent on her
relative velocity in
my frame of reference.
So if her velocity is v,
or the magnitude of her velocity is v
in my frame of reference,
this angle we've already seen
is going to be the inverse tangent
or the arctangent of the ratio
between her relative velocity
and the speed of light.
So this is going to be
equal to the inverse tangent
of v over c.
So the faster she goes,
these two things are going
to start squeezing together,
and if somehow she were
to approach the speed
of light, they would both
approach a 45 degree angle
and actually start to coincide
if they were actually able to approach
the speed of light.
And that's all interesting already,
this idea that space and time are not
as independent, that it's all a continuum
called spacetime, but some
of you have probably said,

Korean: 
일부분은 좀 더 구체적인
숫자들을 다루고 싶을 것입니다
예를 들어, 시공간에서의 이 사건은
제 기준틀에 대해서도
생각해 볼 수 있고,
제 친구의 기준틀에 대해서도
생각해 볼 수 있습니다
제 기준틀에서는
이 좌표를 관찰합니다
이 좌표는 x가 되고,
이곳의 좌표는
ct가 됩니다
이전에 동영상에서 어째서
시간을 ct의 형태로 나타내는지에 대해 설명했습니다
축들의 단위는 미터 단위입니다
우리는 이를 빛-거리라고도 생각할 수 있습니다
이것들은 제 기준틀에서의
좌표축이 됩니다
제 친구의 기준틀에서는
좌표가 어떻게 될까요?
우리는 이미 민코우스키 공간 다이어그램을
어떻게 해석하는지 알고 있습니다
x'축의 좌표를 구하기 위해서는
ct축에 평행하도록 선을 긋습니다
그러면 이것이
다른 기준틀의 x'좌표가 됩니다
ct'축의 좌표를 구하기 위해서는
x'축에 평행하게 선을 긋습니다

English: 
well, I want to deal with some more
tangible numbers here.
For example, if this event right over here
in spacetime, we can think about it
from my frame of reference,
and we can think about it
from her frame of reference.
In my frame of reference,
I would view the coordinates here.
This coordinate would be x,
and this coordinate right over here
would be ct.
We had a whole video on why we think
of time in terms of ct.
The units here literally would be meters.
We could think of it as
light-meters if we like.
So that would be the coordinates
in my frame of reference.
Well, what would be the coordinates
in her frame of reference?
Well, we've already
thought about how to read
these Minkowski spacetime diagrams.
To find her x prime coordinate,
we would just go parallel
to the ct prime axis.
So that would be the x prime coordinate
in her frame of reference.
And to figure out the ct prime coordinate,
we would just go parallel
to the x prime axis.

Thai: 
ฉันอยากได้เลขที่
จับต้องได้ตรงนี้
ตัวอย่างเช่น ถ้าเหตุการณ์นี้ตรงนี้
ในสเปซเวลา เราคิดถึงมัน
จากกรอบอ้างอิงของผมได้
และเราคิดถึง
จากกรอบอ้างอิงของเธอได้
ในกรอบอ้างอิงของผม
ผมมองพิกัดตรงนี้
พิกัดนี้จะเป็น x
และพิกัดนี่ตรงนี้
จะเป็น ct
เรามีวิดีโออธิบายสาเหตุที่เราคิด
ถึงเวลาในรูปของ ct อยู่
หน่วยตรงนี้จะเป็นเมตร
เราคิดเป็นเมตรแสงก็ได้ถ้าต้องการ
นั่นคือพิกัด
ในกรอบอ้างอิงของผม
แล้วพิกัดในกรอบอ้างอิง
ของเธอจะเป็นเท่าใด?
เราคิดวิธีอ่าน
แผนภาพสเปซเวลามินคอฟสกีไปแล้ว
เวลาหาพิกัด x ไพรม์
เราก็ขนานไปกับแกน ct ไพรม์
มันจะเป็นพิกัด x ไพรม์
ในกรอบอ้างอิงของเธอ
แล้วเวลาหาพิกัด ct ไพรม์
เราก็ขนานไปกับแกน x ไพรม์

Bulgarian: 
"Искам да работя с
по-осезателни числа тук.
Например ако това събитие тук
в пространство-времето...
можем да мислим за него
от моята отправна система
и можем да мислим
за него
от нейната отправна система.
В моята отправна система
щях да гледам
координатите тук.
Тази координата ще е х,
а тази координата тук
ще е ct."
Имахме цяло видео за това
защо мислим за времето
по отношение на ct.
Мерните единици тук
ще са метри.
Можем да мислим за това като за
светлинни-метри, ако искаме.
Това ще са координатите
в моята отправна система.
Какви ще са координатите
в нейната отправна система?
Вече мислихме върху това
как да разчитаме
тези пространствено-времеви
диаграми на Минковски.
За да намерим нейната
координата х',
просто ще преминем успоредно
на оста ct'.
Това ще е координатата х'
в нейната отправна система.
За да намерим координатата ct',
просто ще преминем успоредно
на оста х'.

Bulgarian: 
Това ще е координатата
ct'.
Как ще преминеш между тях,
ще трансформираш,
от х в х'
и от ct в ct'?
За да направим това,
в това видео ще се запознаем
с трансформациите
на Лоренц.
И те ни позволяват
да направим
точно това,
което трябва да направим.
Позволяват ни да преминем
от (х; ct)
до (х'; ct').
За да ни помогнат
да помислим за това,
ще въведа някои
променливи
и се надявам,
че това ще покаже
симетрията на
трансформациите на Лоренц.
Може да ги видиш записани
по други начини в други източници
и ще съгласуваме
всички тези в бъдещето.
Но трансформациите на Лоренц –
ще започнем с това,
което наричаме Лоренцов фактор,
понеже той често се появява
в трансформацията.

English: 
So this would be the ct prime coordinate.
Now how do you actually go in between,
transform, from x to x prime
and from ct to ct prime?
And to do that, we're going to introduce
in this video the Lorentz transformations.
And what they do is they allow us to do
exactly what we just needed to do.
They'll allow us to go from x, ct
to x prime
and ct prime.
And to help us think about it,
I'm going to introduce some variables,
and hopefully it will show the symmetry
of the Lorentz transformations.
You might see them written in other ways
in other sources, and we'll reconcile all
of those in the future.
But the Lorentz transformations,
we'll start with what we
call the Lorentz factor
because this shows up a lot
in the transformation.

Korean: 
이것이 ct'좌표입니다
그렇다면 정확히 어떻게
x좌표에서 x'좌표로, ct좌표에서 ct'좌표로
변환할 수 있을까요?
이것을 위해 이 동영상에서는
로렌츠 변환을 소개하겠습니다
이것은 우리가 하려는 것을
정확히 가능하게 만들어 줍니다
이를 통해 x좌표와 ct좌표에서
x'좌표로,
ct'좌표로 변환할 수 있습니다
이해를 돕기 위하여
저는 몇 가지 변수들을 소개하겠습니다
이를 통해 로렌츠 변환의
대칭성을 관찰할 수 있습니다
다른 문헌에서는 다른 형태로
표현되어 있을 수도 있는데,
그것들은 모두 다 같은 이야기입니다
로렌츠 인자라는 것부터
소개하겠습니다
로렌츠 변환에서 매우 많이
등장하는 변수이기 때문입니다

Thai: 
ค่านี้จะเป็นพิกัด ct ไพรม์
ทีนี้ คุณจะไปมา
แปลงจาก x เป็น x ไพรม์
หรือจาก ct ไป ct ไพรม์อย่างไร?
เวลาทำ เราจะแนะนำ
เรื่องการแปลงลอเรนซ์ในวิดีโอนี้
และสิ่งที่มันทำ คือมันทำให้เรา
แก้สิ่งที่เราต้องการได้
มันทำให้เราไปจาก (x, ct)
เป็น x ไพรม์
กับ ct ไพรม์ได้
เพื่อช่วยคิด
ผมจะเพิ่มตัวแปร
หวังว่ามันจะแสดงสมมาตร
ของการแปลงลอเรนซ์ได้
คุณอาจเห็นคนเขียนแบบอื่น
ที่อื่น และเราจะทำให้ตรงกัน
ในอนาคต
การแปลงลอเรนซ์
เราจะเริ่มด้วยสิ่งที่เราเรียกว่า ตัวคูณลอเรนซ์
เพราะมันปรากฎบ่อยมาก
ในการแปลง

Thai: 
ผมจะนิยามมันไว้ล่วงหน้า
ตัวคูณลอเรนซ์ เแทนด้วยตัวอักษรกรีก
แกมมา แกมมาเล็ก
มันเท่ากับ 1 ส่วนรากที่สอง
ของ 1 ลบ v กำลังสองส่วน c กำลังสอง
ทีนี้ บางครั้งคุณอาจเห็นเขาเขียนเป็น
ผมจะเขียนอีกแบบแล้วกัน
บางครั้งคุณอาจเห็นเขาเขียนว่าแกมมา
ขอผมใช้สีเดิมนะ
สีแดงๆ เหมือนเดิม
แกมมาเท่ากับ 1 ส่วนรากที่สอง
ชอง 1 ลบบีต้ากำลังสอง
คุณอาจถามว่า แล้วบีต้าคืออะไร?
บีต้าคือตัวแปรอีกตัวที่ปรากฎ
บ่อยๆ เมื่อเราคิดถึงสัมพัทธภาพพิเศษ
บีต้าก็คืออัตราส่วน
ระหว่างความเร็วสัมพัทธ์
ความเร็วสัมพัทธ์ของเธอ
ในกรอบอ้างอิงของผม
และอัตราเร็วแสง
มันปรากฎบ่อย
แม้แต่มุมอัลฟาตรงนี้
เราบอกได้ว่า มันคืออินเวอร์สแทนเจนต์

English: 
So I'll just define this ahead of time.
So the Lorentz factor,
denoted by the Greek letter
gamma, lowercase gamma,
it is equal to one over the square root
of one minus v squared over c squared.
Now sometimes you might
even see it written like,
well, I'll write it another way.
Sometimes you might see
it written as gamma,
let me do it in that same color,
same reddish color,
gamma is equal to one over the square root
of one minus beta squared.
You might say, well, what is beta?
Well, beta is another
variable that shows up
a lot when we're thinking
about special relativity.
And beta is just the ratio
between the relative velocity,
her relative velocity in
my frame of reference,
and the speed of light.
It shows up a lot,
even this angle alpha here,
we could have said this
is the inverse tangent

Bulgarian: 
Просто ще определя това
предварително.
Лоренцовият фактор,
обозначен с гръцката буква гама,
малка гама,
е равен на
1 върху корен квадратен
от 1 минус v^2
върху с^2.
Понякога може да го видиш
записано така –
ще го запиша
по друг начин.
Понякога може да го видиш
записано като гама –
нека направя това
в същия цвят,
същия червеникав цвят,
гама е равно на
1 върху корен квадратен
от 1 минус
бета на квадрат.
Може да попиташ:
"Какво е това бета?"
Бета е друга променлива,
която често се появява,
когато мислиш за
специалната  теория на относителността.
И бета е просто
отношението
между относителната скорост,
нейната относителна скорост
в отправната ми система,
и скоростта
на светлината.
Често се появява.
Дори този ъгъл
алфа тук –

Korean: 
따라서 이를 먼저 정의하도록 하겠습니다
그리스 소문자 감마로 표현되는
로렌츠 인자는
1 빼기 v제곱/c제곱의 제곱근 분의
1입니다
다른 형태로 표현할 수도 있는데,
지금 적도록 하겠습니다
가끔씩 로렌츠 인자는
위와 같은, 그리스 소문자
감마로 표현되는데,
감마는 루트 1 빼기 베타 제곱 분의
1로 표현됩니다
베타가 무엇일까요?
베타는 마찬가지로 특수상대성이론을
다룰 때 자주 등장하는 변수입니다
베타는 단순히 제 기준틀과
다른 기준틀 간의 상대 속도와
빛의 속도의
비율입니다
매우 많이 등장하는데,
예를 들어 이 각 알파도
그냥 베타의

Korean: 
탄젠트 역함수라고 할 수 있습니다
이는 로렌츠 인자를 사용하게 되면
더 단순하게 됩니다
그리고 실제로 두 좌표 사이의
변환을 보면, 베타가
제가 사용하는 방식에서는
매우 유용함을 볼 수 있습니다
실제로 x'좌표의 값을
어떠한 방법으로
구할 수 있는지를
설명하겠습니다
x'좌표의 값은
로렌츠 인자에
x에
베타에 ct를
곱한 것을 뺀 것을 곱한 것입니다
그리고 ct'의 값을 어떻게 구하는지를
설명하겠습니다
같은 색으로 쓰도록 합시다

English: 
of beta.
This becomes a little bit
simpler when you write
the Lorentz factor.
And when we look at the
actual transformation
between the coordinates,
we'll see that beta
becomes useful again, at least the way
I like to write it.
So if we want to think about what x prime
is going to be, so we can write
x prime is going to be equal
to the Lorentz factor,
let me do it in that red color,
is going to be equal to the Lorentz factor
times x
minus, and now we're going to say
beta times ct,
and ct prime
is going to be equal to
the Lorentz factor gamma,
let me do that same color again,

Bulgarian: 
можем да кажем, че това е
обратно пропорционалния тангенс от бета.
Това става малко по-просто,
когато запишеш Лоренцовия фактор.
И когато гледаме
реалната трансформация
между координатите,
ще видим, че бета отново става полезна,
поне по начина, по който предпочитам
да я запиша.
Ако искам да помисля
какво ще е х'...
Можем да запишем,
че х' ще е равно
на Лоренцовия фактор –
нека запиша това
в този червен цвят –
ще е равно на
Лоренцовия фактор по х
минус – и сега ще кажем
бета по ct –
и ct'
ще е равно на
Лоренцовият фактор гама –
ще запиша това
в същия цвят,

Thai: 
ของบีต้า
สูตรนี้จะเขียนง่ายขึ้นมากเมื่อคุณเขียน
ตัวคูณลอเรนซ์
และเมื่อเราดูการแปลงระหว่าง
พิกัดจริงๆ เราจะเห็นว่าบีต้า
จะมีประโยชน์อีก อย่างน้อยตามที่
ผมชอบเขียน
ถ้าเราอยากคิดว่า x ไพรม์
จะเป็นเท่าใด เราก็เขียน
x ไพรม์ได้เท่ากับ
ตัวคูณลอเรนซ์
ขอผมใช้สีแดงนั้นนะ
จะเท่ากับตัวคูณลอเรนซ์
คูณ x
ลบ ตอนนี้เราจะบอกว่า
บีต้าคูณ ct
และ ct ไพรม์
จะเท่ากับตัวคูณลอเรนซ์ แกมมา
ขอผมใช้สีเดิมอีกครั้ง

English: 
switching colors is sometimes difficult,
gamma times, and we'll see it's just
the other way around.
It is going to be c,
let me do it in that green color,
ct
minus, you might even guess what I'm
about to write based on the symmetry
that we see here,
ct minus beta times x.
And I really want you to appreciate this
because it really shows
that space and time
are really just different directions
in the spacetime and
there's a nice symmetry
to them right over here.
Notice we have an x and we have an x.
We have a ct and we have a ct.
So when we're thinking about x prime,
it's x minus beta times ct,
and we're scaling it
by the Lorentz factor,

Korean: 
ct'의 값을 구하는 과정은
x'을 구하는 과정과 유사합니다
그저 변수를 바꾼 것 뿐입니다
녹색으로 쓰도록 하겠습니다
ct'의 값은
로렌츠 인자 감마에
ct에 베타 곱하기 x'을 뺀 것을
곱한 것입니다
여기서 두 변수 간의
대칭성을 볼 수 있습니다
여러분이 이것의 진가를 보았으면 좋겠습니다
왜냐하면 이것은 시간과 공간이
그저 시공간 위의
서로 다른 방향일 뿐임을
의미하기 때문입니다
이 식에서 x가 이 두 곳에 있고,
ct는 이 두 곳에 있습니다
따라서 x'에 대해 생각할 때는
x에 베타 곱하기 ct를 빼고
로렌츠 인자를 곱해 주는데,

Bulgarian: 
променянето на цветовете
понякога е трудно –
гама по – и ще видим,
че е просто обратното.
Това ще е с...
нека направя това
в зелен цвят –
ct минус –
и може да предположиш
какво ще запиша,
въз основа на симетрията,
която виждаме тук –
ct минус
бета по х.
И искам да
оцениш това,
понеже наистина показва,
че пространството и времето
са просто различни посоки
в пространство-времето
и има хубава симетрия
между тях тук.
Забележи, имаме едно х
и имаме едно х.
Имаме едно ct
и имаме едно ct.
Когато мислим
за х',
това е х минус бета по ct
и го умножаваме 
по Лоренцовия фактор,

Thai: 
การเปลี่ยนสีบางครั้งก็ลำบาก
แกมมาคูณ เราจะเห็นว่ามันก็แค่
กลับกัน
มันจะเท่ากับ c
ขอผมใช้สีเขียวนะ
ct
ลบ คุณคงเดาได้ว่าผมจะ
เขียนอะไรจากสมมาตร
ที่เราเห็นตรงนี้
ct ลบบีต้าคูณ x
และผมอยากให้คุณซาบซึ้งเรื่องนี้
เพราะมันแสดงว่าสเปซกับเวลา
เป็นแค่ทิศ
ในสเปซเวลา และมันมีสมมาตรสวยงาม
ตรงนี้
สังเกตว่าเรามี x และเรามี x
เรามี ct และเรามี ct
เมื่อเราคิดถึง x ไพรม์
มันคือ x ลบบีต้าคูณ ct
เราจะย่อขยายมันด้วยตัวคูณลอเรนซ์

Thai: 
แล้วเมื่อเราคิดถึงเวลา
เราก็ทำกลับกัน
เรายังคงย่อขยายด้วยตัวคูณลอเรนซ์
แต่ตอนนี้มันเป็น ct ลบบีต้าคูณ x
ทีนี้ อันนี้อาจดูน่าประหลาด
และเราใช้ตัวอักษรประหลาดๆ ด้วย
แต่ในวิดีโอต่อไป
ผมจะยกตัวอย่างตัวเลขขึ้นมา
และคุณจะเห็นว่าการหาค่าสิ่งเหล่านี้
เป็นเพียงพีชคณิตตรงไปตรงมา

Bulgarian: 
а после, когато мислим
за времето,
ще направим това
по обратния начин.
Пак го умножаваме
по Лоренцовия фактор,
но сега това е
ct минус бета по х.
Това може да
ти изглежда като написано на гръцки –
и всъщност използваме
гръцки букви –
но в следващото видео
ще използвам някои
примерни числа тук
и ще видиш,
че изчисляването на тези неща
са просто лесни
алгебрични изчисления.

English: 
and then when we're thinking about time,
well we do it the other way around.
We're still scaled by the Lorentz factor,
but now it is ct minus beta times x.
Now this might all seem like Greek to you,
and we actually are using Greek letters,
but in the next video,
I'll actually use some
sample numbers here,
and you'll see that evaluating these
is just a little bit of
straightforward algebra.

Korean: 
시간에 대해서 생각할 때는
순서만 바꾸면 되는 것입니다
로렌츠 변화를 곱하는 것은 같지만
ct에 베타 곱하기 x를 빼는 것입니다
이것은 여러분에게
복잡하고 이해하기 힘들 수 있습니다
그러나 다음 동영상에서는
실제 수들로 예시를 들 것이고
이것들을 계산하는 것은
그냥 단순한 대수학임을 알 수 있을 것입니다
