그림 2. 첫 번째 경우. (출처: 김성철 2013)
그림 5. 좌표계 S에서 본 우주선들의 세계선. (출
는 특수상대성이론의 주장과 상충하며 개 념적으로 모순을 일으키기 때문에 귀류법 추론을 통해 실이 끊어지지 않는다는 주 장을 할 수도 있다. 그러나 민코프스키 시 공간 도표를 이용하여 세세하게 특수상대 성이론에 부합하도록 상황을 살펴봄으로 써, 우주선 사이의 거리를 일정하게 유지 한다는 조건 때문에 두 우주선을 연결한 실이 끊어짐을 보였다.
그렇다면 드원-베란과 벨의 논의는 어 떤 의미를 가질까? 벨은 왜 그리고 어떻 게 드원-베란의 사고실험을 재구성하고 다루었을까? 벨이 우주선 사이의 공간이 아니라 두 우주선을 연결하는 실에만 로 렌츠 수축이 일어난다고 설명한 것은 상 대성이론에 대한 잘못된 이해 때문이었을 까?
실상 벨의 논의에서 가장 핵심이 되는 부분은 피츠제럴드(George F. FitzGerald) 의 아이디어이다. 피츠제럴드에 따르면,
“물체가 에테르를 관통하거나 지나가면서 움직임에 따라, 물체의 길이가 물체의 속 도와 빛의 속도의 비의 제곱에 따라 달라 지는 양만큼 변한다는 가설”만이 마이켈 슨과 몰리 실험의 결과를 설명할 수 있다.
였다. 벨에 따르면, “미시적인 전기력이 물질의 구조에서 중요하기 때문에 빠르게 움직이는 입자의 전기장이 체계적으로 뒤 틀리면 빠르게 움직이는 물질의 내적 평 형을 변형시킬 것이다. 따라서 빠르게 움 직이는 물체의 모양도 달라질 것이라고 예상할 수 있다.” 이것이 피츠제럴드 수축 이며, 실질적으로 두 우주선을 연결하는 실에 대한 벨의 논의는 아인슈타인의 접 근이 아니라 피츠제럴드-라머-로렌츠-푸앵 카레의 접근을 따르고 있다. 따라서 벨의 논의에서는 공간은 수축을 하지 않고 실 과 우주선만이 수축을 한다.
벨이 보기에, 로렌츠의 접근과 아인슈 타인의 접근은 한쪽이 옳고 다른 쪽이 틀 린 것이 아니라 서로 다른 것에 지나지 않 는다. 아인슈타인은 경험적으로 두 관성계 중 어느 쪽이 정지해 있는지 결정할 수 없 기 때문에 상대운동만이 실재라고 선언한 반면, 로렌츠는 그래도 실제로 정지 상태 에 있는 관성계가 있고 그것이 바로 에테 르의 정지 좌표계라고 보았다. 아인슈타인 과 로렌츠의 차이는 물리학적인 것이 아 니라 인식론적인 동시에 존재론적인 것이 다. 로렌츠가 이미 알려져 있거나 추측되
정한 속도로 움직이는 관찰자들에게는 법 칙들이 똑같이 보일 거라는 가설에서 출 발한 것이다. 로렌츠가 증명하려고 했던 것을 아인슈타인은 그냥 가정했을 뿐이며, 이것은 스타일의 차이이지 물리학의 차이 가 아니다. 벨은 피츠제럴드-라머-로렌츠-푸앵카레의 기나긴 도보여행이 상대성이 론을 배우는 사람들에게 불필요한 일이 아님을 강조한다.
참고문헌
[1] 김재영, “벨의 우주선 사고실험과 시공간에 대 한 동역학적 관점의 비판”, 철학사상 49, 141 (2013).
[2] J. S. Bell, “How to teach special rela- tivity”, Progress in Scientific Culture 1 (2), 1 (1976), reprinted in J. S. Bell, Speakable and Unspeakable in Quan- tum Mechanics (Cambridge University Press, 1987), pp 67–80.
[3] J. Ceresuela and J. Llosa, Can. J. Phys.
97, 923 (2019).
[4] E. Dewan and M. Beran Am. J. Phys.
27, 517 (1959).
[5] G. F. FitzGerald, Science 13, 390 (1889).
[6] T. Matsuda and A. Kinoshita, AAPPS Bulletin 14(1), 3–7 (2004).
[7] V. Petkov, Relativity and the Nature of Spacetime (Springer, 2009).
여 좌장이 호스트 역할을 원활하게 수행 Low-D QM: black phosphorus & geo- metric phase
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