03.08 - 요약: 생활속의 상대론(Summary: Living Relativistically) [커세라 강의 페이지]
Earlier in this module, we came to understand how event horizons work by drawing an analogy to a fish falling over a waterfall. At a certain point in its descent, the falling fish can no longer communicate with its friend above because the water is flowing downwards at a greater speed than the speed of sound. Luckily, in the story, we rescued our fishy friend using a rocket pack. This was possible because the speed of sound is not a universal limit.
소리의 속도가 우주의 한계가 아니기 때문 소리의 지평선(sonic horizon)에서 탈출할 수 있었다.
The speed of light on the other hand is. Were we to drop our fishy friend into a real black hole, a rocket pack would be of little use because once you're beyond the event horizon of a real black hole, escape is no longer possible. But don't worry, no fish were harmed in the making of this course.
[중력에 의해 가속되는 폭포수를 블랙홀이 끌어 들이는 에너지로 비유해 봤다. 강력한 블랙홀이라면 가속된 속도가 빛의 속도를 넘을 수도 있지 않을까?] 빛의 속도는 우주의 한계속도다. 실제 블랙홀 이었다면 물고기는 탈출할 수 없다.
We also learned about a revolution in physics which began in the early 1900's. Einstein, in a single year and with four extraordinary papers, turned physics on its head. One of the results of these papers was that space and time are no longer absolutes and in their place was this amalgamation called space-time.
1900년대 초에 아인슈타 인이 발표한 네개의 논문으로 물리학을 완전히 뒤집어 놓았다. 이제 시간과 공간이 절대 적이지 않다.
In this framework, relative motion is what matters and many of our traditional notions about how the universe works no longer apply. Some truly weird things start happening like length contraction, time dilation, and relative simultaneity.
이체제를 시공간(spacetime)이라고 하자. 전통적인 물리학이 더이상유효하지 않다. 빛의 속도는 우주의 상수 이며 빠른 속도로 움직이는 기준 관성 좌표계는 시간의 지연과 거리의 단축을 격게 된다. 그로 인해 '동시성'도 상대적이 된다.
When Einstein went about generalizing his theory of relativity, he realized that there ought to be an equivalence between gravitational fields and the acceleration of a reference system, meaning, if we stuff you in a windowless rocket, you can't tell the difference between a rocket sitting at rest on the surface of the earth or a rocket that is accelerating uniformly upwards at a rate equal to the acceleration due to gravity on Earth's surface.
Under these two conditions, the two are indistinguishable. In addition, general relativity comes with its own quirks, one of which being that mass deforms space-time.
가속에 의해 작용하는 힘과 질량에 의한 중력이 같다는 등가의 원리를 제시하고 이를 일반화한 일반 상대론을 펼쳤다. 질량이 시공간을 왜곡 시킨다.
This is what causes the effect known as gravitational lensing, something not exclusive to black holes but something they are nonetheless known for, that is their ability to bend light rays. In the next module, we'll explore black holes in more detail and learn how to weigh a black hole.
03.07x - 일반상대론의 증거 찾기(The history of the earliest test of general relativity.) [커세라 강의 페이지]
Interview with Dr. Robert Smith, Professor of History at the University of Alberta.
Einstein develops special relativity in 1905, the famous publication. By 1907 though, he's beginning to realize that he would like to generalize special relativity.
No longer talking about reference frames which are moving uniformly with respect to one another. But what about reference frames that are moving in an accelerated fashion with respect to one another? What about rotating reference frames?
So, by 1911, he's got his first, what's called the Prague theory of general relativity and that will change.
By 1913, he's got a version which he thinks is superior. Then, the final version of general relativity that Einstein would develop, he's got by the end of 1915 start of 1916.
But the famous light deflection that he predicts in 1911, comes out of an earlier version of general relativity. So, he calculates how big should the deflection of light be, as light, from a distant star just passes by the sun.
How much will it be affected? The calculation he makes turns out to be an answer of less than one second of arc. An astronomer at the Berlin Royal Observatory, a man called Erwin Finlay-Freundlich, is really interested in Einstein's theory, is one of the very few astronomers who's actually interested in trying to test the results of general relativity. So, Freundlich tries to look at past photographs of eclipses.
Can he look at these earlier photographs and see star images, and compare the positions of those stars with the Sun there at the eclipse? And also when the sun has moved away from the star, because then we should see the deflection. But the images were just not good enough for a range of different reasons, so he decides in 1913 that he would like to engage in an expedition. Go to the Crimea in August 1914, take photographs of the sun during eclipse in order to get the star positions during the eclipse. Take photographs at a different time when the sun is moved away, compare the star positions between the two sets of photographs, and then you've got the measurement of the deflection of light.
Freundlich leads an expedition and they go to Russia, and the eclipse will occur at the end of August 1914. But this is not a good time to be a German traveling in Russia, because World War I breaks out and so Freundlich and his companions and their instruments are taken into custody, they're thought to be spies and they're held in Odessa for several weeks before, in fact, they're released but the instruments are confiscated.
But what is very interesting about this expedition is if they had in fact gone ahead, made the measurements of the deflection of light, they would have come up with an answer which would have been roughly twice the answer that Einstein had calculated, based on one of his earlier versions of general relativity.
So, the actual shift that Einstein predicted later would be 1.75 seconds of arc. At this point, the prediction that Einstein makes is 0.85 seconds of arc. The first measurements made at an eclipse of the deflection of light that are successful anyway, the result is 1.64 seconds of arc.
So, what that means is, if Freundlich had gone ahead, made the observations in 1914, the answer would have been about double Einstein's prediction. Then Einstein would have come along later and redone his calculations, "Oh look, my answer is now double what I pretty much got the amount that the light is deflected by."
Now, would that have aided the acceptance of general relativity? I suspect not because coming in after the fact, after the measurements have been made and say, "Oh, I goofed by a factor of two" is not really a very convincing way to verify your theory I think.
One of the most important realizations Einstein made while developing special relativity is that there is no such thing as a universal time or distance. Instead, special relativity introduced the notion of an invariant spacetime interval.
아인슈타인이 특수 상대론을 발전 시키면서 알아낸 가장 중요한 것은 시간과 거리가 각각 절대적이지 않다는 점이다. 그대신 시공간(spacetime)의 간격이 불변하다는 것이다(시간과 공간의 유기적 결합).
When astronauts travel at different speeds and experience differences in the duration of time intervals, they are effectively trading distance for time or vice versa. They are experiencing a distortion or warping of space and time together. This is required in order for all observers to agree on the speed of light. Einstein realized that he could explain the effects of gravity by combining the equivalence principle with the concept of an invariant spacetime interval used in special relativity. When Einstein developed the general theory of relativity, he came to the realization that gravity is the warping of spacetime. So, stars like our Sun, which have strong gravitational field due to their large mass, actually bend and stretch the fabric of the universe itself. The warping of spacetime causes planets and light to travel on curved paths near massive objects. An early test of general relativity depended on the bent spacetime around the Sun. In 1919, the astronomer, Sir Arthur Eddington, led an expedition to an island of the West Coast of Africa in order to measure how much the gravity of the Sun warped spacetime. They did it by observing a total eclipse of the Sun. During the eclipse, a star could be seen next to the eclipse Sun. Those of you who have observed a total solar eclipse, like I have, know that the Sun looks eerily like a black hole in the sky surrounded by white hair. The locations of all the stars in our neighborhood of the galaxy were mapped more than 100 years ago. So it was known that this star should really be located behind the Sun when viewed from the Earth on the day of the eclipse. So, how did Eddington and his team see the star? The light from the star traveled on a curved path around the Sun to the astronomers' telescopes. This effect was predicted by Einstein's theory of general relativity. The measurement they made confirmed and has since been reconfirmed that the theory of general relativity is accurate and that spacetime itself is bent by matter. This changes our notion of what a straight line is, of course, because if spacetime itself is bent, how can we possibly know that we're going in a straight line? Instead of calling them straight lines, in general relativity, we call them geodesics, which represent the straightest possible path of an object in a curved spacetime. Even though geodesics represent straight lines in curved spacetimes, they wouldn't be considered straight by our standards. Just as the Sun's mass bends the spacetime around it, any light crossing bent spacetime will appear to have its path bent. Since we are talking about curving spacetime, let's consider the surface of this chalk ball as a section of a curved two-dimensional space. This works equally well if you imagine the chalk ball to be the Earth. If I asked you to draw a straight line between two points on opposite sides of the ball, the same thing as asking for the flight path between two cities on Earth, you might be tempted to draw along an equatorial line to join them together. Even though I asked you to draw a straight line, already it's curved. Instead, the smallest distance between two points on a curve surface is considered straight if it's also the shortest line joining the two points together. The smallest distance between two points on a curved surface is called a geodesic. If you look at the flight path of an airplane from Toronto to London, the airplane crosses the ocean near Greenland. The shortest route joining the two cities is a curved path. The same is true for any object traveling through curved spacetime. Now, where do you think the most convoluted curvatures of spacetime in the universe exist? That's right, black holes. Not only do black holes warp spacetime, they warp it to the point that even light will travel on highly curved paths. Photons, by definition, travel on geodesic paths in spacetime. Close to the black hole, the curvature becomes so high that light is bent into paths that all terminate at the black hole singularity. General relativity interprets gravity as the warping of spacetime. When we view a picture of the gravitational field around a massive object, it's usually represented as a depression in space. However, we need to understand that gravity also warps the passage of time. It's strangely difficult for the human mind to grasp the concept of warping spacetime. We understand what it means to bend or warp a material like plastic, but what does it mean when the actual space and time that we live in are bent and twisted? In a sense, warped spacetime means that the paths we choose to cross space and time will be shorter or longer in distance between two points and in the duration it takes to travel between them depending on what the gravitational fields are along the path. Let's focus specifically on how gravitational fields warp the time component in an effect called gravitational time dilation. Let's start with an example by considering two astronauts exploring an unstudied planet around a distant star, perhaps planet e in the nearby Trappist-1 System, which we'll shorten to trappy. One astronaut needs to stay with the ship in order to orbit around the parent star while the astronaut descends to trappy surface. Since we are talking about time, both astronauts will need to carry clocks, which they synchronize before they separate. Far from the surface of the planet, both clocks tick in perfect synchronicity. One astronaut now descends to the surface of trappy. On the surface, he is deep in the planet's gravitational well and therefore, experiences a greater gravitational force. The spacetime in the vicinity of the planet will also be warped. The effect that the warping has on the astronauts' clocks causes it to tick more slowly than the one in orbit. For every tick of the clock on the surface, the orbital clock ticks more rapidly. On the surface of trappy, the astronaut doesn't experience the change in the passage of time because all biological processes are likewise slowed down by the warping of gravity. Just like the ticks of the clock, a distant observer would see the heartbeat of an astronaut on the surface to beat more slowly. Once the surface mission is complete, the two astronauts rejoin one another in orbit around trappy. The astronaut who stayed in orbit will be dismayed. She experienced a longer time than the astronaut who was on the surface. Depending on the duration of the stay and the strength of the gravitational field, the astronaut who went down to the planet's surface will experience fewer ticks of the clock and therefore, be several seconds younger than the one who stayed in orbit. To calculate how time has worked in a strong gravitational field, the following equation is employed. Delta t planet, the elapsed time on the surface of the planet, is equal to Delta t orbit, the elapsed time on the orbiting spaceship, times the square root of one minus two times G times mass divided by radius times c squared. In this formula, the mass and radius refer to the mass and radius of the planet. But if instead of a planet, you were a distance R from a star or a black hole with mass M, you could use the same formula. The important thing in this formula is that the quantity inside the square root sign is smaller than one. So the amount of time that passes when you're in a gravitational well is smaller than if you're out in space far from the gravitating object. Note that this formula doesn't make sense if the ratio of the mass to radius gets too large. This formula only makes sense if R is larger than two times G times mass divided by c squared. You might think that your everyday life is not much affected by time dilation due to special or general relativity. However, you may be surprised to learn that almost everyone carries a piece of technology that would be useless without both theories, GPS. The Global Positioning System that you use every time you navigate with a map on your smartphone depends on Einstein's theory of relativity to function correctly. Handheld GPS works because the device inside your smartphone is capable of measuring and comparing the signals from multiple satellites in orbit around the Earth. These satellites are placed in well-known orbits and carry very precise clocks. By broadcasting a timing signal that can be picked up on a GPS receiver, the difference in timing signals from different satellites can be used to triangulate your position. Since GPS satellite travel at about 14,000 kilometers per hour, they experience a very slight time dilation due to special relativity. Each day, a satellite's clock would appear to slow down by about seven microseconds. That doesn't sound like much, but if you neglected this drift, your GPS would accumulate an error of about two kilometers every day. General relativity predicts that the clocks aboard a GPS satellite traveling at an altitude of 20,000 kilometers would appear to tick faster than clocks on Earth. Every day, a satellite clock would appear to speed up by 45 microseconds compared to clocks on Earth's surface. If this error wasn't corrected, the GPS would accumulate an error of over 13 kilometers a day. Since special relativity works to slow down the apparent rates of the clock on a GPS satellite, and general relativity speeds up their apparent rates, the combined effects add up to a 38 microseconds per day error. Without relativity, our GPS devices would drift by over 10 kilometers every day, roughly the same as 12 centimeters a second. Luckily, we know about the effects of relativity. So we can correct for this drift. GPS devices are some of the most robust tests we have for Einstein's theories of relativity. In the movie "Interstellar", the main character Cooper is sent to retrieve a fellow explorer Mann from the surface of Miller's planet orbiting the nearby black hole Gargantua. On the surface of Miller's planet, an hour of time is equivalent to seven years on Earth. This is an example of the correct use of an effect called gravitational time dilation.
Start transcript at 11 minutes 35 seconds11:35
Since gravitational time dilation slows down the passage of time in intensely strong gravitational fields, it equally effects physical processes that are time-dependent. That means that someone observing an astronaut in orbit around the black hole would see their clocks ticking slow and their hearts beating slower, and everything about them slow down. So, what happens to a beam of light when it's generated deep in the gravity well near a black hole? The beam of light experiences gravitational redshift. Recall the Doppler effect that we discussed earlier. When a moving object like a rocket ship is emitting light, the light can be blueshifted or redshifted depending on the ship's motion towards or away from the observer. If a ship were to accelerate away from you, you would see the light from its engines becoming redder and redder as it accelerated to ever increasing speeds. Light emitted from deep within gravitational well has to work against gravity in order to leave a planet, or a star, or the region near a black hole. When light travels away from a planet, the photon has to convert kinetic energy into gravitational potential energy. If we remember that red photons have less energy than blue photons, we can predict that the photons emitted from the surface of a star will appear redder to an observer far from the star. This effect is called gravitational redshift. The gravitational redshift effect is very small, but it has been measured in the light emitted by a white dwarf star and it agrees with the predictions in general relativity.
Interview with Dr. Jeremy Heyl, Professor at the University of British Columbia.
One fun thing that I did recently with this was to ask the question whether black holes, like if you think of Galileo, the first astronomer, there's this story of him dropping things off towers and whether they fall faster or slower depending on what they're made of, but you can do the same experiment with black holes, because there's black holes in galaxies, and these galaxies are falling through the universe, and you can ask, does the black hole fall any differently than the rest of the galaxy, for example?
최근에 블랙홀에 관해 한가지 재미있는 질문을 해봤어요 (받았어요?). 갈릴레오가, 그는 최초의 천문학자죠, 어느 탑위에 올라 서로 다른 물질로 만든 공을 떨어트려, 떨어지는 속도가 다른지 보려고 실험을 했다는 이야기를 들어봤을 겁니다. 만일 블랙홀을 가지고 이 실험을 하면 같은 결과를 얻을까요? 블랙홀은 은하내에 있고 이 은하들은 우주를 향해 떨어지는 중이 잖아요. 그럼 블랙홀은 은하 내의 다른 것들과 다르게 떨어지지 않겠어요?
Amazingly, I mean, maybe not surprisingly they do, but what's maybe more surprising is that you can actually pose the question that, "Hey, how does a black hole fall? Does it fall like normal stuff or not?" I mean, we're not very precise, they fall like normal stuff to within 50 percent, maybe about as precise as Galileo was, 400 years ago. But I mean, we can get better.
03.06 - 등가의 원리(The Equivalence Principle) [커세라 강의 페이지]
If humans decide to explore other solar systems, we'll need to get there using generation ships. Ships like these can carry a self-sustaining human colony which can survive for many generations. This is the premise of a television series called Ascension. The characters in the show walk around as if they're in Earth gravity, which is generated by the acceleration of their ship.
행성간 이주여행 영화에 '세대 우주선(generation ship)' 등장한다. 우주선을 회전시켜 얻은 가속도를 중력 처럼 활용하는 모습을 보여 준다.
But without windows to see outside, can the characters tell the difference between uniform acceleration of their spaceship or simply being stationary on Earth's surface? Suppose you awaken in just such a situation. You're trapped in a small room unable to remember how you got there and with no way of seeing what's outside. Could you tell the difference between the room being here on Earth or in an accelerating rocket ship.
지속적으로 가속되는 창 없는 방안에 있으면 마치 중력의 영향을 받는다고 느낀다. 끊임 없이 일률적인 가속이 요구된다. 가속의 끝은 무한한 속도다. 그래서 등속 회전으로 원심력을 중력처럼 활용한다.
Einstein realized that these two scenarios are indistinguishable so long as the room is small enough. In an experiment that you could try in your small room is to drop a ball. There are two possible outcomes depending on where the room is. If it's here on earth, the ball will appear to accelerate downwards, falling to the ground due to gravity. In the second scenario, we're in an accelerating rocket ship far away from any sources of gravity, the ball still appears to fall, only this time, it's because the rocket is accelerating upward. If the acceleration of the rocket is precisely 9.81 meters per second squared, the motion of the ball will be indistinguishable from the effects of gravity on Earth.
Nice try, but dropping the ball won't tell you which of the two scenarios you're in. You might say that you dropped the ball by dropping the ball. Not knowing whether it's the rocket ship accelerating or the ball accelerating due to gravity is called the equivalence principle. In fact the formal definition of equivalence principle given by Einstein himself states, we assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system.
등가의 원리는 중력장이 작용하는 지구와 가속 중인 우주선 내의 물리 법칙이 동일하게 적용된다는 것.
What Einstein discovered is that gravity is not a force as it was believed to be by Newton and classical physicists. In small regions of space, gravity is indistinguishable from acceleration. Now we should note that Einstein's statement of the equivalence principle requires that your choice of a reference frame is small. Earth's gravity for example doesn't change much between your toes and your head. However, if you chose a tall reference frame, or an extremely wide reference frame, it would become pretty obvious that you were on Earth. Just by measuring changes in gravity as you moved around.
아인슈타인은 중력이 뉴튼의 고전역학에서 얘기하는 힘이 아니라는 점을 알게됐다. 이 등가의 원리가 중력장에서는 기준 좌표계를 아주작은 규모로 설정했을 때 성립한다.
Gravity would become weaker the higher you were from Earth's surface. The force of the gravity on the surface always points to the center of the Earth. So if you have a large horizontal frame, the direction of the balls will fall becomes different. The converse of our ball analogy is also true. When an astronaut is orbiting the Earth, they appear weightless because they are in free fall. In free fall the force due to gravity is exactly matched by the centripetal acceleration towards the earth. This is similar to riding your favorite drop of doom style amusement park ride where you feel temporarily weightless. Astronauts are in a perpetual drop of doom. This would be indistinguishable from an astronaut who has run out of fuel far from any sources of gravity. Many science fiction shows, including Star Trek, portray artificial gravity. But failed to explain the technology necessary in order to produce these fields. However, some science fiction gets it right. In the movies 2001, A Space Odyssey and Interstellar, gravity is produced by rotating the spacecraft to introduce centripetal acceleration, which mimics gravity, an example of the equivalence principle at work.
If a ball thrown on Earth travels on a curved path due to gravity, we'd expect the same curvature to occur on an accelerating rocket ship. Einstein's explanation of gravity introduces the idea of the thrown ball's trajectory being the shortest possible path through a curved space time. Gravity itself, Einstein believed, was the result of space time being curved by mass and energy.
03.05 - 특수 상대론의 영향 (Effects of Special Relativity) [커세라 강의 페이지]
특수 상대론을 적용하면 어떤 일이 벌어질까? 시간지연(Time Dilation)과 거리수축(Length Contraction) 그리고 쌍둥이 모순(Twin Paradox)
If you decide to hold a party, you need to tell your guests where and when they should arrive. It's not enough to simply tell your friends where the party is without telling them when it occurs or vice-versa. Therefore, when we use the word event, we are using it to describe where and when something is happening. Events can describe things like your arrival at a party, the time you spilled your drink, or even something as simple as snapping your fingers can be an event. I could say that I snapped my fingers about five seconds ago at this location, right here. So, an event must include details of both the position and the time.
"사건(event)"은 말할때는 장소(Position)와 시간(Time)을 명시해 주어야 한다. 파티 초대장에 장소와 시간을 명시하지 않으면 손님이 어찌 찾아오겠는가?
Our universe has three spatial dimensions. So, a defined event could look something like X, Y, Z, and T where X, Y, and Z define the position and T defines the time.
우리는 3차원 공간의 우주에서 살고있다. 그리고 이 우주에서 일어나는 사건은 3차원의 공간과 시간이 포함된 4ㅏ차원으로 기술되어야 한다.
----------------------------------------------
[아래 내용 이해불가]
A good example of this occurs in the popular TV show, Big Bang Theory. In an episode entitled The Cushion Saturation, Dr. Sheldon Cooper explains the first time he sat on his favorite spot on the couch as follows,
"In an ever-changing world, it is a single point of consistency. If my life were expressed as a function on a four-dimensional Cartesian coordinate system, that spot at that moment, I first sat on it would be zero, zero, zero, zero."
Sheldon feels most comfortable and at home at the X, Y, Z coordinates of his spot, all zero, zero, zero. Although he can return to the spot on the couch many times, and he does, he can never return to the exact moment when he first sat on the couch to experience that event again. The reason for this is that the fourth coordinate in the event is time, T, and is always increasing as time passes.
Suppose he originally sat down to enjoy a 40-minutes episode of Star Trek. We can describe the end of the show as an event that happened at zero, zero, zero, 40 minutes. The only way to return to the original event would be to use a time machine such as the one Reto Hofstetter took a ride in, in Big Bang Theory episode "The Nerdvana Annihilation."
If we were to return to Sheldon's first time on the couch and saw Penny riding a skateboard past the scene, Sheldon would see her in his reference frame. Would Penny see the first moment he sits in that spot followed by a 40-minute episode of Star Trek in the same order Sheldon experiences it?
-----------------------------------------
Considering our previous discussion about slicing of space-time, do you think all observers see the two events in the same order or with the same time interval between the events? Let's explore this further using one of Sheldon's favorite objects, trains.
사건의 순서는 같지만 시간의 간격은 다를 수 있다. 관찰자마다 빠르게 혹은 느리게 간다.
Sheldon is preparing for a trip on the Napa Valley Wine Train in his favorite 1915 Pullman-Standard lounge car. Ever the physicist, Sheldon would like to conduct an experiment to test the consequences of a constant speed of light. To do this, he sets up a light source in the center train car and has two of his friends standing in his light detectors in the caboose and the engine at either ends of the train.
While the train is in the station, we say that it is at rest. Here in the station, Sheldon conducts his first experiment by flashing the light and recording the arrival times that his friends measure at each end of the train. Since the distance to the light source is the same from both friends, they each detect the light at the same time. We call this a simultaneous detection.
등속으로 움직이는(관성계) 기차안에서 빛을 발사하여 기차 양끝에 도달하는 시간을 재보자. 광원에서 양측의 관측자 사이의 거리는 동일하다. 실험자(observer)와 관측자 모두 기차에 타고 움직인다. 빛은 동시에 관측된다(Simultaneous Detection).
The train then leaves the station and begins its journey traveling at a constant speed through the mountains. Sheldon prepares the experiment again, this time with the train in motion. Since the train is traveling at a constant speed, once again, the flash of light arrives at each of his friends at precisely the same time. In both the stationary case and the one with the moving train, the observers are at rest with respect to Sheldon and the light source. As a result, they observe the pulses arriving simultaneously on each occasion.
Sheldon wants to know what his experiment would look like if he was stationary with respect to a moving train, so he gets off at the next stop. He gets ahead of the train and get set up to redo his experiment as the train passes at a constant velocity. This time, the light source flashes the moment that it passes Sheldon. Since the train is moving from left to right, Sheldon observes the light pulse arrive at the caboose of the train first followed by the arrival of the pulse at the engine of the train second.
이번에는 실험자가 기차에서 내렸다. 광원과 두 관찰자는 여전히 등속의 기차에 타고 있다. 광원에서 반짝인 빛이 두 관측자에 도달한 시간을 측정하기로 한다. 지상에 고정된 실험자는 기차 뒷칸의 관측자가 먼저 인지했다는 보고를 받게된다. 고정된 관측자의 입장에서 기차 뒷칸의 관찰자에게 빛이 이동한 거리가 짧아지기 때문이다.
Sheldon is puzzled, he observed the light pulse arrive at the back of the train first, while his friends on board report that the light pulse arrives simultaneously. In Sheldon's frame of reference, the light pulses do not arrive simultaneously even though his friend's frame of reference, they do.
실험자의 좌표계가 광원과 함께 움직일 때와 고정되었을 때 동일한 사건이 이상하게도 다르게 관측된다.
This disagreement between observers is a result of light traveling at a constant speed no matter how quickly the source of light moves. This is called the relativity of simultaneity and it describes that stationary and moving observers will report the order of events differently depending on their proper motion with respect to one another.
고전 상대론에서 실험자의 속도에 관측 대상이 움직이는 속도를 더한다. 그런데 빛의 속도는 우주불면이므로 속도를 가감할 수 없다. 따라서 광원이 고정되든 움직이든 동시검출되어야 한다. 동시성의 상대성(relativity of simultaneity) 실험자의 기준 좌표계(frame of reference)가 고정되어 있을 때와 등속운동을 할때 사건의 검출이 달라진 이유를 설명한다.
As strange as it seems, both Sheldon and his friends on the train are right. In some cases, the order of events depends on the motion of the observer. Einstein explained this through the concepts of length contraction and time dilation.
아인슈타인은 이 이상한 현상을 설명했다. 만일 빛이 검출된 시간이 다르다면 두 관측자의 시간 흐름의 간격이 서로 다르던가 거리가 달라져야 한다. [광원에서 두 관측자의 거리가 동일하게 놓고 실험 한 것이므로 거리는 변하지 않아야 한다.]
So, why don't observers in different reference frames agree on the order of events?
그렇다면 실험자의 기준 좌표계가 달라짐에 따라 사건이 일치하지 않는 이유는 뭔가? [관성계에 물리법칙은 동일하게 적용되어야 함에도 불구하고......]
---------------------------------------
Well, think back to our block of cheese space-time analogy. [치즈 썰기에 비유한 내용은 썩 유익하지 않음]
A moving observer relative to another observer actually slices up space-time differently. Not only can they potentially see events in different order than other observers, but they also measure length and time differently.
Have a look at this graph which represents space-time for a stationary observer. A stationary observer sees objects as they naturally are and clocks run as expected. However, a moving observer sees space-time through a different slice. Here's what space-time looks like to a moving observer. Both the moving observer's time axis and distance axis have shifted. Physicists say that the time and space coordinates are rotated due to the motion of the observer.
빛의 속도가 불변이라면 실험자(observer)의 시간과 거리의 좌표축이 다르다고 보자. 고정된 실험자의 좌표축에 비교하여 움직이는 실험자의 시간과 거리 축이 기울어 있다. [치즈썰기에 비유되었다.]
This is a convenient picture to paint, but what other real observable effects of this skewed reference frame? Well, earlier we mentioned that moving observers measure changes in length and time.
찌그러진 기준 좌표계가 서로다른 조건(등속운동)의 두 실험자에게 어떤 영향을 줄까? 앞서 얘기 했지만, 시간 지연과 거리 수축 현상.
Length contraction is given by the equation, L is equal to L zero times the square root of one minus the velocity of the observer divided by the speed of light squared. Well, this equation describes is how the length of the object appears to a moving observer. If I jump into a spacecraft, and I'm moving at nearly the speed of light, objects I observe will appear to shrink in my direction of motion.
앞서 말한대로 움직이는 관측자의 기준에서 길이가 줄어드는 효과(Length Contraction)를 낸다. 속도가 아주 빠른경우 길이 수축이 효과를 낸다. 아주 빠른 우주선에 올라타면 움직이는 방향으로 길이가 수죽된다.
-----------------------------------------
Something like the [inaudible] would pass by the ship appearing to be almost as flat as a pancake. [???????]
-----------------------------------------
It's not just length that changes though, time also changes.
길이뿐만 아니라 시간(측정)도 바뀐다. [길이와 시간 측정 장치의 눈금(텐서, tensor)이 다르다.]
Time dilation is given by the equation t is equals to t zero divided by the square root of one minus the velocity of the observer divided by the speed of light squared. In this case, time is modified by dividing by these terms under the square root sign. So, instead of decreasing, the time observed by the moving observer increases. So, the moving observers see all external clocks slowing down the faster they move.
움직이는 실험자의 시계가 느리게 가는 효과(Time Dilation)를 보여준다.
Both length contraction and time dilation are effects that are measured by a moving observer, the faster the observer moves with respect to any object such as a clock, the thinner it appears and the slower it ticks. Hopefully, your head isn't spinning too much yet because we have to discuss an important issue with special relativity. Since a moving observer appears to be stationary in their own frame of reference, who can we trust when we say that the lengths have been contracted and the clocks have been slowed? To illustrate this problem, we need to introduce you to the twin paradox.
움직이는 실험자는 길이 수축과 시간 지연의 효과를 경험하게 된다. 그렇다면 이동하는 실험자의 입장에서 자신의 기준 좌표계를 잡으면 (물리현상은) 서있는 것과 다를바없다. 과연 누가 길이 수축과 시간 수축을 말해줄 수 있을까? 특수 상대론의 대표적인 논쟁꺼리인 쌍둥이 모순(twin paradox)을 살펴보자.
----------------------------------------------
Like to imagine that twins named Leia and Luke are preparing for an interstellar voyager. Leia will stay behind on the earth to monitor the journey while Luke, the adventurous one, takes off in his spaceship capable of reaching nearly the speed of light.
쌍둥이의 이름은 '레아'와 '루크'다. 이란성 쌍둥이는 우주여행을 준비하고 있다. 레아는 지구에서 루크가 빛의 속도에 가까운 빠른 속도로 우주 여행을 지켜보기로 한다.
Since Leia stays on the earth as Luke speeds away, Luke's clock appears to slow down the faster he zooms off his ship.
'레아'는 지구에서 머물며 루크가 빠르게 멀어져가는 것을 관측한다. 루크의 시계가 느리게 가고 있다고 관측한다.
But to Luke, Leia appears to be speeding away, so to Luke, Leia clocks have slowed down.
'루크'의 입장에서는 레아가 멀어지고 있으므로 그녀의 시계가 느리게 간다고 관측한다.
Both observers see the other clock as being slow. While our own clocks are at regular speed, how can that be? Surely both observers can't be right.
양측의 입장에서 보면 (서로) 상대방의 시계가 느리게 간다고 말한다. 우리가 가진 시계는 정상적으로 흘러 간다. 어떻게 그럴수 있을까? 두 관측자 모두 틀린것리 분명하다.
----------------------------------------------
Welcome to the twin paradox, proposed by Einstein, not as a paradox but as a peculiarity of special relativity.
아인슈타인이 제시했던 쌍동이 모순에 대해 알아보자. 사실 모순(paradox)이라기 보다 특수 상대론의 가설(peculiarity)이다.
In Einstein's 1905 paper, he reasoned that if two clocks were synchronized and one of them where to go on a lengthy journey, the traveling clock would return to the original location with its time lagging behind the stationary clock.
아인슈타인은 1905년의 논문에서 느리게 가는 여행자의 시계가 원래 자리로 되돌아 왔을때 고정된 시계보다 여전히 늦게 간다는 모순을 설명 하였다.
However, since relativity says that either clocks could view the other as being the one in motion, that is the traveling clock could consider itself at rest and the stationary clock would therefore be the one moving away. Shouldn't the stationary clock be the one lagging behind when the other returns again?
여행을 떠났다가 다시 제자리로 돌아온 시계는 머물러 있던 시계보다 느리게 간다. 왜 그럴까?
Let's watch as Luke flies to a nearby star system six light years away while Leia stays behind on the earth. Luke can travel at a significant fraction of the speed of light, say north 0.6 c.
루크가 6광년 떨어진 별로 여행을 간다. 레아는 지구에 남아 있다. 루크의 속도는 아주 빨라서 빛의 0.6배다. 루크가 떠나기전 두 사람의 시계를 맞춰 놨다.
When we say that something is traveling at one c. It is the same as saying that it goes one light year per year. So, if Luke travels at 0.6 c he will travel north 0.6 of a light year for each year of travel. As such, Leia will say that Luke's journey takes 10 years.
이 속도로 6광년 떨어진 별로 여행을 가면 레아의 입장에서 가는데 10년이 걸리는 것으로 계산된다.
However, let's carefully assess what Luke observes on his particular journey. Luke sets his spaceship to travel at north 0.6 c. In doing so, the distance to his destination changes, at north 0.6 c, the length between the earth and the destination has shortened by 20 percent. So, instead of six light years, the star appears to be only 4.8 light years away from Luke's perspective.
루크가 탄 우주선의 속도는 매우 빠르다. 광속의 0.6배나 된다. 이 속도라면 루크가 여행할 거리는 4.8 광년으로 줄어든다.
At north 0.6 c, Luke's time of arrival is only eight years after his departure from the earth.
루크의 관점으로 보면 6광년의 거리가 4.8 광년으로 줄었다. 광속의 0.6배로 비행하면 도착하는데 8년이 걸린다.
Meanwhile, Luke has tend to shift around and begins his journey back to the earth again at 0.6 c. So, the same length contraction applies instead of flying across six light years of space, Luke only flies the length contracted, 4.8 light years, and he is back from his distance star system after another eight year journey.
별로 여행갔던 루크는 다시 같은 속도로 지구로 되돌아 오기로 한다. 루크의 입장에서 되돌아 오는 여정은 역시 4.8광년으로 여행시간은 8년이다.
For Leia, Luke has been gone for 20 years, but from Luke's perspective he has only been gone 16 years. Luke is now four years younger than Leia.
왕복 여행에 걸린 시간을 보자. 루크의 시계로는 16년, 레이의 시계로는 20년이 흘렀다.
---------------------------------------
Hopefully, you can now see why Einstein said this was a peculiarity and not a paradox. Luke is the moving observer, sees space itself foreshortened, but in Leia's reference frame, the distances haven't changed, merely the shape of Luke's ship.
아인슈타인이 왜 쌍둥이 모순이라 하지 않고 쌍둥이 가설이라고 했는지 이해 했길 바란다. 루크는 움직이는 관측자로 길이 수축의 영향을 받았고 레아의 표준 좌표계에서는 거리 수축이 없다.
---------------------------------------
We've seen this square root equation come up twice already.
So, what is it? Well, this is a useful little equation that represents the strength of the time dilation or length contraction based on the speed of the moving observer. It's more commonly found in this form called the Lorentz factor or the gamma factor.
The Lorentz factor is a convenient tool when discussing length contraction and time dilation because it converts these equations into these vastly simpler forms.
So, someone traveling at 10 percent of the speed of light or north 0.1 c sees a north 0.5 percent shortening in the length of a stationary object and a north 0.5 increase in the flow of time. That's not that much and even at half the speed of light, it's only a 15 percent change. You need to be traveling at almost the speed of light to see significant changes. At 90 percent of the speed of light, the Lorentz Factor is more than two. Here is a graph illustrating how quickly the Lorentz factor changes at very high speeds.
속도에 따른 로렌츠 인자의 변화를 보자. 속도가 광속에 가까울 수록 급격히 증가하는 모습을 볼 수 있다.
-------------------------------------------
We should note that Einstein developed special relativity to describe physics for observers who are not experiencing a strong gravitational force. But what happens near an object with a strong gravitational field such as a black hole?
아인슈타인이 광속에 관한 특수상대론을 전개한 이후 강력한 중력의 영향을 받는 관측자에게 미치는 물리현상이 포함 되지 않았다는 것을 깨닳았다. [특수 상대론 > 광속불변 > 시간 지연과 거리 단축> 중력에 의한 시공간 왜곡 > 일반 상대론]
Einstein realized that he had to modify his theory of special relativity to make it more general and to allow for gravity, Einstein called this relativistic theory of gravity, general relativity. In order to understand the theory of general relativity, we'll begin with Einstein's first ponderings on the subject, something called the equivalence principle.
03.04x - 다른 차원이 있다고? (Could there be extra dimensions?) [커세라 강의 페이지]
Could there be extra dimensions? Interview with Dr. Douglas Gingrich, Professor at the University of Alberta
We all know four dimensions or three dimensions, and the idea is that if we do have extra dimensional space, where is it?
사람들은 3차원과 4차원에 대해 이야기합니다. 공간의 3차원 이외에 한개의 차원이 더 있다고 하는데 그게 어디에 있는거죠?
So it has to be, first of all, small, otherwise will be detected. If it was infinite like our other three dimensions then, of course, we would see it. So they are very small and they are finite in the sense that they don't extend to infinity. They're very small and so we think of extra dimensions as curled up so that if you traveled in them, if you could, you would come around after a while to where you started from.
아마 아주 작게 존재하는 걸겁니다. 안그랬으면 벌써 알아 봤겠지요. 3차원 공간처럼 무한하다면 벌써 알아봤을 겁니다. 그러니까 4차원은 아주 작고 무한히 확장되지도 않는다고 봐야겠지요. 공간의 차원에 한 차원이 추가된 4차원은 아주 작고 난해하여 쉽게 와닿지 않습니다. 그래도 할 수만 있다면 지금부터 한번 생각해 봅시다.
If you make them small enough, you don't see them, yet they're still allowed in the sense that they don't change the observable physics enough, that you could still have them yet they will be undetectable till now or hopefully in the near future.
아주 작아서 보이지 않는 크기를 생각해 봅시다. 가까운 장래에 측정가능하게 되겠지만 어쨌든 지금의 과학으로는 볼 수 없는 아주작은 크기입니다. 하지만 보이지 않더라도 지금의 물리법칙이 변함 없이 적용 됩니다.
Well, the small dimensions allow gravity to go into those dimensions but not other particles. So if you imagine the electrons and the older particles that interact by electromagnetic and strong nuclear forces, they can't go into the extra dimensions otherwise we would see matter disappearing or come into the extra dimensions and we'd see it appearing.
이런 작은 규모에도 중력은 작용합니다. 하지만 입자들은 다르죠. 전자기력이나 강한 핵력과 작용하는 전자나 전통적인 입자들은 예외죠. 그렇지 않았더라면 우리는 그 물질들이 보였다 사라지는 모습을 봤을 겁니다. [입자를 직접 본적은 없다. 단지 입자들이 전자기력등과 상호작용하여 보여주는 현상을 측정하여 입자의 존재를 알고 있을 뿐이다]
So the idea is that, matter as we know it exists in the four dimensions, but gravity can go into the extra dimensions. This is beneficial because it explains that gravity is very weak on the sub-atomic scales which it is. It is a very weak force compared to all the other forces at very small scales or distances, and so that allows us to also justify why gravity or explain why gravity is so weak at such small distances.
이 한차원이 추가된 곳에 중력은 끼어들지 못하지만 사차원 세계에 존재하는 물질이 있다고 믿고 있죠. 이런 (4차원의 존재에 한다는)생각은 중력의 영향이 아주약한 원자보다 작은세계를 설명하는 데 유용합니다. 아주 작은 크기 혹은 짧은 거리(입자들의 세계)에서 중력의 역활은 다른 힘들에 비해 아주 미미하죠.
Last section ended with the idea that the speed of light is the same in all inertial frames. Now let's connect this to the idea of spacetime and events.
전편에서 모든 관성 기준좌표계에서 (측정한) 빛의 속도는 같다는 점을 이야기했는데 이 번편에서는 시공간과 사건을 연관지어 생각해 보기로 하자.
Two astronauts moving at constant speeds relative to one another will measure the speed of light from all sources of light to have the exact same value which we write as a lowercase c. A constant speed is just the distance traveled by the time that has elapsed. Einstein realized that one way to explain why two astronauts moving relative to each other measure the same speed of light is because the two astronauts do not agree on the definitions of space and time. Instead of thinking about space and time as separate concepts, Einstein realized that he needed to consider the combination of both space and time into a concept he called spacetime.
속도는 이동한 거리를 이동에 소요된 시간으로 나눈다. [이 속도에 대한 전통적 정의는 새로운 이론에서도 적용되어야 한다.] 아인슈타인은 서로 다른 관성계에서 빛의 속도가 같으려면 시간과 공간을 분리해서 정의한 개념을 바꿔야 한다고 생각했다. 시간과 공간을 별개가 아닌 서로 연관된 개념으로 시공간(spacetime) 이라고 불렀다.
The universe consists of four dimensions. Three of those dimensions are spatial moving in the up-down dimension, the left-right dimension, and the forward back dimension. The last dimension is time, the past future dimension. Although, we don't say something moves in time, just that the flow of time itself moves us towards the future and away from the past at a speed of one second per second.
세상은 네개의 차원(dimensions)으로 이뤄졌다. 공간은 전후, 좌우, 상하로 세방향 움직임이 매우 직관적이다. 그런데 나머지 시간이라는 차원은 미래를 향해 나갈 뿐이다. 과거를 회상하거나 미래를 예상할 수는 이다 [회상과 예상 모두 생각이다. 공간은 바꿀 수 있지만 시간은 늦출 수 있을 뿐]
--------------------
Let's exercise our imagination to better understand how humans perceive time. Our senses collect information from the space around us but we exist only at a single moment in time. None of our senses can perceive the passage of time directly or changes in time for that matter. The best humans can do is to create memories of the past which allows us to affect change in their future environment. In that sense, we only experience a narrow slice of time.
우리는 시간을 어떻게 인지 할까? 우리는 시간을 직접 인지하지 못한다. 다만, 매순간마다 주변의 상황 변화(사건)을 기억하므로써 시간의 흐름을 안다.
So, how do we effectively imagine what a four-dimensional spacetime looks like? Well, let's start by considering an easier picture with fewer dimensions altogether. Suppose my fingers are limited to motion in only one spatial dimension like walking along my arm. I can move them forwards along my arm or backwards along my arm. But it's too narrow for left and right and my fingers are too weak for up and down. In essence, I've compressed three dimensions of space into a single dimension. So now, my fingers' position can be characterized by a single point along a line. If the fingers walk along my arm from elbow to hand, it takes some amount of time. Since we've got my fingers' distance on the horizontal axis, let's now plot time along the vertical axis. This diagram is called the spacetime diagram. Since we humans only see a narrow slice of the spatial dimensions, we need to reveal how my fingers' position changes with time. This curve, for example, shows that my fingers walk back and forth across my arm and also move forward in the time dimension. If we mask everything but a narrow slice, we get back to the original representation of my fingers position in space. This path is my fingers worldline.
네개의 차원을 가진 시공간은 어떻게 보면 좋을까? 논의를 단순화하기 위해 공간을 1개의 차원으로 줄여 보자. 그리고 가로축을 1차원 공간으로 세로축을 시간의 차원으로 두자. 이 그래프는 시간에 따라 움직임을 그린 것과 같다. 말하자면 이 시간 대 공간의 좌표축(시공간 도, spacetime diagram라고 부르자.)에 표시된 곡선의 경로는 시간에 따라 물체가 공간에서 이동한 모습을 보여주는 것으로 세계선(worldline)이라고 하자. [굽은 경로는 물체의 운동이 가속되었다는 뜻이다. 이 때 기준 좌표계는 지면으로 설정되었다. 앞으로 등속도로 움직이는 기준 좌표계 (관성계)를 다룰 것이다.]
Since photons must travel at the speed of light, a plot of position of a photon on a spacetime diagram will zoom outwards in a perfectly straight line. Normally, this line is drawn so that the light ray makes a 45-degree angle from the space and time axes. Anything that travels at speeds less than light such as people and rockets have worldlines that stay in the region between the time axis and the worldline of the light ray. The only way to escape from this region is to move faster than the speed of light. This diagram only shows light moving to the right. But light can also move to the left. And the left moving light will also be represented by a line that makes a 45-degree angle to the space and time axis.
빛의 속도로 움직이는 광자의 세계선을 시공간도 상에 그려보자. 빛의 속도는 상수이므로 45도의 직선이 된다. 광자 보다 낮은 속도, 현실속의 움직임들 제아무리 빠른 로켓도 빛보다 느리다. 이런 현실속의 속도는 광자의 세계선과 시간 축 사이에 놓인다.
This diagram shows only one dimension, the left-right dimension. But there is also a back and forth dimension that comes in and out of the screen that we aren't showing. Light also travels at 45-degree angles to the back and forth dimension's axis. The two-dimensional surface that light can travel on is called the light cone. In addition, there is a third dimension, up and down and it would be really difficult to show this dimension in a drawing of this sort. In a spacetime diagram, the light cone defines the boundary of spacetime events that a person or any object that travels at speeds slower than light can experience. People can travel upwards in the time dimension in directions that stay inside the light cone. Experiencing events outside of the light cone would require that we can travel faster than light. This means that people and all objects with mass are confined to our own personal light cones.
-----------------------------------------------
실제로 시공간이 무엇인지 설명하기는 매우 어렵다. 더구나 3차원 공간에 시간의 차원을 더한 시공간을 보여 주기는 곤란하다.
It's hard to convey what spacetime actually is. One way to visualize spacetime is to imagine a three-dimensional object and then try to extend its dimensionality across time. A person is human-shaped in three dimensions but in four-dimensional spacetime, a person is a long tube that includes the person in the past, present, and future. If you slice this four-dimensional tube in the time dimension, a three-dimensional version of the person at that moment in time is the slice.
The four-dimensional spacetime we live in is similar to a block of cheese if we reduce spacetime to only two dimensions. We can imagine the ends of this cheese as the two space dimensions and the length of the cheese as the time dimension.
So a hole in Swiss cheese becomes a cheese being, living inside of a block of cheese time or space cheese or space cheese time. You get the idea. A cheese being at rest thinks of time running along the long axis of the cheese and the two-dimensional space that it lives in is the flat end of the cheese. Humans are all powerful higher dimensional beings with a cheese knife and we can slice up the block of cheese into thin slices. Each slice of cheese represents a single moment of time as experienced by the cheese being. At one end of the cheese there are no cheese beings but as we slice through their time dimension, we discover the birth of a cheese being growing to larger sizes and eventually disappearing.
Just like our four-dimensional human tube. From our perspective, a cheese being has been born, lived a fruitful life and died a cheesy death. Here's where things get interesting though. A different cheese being that moves at a constant speed through the cheese will slice up the cheese in different direction. The moving cheese being will see different size slices and think the times and sizes are different as if the cheese spacetime itself were somehow warped. However, if we were to take the same cheese block and slice it up in yet another direction, we can do it such that both observers agree on where the bubbles are in spacetime but they can't agree on how it was sliced. We can only speculate whether Einstein used cheese to describe spacetime but if he did surely we can all agree that it must have been tasty.
03.03 - 특수 상대론의 도입(Introducing Special Relativity Theory) [커세라 강의 페이지]
Just as sound waves propagate in water, it was once believed that light waves propagate in a medium called aether. This presented an opportunity for experimental physicists to measure the motion of the earth with respect to the aether. In 1887, two scientists named Michelson and Morley conducted an experiment to do just that. But no matter which the direction they pointed their apparatus, they measured the same speed of light through the aether. This forced them to conclude that the aether did not exist and that light would always be seen traveling at the same speed.
This puzzled scientists worldwide, well, except for one, Einstein. Einstein imagined what it would be like to see the universe from the perspective from a beam of light. He asked questions like how would a photon perceive the passage of time? And will distances shrink and stretch depending on the motion of an observer? Of relevance to him was the fact that experiments had proven that light waves were special compared to sound waves or water waves. In that they didn't require a medium through which to propagate.
에테르가 존재하지 않는다는 사실은 많은 과학자들을 혼란케 했지만 아인슈타인은 달랐다. 그가 가진 의문은 시간의 흐름에 광자는 어떻게 변할지, 관측자의 운동에 따라 (광자가 이동한) 길이가 줄거나 늘지 않을까 라는 것이었다. [빛은 매질 없이 전달된다. 매질이 없으므로 빛(광자)의 운동은 물속의 음파 전달의 경우 처럼 매질의 속도에 더해지거나 빼지 않는다. 빛의 속도는 불변이다. 움직이는 물체에서 출발한 광자나 정지한 물체에서 출발한 광자든 속도가 불변이다. 동시에 출발한 광자는 동일한 지점에 도달해야 한다. 이동한 거리가 늘어나거나 시간이 느리게 가야 한다. 빛의 속도로 움직이는 광자의 입장에서 시간과 공간(시공간, spacetime)이 왜곡된다.]
In helping us to understand these new revelations, Einstein had to tackle problems which few could ever even consider. In one of Einstein's most famous papers entitled On the Electrodynamics of Moving Bodies, he introduced two very important ideas. Ideas which are now among the foundation of modern physics.
이런 (빛의 속도 불변으로 제기된) 문제를 풀기위해 아인슈타인은 누구도 하지 못했던 생각을 '이동하는 물체의 전기 동역학에 관하여'라는 논문으로 냈다. [빛은 전자기파다.] 이 논문에는 현대 물리학의 근간이 된 중요한 이론을 세웠다.
They are, 1, the laws of physics are the same in all inertial frames of reference. And 2, light moves at the same speed relative to all observers. That first postulate seems reasonable.
------------------------------------------------
1. 모든 관성계에서 물리법칙은 동일하다.
The laws of physics are the same for me here as they are for you sitting there. The laws of physics are the same on the moon as they are here on Earth. In physics, this principle is essential, as we use it all the time in order to learn about places that are distant from us.
물리법칙은 위치에 상관없다. 지구에 있든 달에 가 있든 모두 같은 물리법칙의 지배를 받는다.
An inertial reference frame is either an experiment at rest or one moving with a constant velocity. Inertial frames are not accelerating. For example, someone standing in a high speed train would experience the same laws of physics as someone stationary on the ground, so long as neither are accelerating. The first postulate is intuitive to human beings which makes the second one impossibly hard to believe at first glance.
등속운동하는 곳 어디에 기준 좌표계를 설정해도 물리 법칙은 같다. 관성 좌표계는 가속하지 않는다.
---------------------------------------------------
2. 관측자(등속운동을 하든 정지해 있든)에 상관없이 빛의 속도는 같다.
Einstein's second postulate was that light moves at the same speed relative to all observers. So if we were to measure the speed of light from a fast moving astronaut, we don't add the astronaut's speed to the speed of light. Weird, right? The speed of light always comes out to the same value, no matter how fast the astronaut is traveling. Einstein realized that if the laws of physics are the same for all observers, then all observers must agree on the value of the speed of light.
상대운동, 서로 다른 속도로 (하지만 등속으로) 움직이는 관측자에 따라 관측되는 속도가 다르다.
You've probably experienced some of the strange effects of changing reference frames before. Have you ever been in a parked car when an adjacent car starts moving? In some cases, your brain tricks you into thinking that you're moving instead of the other car. Since motion is relative, we can always choose a reference frame that is stationary, even if there's relative motion to something else. Let me explain.
Suppose you're riding in a self-driving car. Some fast cars are passing you in the left lane and you are passing some slow cars in the right lane. If all the cars are moving at a constant but different speed, each car is their own inertial reference frame. If you observe the cars from the ground they will all appear to be moving.
If, however, you choose a reference frame of the car in the middle lane, the cars on the left appear to be moving forward. While the cars in the right lane appear to be moving backwards. Without the road in the background, we can't figure out how fast the cars are traveling. The only thing we can tell is how fast they're traveling with respect to one another.
---------------------------------------------
누구에게나 빛의 속도는 같다는 개념을 도입하니 상대속도를 설명하기 어려워졌다.
However, this becomes problematic when light is introduced. Instead of driving during the day, what if our cars are driving at night? They'll need to turn their headlights on. And If the center car turns on their headlights, they'll see photons leaving at the speed of light, c.
Let's consider the headlights of the cars in the left lane. Does the speed of light coming from the fast car appear faster due to the relative motion? No, even though the red car is moving faster, the photons coming out of the headlights always appear to move at the speed of light, c. The speed of light from the middle car is not c minus 10 kilometers due to the motion of the cars. And the same is true for the slower blue car. The speed of light is always measured as c.
Weird? Einstein thought so, too. Clearly, if Einstein's second postulate, that all observers measure the speed of light as a constant, is to hold true, we need some other kind of transformation group, so that every observer can see the light beams moving relative to themselves, at c. In order to do such a thing, Einstein realised that our intuitions about space and time must be incorrect. And that a new theory is required to describe how all observers, moving at different speeds, can measure the speed of light to be a constant.
모든 관찰자(등속운동을 하는)에게 빛의 (측정한) 속도는 같다. 아인슈타인도 이를 그냥 받아들이기 어려웠다. 그래서 새로운 이론을 세워야만 했다. [솜씨 좋은 목수가 궁한 물건을 만들어 쓰듯이 아인슈타인은 이해가 않되면 이론을 만들어 냈다. 나만 편하면 되는 것이 아니라 우주를 통찰하는 이론이다. 그는 '끕'이 다른 재주꾼 이라고 해야겠다.]
