
English: 
This episode is supported by
 "The Great Courses Plus".
The Planck constant defines the size scale at which
 the familiar physics of our macroscopic reality...
...gives way to the weirdness
 of the quantum world.
You might not expect
 the quantum behaviour of the microscopic...
...to be observable on all scales
 of the universe,...   BUT IT IS.
In fact, you can see the effect
 of this quantum behaviour,...
...and even measure the Planck constant,...
...just by observing the colour of sunlight.
Zeno's famous paradox tells us
 that it's impossible to overtake a tortoise.
Run as fast as you like.
By the time you reach the tortoise's initial position,
 it'll have moved forward.
Reach that second position,
 it'll have moved forward again.
To overtake a tortoise, you need to travel
 to its previous position infinite times.

Modern Greek (1453-): 
Το επεισόδιο έχει χορηγό το Great Courses plus.
Η σταθερά του Πλανκ ορίζει την κλίμακα του μεγέθους
στην οποία η γνωστή Φυσική στη μακροσκοπική μας πραγματικότητα
δίνει χώρο στον παράξενο κβαντικό κόσμο.
Ίσως νομίζετε ότι η κβαντική συμπεριφορά των μικροσκοπικών πραγμάτων
δεν παρατηρείται σε κάθε κλίμακα μεγέθους, αλλά τελικά παρατηρείται.
Μάλιστα μπορείτε να δείτε το αποτέλεσμα αυτής της κβαντικής συμπεριφοράς
και να μετρήσετε ακόμη και τη σταθερά του Πλανκ απλώς
παρατηρώντας το χρώμα από το φως του ήλιου.
Το γνωστό παράδοξο του Ζήνωνα μας λέει ότι είναι αδύνατο
να προσπεράσεις μια χελώνα.
Τρέξε όσο γρήγορα θες, αλλά την στιγμή
που θα φτάσεις στην αρχική θέση της χελώνας,
εκείνη θα έχει προχωρήσει λίγο μπροστά.
Μόλις φτάσεις για δεύτερη φορά στη θέση της,
εκείνη θα έχει προχωρήσει κι άλλο πάλι.
Για να προσπεράσεις μια χελώνα, πρέπει να φτάσεις
στην θέση που βρισκόταν κάθε φορά, άπειρες φορές.

English: 
This episode is supported
by "The Great Courses Plus."
The Planck constant
defines the size scale
at which the familiar physics
of our macroscopic reality
gives way to the weirdness
of the quantum world.
You might not expect the quantum
behavior of the microscopic
to be observable on all scales
of the universe, but it is.
In fact, you can see the
effect of this quantum behavior
and even measure the
Planck constant just
by observing the
color of sunlight.
Zeno's famous paradox
tells us that it's
impossible to
overtake a tortoise.
Run as fast as you
like, by the time
you reach the tortoise's
initial position,
it'll have moved forward.
Reach that second
position, it'll
would moved forward again.
To overtake a tortoise,
you need to travel
to its previous
position infinite times.

Korean: 
 
이 에피소드는 "The Great Courses Plus" 가 후원합니다.
플랑크 상수는 우리가 친숙한 거시적 실재의 물리법칙이
양자세계의 기묘함으로 바뀌는
부피의 단위를 정의합니다.
미시적인 양자의 성질을  거시적 현실에서 관찰이 불가능하다고
예상하실지 모르겠지만, 실제로 관측은 가능합니다.
실제로 이러한 양자성질의 효과의 관측도 가능할 뿐만 아니라
태양빛의 색을 관찰하므로써
플랑크 상수의 측정까지 가능합니다.
 
잘 알려진 제논의 역설에서는 거북이를
따라잡는 것은 불가능하다고 말합니다.
최대한 빠르게 달려도,  거북이의 초기 위치에
도달할 때 쯤이면,
거북이는 이미 전진해있기 때문이죠,
두번째 위치에 도달해도,
거북이는 더 앞으로 전진해있을 겁니다.
거북이를 추월하기 위해선 거북이의 전 위치로
무한대의 이동이 필요합니다.

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Korean: 
각 이동은 바로 전의 이동보다 더 짧아지겠지만,
여전히 무한대로 더 이동이 필요하죠.
이 역설에는 몇가지 문제점이 있습니다.
첫째로, 공간을 무한대로 분할할 수 있다고 가정하는 것이죠.
이건 사실이 아닙니다.
거북이와의 거리가 상상할 수 없을만큼 작아지게되면,
당신의 위치에는 양자적 불확실성이 일어나게 됩니다.
일정수준 이상 가까워지게 되면, 이 양자적 모호함으로
당신의 위치가 거북이의 전방인지 후방인지 조차
확인이 힘들게 만들죠.
최근 드브로이 파장에 관해서 이야기 할 때
이 문제에 대해서 더 이야기한 바 있습니다.
그리고 더 공식적으론,  하이젠베르크의 불확정성의 원리는
거리의 최소단위를 표현하므로써
물체의 유효한 위치를 정의할 수 있게합니다.
이 작은 플랑크 상수  6.63 * 10³⁴J  초는
양자적 모호함이 발생하는 단위를 설정합니다.
그러므로,  현실의 픽셀 단위라고 봐도 되겠네요.

Modern Greek (1453-): 
Το κάθε βήμα γίνεται πιο μικρό από το προηγούμενο,
αλλά πάντοτε μεσολαβούν άπειρα βήματα.
Το παράδοξο έχει κάποια προβλήματα,
ένα από αυτά είναι η παραδοχή ότι ο χώρος διαιρείται επ' άπειρον.
Δεν ισχύει αυτό.
Όταν η απόσταση από τη χελώνα γίνει εξαιρετικά μικρή,
εμφανίζεται μια κβαντική αβεβαιότητα στη θέση.
Πλησιάζοντας αρκετά, αυτή η κβαντική "θολούρα"
σημαίνει ότι δεν μπορείς να ξεχωρίσεις αν η θέση σου βρίσκεται
πίσω ή μπροστά από την χελώνα.
Μιλήσαμε για αυτό πρόσφατα στη συζήτηση για το
μήκος κύματος Ντε Μπρολί.
Αυτό και, πιο σωστά, η αρχή αβεβαιότητας του Χάιζενμπεργκ
περιγράφει την ελάχιστη απόσταση για την οποία
η θέση ενός αντικειμένου έχει νόημα να προσδιοριστεί.
Η πολύ μικρή σταθερά του Πλανκ, 6,63 επί 10 υψωμένο στην δύναμη -34 Joule·s
δηλώνει αυτή την κλίμακα όπου αρχίζει η κβαντική "θολούρα".
Κατά κάποιο τρόπο οριοθετεί το μέγεθος ενός "πίξελ" πραγματικότητας.

English: 
Each of those steps is
shorter than the last,
but there are still an
infinite number of them.
There are a few problems
with this paradox,
but one is that it assumes that
space is infinitely divisible.
This is not true.
As your distance to the tortoise
becomes unthinkably small,
there arises a quantum
uncertainty in your location.
Get close enough to it,
and this quantum blurriness
means it's impossible to say
whether your location is really
behind or in front
of the tortoise.
We talked about this recently
when we discussed the de
Broglie wavelength.
This, and more formally,
the Heisenberg uncertainty
principle, describes
the smallest distance
for which an object's location
can be meaningfully defined.
The tiny Planck constant, at
6.63 by 10 to the minus 34
joule seconds, sets the scale
of this quantum blurriness.
So it also sort of defines
a pixel scale to reality.

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

English: 
Each of those steps
 is shorter than the last,...
...but there are still
 an infinite number of them.
There are a few problems
 with this paradox,...
...but one is that it assumes
 that space is infinitely divisible.
This is not true.
As your distance to the tortoise
 becomes unthinkably small,...
...there arises a quantum uncertainty
 in your location.
Get close enough to it,
 and this quantum blurriness...
...means it's impossible to say whether your location
 is really behind or in front of the tortoise.
We talked about this recently,
 when we discussed the de Broglie wavelength.
This, and more formally,
 the Heisenberg uncertainty principle,...
...describes the smallest distance...
...to which an object's location
 can be meaningfully defined.
The tiny Planck constant,
 at 6.63x10^(-34) Joule.seconds,...
...sets the scale of this quantum blurriness.
So, it also sort of defines
 a pixel scale to reality.

Modern Greek (1453-): 
Από πολλές απόψεις, ορίζει την διαιρετότητα
του κβαντικού κόσμου.
Στην πράξη η σταθερά του Πλανκ εμφανίζεται
σχεδόν σε κάθε εξίσωση
που περιγράφει κβαντικά φαινόμενα.
Η αρχή αβεβαιότητας του Χάιζενμπεργκ και το μήκος κύματος
ντε Μπρολί, αλλά επίσης και η εξίσωση Σρέντινγκερ,
οι ενεργειακές στάθμες των τροχιών των ηλεκτρονίων και, κυρίως,
η σχέση ανάμεσα στην ενέργεια και την συχνότητα
του φωτονίου.
Επίσης οριοθετεί το μέγεθος του "μήκους Πλανκ", το οποίο
είναι, υποθετικά, το μικρότερο μήκος, κάτω από το οποίο η έννοια
του μήκους χάνει το νόημά της.
Μπορεί να ορίζει την κλίμακα μεγέθους της κβαντικής πραγματικότητας,
όμως η επίδραση της σταθεράς του Πλανκ
είναι ορατή και στη δική μας κλίμακα μεγέθους.
Για παράδειγμα, με την θερμοκρασία που έχει ο ήλιος
η σταθερά Πλανκ προσδιορίζει το χρώμα για το φως του.
Αν η σταθερά Πλάνκ ήταν 25% πιο μικρή,
τότε ο ήλιος θα αποκτούσε βιολετί χρώμα, εφόσον τίποτε άλλο δεν άλλαζε.
Στην πραγματικότητα, το ίδιο το ερώτημα γιατί λάμπουν, στο χρώμα που λάμπουν, τα αντικείμενα

Korean: 
많은 면에서 플랑크 상수는 양자세계의
분리성을 정의합니다.
사실, 플랑크 상수는 필연적으로
양자 현상을 표현하는
모든 수식에 등장합니다.
하이젠베르크 불확정성의 원리
드브로이 파장공식
그리고 또한 슈뢰딩거의 방정식에서도 등장하죠.
전자궤도의 에너지수준 그리고 더욱 중요하게
광자의 진동수와 에너지의 관계성에서도 말이죠
광자의 진동수와 에너지의 관계성에서도 말이죠
상수는 또한,  가설적으로 '거리'라는 개념 자체가
의미를 잃어버린 정도로 짧은 거리인 플랑크 거리의
단위를 설정하기도 합니다.
양자적 현실의 단위를 정의할 수도 있지만,
플랑크 상수의 영향은 우리의 현실에서도
관측이 가능합니다.
예를 들어, 태양의 온도와 함께,
태양빛의 색깔을 정해주기도 합니다.
만약 플랑크 상수가 25%정도 작았다면,
태양은 다른 것은 다 똑같아도 태양은 보랏빛이였을테죠.
사실, 왜 뜨거운 물질이 특정 색을 내며 빛을 발하는가에 대한

English: 
In many ways, it defines
 the divisibility of the quantum world.
In fact, the Planck constant appears in essentially
 all equations that describe quantum phenomena.
The Heisenberg uncertainty principle
 and the de Broglie wavelength,...
...but also the Schrödinger equation,...
...the energy levels of electron orbits,...
...and, importantly, the relationship
 between the energy and frequency of a photon.
It also sets the size
 of the Planck length,...
...which is, hypothetically, the length below which
 the concept of length loses meaning.
It may define
 the scale of quantum reality,...
...but the influence of the Planck constant
 can be seen even on our scale.
For example, along with the sun's temperature,
it sets the colour of sunlight.
If the Planck constant were 25% smaller,
 the sun would be violet, all else being equal.

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

English: 
In many ways, it
defines the divisibility
of the quantum world.
In fact, the Planck
constant appears
in essentially
all equations that
describe quantum phenomena.
The Heisenberg uncertainty
principle and the de Broglie
wavelength, but also the
Schrodinger equation,
the energy levels of electron
orbits, and importantly,
the relationship between
the energy and frequency
of a photon.
It also sets the size of
the Planck length, which
is, hypothetically, the
length below which the concept
of length loses meaning.
It may define the scale
of quantum reality,
but the influence of
the Planck constant
can be seen even on our scale.
For example, along with
the sun's temperature,
it sets the color of sunlight.
If the Planck constant
were 25% smaller,
the sun would be violet,
all else being equal.
In fact, the mystery of why hot
things glow the color that they

Korean: 
의문 자체가 양자우주의 발견을 이끈 원인었죠.
의문 자체가 양자우주의 발견을 이끈 원인었죠.
과학적 사실 - 우주의 모든 것은
그 자신의 내부의 열로 인해 빛을 내뿜습니다.
열이란 그저 물체를 구성하는 입자들의 불규칙적 운동 속의 에너지일 뿐입니다.
열이란 그저 물체를 구성하는 입자들의 불규칙적 운동 속의 에너지일 뿐입니다.
가속 된 전하는 전자기적 방사능을 생성합니다.
바로 빛이죠.
그러므로  진동하는 전하입자들로 이루어진 물체,
즉 전자와 양성자들은 빛을 내게 됩니다.
물체가 뜨거울 수록, 입자들은 더욱 빠르게 진동하죠.
그래서 빛, 광자의 평균 진동수는
온도와 함께 증가합니다.
이 평균 진동수가 우리가 보는 색을 정의하게 되죠.
태양은 황색인 이유는 표면의 6000캘빈이라는 온도가
녹색과 황색의 전자기적 스펙트럼을 가장 많이 방출하기 때문이죠
녹색과 황색의 전자기적 스펙트럼을 가장 많이 방출하기 때문이죠
청색거성인 리겔은 12,000켈빈이므로

English: 
In fact, the mystery of why hot things
 glow the colour that they do,...
...led us to discover
 the quantum universe in the first place.
Science fact: everything in the universe
 glows with the light of its own internal heat.
Heat is just the energy in the random motion
 of particles comprising an object.
Accelerated charges
 produce electromagnetic radiation - light.
And so, an object made of jiggling charged particles, like electrons and protons, glows.
The hotter an object is,
 the faster its particles jiggle.
And so the average frequency
 of the resulting particles of light, of photons,...
...increases with temperature.
This average frequency
 defines the colour that we see.
The sun is yellow...
...because its 6000 Kelvin surface...
...produces more photons in the green-yellow
 part of the electromagnetic spectrum...
...than anywhere else.
The blue super giant star Rigel
 is 12,000 Kelvin,...

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

English: 
do led us to discover
the quantum universe
in the first place.
Science fact-- everything
in the universe
glows with the light of
its own internal heat.
Heat is just the energy in
the random motion of particles
comprising an object.
Accelerated charges produce
electromagnetic radiation--
light.
And so an object
made of jiggling
charged particles, like
electrons and protons, glows.
The hotter an object is, the
faster its particles jiggle.
And so the average frequency
of the resulting particles
of light, of photons,
increases with temperature.
This average frequency
defines the color that we see.
The sun is yellow because its
6000 Kelvin surface produces
more photons in the
green yellow part
of the electromagnetic
spectrum than anywhere else.
The blue super giant star
Rigel is 12,000 Kelvin,

Modern Greek (1453-): 
που είναι πολύ ζεστά, μας οδήγησε στην ανακάλυψη του κβαντικού σύμπαντος
όταν αρχίσαμε να το ψάχνουμε.
Είναι επιστημονικό γεγονός: όλα τα αντικείμενα στο σύμπαν
λάμπουν με το φως από την εσωτερική τους θερμότητα.
Η θερμότητα είναι η ενέργεια εξαιτίας των τυχαίων κινήσεων των σωματιδίων
από τα οποία αποτελείται ένα αντικείμενο.
Επιταχύνσεις των φορτισμένων σωματιδίων δημιουργούν ηλεκτρομαγνητική ακτινοβολία,
δηλαδή, φως.
Επομένως κάθε αντικείμενο που έχει φορτισμένα
σωματίδια που τρεμοπαίζουν, όπως ηλεκτρόνια και πρωτόνια, λάμπει.
Όσο πιο θερμό είναι το αντικείμενο, τόσο γρηγορότερα τρεμοπαίζουν τα σωματίδια.
Οπότε και η μέση συχνότητα των σωματιδίων φωτός που εκπέμπονται,
τα φωτόνια δηλαδή, αυξάνεται με την θερμοκρασία.
Αυτή η μέση συχνότητα καθορίζει το χρώμα που αντικρίζουμε.
Ο ήλιος είναι κίτρινος επειδή τα 6000 Κέλβιν της επιφανειακής του θερμοκρασίας
δημιουργεί περισσότερα φωτόνια στην πράσινο-κίτρινη μεριά
του ηλεκτρομαγνητικού φάσματος, από όσα οπουδήποτε αλλού.
Το αστέρι Ριγκέλ είναι ένας μπλε γίγαντας στα 12000 Κέλβιν,

Korean: 
더 고진동수인 푸른빛과 심지어는 보랏빛도 발산하기도 하죠
더 고진동수인 푸른빛과 심지어는 보랏빛도 발산하기도 하죠
인체의 온도는 310켈빈 정도이므로,
당신의 열로 인한 빛은 대부분 낮은 진동수인 적외선 광자들입니다.
아이작 뉴턴경은 1660년대에  이러한 열발산을
태양빛을 프리즘으로 분광시켜 처음 관측한 인물이었죠
태양빛을 프리즘으로 분광시켜 처음 관측한 인물이었죠
하지만 그는 이 색들의 상대적 밝기가 양자세계의 열쇠를 쥐고 있다는 사실은
인지하지 못했습니다.
1800년대 후반에
뜨거운 물체로부터 생성 된 진동수와 발기의 분배는
흑체 방사선에 대한 연구로 세부적으로 분류되었습니다.
흑체 방사선에 대한 연구로 세부적으로 분류되었습니다.
그 결과로 나온 흑체복사 스펙트럼은 한쪽으로 쏠린
종 모양의 곡선입니다.
하지만, 이러한 형태를 나타내는 물리적 근거는 밝혀지지 않았었죠.
이러한 의문을 해결할 수 있었던 열쇠는
흑체복사 스펙트럼에 대한 수학적 설명을

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

English: 
...and so it pumps out
 lots of high frequency blue light,...
...and even more ultraviolets.
Your temperature
 is around 310 Kelvin,...
...so your heat glow is mostly
 in low frequency infrared photons.
It was Sir Isaac Newton who first analysed
 this heat glow in the 1660s,...
...when he used a prism to split sunlight
 into its component colours.
But he didn't realise
 that the relative brightnesses of those colours...
...held the key to the quantum world.
By the late 1800s,...
...the distribution
 of brightnesses with frequency,...
...produced by hot objects,...
...had been mapped
 in careful experiments...
...that blacked out
 anything but the glow of heat.
The resulting blackbody spectrum...
...looks like a lopsided bell curve.
However,...
...the deep physics behind this shape
 remained a mystery.
The key to unlocking the mystery...

Modern Greek (1453-): 
οπότε εκπέμπει την ενέργειά του σε υψηλότερης συχνότητας μπλε φως
και ακόμα περισσότερο υπεριώδες.
Η θερμοκρασία σας είναι περίπου 310 Κέλβιν,
οπότε η λάμψη της θερμότητάς σας βρίσκεται σε χαμηλής συχνότητας φωτόνια στο υπέρυθρο.
Ήταν ο Σερ Ισαάκ Νιούτον ή Νεύτων που πρώτος ανάλυσε αυτή την λάμψη της θερμότητας
στη δεκαετία του 1660, όταν πήρε ένα γυάλινο πρίσμα και διαχώρισε το ηλιακό φως
στα χρώματα από τα οποία αποτελείται.
Αλλά δεν συνειδητοποίησε ότι οι σχετικές διαφορές στη λαμπρότητα
των χρωμάτων εκείνων, είναι το κλειδί για τον κβαντικό κόσμο.
Στα τέλη του 19ου αιώνα, η κατανομή
της λαμπρότητας με την συχνότητα που εκπέμπουν τα θερμά αντικείμενα
καταγράφτηκε σε προσεκτικά πειράματα που συσκότιζαν
κάθε άλλη ακτινοβολία εκτός από αυτή τη λάμψη της θερμότητας.
Το αποτέλεσμα ήταν το λεγόμενο φάσμα "μελανού σώματος" που μοιάζει με στραβή καμπάνα.
Ωστόσο η φυσική εξήγηση αυτού του σχήματος παρέμενε ένα μυστήριο.
Το κλειδί για να ξεκλειδωθεί το μυστήριο ήταν
να βρεθεί η μαθηματική περιγραφή

English: 
and so it pumps out lots of high
frequency blue light and even
more ultraviolets.
Your temperature is
around 310 Kelvin,
so your heat glow is mostly in
low frequency infrared photons.
It was Sir Isaac Newton who
first analyzed this heat glow
in the 1660s when he used
a prism to split sunlight
into its component colors.
But he didn't realize that
the relative brightnesses
of those colors held the
key to the quantum world.
By the late 1800s,
the distribution
of brightnesses with frequency
produced by hot objects
had been mapped in careful
experiments the blacked
out anything but
the glow of heat.
The resulting blackbody spectrum
looks like a lopsided bell
curve.
However, the deep physics behind
this shape remained a mystery.
The key to unlocking
the mystery lay
in finding a
mathematical description

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Korean: 
찾는데 있었죠.
20세기 초에,
레일리, 제임스 진과 같은 영국 연구자들은
당시 상대적으로 새로이 등장한 개념으로 이 문제를 해결하려 시도했습니다.
바로 에너지 등분배 법칙이었죠.
이 법칙은 물체의 열에너지는 결국
물체의 모든 입자들을 진동가능한 모든형태로
로 진동시킬 것이라고 했죠.
물리학적으로 말하면- 평형적으로,
에너지가 모든 가능한 에너지상태로 확산되었다는 말입니다.
이 단순한 개념은 우리의 영국연구가들로 하여금
이러한 열운동으로부터 생성 된
광자의 진동수를 확인할 수 있도록 해주었습니다.
레일리-진 법칙은
흑체스펙트럼을 완벽히 설명했습니다.
적외선과 같은 저진동수에서는 말이죠.
하지만 더 높은 진동수, 가시광선이나 자외선의 경우엔
너무 지나치게 높은 밝기를 예측했죠.
더 심각하게, 그 강도가 결국엔
진동수가 증가하면서 무한대에 이르리라고 예측했습니다.

English: 
for the blackbody spectrum.
At the beginning of
the 20th century,
a couple more Brits, Lord
Rayleigh and Sir James Jeans,
attacked the problem with a
relatively new idea called
the equipartition theorem.
It states that an object's
heat energy will end up
juggling all of its
particles in all the ways
that they can be jiggled.
In physics speak--
at equilibrium,
energy is evenly spread between
all possible energy states.
This simple idea allowed
our good Englishmen
to figure out the frequencies
of the photons produced
by all of this thermal motion.
The resulting
Rayleigh-Jeans law described
the blackbody
spectrum perfectly.
For low frequency,
infrared light.
But for higher frequencies,
like visible and ultraviolet,
it predicted brightnesses
that were way too high.
Worse, it predicted that the
intensity should eventually
approach infinity as
frequency increased.

English: 
...lay in finding a mathematical description
 for the blackbody spectrum.
At the beginning of the 20th century,...
...a couple more Brits, 
Lord Rayleigh and Sir James Jeans,...
...attacked the problem
 with a relatively new idea,...
...called the equipartition theorem.
It states that an object's heat energy
 will end up...
...jiggling all of its particles
 in all the ways that they can be jiggled.
In physics' speak: ...
...at equilibrium, energy is evenly spread
 between all possible energy states.
This simple idea
allowed our good Englishmen...
...to figure out the frequencies of the photons
 produced by all of this thermal motion.
The resulting Rayleigh-Jeans law...
...described the blackbody spectrum perfectly...
...for low frequency, infrared light.
But for higher frequencies,
 like visible and ultraviolet,...
...it predicted brightnesses
 that were way too high.
Worse: it predicted that the intensity...
...should eventually approach infinity,
as frequency increased.

Modern Greek (1453-): 
για το φάσμα του "μελανού σώματος".
Στις αρχές του 20ού αιώνα
δυο Βρετανοί ακόμη, ο Λόρδος Rayleigh και ο Σερ James Jeans,
προσέγγισαν το πρόβλημα με μια σχετικά καινούργια ιδέα, που αποκάλεσαν
«θεώρημα ισοκατανομής» της ενέργειας.
Θεωρεί ότι η θερμική ενέργεια ενός αντικειμένου οδηγεί τελικά
όλα του τα σωματίδια να ταλαντώνονται με κάθε
δυνατό τρόπο ταλάντωσης.
Αν το διατυπώσουμε με περισσότερη Φυσική, στην ισορροπία
η ενέργεια θα έχει ομοιόμορφα κατανεμηθεί ανάμεσα σε όλες τις ενεργειακές καταστάσεις.
Αυτή η απλή ιδέα επέτρεψε στους δυο αυτούς Άγγλους
να υπολογίσουν τις συχνότητες των φωτονίων που παράγονται
από αυτή την θερμική κίνηση.
Ο νόμος Rayleigh-Jeans, που προέκυψε, περιέγραψε
το φάσμα του "μελανού σώματος" τέλεια...
...για τις χαμηλές συχνότητες του υπέρυθρου φωτός.
Αλλά στις υψηλές συχνότητες όπως το ορατό φως και το υπεριώδες,
προέβλεπε λάμψη κατά πολύ ισχυρότερη από την πραγματική.
Κι ακόμη χειρότερα, έκανε την πρόβλεψη ότι η ένταση τελικά
θα έφτανε το άπειρο με την αύξηση της συχνότητας.

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Modern Greek (1453-): 
Σχηματίζει μια τρελή εικόνα για το σύμπαν
όπου θα έχει ακραία άπειρη ενέργεια από ακτινοβολία γάμμα.
Μάλλον δεν ισχύει κάτι κάτι τέτοιο.
Αυτό αποκλήθηκε «η καταστροφή στο υπέρυθρο».
Ήταν καταστροφικό διότι έδειχνε ότι κάτι ήταν
θεμελιωδώς εσφαλμένο στην κλασική Φυσική,
μέσα στον νόμο Rayleigh-Jeans.
Το πρόβλημα προέκυψε τελικά επειδή στην κλασική Φυσική,
όλα μπορούν να διαιρεθούν άπειρες φορές.
Δεν υπάρχει τίποτε που να είναι το μικρότερο.
Ο υπολογισμός των Rayleigh-Jeans επιτρέπει
στα σωματίδια να ταλαντώνονται με οσηδήποτε ποσότητα ενέργειας
μέχρι και τις πιο ασήμαντες διαταράξεις.
Όταν προσπάθησαν λοιπόν προσπάθησαν με τα μαθηματικά να βρουν την κατανομή
της θερμικής ενέργειας στις ίσες διαμερίσεις όλων των ενεργειακών καταστάσεων,
υπολογίστηκε να στριμώχνεται πολλή περισσότερη ενέργεια μέσα σε καθεμία από τις
αμέτρητες και πολύ μικρές ενεργειακές καταστάσεις των υψηλών συχνοτήτων.
Από μαθηματική άποψη, ο Rayleigh και ο Jeans
κυνηγούσαν την χελώνα του Ζήνωνος, αφού διαιρούσαν άπειρες φορές

English: 
It paints the crazy
picture of a universe
full of infinite extreme
energy gamma radiation.
This appears not to be the case.
This was called the
ultraviolet catastrophe.
It was catastrophic because
it meant that something
was fundamentally wrong with
the classical physics that went
into the Rayleigh-Jeans law.
The problem turned out to be
that in classical physics,
everything can be
infinitely divided.
There's no smallest anything.
The Rayleigh-Jeans
calculation allows
particles to vibrate with
any amount of energy,
all the way down to
infinitesimally tiny wiggles.
When they tried to
mathematically distribute
heat energy to equipartitionates
across possible energy states,
way too much energy got packed
into the countless very tiny
energy states at
high frequencies.
Mathematically,
Rayleigh and Jeans
were chasing Zeno's
tortoise, infinitely dividing

Korean: 
이러한 우주는 상상할 수 없는 형태였죠.
무한한 숫자의 감마방사선으로 가득찬 우주라니요.
실제 현실이 그렇지는 않아보였죠.
이 문제는 자외선 파탄이라고도 불립니다.
이게 파탄인 이유는 이것이 의미하는 바가 결국
레일리-진 법칙에 사용된 고전물리학의 어떤 부분이
근본적으로 잘못되었다는 것을 의미했기 때문이었습니다.
문제는 결국 고전물리학에선
모든 것들이 무한대로 분할될 수 있기 때문이라는 것이 밝혀졌습니다.
하지만 그런 일은 존재하지 않죠.
레일리-진의 계산은
입자가 에너지량에 관계없이 진동할 수 있도록 허용합니다.
무한대로 작은 진동까지요.
그들이 수학적으로 모든 에너지 상태에 대해서
열에너지를 등분배하려고 했을 때
셀 수 없이 작게 쪼개진 고진동대의 에너지 상태에 영역에
너무나도 많은 에너지가 축적되게 되었죠.
레일리와 진은 수학적인 의미에서
제논의 역설을 경험하고 있었던 겁니다.
가장 작은 에너지 상태가 무한대로 나뉘어서

English: 
It paints the crazy picture of a universe...
...full of infinite, extreme energy,
gamma radiation.
This appears not to be the case.
This was called
 "the ultraviolet catastrophe".
It was catastrophic,...
...because it meant
 that something was fundamentally wrong...
...with the classical physics
 that went into the Rayleigh-Jeans law.
The problem tuerned out to be
 that in classical physics,...
...everything can be infinitely divided.
There is no "smallest" anything.
The Rayleigh-Jeans calculation allows particles
 to vibrate with any amount of energy.
All the way down
 to infinitesimally tiny wiggles.
When they tried
 to mathematically distribute heat energy...
...to "equipartitionates"
across possible energy states,...
...way too much energy
 got packed into the countless,...
...very tiny energy states
at high frequencies.
Mathematically, Rayleigh and Jeans
were "chasing Zeno's tortoise",...

Korean: 
가장 작은 에너지 상태가 무한대로 나뉘어서
결국 그 끝이 있을 수가 없었죠.
독일 물리학자인 막스 칼 루트비히 플랑크는
이 문제를 거의 우연적으로 해결했습니다.
흑체복사 스펙트럼에 대한
새로운 수학적 접근법을 찾는 도중에
그는 소위 무한대의 에너지상태의 숫자를 세기 위해서
일종의 수학적 꼼수가 필요했습니다.
그의 표현에 의하면 '절망의 순간' 에
꽤 바보같은 시도를 했죠.
그는 이러한 입자들이 어떤 최소 에너지의
배수로 밖에 진동할 수 없다고 정해버렸죠.
그는 에너지상태를 양자화시켰습니다.
그는 이 최소에너지를 입자의 진동수에 아주 작은 값을 곱했습니다.
이 값은 아직 측정된 적이 없는 값이었죠.
그 값이 바로 플랑크 상수가 되었습니다.
이것은 마치 컴퓨터가 멈췄을 때
키보드를 마구 누르는 것과 비슷한 행동이었는데
이게 통해버린거죠.

English: 
...infinitely dividing
 the smalles remaining energy states,...
...and so never ever
finding an end to them.
German physicist
 Max Karl Ernst Ludwig Planck...
...resolved the catastrophe
 almost by accident.
While searching for a new mathematical approach
 to deriving the blackbody spectrum,...
...he needed some sort of "math trick"...
...to count
 the supposedly infinite energy states.
In what he described as
"a moment of desperation",
...he tried something pretty silly.
He decided that those particles...
...could only vibrate with energies...
...that were a multiple
 of some minimum energy.
He "quantised" the energy states.
He set this minimum energy...
...to be the frequency of the particles' vibration
times a very, very small number.
A number
that had yet to be measured.
That number became the "Planck constant".
It was a move similar to smooshing your hands
 on the keyboard when your computer freezes,...
...but it worked!

Modern Greek (1453-): 
τις πιο μικρές από τις υφιστάμενες ενεργειακές καταστάσεις,
και έτσι δεν μπορούσαν να βρουν πώς να ολοκληρώσουν την διαδικασία.
Ο Γερμανός φυσικός Μαξ Καρλ-Ερνστ Λούντβιχ Πλανκ
έλυσε το πρόβλημα της «καταστροφής στο υπέρυθρο» σχεδόν από τύχη.
Ενώ διερευνούσε μια διαφορετική μαθηματική προσέγγιση
για να υπολογίσει το φάσμα του "μελανού σώματος",
εφάρμοσε ένα είδος μαθηματικού κόλπου
ώστε να "μετρήσει" τις υποτιθέμενα απειράριθμες ενεργειακές καταστάσεις.
Σε μια στιγμή απελπισίας, όπως το περιέγραψε,
δοκίμασε κάτι που ήταν χαζό.
Αποφάσισε να θεωρήσει πως τα σωματίδια μπορούσαν μόνο έτσι να ταλαντώνονται
με τόση ενέργεια καθένα, όση κάποιο πολλαπλάσιο
μιας ελάχιστης ποσότητας ενέργειας.
Ποσοτικοποίησε - κβάντισε τις ενεργειακές καταστάσεις.
Έθεσε αυτή την ελάχιστη ενέργεια να είναι μια συχνότητα ταλάντωσης
ενός σωματιδίου, πολλαπλασιασμένη με ένα πολύ πολύ μικρό αριθμό,
ο οποίος μπορούσε και χρειαζόταν να μετρηθεί.
Αυτός ο αριθμός έγινε η «σταθερά του Πλανκ».
Ήταν μια αντίδραση ανάλογη του να κοπανάς τα χέρια
στο πληκτρολόγιο όταν ο υπολογιστής "παγώνει",
αλλά τελικά δούλεψε!

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

English: 
the smallest remaining
energy states,
and so never ever
finding an end to them.
German physicist Max
Karl Ernst Ludwig Planck
resolved the catastrophe
almost by accident.
While searching for a
new mathematical approach
to deriving the
blackbody spectrum,
he needed some
sort of math trick
to count the supposedly
infinite energy states.
In what he described as
a moment of desperation,
he tried something pretty silly.
He decided that those
particles could only
vibrate with energies
that were a multiple
of some minimum energy.
He quantized the energy states.
He set this minimum energy to
be the frequency of a particle's
vibration times a very, very
small number, a number that
had yet to be measured.
That number became
the Planck constant.
It was a move similar
to smooshing your hands
on the keyboard when
your computer freezes,
but it worked.

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

English: 
It allowed Planck to equipartition energy
in a way that solved the ultraviolet catastrophe.
Why?
Because it limited how much energy
 those high frequency vibrations could hold.
Planck's new equation...
...described the shape
 of the blackbody spectrum EXACTLY,...
...across all frequencies of light.
It became Planck's Law.
Now, Max Planck didn't originally think
that these quantised leves were real.
It was supposed to be a math trick.
He expected his new constant
 to turn out to be zero,...
...which would mean
 no interval between energy states,...
...no quantisation,...
...no minimum energy.
In that case,...
...the Planck constant
 would have cancelled out in the final equation,...
...but it DIDN'T.
The Planck constant is firmly entrenched
in the Planck blackbody law.
Energy quantisation is real.
Now, the actual value of the Planck constant
 still had to be measured.

English: 
It allowed Planck to
equipartition energy
in a way that solved the
ultraviolet catastrophe.
Why?
Because it limited how much
energy those high frequency
vibrations could hold.
Planck's new equation
described the shape
of the blackbody
spectrum exactly,
across all frequencies of light.
It became Planck's law.
Now Max Planck didn't
originally think
that these quantized
energy levels were real.
It was supposed to
be a math trick.
He expected his new
constant to turn out
to be 0, which would mean
no interval between energy
states, no quantization,
no minimum energy.
In that case, the Planck
constant would have canceled
out in the final
equation, but it didn't.
The Planck constant
is firmly entrenched
in the Planck blackbody law.
Energy quantization is real.
Now the actual value
of the Planck constant
still had to be measured.

Korean: 
이것을 통해 플랑크는 자외선 파탄을 해결하는 방향으로
에너지를 등분배할 수 있었습니다.
왜일까요?
고진동대 주파수가 가질 수 있는 에너지에 한계를 부여했기 때문이었죠.
고진동대 주파수가 가질 수 있는 에너지에 한계를 부여했기 때문이었죠.
플랑크의 새로운 방정식은 흑체복사 스펙트럼의 형태를
모든 빛의 주파수대에서 동일하게 표현합니다.
플랑크의 법칙이죠.
하지만, 막스 플랑크는 당시 이 양자화 된 에너지 수준이
실제로 존재하는 것이라고 생각치는 않았습니다.
이것은 일종의 수학적 꼼수였죠.
그는 그의 이 새로운 상수의 값이
0일 것이라고 예상했습니다.즉 에너지 상태 간에
간격, 양자화, 최소 에너지도 없는 것이죠
그랬다면,  플랑크 상수는 최종결과에서 상충되는 값을 도출해야했지만, 그렇지 않았죠.
플랑크 상수는 플랑크 흑체 법칙에
완전히 들어맞습니다.
에너지의 양자화는 실제였죠.
플랑크 상수의 실제 값은 여전히 측정이 필요한 상황이었습니다.
플랑크 상수의 실제 값은 여전히 측정이 필요한 상황이었습니다.

Modern Greek (1453-): 
Επέτρεψε στον Πλανκ να ισοκατανείμει την ενέργεια
με τέτοιο τρόπο που έλυνε το πρόβλημα της «καταστροφής στο υπέρυθρο».
Γιατί όμως;
Επειδή περιόρισε το πόση ενέργεια μπορούν να διαθέτουν
οι ταλαντώσεις στις υψηλές συχνότητες.
Η νέα εξίσωση του Πλανκ έκανε την περιγραφή
του φάσματος του "μελανού σώματος", με ακρίβεια,
σε κάθε συχνότητα φωτός.
Έγινε ο Νόμος του Πλανκ.
Ο Μαξ Πλανκ βέβαια αρχικά δεν πίστευε ότι
οι κβαντισμένες ενεργειακές στάθμες υπήρχαν πραγματικά.
Υποτίθεται ότι ήταν ένα μαθηματικό κόλπο.
Περίμενε ότι η δική του σταθερά να προκύψει
μηδέν, που θα σήμαινε ότι δεν υπάρχουν διαστήματα ανάμεσα στις
ενεργειακές καταστάσεις, ούτε κβάντιση, ούτε ελάχιστη ενέργεια.
Αν ήταν έτσι όμως, η σταθερά του Πλανκ
θα είχε απαλειφθεί από την τελική εξίσωση, κάτι που δεν έγινε.
Η σταθερά του Πλανκ έχει ριζωθεί βαθιά
στον νόμο για τα "μελανά σώματα" του Πλανκ.
Η ενεργειακή κβάντιση είναι μια φυσική πραγματικότητα.
Όμως η αριθμητική τιμή της σταθεράς του Πλανκ
έπρεπε να μετρηθεί.

Korean: 
그러나 흑체복사 스펙트럼을 위한 수학적 형식으로
플랑크의 법칙이 실제 관측되는 스펙트럼과 일치하게
플랑크 상수를 조절하면 되는 문제였죠.
플랑크의 법칙과 물체의 온도를 알고 있다면
우리는 이제 플랑크 상수를
물체의 열발산에서 가장 밝은 지점을 찾기만 하면 구할 수 있게 되었습니다.
예로, 태양에서 오는 빛의 색을 관찰하는 것처럼 말이죠.
언제나처럼, 플랑크의 기묘한 양자화된 진동의 물리에
대한 이해는 아이슈타인이 이뤄냈습니다.
아이슈타인은 이것이 바로 실제로 빛이
양자화 된 것이라는 것을 깨달았죠.
이 작고 진동하는 입자들은 양자화된 에너지를 가지고 있는데,
그 이유는 입자들이 빛의 입자를 한번에 하나씩
흡수하거나 발산하기 때문입니다.
그리고 이 빛의 입자는 더이상 분할될 수 없는 에너지 단위입니다.
플랑크의 발견은 곧 아이슈타인이 .

English: 
But given a mathematical form
for the blackbody spectrum,
it was possible to do this
just by varying the constant
until the Planck law matched
the observed spectrum.
But once you know the Planck
law and an object's temperature,
you can calculate the
Planck constant just
by finding the brightest
part of an object's heat
glow, for example, by
observing the color of the sun.
As usual, it took Albert
Einstein to fully understand
the physics behind Planck's
strange quantized vibrations.
Einstein realized that
it's actually light
that is quantized.
Those little vibrating particles
do have quantized energies,
but it's because they can
only gain or lose energy
by absorbing or emitting one
particle of light at a time.
And that light comes in
indivisible energy packets.
Planck's discovery
was the clue Einstein
needed to hypothesize the
existence of the photon-- part

Modern Greek (1453-): 
Όμως με την μαθηματική μορφή του πραγματικού φάσματος του "μελανού σώματος"
κατέστη δυνατό να υπολογιστεί δοκιμάζοντας διάφορες τιμές της σταθεράς,
ώσπου ο Νόμος του Πλάνκ να ταίριαζε με την παρατηρημένη μορφή του φάσματος.
Οπότε εφόσον γνωρίζεις τον Νόμο του Πλανκ και τη θερμοκρασία ενός αντικειμένου,
υπολογίζεις την σταθερά του Πλανκ, αρκεί
να βρεις το πιο λαμπερό σημείο από την θερμική του
ακτινοβολία· για παράδειγμα, παρατηρώντας το χρώμα του ήλιου.
Ως συνήθως, χρειάστηκε να έρθει ο Αλβέρτος Αϊνστάιν για να καταλάβουμε πλήρως
τη Φυσική πίσω από τις παράξενες κβαντισμένες ταλαντώσεις του Πλανκ.
Ο Αϊνστάιν συνειδητοποίησε πως το φως είναι αυτό
που στην πραγματικότητα είναι κβαντισμένο.
Αυτά τα μικροσκοπικά ταλαντευόμενα σωματίδια έχουν κβαντισμένες ενέργειες
επειδή μπορούν να λάβουν ή να δώσουν ενέργεια
εκπέμποντας και απορροφώντας αντίστοιχα ένα σωματίδιο φωτός κάθε φορά.
Και το φως αυτό αποτελείται από αδιαίρετα ενεργειακά πακέτα.
Η ανακάλυψη που έκανε ο Πλανκ ήταν το στοιχείο που ο Αϊνστάιν
χρειάστηκε για να κάνει την υπόθεση της ύπαρξης του φωτονίου: κατά μέρος κύμα,

English: 
But given a mathematical form 
for the blackbody spectrum,...
...it was possible to do this...
...just by varying the constant,
 until the Planck law matched the observed spectrum.
For once you know Planck's law,
and an object's temperature,...
...you can calculate the Planck constant
 just by finding the brightest part...
...of an object's heat glow.
For example, by observing
 the colour of the sun.
As usual, it took Albert Einstein...
...to fully understand the physics
behind Planck's strange quantised vibrations.
Einstein realised
 that it's actually light that is quantised.
Those littles vibrating particles
do have quantised energies,...
...but it's because
 they can only gain or lose energy...
...by absorbing or emitting
one particle of light at a time.
And that light comes
in indivisible energy packets.
Planck's discovery
 was the clue Einstein needed...
...to hypothesise
 the existence of the photon,...

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Modern Greek (1453-): 
κατά μέρος σωματίδιο, φέροντας ένα "κβάντο" ενέργειας
ίσο με την γνωστή συχνότητα του κύματος,
πολλαπλασιασμένο με τη σταθερά του Πλανκ.
Ο Αϊνστάιν έκανε την απόδειξη μέσω του φωτοηλεκτρικού φαινομένου.
Πήρε το Βραβείο Νόμπελ Φυσικής το 1921 για αυτό,
ακολουθώντας το Νόμπελ του Πλανκ το 1918.
Οι ανακαλύψεις αυτές πυροδότησαν ένα φρενήρη ρυθμό
επιστημονικής δραστηριότητας που οδήγησε στην
κβαντική επανάσταση της δεκαετίας του 1920.
Κι αυτός ο μικροσκοπικός αριθμός που βρήκε ο Μαξ Πλανκ,
στη στιγμή της απελπισίας του,
η σταθερά του Πλανκ, παραμένει στην καρδιά
όλων των κβαντικών πραγμάτων.
Και όχι μόνο των κβαντικών.
Σκιαγράφοντας το σχήμα του φάσματος του "μελανού σώματος",
η σταθερά του Πλανκ μπορεί να αναγνωριστεί στο χρώμα
του ήλιου και των αστέρων, στη φωτεινότητα
των διαφορετικών χρωμάτων του ουράνιου τόξου.
Και σε συνδυασμό με μια χούφτα ακόμη
από άλλες θεμελιώδεις σταθερές,
κυβερνά την συμπεριφορά των πάντων μέσα σε αυτόν τον χωρόχρονο.
Ευχαριστούμε την "The Great Courses Plus"

English: 
wave, part particle,
carrying a quantum of energy
equal to the now familiar
frequency of the wave
times the Planck constant.
Einstein proved this through
the photoelectric effect.
It got him the 1921
Nobel Prize in Physics,
shortly following
Planck's Nobel of 1918.
These discoveries
sparked a frenzy
of sciencing that
led to the quantum
revolution of the 1920s.
And that little number
that Max Planck came up
with in his moment
of desperation--
the Planck constant--
remains at the heart
of all things quantum.
But not just quantum.
By defining the shape of
the blackbody spectrum,
the Planck constant can
be read in the color
of the sun and the
stars, in the brightness
of the different
colors of the rainbow.
And combined with
a small handful
of other fundamental
constants, it
governs the behavior of
everything in this space time.
Thanks to "The
Great Courses Plus"

Korean: 
광자의 존재를 가정할 수 있게한 단서였습니다
부분 입자, 부분 파동이면서,
파동의 주파수에 플랑크 상수를 곱한 값과 동일한
수치를 지닌 양자에너지를 말이죠.
아이슈타인은 이 내용을 광전효과 실험을 통해 증명했고
그로 인해 1921년 노벨물리학 상을 받았습니다.
1918년에 플랑크의 노벨상을 뒤이어서 말이죠.
이 발견들은 결국
1920년대에 양자혁명이라고 불리는
시기의 도화선이 되었습니다.
그리고 플랑크가 정말의 순간에 넣어놨던
그 작은 숫자들은
모든 양자인 것들의 핵심에
아직도 자리잡고 있습니다.
하지만 양자적인 것 뿐만 아니라
흑체복사 스펙트럼의 형태를 정의함으로써,
플랑크 상수는 태양이나 항성,
무지개 색간의 밝기 정도에서도
값을 구할 수가 있고
다른 몇몇 근본적인 상수들과 함께
다른 몇몇 근본적인 상수들과 함께
시공간의 모든 것들의 행동을 조절합니다.
"Great Course Plus" 에 이 비디오의 스폰서에

English: 
...part wave, part particle,...
...carrying a quantum of energy
equal to the now familiar...
...(frequency of the wave) x (the Planck constant).
Einstein proved this
 through the photoelectric effect.
It got him
 the 1921 Nobel Prize in Physics,...
...shortly following
Planck's Nobel of 1918.
These discoveries sparked
 a frenzy of science...
...that led to the quantum revolution
 of the 1920's.
And that little number that Max Planck 
came up with in his moment of desperation,...
...the Planck constant,...
...remains at the heart
 of all things quantum.
But not just quantum.
By defining the shape
 of the blackbody spectrum,...
...the Planck constant can be read
 in the colour of the sun,...
...and the stars,...
...and the brightness 
of the different colours of the rainbow.
And, combined with a small handful
of other fundamental constants,...
...it governs the behaviour of everything...
...in this spacetime!

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Korean: 
감사드립니다.
"The Great Courses Plus"는
아이비리그 교수부터 세계의 다른 교육자들로부터
여러 주제에 대해서 배울 수 있는 서비스 입니다.
과학, 수학, 역사, 문학에 대한 다양한 영상강의를 들어보세요
과학, 수학, 역사, 문학에 대한 다양한 영상강의를 들어보세요
또는 요리, 놀이, 체스, 사진가가 되는 법까지
매월 새로운 강의, 주제들이
업로드 되고 있습니다.
"The Great Cousre Plus" 와 함께
어떠 시험도 필요없이 당신이 원하는 때에 원하는 만큼
원하는 강의를 볼 수 있습니다.
"Space Time' 채널을 thegreatcourseplus.com
에 가셔서 한달 trial에 등록해 지원해주세요.
지난 주에 우리는, 중력 렌즈에 관해 이야기했습니다.
그리고 모두 좋은 질문들이었습니다.
많은 분들이 왜
아이슈타인의 십자가가 십자가인지
왜 고리형태가 될  수 없는지 질문을 받았습니다.
만약 빛의 출발점과, 렌즈 그리고 망원경이 완벽히
정렬되어 있고, 렌즈가
이 세개를 연결하는 선, 광학축에서

Modern Greek (1453-): 
για την χορηγία της σε αυτό το επεισόδιο.
Η "The Great Courses Plus" είναι μια διαδικτυακή υπηρεσία
με την οποία μπορείτε να μάθετε μια γκάμα θεμάτων, από καθηγητές κλάσεως "Ivy League"
καθώς και άλλων εκπαιδευτών από διάφορες σχολές του κόσμου.
Πηγαίνετε στον ιστότοπο:
http://thegreatcoursesplus.com/spacetime
για να αποκτήσετε πρόσβαση σε μια βιβλιοθήκη από διαλέξεις σε βίντεο,
με θεματολογία από τις επιστήμες, τα μαθηματικά, την Ιστορία και την λογοτεχνία,
ή ακόμη και την μαγειρική, το σκάκι, ή πώς να γίνετε φωτογράφος.
Νέα θέματα, νέα μαθήματα και καθηγητές
προστίθενται κάθε μήνα.
Με το "The Great Courses Plus", μπορείτε να παρακολουθήσετε
όσα διαφορετικά μαθήματα θέλετε,
οποτεδήποτε και οπουδήποτε, δεν δίνετε εξετάσεις.
Υποστηρίξτε το κανάλι μας "Space Time" (Χωρόχρονος) με μια δοκιμή ενός μήνα
που θα κάνετε στον ιστότοπο http://thegreatcoursesplus.com/spacetime
Την περασμένη εβδομάδα μιλήσαμε για βαρυτικούς φακούς
και κάνατε πολύ καλές ερωτήσεις.
Λοιπόν, πολλοί από εσάς θέλετε να ξέρετε γιατί
ο αστερισμός "Σταυρός του Αϊνστάιν" σχηματίζει σταυρό και όχι
ένα πλήρη κύκλο (όπως στους οπτικούς φακούς).
Αν η πηγή του φωτός, ο φακός και το τηλεσκόπιο που παρατηρείτε
έχουν ευθυγραμμιστεί τέλεια και ο φακός
είναι τέλειος κύκλος γύρω από την ευθεία

English: 
Thanks to "The Great Courses Plus"
for sponsoring this episode.
The Great Courses Plus is a service
 that allows you to learn about a range of topics...
...from Ivy League professors,
 and educators from other schools around the world.
Go to 
thegreatcoursesplus.com/spacetime,..
...and get access to a library
 of different video lectures about...
...Science, Math, History, Literature,...
...or even How to Cook, Play Chess,
Become a Photographer.
New subjects, lectures, and professors
 are added every month.
With "The Great Courses Plus" you can watch
 as many different lectures as you want,...
...any time, anywhere,
without any tests or exams.
Help support "Space Time"
and start your 1-month trial...
...by going to
 thegreatcoursesplus.com/spacetime
Last week, we talked about
 "gravitational lensing".
And you guys asked
 all the good questions.
Okay.  A lot of you want to know why it is
 that the Einstein cross is a CROSS,...
...rather than a full ring.
So, if your light source,
your lens, and your telescope...
...are all perfectly lined up,...

English: 
for sponsoring this episode.
"The Great Courses
Plus" is a service
that allows you to learn about a
range of topics from Ivy League
professors and educators from
other schools around the world.
Go to thegreatcoursesp
lus.com/spacetime,
and get access to a library of
different video lectures about
science, math,
history, literature,
or even how to cook, play
chess, become a photographer.
New subjects, lectures,
and professors
are added every month.
With "The Great
Courses Plus," you
can watch as many
different lectures
as you want any time, anywhere,
without any tests for exams.
Help support "Space Time" and
start your one-month trial
by going to thegreatcoursesp
lus.com/spacetime.
Last week, we talked about
gravitational lensing,
and you guys asked all
the good questions.
OK, a lot of you
wanted to know why
it is that the Einstein
cross is a cross rather
than a full ring.
So if your light source,
your lens, and your telescope
are all perfectly
lined up, and your lens
is perfectly circular
around the line

English: 
...and your lens is perfectly circular
around a line connecting the three,...
...-- the optical axis --,...
...then the light source
 will be stretched out into a circle.
We call that an "Einstein Ring".
In that case, all the paths 
around the lens are equally good,...
...and so light from the source
can travel all of them.
But perfect alignment is almost impossible
 for something as small as a quasar.
The quasar is always
 slightly offset from the optical axis.
Also, the lens mass distribution...
...is never perfectly
 circularly symmetric around its axis.
It's elongated in one direction or another.
The result is that
 only a few paths around the lens...
...get deflected directly back to us.
If the alignment is still pretty close,...
...then you see 4 images.
In fact, there is really 5,...
...4 magnified images
 and 1 heavily demagnified image...
...in the centre, that we can't see.
On the other hand,
 if the light source is large,...
...for example, an entire galaxy,...
...then it's easy
 for at least part of the galaxy...

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

English: 
connecting the three--
the optical axis--
then the light source will be
stretched out into a circle.
We call that an Einstein ring.
In that case, all of the
paths around the lens
are equally good, and
so light from the source
can travel all of them.
But perfect alignment is
almost impossible for something
as small as a quasar.
The quasar is away slightly
offset from the optical axis.
Also, the lens mass distribution
is never perfectly circularly
symmetric around its axis.
It's elongated in one
direction or another.
The result is that only a
few paths around the lens
get deflected
directly back to us.
If the alignment is
still pretty close,
then you see four images.
In fact, there's really
five-- four magnified images
and one heavily demagnified
image in the center
that we can't see.
On the other hand, if the
light source is large,
for example, an entire
galaxy, then it's
easy for at least
part of the galaxy

Modern Greek (1453-): 
που συνδέει αυτά τα τρία πράγματα, ο λεγόμενος "οπτικός άξονας",
τότε μια πηγή φωτός θα παραμορφωθεί σε κύκλο.
Τον αποκαλούμε "δακτύλιο του Αϊνστάιν".
Σε τέτοια περίπτωση, όλες οι πορείες γύρω από το φακό
είναι εξίσου καλές για το φως, οπότε και το φως της πηγής
τις ακολουθεί όλες μαζί.
Αλλά μια τέτοια τέλεια ευθυγράμμιση είναι σχεδόν αδύνατη
για κάτι μικρό όσο ένα κβάζαρ.
Το κβάζαρ έχει μια μικρή απόκλιση από τον οπτικό άξονα.
Επίσης η κατανομή της μάζας στο φακό δεν είναι ποτέ τέλεια κυκλικά
συμμετρική γύρω από τον άξονα.
Έχει μια επιμήκυνση σε κάποια διεύθυνση.
Το αποτέλεσμα λοιπόν είναι ότι λίγες από τις πορείες γύρω από τον φακό
που μπορεί να πάρει το φως, φέρνουν το φως προς το μέρος μας.
Αν όμως είναι κάπως καλή η ευθυγράμμιση
τότε θα δείτε τέσσερα είδωλα.
Στην πραγματικότητα υπάρχει και πέμπτο. Είναι τέσσερις εικόνες μεγεθυσμένες
και μια τελείως "απομεγεθυσμένη" εικόνα στο κέντρο
που δεν μπορούμε να δούμε.
Από την άλλη μεριά, αν η πηγή φωτός είναι μεγάλη,
για παράδειγμα ένας ολόκληρος γαλαξίας, τότε είναι
ευκολότερο ένα τουλάχιστον μέρος του γαλαξία

Korean: 
완전한 구형을 이룬다면
빛은 출발점에서 원형으로 펼쳐지게 됩니다.
이것을 아이슈타인 고리라 부르고, 이 경우에 렌즈를 둘러싼 모든 길은
동일하기 때문에, 빛은 이 모든 곳을
통과할 수 있습니다.
하지만 완벽한 정렬은
퀘이사 같이 작은 것에는 거의 불가능합니다.
퀘이사는 항상 광학축이 약간 뒤틀려있죠.
또한, 렌즈의 질량 분배 또한  광학축에 대해서
대칭적이지 않죠.
한 방향이 항상 더 길게 되어있죠.
결과적으로 오직 렌즈로부터 몇몇의 빛만
우리에게 반사되게 됩니다.
만약 정렬의 상당히 정확하다면
4개의 이미지를 보게됩니다.
사실 5개인데,  4개의 확대 된 이미지와
중앙의 확대되지 않은 이미지이지만, 이건 볼 수가 없죠.
중앙의 확대되지 않은 이미지이지만, 이건 볼 수가 없죠.
반면에 만약 빛의 근원이 아주 거대한 것이라면,
예를 들어서 은하계 전체의 경우
최소한 은하계의 특정 부분이라도

Modern Greek (1453-): 
να τοποθετηθεί πάνω στον οπτικό άξονα.
Τότε θα αντικρίσετε το δακτύλιο του Αϊνστάιν.
Υπάρχουν περιπτώσεις που φαίνονται τέσσερις εικόνες ενός και μόνο κβάζαρ
αλλά συνδέονται με ένα δακτύλιο Αϊνστάιν.
Αυτός ο δακτύλιος είναι ο γαλαξίας
στον οποίο βρίσκεται το κβάζαρ.
Ο Gary Palmer θα ήθελε να μάθει πώς είμαστε τόσο σίγουροι
για την μέτρηση της μάζας ενός βαρυτικού φακού
δεδομένου ότι δεν γνωρίζουμε τη σύσταση αυτού του φακού.
Είναι αλήθεια ότι για κάποιον φακό
υπάρχουν διάφορες διαμορφώσεις της μάζας
που δημιουργούν την ίδια κατανομή του φωτός
όπως φαίνεται από τον φακό, δηλαδή τις θέσεις των ειδώλων και τη φωτεινότητά τους.
Αλλά άμα γνωρίζεις την απόσταση από την πηγή του φωτός
και την απόσταση από τον φακό, υπολογίζοντας από τη μετατόπιση προς το ερυθρό (redshift),
τότε μπορείς να κάνεις αναζήτηση σε μια μεγάλη γκάμα κατανομών μάζας
για το φακό, με τη βοήθεια προσομοιώσεων σε υπολογιστή.
Οπότε καταλήγεις σε ένα σύνολο ισοδύναμων αποτελεσμάτων για τους φακούς,
το οποίο να συμφωνεί με τις παρατηρήσεις.
Από αυτό το σύνολο προκύπτει μια γκάμα από μάζες,
αλλά συνήθως είναι μια στενή γκάμα.

English: 
...to be located
 directly on the optical axis.
Then you'll see an Einstein ring.
There are some cases...
...where you see
 4 individual quasar images...
...connected by an Einstein ring.
That Einstein ring is actually
 the galaxy that hosts the quasar.
Gary Palmer would like to know
 how we can really be confident...
...measuring the mass
of the gravitational lens,...
...given that we don't really know
 the composition of that lens.
Well, it's true that for a given lens...
...there could be a range
 of different configurations of matter...
...that produce the same distribution
 of light seen in the lens.
So, image positions
 and brightnesses.
But, if you know the distance
 to the light source,...
...and the distance to the lens,
both from redshift,..
...then you can explore an enormous range
 of possible lens mass distributions,...
...with computer simulations.
So you end up with a set
of virtual lenses...
...that can reasonably
produce the observations.
That set will span
a range of masses,...
...but that range
is usually pretty small.

English: 
to be located directly
on the optical axis.
Then you'll see
an Einstein ring.
There are some cases where
you see four individual quasar
images connected by
an Einstein ring.
That Einstein ring is
actually the galaxy
that hosts the quasar.
Gary Palmer would like to know
how we can really be confident
measuring the mass of
a gravitational lens,
given we don't really know
the composition of that lens.
Well, it's true that
for a given lens,
there could be a range of
different configurations
of matter that produce the
same distribution of light
seen in the lens, so image
positions and brightnesses.
But if you know the distance
to the light source,
and the distance to the
lens, both from redshift,
then you can explore an enormous
range of possible lens mass
distributions with
computer simulations.
So you end up with a
set of virtual lenses
that can reasonably
produce the observations.
That set will span
a range of masses,
but that range is
usually pretty small.

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Korean: 
광학축에 정확히 위치하도록 만들 수 있죠.
이 경우엔 아이슈타인 고리를 관측할 수 있습니다.
가끔 4개의 퀘이사 이미지가
아이슈타인 고리로 연결된 경우를 볼 수가 있는데요.
그 아이슈타인 고리는 실제로 그
퀘이사의 은하계입니다.
Gary Palmer 는 우리가 어떻게
중력 렌즈가 정확히 무엇으로 이뤄진지 모르는 상태에서 어떻게
렌즈의 질량 측정 값을 신뢰할 수 있는지 질문했는데요.
이 렌즈의 경우에
동일한 빛의 분배 , 즉 밝기나 위치, 를 보여주는  다른 물질의 배열 상태가 있을 수 있습니다.
동일한 빛의 분배 , 즉 밝기나 위치, 를 보여주는  다른 물질의 배열 상태가 있을 수 있습니다.
동일한 빛의 분배 , 즉 밝기나 위치, 를 보여주는  다른 물질의 배열 상태가 있을 수 있습니다.
하지만 우리가 빛의 출발점까지의 거리와
출발점으로 렌즈까지 거리를 알고 있다면,
두 경우의 적색편이를 통해 서
엄청난 범위의 가능한 렌즈 질량분배를
컴퓨터 시뮬레이션을 통해 알 수 있습니다.
결과적으로 관측을 어느정도 수행할 수 있는
가상의 렌즈질량을 얻게 되죠.
그 질량값은 그 범위가 있지만
보통은 매우 작은 범위를 지닙니다.

Korean: 
그래서 우리는 결과적으로 가장 최선의 질량과 그리고
그 범위로 계산되는 오류편차를 갖게되죠.
Prasad Deshmukh님과 몇몇 분들이
우주배경복사선도 중력렌즈 효과에 영향을 받았는지?
라고 질문하셨는데요.
맞습니다.
우주배경복사는 미세중력렌징에 영향을 받는데
복사의 모든 부분이 아주 미세하게 왜곡되어있죠.
이러한 왜곡은 스펙트럼의 분배,크기의 강도를 바꿀 수가 있는데
이러한 왜곡은 스펙트럼의 분배,크기의 강도를 바꿀 수가 있는데
우주적 인자값들을 측정하는데 매우 중요한 내용들이죠.
이것은 또한 잠재적으로 B-mod 극성화를 일으킬 수 있는데요.
이것은 태초의 중력파가 일으켰을 소용돌이와 정확히
동일한 소용돌이이죠
그러므로, 우주배경복사에서 이러한 왜곡효과에 보정을 해야합니다.
Ed Eggermont님은 중력파도 중력렌즈와 관련 있는 주제인지 궁금해하셨는데요.
Ed Eggermont님은 중력파도 중력렌즈와 관련 있는 주제인지 궁금해하셨는데요.
당연히 그렇습니다.
중력파는 시공간 구조의 물결과 같은 것으로
시공간이 가는 곳이라면 따라가게 되어있죠.

English: 
So we end up
with a "best mass",...
...and error bars defined by that range.
Prasad Deshmukh
 and a few others asked...
..."Is the cosmic microwave
 background radiation..."
"...gravitationally lensed?"
Actually, yes!
The CMB is affected by "weak lensing".
So, all of its blobs
 are very slightly distorted.
This can change the power spectrum,...
...so, the distribution
 of the sizes of its blobs,...
...which is really important
for measuring cosmological parameters.
It could also potentially introduce
B-mode polarisations.
That's exactly
 the same type of squirrelliness...
...that primordial gravitational waves
 should produce.
So yeah, we are going to need to correct
 for lensing in the CMB.
Ed Eggermont wonders if gravitational waves
are also subject to gravitational lensing.
Well, yeah!
Gravitational waves
 are ripples in the fabric of spacetime.
So they've to go
 where the spacetime goes.

English: 
So we end up with a best
mass and error bars defined
by that range.
Prasad Deshmukh and
a few others asked,
is the cosmic microwave
background radiation
gravitationally lensed?
Actually, yeah.
The CMB is affected
by weak lensing.
So all of its blobs are
very slightly distorted.
This can change the power
spectrum, so the distribution
of the sizes of
its blobs, which is
really important for measuring
cosmological parameters.
It could also potentially
introduce B-mode polarizations.
That's exactly the
same type of swirliness
that primordial gravitational
waves should produce.
So yeah, we're going to need to
correct for lensing in the CMB.
Ed Eggermont wonders if
gravitational waves are also
subject to
gravitational lensing.
Well, yeah.
Gravitational waves are ripples
in the fabric of space time,
so they have to go where
the space time goes.

Spanish: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Modern Greek (1453-): 
Έτσι οδηγούμαστε στην βέλτιστη εκτίμηση για τη μάζα, βάζοντας κάποιο διάστημα σφάλματος
σε αυτή την γκάμα.
Ο Prasad Deshmukh και μερικοί άλλοι ρωτούν:
Υφίσταται η κοσμική μικροκυματική ακτινοβολία υποβάθρου
παραμόρφωση από βαρυτικούς φακούς;
Η απάντηση είναι, ναι.
Η ακτινοβολία υποβάθρου επηρεάζεται από αδύναμους φακούς.
Οπότε όλες οι περιοχές της έχουν μια μικρή παραμόρφωση.
Αυτό μπορεί να αλλάξει το φάσμα, όπως και την κατανομή
των μεγεθών αυτών των περιοχών, που είναι
πολύ σημαντικό στην μέτρηση των κοσμολογικών παραμέτρων.
Θα μπορούσε επίσης να εισαγάγει περισσότερη πολικότητα B στην ακτινοβολία υποβάθρου.
Κι αυτή ακριβώς είναι η "στροφικότητα" που περιμένουμε
να έχουν παραγάγει τα πρωταρχικά βαρυτικά κύματα.
Οπότε βέβαια, θα χρειαστούμε να κάνουμε διορθώσεις από βαρυτικούς φακούς της ακτινοβολίας υποβάθρου.
Ο Ed Eggermont αναρωτιέται αν τα βαρυτικά κύματα υφίστανται
και αυτά επίδραση από βαρυτικούς φακούς.
Λοιπόν, ναι.
Τα βαρυτικά κύματα είναι ρυτιδώσεις της υφής του χωρόχρονου,
επομένως πηγαίνουν όπου πάει και ο χωρόχρονος.

Korean: 
Dylan T 님은 SpaceTime 채널을 추천하다가
현재 아내분을 만나셨다고 하는군요.
저희가 두분을 "얽히게" 해드려서 기쁩니다.
 
 

English: 
Dylan T tells us that he
met his wife by suggesting
that they Space Time and Chill.
I'm glad we could help
you guys get entangled.
[THEME MUSIC]

Spanish: 
 
 
 
 
 

Modern Greek (1453-): 
Ο Dylan T μας λέει ότι γνώρισε την σύζυγό του προτείνοντάς της
να κάνουν Χώρο στο Χρόνο τους για καλοπέραση.
Είμαι πολύ χαρούμενος που αποκτήσατε διεμπλοκή!

English: 
Dylan T tells us that he met his wife
 by suggesting that they "spacetime and chill".
I'm glad we could help
 you guys get entangled!
