나뮈키에는 지구에서 출발해서 지구로 돌아올 때 일반상대성원리(가속) 때문에 우주선에 있는 사람이 더 젊다고 써있길래 둘 다 우주선에 탑승해 있다면 어떻게 되는지 궁금해졌음.
영어 잘하지는 못해서 구글번역으로 물어봤음. 근데 결론이 서로 다르게 움직였던 계는 정지해도 동일한 측정이 불가능하다는 식인거 같은데 이게 맞나싶음
Relativity Time Age Question
나
When the twins each boarded the light-speed spacecraft going in opposite directions, and they came back and met, who would be older?
(쌍둥이 우주선에 태웠단 얘기)
챗
Relative to each other, both twins would be the same age, regardless of their experiences in different inertial frames. According to the theory of special relativity, time passes differently for objects in different states of motion relative to each other, but there is no objective way to say that one twin is "older" than the other.
(아마 같은 나이일 것이며 동일한 시각이란 게 있을 수 없기 때문에 누가 늙었음은 의미가 없음)
나
You mean we can't calculate time difference in different inertial frame?
(시간차는 계산이 불가하다고?)
챗
Correct, time dilation, as described by special relativity, means that time passes differently for objects in different states of motion relative to each other. However, there is no unique or absolute measure of time that applies to all observers in different states of motion. Each observer will measure time differently based on their relative motion, and there is no way to determine which observer has the "correct" measure of time. The concept of a unique and universal time does not exist in special relativity.
(시간이 다른 속도로 흐르는 것은사실이지만 서로 자기기준으로 측정하기 때문에 시간측정의 "올바른" 기준은 없다)
나
Is it like Schrödinger's cat? Even GPS compensates for the time difference by special relativity and general relativity. Suppose we put uranium in a satellite and launch it. Shouldn't the result come out when you check the inside when you collect it after a few years?
(gps도 이미 상대성원리 쓰는 걸로 아는데 왜 측정할 수가 없다는 거냐는 물음, 위성에 우라늄을 넣었다 치면 반감기로 체크 가능하지 않음?)
챗
The GPS system indeed takes into account the effects of both special and general relativity to ensure accurate timekeeping. However, the situation with the uranium in a satellite is not comparable to Schrödinger's cat. In the case of the uranium, the passage of time can be objectively and unambiguously measured, both inside and outside the satellite. The effects of special and general relativity modify the rate at which time passes, but they do not introduce any fundamental ambiguity or indeterminacy into the nature of time itself.
So, if you were to measure the decay of the uranium both before and after it was launched into space, you would observe a difference in the rate of decay due to the effects of special and general relativity, but the concept of time itself would not be affected by these effects in the same way that the state of the cat in Schrödinger's thought experiment is indeterminate until observed.
(내가 슈뢰딩거드립을 쳐서 전혀다르다고 팩폭)
나
Suppose there are light-speed spaceships traveling in opposite directions carrying the same uranium. After some time has passed, if they move toward each other again and meet in the middle, you can compare the amount of uranium drop. According to the principle of relativity, isn't it true that one of the two is definitely decreasing?
(두 광속 우주선에 우라늄 넣어놓고 각기 왕복 시켜서 한자리에 놓으면 누군가는 줄었든 해야하는 게 아님?)
챗
According to the theory of special relativity, time passes differently for objects in different states of motion relative to each other. In this scenario, the two light-speed spaceships would experience time differently while they were moving apart from each other, and this would result in a difference in the rate of decay of the uranium on board each ship.
However, when the two ships meet again in the middle, there would be no objective way to determine which ship has the greater or lesser amount of decay. Both observers would see the other ship's clock as ticking more slowly, and both would see the other ship's uranium as having decayed less. This is because the effects of special relativity are relative, and there is no unique or absolute reference frame that can be used to determine a "correct" measure of time or decay. The relative difference between the two ships would be observer-dependent, and there is no way to determine which observer's measure is correct.
(둘 모두 상대가 느리게 흐르며 우라늄이 덜 줄었을 것으로 느낀다. 하지만 만났을 때에도 관찰자기준으로 밖에 측정할 수 없기 때문에 완벽한 측정은 불가능함)
나
You can measure the mass or volume of it, don't you
(그냥 질량과 부피만 측정하면 되잖아?)
챗
Yes, you can measure the mass or volume of the uranium after the two light-speed spaceships meet in the middle. This would allow you to determine the difference in the amount of decay that has taken place on each ship. However, it is important to note that the measurement of the mass or volume of the uranium would be subject to the same relative differences as the measurement of time. Both observers would see the other ship's measurements as being contracted along the direction of motion, and the results of the measurement would depend on the reference frame of the observer.
In general, the theory of special relativity predicts that all physical measurements, including the measurement of mass and volume, will be affected by the relative motion of the observer and the object being measured. The effects of special relativity are relative, and there is no absolute reference frame that can be used to determine a "correct" measure of these quantities.
(모든 물리 측정 방식은
관찰자 각각의 상대적 운동에 따라 어그러질 수 밖에 없다. 그래서 "올바른" 방식은 존재하지 않는다.)
나
When they meet, they are stationary, so why does the theory of relativity affect the measurement then?
(만나면 정지 상태인데 무슨 상대성원리가 적용된다는 거임)
챗
The effects of special relativity persist even when two objects are stationary relative to each other. This is because the relative velocity between two objects is not the only factor that determines the effects of special relativity.
In the scenario you describe, where the two light-speed spaceships meet and become stationary relative to each other, the relative velocity between the two ships is zero, but the effects of their previous motion still persist. The twin paradox is a classic example of how the effects of special relativity can persist even in the absence of relative motion.
According to the theory of special relativity, time dilation and length contraction are relative effects that depend on the relative velocity between the observer and the object being measured. Even when two objects are stationary relative to each other, the effects of their previous relative motion will persist, and each observer will measure time and length differently based on their own frame of reference. There is no absolute or objective measure of time or length that applies to all observers in different frames of reference.
(정지 상태가 되어도 이전의 상대적운동 효과는 영구적이어서 정지상태에도 적용됨)
여기서 나는 사고정지가 와서 끝남
근데 이게 맞는 건가? 뭔 다중우주도 아니고 왜 측정이 안되는 건지 이해가 안감....
식견이 짧아서 수학은 잘모르지만 개념적으로 이해하고 싶음...
