시리즈의 첫번째 (1)번 글에서 시간과 공간의 개념이 현재의 물리학자들에게도 여전히 미스테리로 남아있고 아직도 좀더 정확한 이해를 필요로 하고 있다고 소개했다. 이 시리즈물은 보다 정확한 시간과 공간의 개념에 대해 소개하고 이를 바탕으로 현대 물리의 다양한 미스테리들을 어떻게 보다 직관적으로 이해할수 있을지 가능성을 소개하기 위해 만들어졌다. 잠깐, 양자역학과 같은 현대 물리에서 논의되는 다양한 문제점을 직관적으로 이해한다고? 만일 독자가 양자역학에 대해 어느정도 배경지식을 가지고 있다면 거의 모든 대부분의 독자들이 이런 말도 안되는 사기꾼 아니냐며 이런 질문을 할것이다. 

나는 충분히 이해한다. quantum entanglement나 하이젠버그의 불확정성원리에서 얘기하는 매우작은 입자들의 위치와 운동량을 동시에 정확하게 알수 없다는 등의 고전역학에서는 상상하기 힘든 어려운 일들이 벌어지고 있는데 이런 이상한 현상들을 직관적으로 이해할수 있다는 사기꾼이 쓰는 내용을 믿을 충분한 이유를 찾기가 힘들 것이다. 그것보다 직관적이라는 단어가 엄밀함과 동떨어진 단어로 과학과 수학에서는 될수 있으면 멀리하려는 경향성을 보이기에 독자들 또한 별로 탐탁치 않게 여길 것이다.

독자들의 우려를 충분히 알고 있음에도 필자는 무모하게도 직관성이 인류과학 발전에 가져다준 혁명적 진보의 실사례를 알고 있다. 바로 아인슈타인이 그 한 사례를 보여줬다. 아인슈타인은 사실 수학적으로 그렇게 뛰어난 사람은 아니었다. 물론 평범한 사람들보다는 수학능력이 뛰어났지만 당대의 뛰어난 수학자들수준정도의 실력을 갖췄다고 보기는 어렵다. 대신 그는 누구도 따를수 없는 직관성을 보여줬다. 누구보다도 뛰어난 직관력으로 그는 시간과 공간 상에서의 빛의 실체에 대해 뉴튼이래 그때까지 믿어져 왔던 절대적인 시간과 공간 개념에 벗어나서 관측자의 운동상태에 따라 관측가능한 시간과 공간이 변할수 있음을 최초로 발견해내었다. 또한 일반 상대성이론을 도출하는 과정에서 물체의 가속과 중력을 분간해내기 힘듬또한 알아 내었는데 이것 또한 그의 천재적인 직관성이 이룩해낸 성과물이었다. 일반상대성이론의 완성에 있어서 그의 직관적인 인지능력이 없었다면 이론에 대한 아이디어를 꺼낼수도 없었을 것이라는 점과 일반 상대성이론의 기반인 수학적인 엄밀성은 그의 부족했던 수학능력을 채워줄 많은 수학자들의 도움을 받아서야 비로서 이룩해낼수 있었던 점을 같이 고려해서 보면 일반상대성이론이라는 현대 물리학의 두가지 핵심 기본 원리를 발표한 시점까지를 아인슈타인 전반기로 보았을때 그의 뛰어난 업적은 탁월한 직관력에 기인했다고 할 수 있을 것이다.

하지만 아인슈타인의 하반기 인생 즉 전자기력과 중력을 통합하기 위한 노력은 실패로 끝났다. 일반상대성이론에서 쌓은 수학적 기반과 더불어 그의 전성기에 시작되고 진행되었던 양자역학의 성과물을 가장 근거리에서 지켜봤던 그였지만 그는 상대성이론과 양자역학을 성공적으로 결합시키는데 실패했다. 물론 모든 물리학자들이 실패했고 아직 누구도 성공하지 못하고 있다. 수학적으로 뛰어난 능력자들이 즐비하지만 성공하지 못하고 있다는 점에서 우리는 직관성이 여기에 빠져 있을수 있다는 가능성에 주목해야 한다. 아인슈타인 또한 상대성이론과 양자역학을 성공적으로 결합시키기 위해 필요한 직관적인 아이디어를 가지고 있지 못했었기에 제대로 된 방향 조차 설정하지 못하고 죽는 날까지 노력했지만 성과없이 생을 마쳤던 것이다. 

시간과 공간에 대한 가장 정확한 개념은 현대물리에서는 아인슈타인의 상대성이론에서 정립되었다고 보는게 정설이다. 아인슈타인의 상대성이론은 그 누구보다도 정확한 운동의 예측을 가능하게 해주었고 아직까지 공식적으로는 그의 이론의 정확성을 부정받은 적이 없기에 누구도 부정확성을 의심하지 않고 있다. 하지만 일반상대성이론이 현실에 존재하는 인간이 접근가능하고 검출가능한 영역에서 실험한 결과에서 결점이 한번도 드러난 적없다고 해서 결점이 없는 것만은 아니다. 일반상대성이론에 따르는 결과인 블랙홀에서의 운동은 현재로선 인간이 직접적으로 검출가능하지 않고 또 그 운동의 예측 또한 현재 불가능한 상태에 놓여 있다. 이것은 상대성이론에서 제공하는 시간과 공간의 개념이 양자역학에서 관심을 가지는 미립자 세계의 그것과 틀리다는 점에 있고, 이는 아직 인간이 시간과 공간에 대한 정확한 이해를 못하고 있다는 것을 보여준다. 

현재까지 물리학자들의 연구 결과는 양자역학과 상대성이론을 접목시켜서 하나의 커다란 통일이론이 생각보다 쉽지 않고 커다란 극복하기 어려운 벽에 막혀 있는 듯한 느낌을 주고 있으며 몇몇 학자들은 이의 극복을 위해서는 전혀 새로운 아이디어를 필요로 할지 모른다고 얘기하고 있다. 필자 또한 이러한 생각에 동의하고, 19세기 말 맥스웰 방정식과 갈릴레이 변환이 서로 충돌할때 이를 해결하기 위해 젊은 아인슈타인이 시간과 공간의 실체 파악에 보여줬던 천재적인 직관적 능력이 이번에도 다시 한번 발휘되어야 궁극적인 통합 이론(Theory of Everything)이 나올수 있다고 주장한다. 통일이론의 첫걸음은 가장 근본이 되는 개념부터 기존의 모든 선입관을 배제하고 되집어볼때 가능할 수 있을 것이다. 앞서 언급한 일반상대성이론과 양자역학에서의 시간과 공간 개념이 서로 일치하지 않는 것처럼 보인다는 점에 착안하여 도대체 아인슈타인이 시간과 공간 개념을 도출할때 혹 무엇인가 빠뜨린 부분이 없진 않았는지 다시 한번 되돌아볼 실낱같은 가능성을 필자는 지금부터 시도해보려고 한다. 아니 필자는 이미 확신하고 있다. 분명 아인슈타인이 간과하고 넘어간 부분이 있음을 필자는 지금부터 설명하고 보다 더 나은 해석을 제공하고자 한다. 일차적으로는 시간과 공간 개념에 대해 충분히 설명한뒤 새롭게 다져진 개념을 기반으로 어떠한 유익한 결론을 순차적으로 도출해낼수 있는지 보이고자 한다. 그 결론은 확률기반의 양자역학을 직관적으로 이해할수 있는 고전역학으로의 포섭이 될 것이며 이는 궁극적인 통합이론을 만드는데 필수적인 기반이 될 것이다. 

시간과 공간 개념 되집어 보기

고전역학의 기본은 물체의 운동에 대한 규칙을 알아내는 것이다. 물체의 운동을 안다는 것은 물체가 시간의 흐름에 따라 공간에서의 위치의 변화를 모두 알고 있다는 말과 동급이다. 물체가 관성운동을 하고 있다는 말은 물체가 변화하지 않는 속도에 따라 공간속에서 자연히 움직이고 있다는 말이다. 만일 물체 A가 3차원 공간상에서 x축의 방향으로 속도 1m/s로 관성운동을 하고 있다고 할때 t=0일때 원점에 있었다면 t=1일때 물체의 위치는 원점에서 x축방향으로 1m떨어져 있을 것이라는 예측을 가능하게 해주고 실제 물체의 위치를 확인해보면 예측치과 확인 결과가 동일할때 비로소 우리는 물체의 운동에 대해 알고 있다고 말할수 있을 것이다. 이렇듯 고전 역학에서는 물체의 운동을 안다라는 표현이 구체적으로는 물체의 시간과 공간 좌표계에서의 물체의 궤도를 그려볼수 있다는 것과 동일 표현임을 우리는 알수 있다. 필자가 아는 한 물체의 시공간좌표계에서의 궤적(Trajectory in the coordinate of space and time)을 가지지 않는 고전역학에서의 탐구대상은 없다.

고전역학에 부합하지 않는 물리학의 탐구대상이 미립자들이다. 미립자들은 입자라는 고전역학에서 친근한 이름이 붙여져 있긴 하지만 양자역학에서 이들의 궤적은 없는 것으로 간주되고 있다. 양자역학이 확고한 기반을 갖추기까지 핵심적인 역할을 했던 보어의 코펜하겐 해석에 따르면 인간이 미립자를 관측하기 이전에 미립자의 상태에 대해 말하는 것은 의미없다고 얘기된다. 양자역학은 관측이전에는 미립자는 오직 확률적으로 공간상에 존재하고 관측직후 잠깐 그의 위치가 결정되기에 궤적은 찾을수 없다고 얘기한다. 실례로 그림2-1은 미립자의 일종인 전자가 조건에 따라 다양한 원자내 공간 궤적을 가지고 있는데 색의 차이에 따라 원자내 공간에서 위치가 발견될 확률이 달라짐을 보여주고 있다. 밝은 영역은 전자가 발견될 확률이 높다는 것을 의미하고 어두운 색영역으로 갈수록 적어짐을 보여준다. 

그림 2-1

이와 같은 확률분포는 수소원자가 안정적으로 구조를 유지하는 한 시간에 대해 불변이고, 이 우주 어디에 가서 놓여있다하더라도 변함없이 고정적이다.  다시 얘기하면 인간이 알고있는 지식 수준내에서는 원자내의 전자라는 입자의 궤적은 시간에 따라 변화하지 않는 것처럼 보이며 더 나아가 시간이란 개념을 아예 지워도 무방한 것 처럼 보인다는 점이다. 시간에 따라 확률분포가 변화하지 않을 때 굳이 시간이란 없어도 무방한 인자를 넣어 생각할 필요가 없으니 시간이 없는 것과 마찬가지라는 얘기다. 이처럼 

 입자의 시공간좌표계에서 시간과 1:1로 유일하게 상응하는 공간내 위치들의 집합인 궤적을 확인할수 없으면 그것은 고전역학이 다루는 범주를 벗어나게 되는 것이고 이는 전혀 다른 역학계가 존재한다는 걸 의미한다. 

인간의 직관적인 관점과는 동떨어진 확률적인 세계인 양자역학의 세계가 고전역학세계와 공존하는게 필자를 포함한 몇몇 사람들에게는 불편하게 느껴진다. 빅뱅이론에 따르면 모든 세계는 본디 하나의 점에서 시작했고 그때 모든 법칙은 단순했을 것이다. 아니 인간의 감성은 보다 단순한 법칙을 선호하게끔 유전적으로 만들어져 있다. 그래서 두개의 서로다른 역학계보다는 하나의 역학계를 더 선호하게 된다. 만일 인간의 직관과 동떨어진 양자역학을 직관적인 고전역학에 친숙한 방식으로 이해할수 있게 된다면 그것이 가능하다면 두개의 서로다른 역학계의 공존이 가져다주는 불편함을 해소할수 있을 것이다. 정말 앞서 언급한 고전역학적 성질인 물체의 시공간상에서의 궤적을 미립자를 상대로 볼수 있을까라는 실낱같은 가능성을 좀더 살펴보고자 한다.

아인슈타인의 시간과 공간개념의 미흡함.

(추가 예정)

이 글은 철학과 물리학에서 가장 큰 미스테리인 시간과 공간에 대한 새로운 이해를 돕기 위해 씌여졌다.  다소 철학적이고 복잡한 주제를 담고 있기에 표현이 보다 자유로운 한글로 작성하는 바이다. 

새로운 시공간 개념에 대한 이해가 왜 필요한가?

시간과 공간에 대한 제대로 된 이해에 대한 필요성은 물리학을 지탱하는 두개의 큰 원리들인 양자역학과 상대성 원리에 아직 남아있는 문제점을 풀고싶어하는 모든 물리학자들이 가장 절실히 느끼고 있다. 이 두개의 원리를 통합하기 위해 물리학자들은 아직 개발단계인 양자 중력(Quantum gravity) 분야에서 씨름하고 있으나, 사실 이들 대부분의 물리학자는 완전한 통합이론을 배출하기엔 극복하기 어려운 커다란 난관에 봉착해 있다. 그 이유들중 가장 큰 것은 양자역학에서 이용되는 시간과 공간의 개념과 상대성원리에서 이해하는 시간과 공간의 개념이 서로 맞지 않는 것에서 기인한다. 

양자 역학에서의 시간과 공간 개념은 시간의존적인 슈뢰딩거 파동 방정식(Time dependent Schrodinger equation)에서 확인할 수 있는 것처럼 독립적이고 절대적이다. 여기서 하나의 소립자의 모든 상태의 변화는 슈뢰딩거 공식에 의해 결정된다고 볼때 공식에 포함되어 있는 시간과 공간 변수(parameter)는 다른 관측자의 존재 유무와 관계없이 단독으로 유효하다. 다시 말해 시간 의존적 슈뢰딩거 파동방정식은 타자에 의존적이지 않고 그 자체로서 완전하게 입자의 운동을 기술할수 있다는 말이다. 여기서 코펜하겐해석에서는 다른 관측자의 관측이전에는 어떤 것도 알수 없다고 기술하고 있지만 입자가 공간에서 발견될 확률적 발생빈도가 관측이전에 결정되어 있는 사실을 비추어 보면 실체는 있다고 봐야 한다. 

반면에 상대성 원리에서는 물체의 운동의 기술 또는 물질의 상태 변화는 필수적으로 시간과 공간 좌표에 의해 기술될수 밖에 없는데 이 물질이 기술될 시간과 공간은 제2의 물질에 의해 왜곡될수 밖에 없다고 보기에 타자의 존재에 의해 언제든지 달라질수 있다고 보기 때문이다. 다시말하면 상대성원리에서는 물체의 운동은 단독으로 결정되는 것이 아니라 제2,3의 질량을 가진 물체의 존재 여부에 따라 달라지기에 상대적으로만 기술될수 있다는 입장을 가진다. 예를 들면 빈 우주 공간에 어떤 물체가 관성운동을 하고 있고 관측자가 물체의 운동을 기술하고자 할때 물체의 운동은 공간내의 제3의 물질의 존재 유무에 따라 관측대상과의 직접적인 상호동작이 없음에도 불구하고 다르게 기술될 수 있다고 본다. 다른 물질의 존재가 관측대상의 시간과 공간 축척을 왜곡시킬수 있기에 타자에 의존적이라 할수 있다.

이 두개의 관점에서 보면 시간과 공간의 축척이 다른 입자나 물질과의 직접적인 충돌이 없음에도 불구하고 존재 여부에 독립적이냐(양자역학) 또는 의존적(상대성원리)이냐 로 갈린다는 것을 보면 양대원리에서의 시간과 공간의 개념이 합치될 여지가 없어 보인다는 점이 현재 물리학자들이 가지고 있는 최대의 고민이다. 어떻하든 이 서로 다른 두 개념을 합하려고 하는 모든 물리학자들의 시도는 아직까지 계산 결과가 무한값으로 나오게 되는 실패로 끝나왔다. 자연에서 존재하는 힘의 종류중 가장 먼저 알려진 중력은 우리에게 가장 친근한 개념이고 쉬운 개념이지만 물리학에서는 가장 미스테리한 힘으로 남아 있고 현재까지 가장 성공적인 표준입자물리론에 통합되기를 거부하고 있는 중력을 극복하기 위해서는 제대로 된 시간과 공간에 대한 보다 정확한 이해가 절실하고 모든 물리학자들이 찾고 있으나 아직까지 성공하지 못하고 있다. 이에 몇몇 물리학자들에게 있어서 이문제는 극복하기 어려운 장벽으로 이를 해결하기 위해서는 새로운 원리나 개념이 필요하다고 느끼는 사람들이 많아 지고 있는 실정이다.

필자는 이러한 새로운 원리의 도입에 대한 필요성에 절대적으로 공감하고 새로운 돌파구를 제시할 개념을 소개하고자 한다.

시공간에 대한 새로운 해석

양자역학에서의 시공간 개념은 주로 연구대상들이 빛입자나 소립자들의 운동처럼 가벼운 입자들이었기 때문에 시공간의 왜곡이 상대적으로 작거나 거의 없기에 시공간의 왜곡을 무시하고서도 비교적 정확하게 입자의 운동을 기술할수 있었다는 이점을 누렸다는 점에서 비교적 원시적이이라고 할수 있다. 고대로부터 아인슈타인 이전까지는 시공간의 왜곡이 없다고 가정하고 물체의 운동을 기술하였기에 원시적이거나 단순하고 절대적인 시공간 개념만이 유효했던 반면, 아인슈타인의 상대성원리에 의해 시공간이 물질의 존재에 따라 왜곡될수 있다는 사실을 인지하기 시작하면서부터 시공간이 절대적이기 보다는 상대적이고 사려깊은 고려를 필요한다는 점에서 보다 진보된 개념을 가지고 있다고 할수 있다. 

문제는 시공간에 대한 보다 진보된 관점을 가지고 원시적인 관점을 가진 양자역학을 고치려 할 경우 다시 말해서 보다 진보된 시공간 개념을 양자역학에 도입하려 할 경우 이론적으로 말도 안되는 결론을 얻게 된다는 점이다. 그래서 아직까지 우리는 하나의 통합된 이론이 아니라 소립자에 대한 운동의 기술을 위해서는 양자 역학을, 무거운 물질의 운동에 대한 기술에서는 상대성이론이라는 두개의 별도의 원리를 가지고 있지만 이것이 사람들을 불편하게 만든다. 왜 두개의 이론을 합칠수 없는가? 블랙홀이나 빅뱅의 운동을 기술하고자 할때 우리는 이 두개의 이론을 동시에 적용해야 하는데 통합이론이 없는 관계로 아직까지는 정확한 운동을 기술할수 없는 상황이다. 통합이론의 걸림돌은 무엇인가?

두개의 원리는 각자 자신의 분야에서 수도 없는 검증을 거쳐왔고 살아남았고 많은 상태의 변화에 대한 예측을 가능하게 해주었기에 거의 절대적으로 옳은 관점을 가진다고 봐야 한다. 즉 다시말해서 각각의 원리가 가지는 시공간 개념에 대한 기득권을 인정해야 한다고 본다. 거듭 얘기하지만 모든 물리의 연구대상은 관측대상의 시공간에서의 상태변화가 전부로 무엇보다도 본질적인 개념이 시공간인 것이다. 그러한 기본개념을 바탕으로 모든 운동을 예측할수 있다고 한다면 그러한 개념의 적용은 성공적인 것이고 그러한 이유로 그 존재에 대한 타당성이 인정된다고 할수 있다. 다시 말해서 양자역학에서의 절대적 시공간의 개념을, 상대성원리에서의 상대적 시공간의 개념을 각각 인정해야 한다는게 필자의 주장이다.

새로운 시공간 개념을 지지하는 두개의 철학 사상

그러면 절대적 시공간의 개념과 상대적 시공간의 개념이 어떻게 연관될수 있어야 하는지 그 근거를 대는건 필자의 몫이 될것이다. 이 관계를 이해할수 있다면 필자의 경험에 비추어 볼때 독자들 역시 아마도 세상을 보는 관점이 혁명수준으로 바뀌게 됨을 경험하게 될 것이다. 세상에서 가장 기본적인 개념들이 시간, 공간, 질량들일 것인데 이러한 개념들은 철학에서 부터 비롯되었다고 할수 있고 이들 개념들의 원형이 나오는 고대 그리스의 철학연구결과를 돌이켜 봄으로써 보다 정확한 이해를 할수 있었다는 점을 고백하지 않을 수 없다. 필자가 두개의 서로 다른 개념을 연결짓는데 핵심적인 역할을 했던 철학은 두가지가 있는데 하나는 파르메니데스(Parmenides of Elea)의 존재론(Ontology)이고 다른 하나는 피타고라스의 만물은 수이라다는 사상으로 이 두개를 염두에 두고 있으면 필자의 서로 다른 시공간의 개념을 연결짓기 위한 설명이 보다 쉽게 이해 될수 있을 것이다. 물론 아직 감이 잡히지 않겠지만 설명을 진행해 나가면서 서서히 감이 잡히게 될 것이고 이해가 완전하게 될 때 연결의 간결함이 가져다 줄 아름다움에 눈을 뜨게 될 것이다.

존재론(Ontology)에서 내거는 사상에 대해 좀 알아볼 필요가 있다. Parmenides는 '것' 또는 실체(thing)가 무엇인가에 대한 고민을 그의 사상에서 엿볼수 있다. 그는 실체는 확인할수 없고 사람의 감각은 실체의 왜곡된 면만을 감지 할수 있다고 보았다. 사람은 '것'에 대해 감각기관으로 감지하거나 두뇌에서 추론으로 이해하지만 그로 인한 이해는 실체의 전부를 담고 있다고 보지 않고 실체의 일부나 또는 생각의 주체인 사람에 의해 왜곡된 형상으로 인지된다고 보았기에 사람의 감각기관이 '것'을 왜곡시킨다는 사상을 피력했다. 이러한 사상이 시공간에 적용된 사례를 뉴튼에게서 찾아 볼수 있다.

뉴튼이 쓴 책중 가장 유명한 것이 Principia로 여기에서의 주석에 따르면 뉴튼은 다음과 같은 취지의 표현을 했다.

(https://en.wikipedia.org/wiki/Absolute_time_and_space)

Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time ...

여기에서 보면 뉴튼은 '때'(Time)에 대한 실체는 그 자체로 존재하나 '때'의 또다른 표현 '때차이'(duration)는 사람에게 인지될수 있는 상대적인 개념으로 일반적으로 때에 대한 대치물로 이용된다고 보고 있다. 다시 말해서 '때'는 사람이 인지하지 않더라도 그 자체로 존재하고 그 어느것에도 구애받지 않고 고정된 비율로 항상 흐르고 있다고 보며, 사람이 때의 개념을 인지하는 경우는 특정 두개의 사건의 '때차이'를 감지할 때 가능해진다는 존재론의 사상을 뉴튼이 가지고 있었음을 보여주고 있다. 이 문구는 200년뒤 아인슈타인이 발견한 상대적 시공간 개념을 뉴튼도 이미 어느 정도는 가지고 있었음을 보여준다. 단지 뉴튼은 아인슈타인이 확인한 상대적 시공간개념에서의 축척이 '때'의 축척과 달라질수 있다는 점을 몰랐을 뿐이라고 필자는 생각한다.

아인슈타인은 관측될수 있는 시공간의 축척이 상대적이고 이 관측가능한 시공간이 뉴튼의 운동법칙에서 사용된 절대적 시공간 개념과는 차원이 틀린 상대적 관념이라는 점을 처음 발견한 사람이다. 그래서 상대적인 시공간 관념인 관측가능한 시공간의 개념으로 모든 물체의 운동을 기술할수 있다고 봤다. 그래서 뉴튼의 절대적 시공간개념은 유효하지 않고 보다 선진화된 상대적 시공간 개념만을 사용해야 한다고 주장한 것이고 이것이 지금 주류물리학자들의 인식이다.

필자는 뉴튼과 아인슈타인의 시공간 개념을 절충해야 한다고 주장한다. 아니 물리학자들이 당면한 장벽을 넘기 위해서 이것은 무조건적으로 필요하다고 본다. 과연 어떻게 절충할수 있을까. 답은 질량에 있다. 상대적 시공간의 축척은 절대적 시공간의 존재로부터 기인하고 그 변화는 질량에 따른다는 게 필자의 핵심주장이고 이에 대한 설명은 다음편에서 하도록 하겠다.

향후 이어짐...

This is a supplementary to the last episode concerning the searching for the theory of everything. The postulates introduced in the previous episode are made to describe the most strange behavior observable in our universe, double slit experiment but are lack of enough explanations and motives on why those are necessary to understand the strange behaviors in quantum mechanics such as particle-wave duality, superposition, the conflict of notion of time and space between quantum mechanics and general relativity and so on. 

To most readers who know what Feynman mentioned on the strange behaviors in quantum mechanics, my postulates may sound like just a stupid and false information and will be put into a trash. I agree that it may be highly likely the case. But I hope that everyone is on same page with me and I still believe time is on my side which means I am crazy now. I am pretty sure that everyone will agree with my view someday because it would be only game in town which means it will be the only one model existing so far to make one understand intuitively all strange behaviors observable in the double slit experiment. 

The main point here is that we need to revisit every notion of the most fundamental property in our universe such as time, space and mass and the re-conceptualization on those notions is crucial to understand the unanswered problems in quantum mechanics and general relativity. The necessity for the re-conceptualization of notion of the most fundamental properties have been expressed by many other brilliant persons including scientists and philosophers who are involved in the development of quantum gravity.

Quantum gravity is a physical theory not finished yet trying to unify all 4 forces, strong/weak forces, electromagnetic force and gravitational force. Although quantum gravity have been studied by many physicists for almost 100 years, it is still on-going process. String theory and loop quantum gravity, which are both trying to unify all forces within a single theoretical framework are all considered as a possible candidate for the theory of everything but still far from the perfect theory. Difficulty to reconciling quantum mechanics and gravity came from the different notions for time and space and is described in [2]. Why is that? In my view, it is because the current understanding of time and space is incomplete and Einstein himself who introduced the latest description for gravity, curvature of space-time, expressed a similar view. In 1916, shortly after publishing the theory of general relativity, he wrote "Due to the intra-atomic movement of electrons, atoms would have to radiate not only electromagnetic but also gravitational energy, if only in tiny amounts. As this is hardly true in nature, it appears that quantum theory would have to modify not only Maxwellian electrodynamics, but also the new theory of gravitation.”

Gravity is described by Einstein's equations, which amount to constraints on the curvature of space-time due to the presence of mass and energy and the necessity for modifying the theory of gravitation means that we need to rethink about the true nature of time and space. Similar views have been shared among physicists. According to [1], Matvei Bronstein, one young Russian scientist, expressed a similar view in his a short paper published in 1934 by concluding that the difficulty of quantizing gravity brought the entire nature of space and tme into question: "The elimination of the logical inconsistencies ... requires a radical reconstruction of the theory, and in particular, the rejection of a Riemannian geometry dealing, as we have seen here, with quantities which are unobservable in principle, and perhaps also the rejection of our ordinary concepts of space and time, replacing them by some much deeper and nonevident concepts. Wer's nicht glaubt, bezahlt einen Thaler."

In order to open the next door leading to a working theory for quantum gravity, I think a new philosophical thinking on the true nature of time and space is also necessary as can be seen [2]. 

Tian Cao argues that quantum gravity offers up a unique opportunity for philosophers of physics, leaving them “with a good chance to make some positive contributions, rather than just analysing philosophically what physicists have already established” (Cao, 2001, p. 138). This sentiment has in fact been echoed by several physicists, not least by Carlo Rovelli (a central architect of the approach known as loop quantum gravity), who complains that he wishes philosophers would not restrict themselves to “commenting and polishing the present fragmentary physical theories, but would take the risk of trying to lookahead” (Rovelli, 1997, p. 182)

It would be worth to introduce one more writing (refer [3])  mentioning the existence of absolute time and space which I agree:

...

Flat (Minkowski) spacetime is a trivial example, but empty spacetime can also be curved, as demonstrated by Willem de Sitter in 1916. There are even spacetimes whose distant reaches rotate endlessly around the sky relative to an observer's local inertial frame (as discovered by Kurt Gödel in 1949). The bare existence of such solutions in Einstein's theory shows that it cannot be Machian in the strict sense; matter and spacetime remain logically independent. The term "general relativity" is thus something of a misnomer, as pointed out by Hermann Minkowski and others. The theory doesnot make spacetime more relative than it was in special relativity. Just the opposite is true: the absolute space and time of Newton are retained. They are merely amalgamated and endowed with a more flexible mathematical skeleton (the metric tensor).

...

If one goes beyond classical physics and into modern quantum field theory, then questions of absolute versus relational spacetime are rendered anachronistic by the fact that even "empty space" is populated by matter in the form of virtual particles, zero-point fields and more. Within the context of Einstein's universe, however, the majority view is perhaps best summed up as follows: Spacetime behaves relationally but exists absolutely.

So I hope that one recognize that there exists a need to re-conceptualize the notion of time and space shared by a group of physicists at least and let me introduce my own reasoning in the following sections.

[will be updated soon]

.....

References:

[1] http://blogs.scientificamerican.com/guest-blog/why-is-quantum-gravity-so-hard-and-why-did-stalin-execute-the-man-who-pioneered-the-subject/

[2] http://plato.stanford.edu/entries/quantum-gravity/

[3] https://einstein.stanford.edu/SPACETIME/spacetime2.html

Challenging to solve the double slit experiment puzzle

Oh YeungJong (dmqcka _at_ gmail _dot_ com)

Note: This paper is intended to introduce my private view in a hope helping others to build the theory of everything. Please be noted that this has some radical or crazy ideas and may have wrong statements. I want to celebrate the 100 anniversary Einstein's general theory of relativity before the end of 2015. Welcome any comment and further discussion.

One of the weirdest things in Quantum Mechanics (QM) would be the subatomic particle’s behavior which can be observable in the double slit experiment. The microscopic scale particle such as photon and electron appears as a particle whenever we measure them but if single subatomic particle is not observed, then it seems to exist at multiple places at the same time. This observation confused many scientists. One major figure in modern physics, Richard Feynman mentioned in his physics lecture series [1] that (this) “phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot explain the mystery in the sense of “explaining” how it works.” For now, it is common belief that there is no one who can explain “how it works” in the double slit experiment similar to the Figure 1 introduced in his lecture.

With Schrödinger's Cat thought experiment, they are showing one famous counter-intuitive feature about quantum superposition and collapse. In quantum mechanics, superposition is a fundamental principle stating that a point like particle such as photon or electron exists in several different positions at the same time and collapse means that measurement gives a result corresponding to only one of the possible state. This observation has been so weird to many physicists including Feynman but it is a fact no one can deny.

How can a point like particle exist several places at the same time? This question based on the reality has confused many physicists since the discovery of quantum mechanics and still remains unanswered. Problem is that even though many physicists tried to understand the weird behavior during last few decades, there is no working model which can give us a reasonable explanation of the quantum superposition yet. Is it possible to think about such a physical model explaining quantum superposition and collapse using two great principles of quantum mechanics and theory of relativity?

Figure 1: Double slit experiment with electrons. [1]

Here I present a bold argument that there is another essential principle missing in building a theory of everything which will unify quantum mechanics and relativity. Without serious consideration for it, I argue no one will have clear picture on the fundamental structure beneath Quantum mechanics. I am pretty sure that if many scientists seek for something beyond the standard model to build the theory of everything, the first candidate must be the chaos theory and I hope the following discussion will make it clear. To show the usefulness of chaos theory, I begin by introducing a classical example which could be a hint for particle superposition similar to the quantum superposition and collapse.

Before delving into the discussion of a new model concerning quantum superposition, it would be helpful for understanding it to consider an mechanism to display Arabic number with a 7 segment display as a classical example which can show the same pattern with the superposed particle.

Figure 2: An example for particle superposition effect in 7 segment display utilizing Persistence of Vision

In the left of Figure 2, a typical numeric display device known as 7 segment display is shown and in it there are 7 lights which are tagged as a, b, c, d, e, f and g. It is used to display any single Arabic number among 0-9. In order to display number 5 as in the figure 2, we can choose one of two possible options. First is to turn on all 5 lights at a, c, d, f and g at the same time. It obviously consumes 5 times energy than turning on single light. To reduce the required energy, with help of persistence of vision, we can take the second option to turn on only one light at any instance time. The right of the Figure 2 shows the timing sheet showing how to schedule to turn a light in 7 segment display. The used algorithm is something like as follows.

Let suppose there is a system which can display a number 5 with 7 segment display and it has 7 states named from a to g. It is assumed to be in one state at certain instance time and change its state at a discrete time interval or tick t. With these limitations, it requires 7 ticks in minimum to visit all states so let assume its transition is always periodic with period 7. Basically it is scheduled to turn on ‘a’ during first tick out of period 7 and ‘b’ during second tick and so on. In order to display 5, it can visit ‘a’, ‘c’, ‘d’, ‘f’, and ‘g’ sequentially except ‘b’ and ‘e’. As described in the previous assumption, it is scheduled to keep the previous state during interval for ‘b’ and ‘e’.

With these preparations, when we exploit the persistence of vision, one characteristic of the human eyes, we can experience the same effect as in the first method. If the unit period time T is decreased below a certain threshold value, fairly less than 1/60 second, human eye feels difficult to distinguish the observed behavior of it from one of turning on all lights and its appearance will be almost same as the interval of unit time tick is decreased to zero. Even though human eye can see the same effect as all lights are turned on with extremely short interval of unit time tick, whenever we try to stop the system running and see what state it show, we always observe one state instead of many states. Here the probability we can calculate and measure for all possible states are shown in Table 1. The example model used here gives us a hint in building a model deceiving us that a single particle can show up multiple places at the same time with the predictable probabilities but is detected at only one place.

Table 1 Probability to be in one state out of 7 states of 7 segment display system showing number 5.

A physical model explaining quantum superposition and collapse

My purpose here is to introduce a model describing properties of the most fundamental building block in our universe probably scale down to the plank scale distance using three theoretical frameworks; quantum gravity, relativity and chaos theory. It is expected to explain many weird behaviors what many physicists want to understand and the nature of time, space and mass. As like other great theories require certain number of postulates, my model needs many postulates but I think the number need to be decreased significantly as study goes.

Postulates

1.     Revival of Newton’s absolute time. Newton’s view on absolute time that absolute time exists independently of any perceiver and progresses at a consistent pace throughout the universe is a basis for further reasoning. Full range of absolute time can be mapped into continuous real number and absolute time flows always to the future at a uniform rate independently of any inertial frame of reference.

2.     Revival of Newton’s absolute space. According to Newton, “absolute space, in its own nature, without regard to anything external, remains always similar and immovable.” Full range of absolute space can be mapped into continuous real number.

3.     Similar to what string theory suggests, the time evolution of every elementary entity in 3 spatial dimensional space defined in the standard model such as electron, photon, dark matter and dark energy can be described as mathematical language and all share a common mathematical form and the general form can be rearranged as a set of first order differential equations defined in 11 dimensional space whose Eigen vectors include:

A.     3 absolute spatial vectors x, y, z

B.      1 absolute time vector t

C.      3 spinning forces f_r, f_g, f_b at position p= (x, y, z).

D.     3 directional forces f_x, f_y, f_z at position p= (x, y, z).

E.      1 energy vector E as a power source driving the time evolution.

4.     The general form in 3 for any elementary entity in can be simplified as follows:

, where h is plank constant, ν is light frequency, c is the speed of light in empty space and m is mass. This equation reflects the wave-particle duality. For a pure photon with energy E=hν, if it is got absorbed by a balckhole, it's wave like energy will turn into a pure mass form with $$E=mc^2$$. So m and ν are related as $$E=hν=mc^2$$.

5.     The p and q in equation (2) has the relation of

6.     Dark matter which is well known term in cosmology is assumed to be a point like particle with q=1 in the equation (2) and the pure photon with constant light velocity is considered as a point like particle with p=1 in the equation (2).

7.     Of any elementary particle system, Einstein’s relative time t_r and relative space x_r are related with Newton’s absolute time t and x as in what follows:

, where m is the mass term and m^-1 is called as a world evolving rate. For a photon, m=0.

8.     Of any system of elementary particle, the mass term m in equation (3) and (2) is defined as a sum of all interaction with dark matters included within its bounded area over a unit interval of absolute time domain. The full set of possible states of the system governed by the rule of equation (1) is known to be finite or bounded in the state space. [Refer to 2].

9.     The definition of measurement is to synchronize two different world evolving rates of two different inertial reference frames. For example, If a detector system with the world evolving rate r1 try to measure or detect a photon with the evolving rate r2=∞, then the measurement can be completed only after setting r2 to r1.

[2016-206. Added]

10.     The term "dark matter" mentioned in the postulate 8 can be thought as a particle having a tendency to stand still to a inertial reference frame and its role is generally to put some amount of mass to an encompassing particle. It is defined as the linear sum of 3 spinning forces f_r, f_g, f_b at a spatial position p= (x, y, z). 

Explanation for the postulate 10.

In my view, the dark matter seems to play the same role what the "Higgs particle" is expected to show. The most important thing is this dark matter is also the source of gravitational lensing effect such as bending space-time as most physicists think. My understanding is that the major view point shared by most physicists are that Higgs particle and dark matter are two different things and not the same one but I argue they are the same thing. Then the question is how it, whatever is called as dark matter or Higgs particle, can play both roles; putting a some amount of mass to a particle or bending space-time.

I think if the dark matter particle is included within the bounded area of a particle or object, then the object will get the mass equal to the sum of the interaction with the dark matter particle. So the mass of our body is believed to be the sum of interaction with the dark matter enclosed by our body. In this view, any physical shape including us are the total sum of lights, massless particle, interacting with the dark matter particles within a bounded area in 3 dimensional space. If a massive rigid body occupying a finite area in space is in a consistent motion with the same velocity, we say it is associated with a inertial reference of frame IRF and the dark matter particles contributing the mass of it tend to standing still to IRF. This view shows the role of Higgs particle is expected to play. I think the mass created from the interaction with dark matter particles bounded within a thing(i.e electron, proton and etc) is the rest mass or invariant mass of the thing most physicists mean.

Another role which dark matter plays is to change the motion of a particle or bend the space-time. Let me describe what I have in mind. Dark matter can reside any point in 3D space and shows a tendency to stay still relative to a inertial reference of frame. It makes me to think the eye of typhoon, a floating force trying to pull everything nearby into its center. The dark matter distributed not only within the bounded area of a rigid body but also near out side of the rigid body constituting a field. The distribution of dark matter near a massive body of mass M is believed to meet the condition described in the postulate 5 and suggested by general relativity. 

For better understanding, let me give you a classical analogy. Suppose, in the center of ocean, that a ship is sailing with constant velocity v and will pass nearby a whirlpool strong enough to change the sailing direction of a ship. In this case the future life of the ship will be determined by the closet distance between the ship and the center of whirlpool with the assumption that the the whirlpool power is constant and no driver controlling the ship on board. As it gets to the center of the whirlpool, it will need more energy to escape from it. Here we need to change our classical view that the eye of typhoon is just one. Instead, we can think there are finite but infinitely many number of eyes within the bounded area of typhoon and each eye having different magnitude is orderly distributed so that its pulling power is inversely proportional to the distance to the center of typhoon. This view resolves the problem of acting with object at a distance which Newton want to know. I believe this classical example helps readers understanding intuitively the space-time curvature what Einstein recognized firstly 100 years ago.

So it is the source to give rise in the rest mass of a rigid body that the dark matters enclosed by it and standing still relative to the center of mass of it. The minimum distance between two dark matters is estimated to be the Planck scale distance 10^-35m. No matter where the rigid body moves, its paired dark matter will follow standing still to the IRF of it so there will be no change in the rest mass. Of course, near out side of the rigid body, there will be dark matters distributed consisting a gravitational field due to the rigid body. Returning to the classical example of the ship sailing near by a whirlpool, the ship can be thought as the rigid body and whirlpool as a black hole exerting humongous gravitational field. In such case, the space-time curvature what Einstein described in his general relativity can be described as the distribution of two groups of dark matters which are originated from the rigid body and black hole in space. This distribution which is continuous in space can provide definitely the guiding passage for the rigid body in its world line. Unfortunately, I don't have enough skills to describe it with a strict mathematical form for now but I believe some experts can derive it easily based on the description above.

It would be worth to note one additional philosophical view that nature hates sudden discontinuity and I agree on that. On the boundary of a massive rigid body, I think it would be nice and beautiful that the distribution of dark matter is decreased gradually as the distance from the boundary increases.

The dark matter seems to be a singularity attractor pulling any particle moving near by and black hole is believed to be a dark matter particle with huge energy. I borrowed the concept of attractor from the chaos theory. Some characteristics found in attractor such as the new concept of frequency of a strange attractor are especially important to understand the true nature of our universe but I will leave it here and discuss in another thread. 

In my view, all Higgs particle and dark matter and black hole are actually the same thing with magnitude variations: a energy force trying to pull any object passing near by into its center. I think most physicists will agree on that a physical model with fewer assumptions is better than one with more assumptions. From my intuition, it seems to prevent the time evolution of a particle and shrink its perception on the spacial space similar to what special relativity proposes.  

[/2016-206. Added]

How can quantum superposition and collapse be interpreted using the above postulates?

For simplicity, I will begin with the most basic element particle, a massless photon, other than electron with rest mass. From postulate 3 and 8, a photon evolves in time in a bounded volume of 3 spatial dimensional space deterministically ruled by a set of ordinary differential equation. Bounded area means that the photon oscillate within a bounded area or has a finite size instead of a point independently of any perceiver.

As quantum mechanics already discovered that the probability to find a photon at certain volume area can be predicted, the previous work with chaos theory [3] showed that the probability distribution of a particle moving along the trajectory of chaos system such as Lorentz system can be determined by means of numerical analysis before actual measurement.

The size of a photon is appeared as almost zero to any perceiver close to human scale but in absolute time and space, the bounded area of a photon is non-zero volume and remains unchanged if there is no interaction with any external energy form.

What is the frequency of light in free space and is it quantizable?

This is next topic.

[Added 2016-01-03]

See the recent comments in the additional part in 2016-2-06.

I missed one important postulated so here I add more postulate about the distribution of dark matter in absolute space. Dark matter which is known as a hypothetical kind of matter causing gravitational effect in cosmology is, in my model, a sort of frictional like energy particle instead of matter. It is made up of the linear combination of f_r, f_g, f_b. It is same with the inertial mass in classical mechanics.

Postulate 10.

Given a point like matter with mass m, assuming 1 directional space, dark matter is distributed around it in decreasing way as the distance r from the mass position: Unfortunately, I don't have the exact equation for the dark matter distribution but my guess is that it could be a equation whose integrals from 0 to infinity distance is matched with the rate of percentage of dark matter over visible matter: 

Figure 3. Conceptual image for dark matter distribution. The integral of the distribution between 0 to infinity is expected to be matched with the rate between the percentage of dark matter and visible matter. 

Understanding quantum superposition in double slit experiment with the new model.

From postulate 3, it is known that any particle system of which time evolution is governed by the set of ordinary differential equations is oscillating in a bounded area in absolute time space in similar way to the strange attractor. It means it is possible that the bounded area of the particle is bigger than the distance between two slits. Figure 5 shows such a case. 

Figure 4. A conceptual image. An oscillating particle in the bounded area is passing through double slits with light velocity c. The trajectory of the particle is big enough to contain the wall between two slits.

As can be seen in the previous example of 7 segment display system, for a system which can have only one state at any instance time, it can produce an illusionary effect as if it can have multiple states at the same time by reducing the duration of a unit tick to zero. Same principle can be applied with the double slit experiments with photon. What important information is that a photon has no mass and a world evolving rate $$ \alpha = \frac{t}{t_r} = \infty $$

What the world evolving rate α of a system is infinity means that it takes no time to complete the evolution which is analogous with increasing the clock speed of CPU to infinity or decreasing the duration of a unit tick. It should be noted that any system experience only relativistic time and space and there is no way to measure or observe the absolute time and space. It is similar to what we are unable to measure π. Instead of using ideal symbol, we can only use the approximated value of π in a calculation and the approximated value is normally relativistic to who make a decision of the level of approximation. 

Back to the double slit experiment, due to the mass of wall included in the bounded area of photon particle, the world evolving rate will be decreased but negligible because the mass is small and still it's moving from one slit to other along its trajectory will take almost zero time. 

I think the model described so far using chaos theory and special relativity is the only available non-mathematical explanation about the quantum superposition and easy to understand.

[/Added 2016-01-03]

1.      [↑] Feynman, R.P., Leighton, R.B., and Sands, M. (1965). The Feynman Lectures in Physics Volume 3, Section 1–1, Addison–Wesley.

2.     Chaos. http://plato.stanford.edu/entries/chaos/

3.      Jos Leys, É. G. (n.d.). Chaos-viii-statistics. Retrieved from CHAOS: http://www.chaos-math.org/en/chaos-viii-statistics

This post will be the first step to the ultimate one theory which will unify Quantum mechanics and Relativity. The two great principles in modern physics work well when they are separate from each others domain but when we try to study the case both should be considered at the same time, for example behavior of black hole and big bang, they conflict each other and physicists failed to produce a solid consistent explanation. The most difficulty in marrying both principles come from the difference of the notion of time and space, the most fundamental ingredients of our universe.

Current understanding of time and space was available when Einstein introduces Special relativity and general relativity in the early decades of twentieth century. In his theories, he reconceptualized the notion of time and space by revealing their relativistic nature instead of absolutivity of time and space which Isaac Newton proposed. But Einstein's relativistic view of time and space is not useful to explain the microscopic scale movements which are understood fairly enough with the help of Quantum mechanics. So it is obvious that we need to redefine clearly the notion of time and space playing as a common base in every scale universe. That is why I revisited Special Relativity(SR) which is the starting point in formulating current understanding of time and space. Here I focus to explain why SR is incomplete and propose a way view to solve the incompatibility of time and space.

I argue that two postulates used in Special relativity is not enough to make it a consistent theory and it must be modified to be perfect. Why? Because in SR, there is no way to figure out whether any Inertial Reference Frame(IRF) is moving or stationary. SR can talk only about the relative motion of other inertial reference frame compared to my IRF. Let suppose that in the empty space there exist only two objects, me and you, and each can see the position of other with help of light, let say we are getting closer in time and there is no change in IRF to both which means both are in the motion with constant velocity. In this case, we cannot tell who is moving and stationary if we are given only two postulates (see below quote) which Einstein proposed in SR. There are three possible cases: 1) me stationary and you moving 2) me moving and you stationary 3) both moving. Depending on the cases listed here, as predicted by SR and verified in every experimental result, i will have different experience about aging. 

From wiki, two postulates are as follows:

This logical deduction above contradicts with the first postulate, principle of relativity. In result 1), I is getting older than you but in 2) you are getting older than me. If we live in a single universe and there is only one event happening and we are ruled by the law of physics, there should be only one result observed by both me and you. But depending on our choice on the view points listed above which are all equally valid within the view point of SR, it is unavoidable to observe different results instead of the same result in all inertial frames of reference. We can notice that, in Einstein's 1905 paper, he assumed he know which IRF is stationary but knowing whether any IRF is stationary or moving is not an easy task and we need to be very careful to do so. This means that SR is incomplete and need to be complemented or modified to produce no contradiction. 

Note: The definition of IRF used here is the coordinate system of which origin is always sticking to the center of any rigid body or particle including photon in unchanging motion.  As long as object is in the motion of constant velocity, then there is no change in the Inertial Reference Frame of it.

In the next post, I will propose a new way to complement SR.

[Series #5] How a massless photon gets massive?

This post is continued from the last series #4 to explain more the mechanism how a point like massless particle get massive within the gravitational field conceptually. Again I am neither a mathematician nor a physicist so proving something with precise mathematic equations is beyond my capability. Instead I will try to provide some conceptual ideas such that ordinary people like me can grasp and understand it. Additionally in the end I will propose an experimental way to verify whether my view is correct or wrong. In this series, I will focus to explain the mechanism conceptually on how a massless particle such as a photon moves though the space filled with a rotational force element.

As the string theory suggests that the most fundamental building blocks are all vibrating strings, similarly I assume every subatomic particle should be an oscillating point-like particle whose trajectory in the 11 dimensional space is something like a strange attractor which do not intersect itself such that it looks like an open ended string within a bounded area. My assumption is a possible scenario because there are many examples in various areas as studied in Chaos theory.

My story begins with the conceptual visualization of the internal structure of a massless particle with velocity C such as a photon as can be seen in the Figure 1(a). Basically in my view, a photon is assumed to be in a bounded volume in 3d space such that the probability to find the particle P within the bounded area is 1. Within the bounded area, a point-like particle P is orbiting its trajectory in the 11 dimensional space exactly governed by the rule shown in the series #2 and it means that it is a deterministic system. As a real photon has a definite frequency, the assumed photon-like particle in my model also is assumed to have a sort of frequency. This periodicity sounding crazy to readers will be explained later in detail and for now I will skip it. I believe that the periodicity of light can be understood fully only when considering both time and space simultaneously as Einstein did in the SR.

Figure 1. A conceptual visualization. The mechanism on how the gravitational field changes the movement direction of a massless particle. In (a), a massless particle B moves at constant speed C along x direction. For simplicity it is assumed to have a frequency 10 per a unit time T. In (b), B enters in the region where F is influential enough to attract nearby massive objects to its center like a whirlpool. P which is influenced by F is orbiting the modified route with a less frequency 9 while staying around F at a rate of 1. Here P gets non-zero stickiness or inertial mass.

So under the current scenario my photon is initially assumed to have a frequency 10 per a unit time T in empty space as in Figure 1-(a) and it means that the point-like particle P orbits 10 times around each steady convections per a unit time T. Here the meaning of the unit time T will not be clear to readers but it means the infinity is the unit time and this crazy mind blowing idea will be discussed in other post.

In the figure 1, the photon moves with light speed C from left to right and no mass if it has no interaction with the rotational force element F. If it enters the region in where there exist interactions with the rotational force element F, then it gets massive and its moving direction is curved as in the Figure 1-(b). To sum up, in my model, a massless photon gets massive and bent within the gravitational force field. Let me describe more what happens to a massless particle moving at the speed of light in the gravitational force field.

Again due to my lack of mathematics, it is hard to formulate the exact equation describing correct movement of the photon. Instead I will focus on the concept what a photon will behave. If someone gives me a hint or lesson about the necessary math to precisely calculate values, we can help each other to make some outputs which will be almost impossible solely.

In the region where influenced by F, P travels the modified orbit with a frequency less than one in the Figure 1-(a). It is assumed that P is attracted to F and orbit around F at a rate 1/T and 9/T around each convection points. It means P needs to spend 1/T circulating around F and 9/T orbiting around each convection point. From the view point of two convections, the frequency of P is decreased.

What is important here is that P gets stickier near F in the right of Figure 1. Let us assume the bounded area is a solid body which can be pushed or pulled and trying to move it downward. If we compare the energies needed to move P downward for both cases, then we notice those will be different and the energy used in moving the body downward in the right of figure 1 will be higher than the one in the left. If the power of F is so strong, i.e. a black hole, then P will be attracted to F and will orbit around F all times so that the probability to find P around F would be 1. If P is captured by a black hole and unable to escape out of the event horizon of the black hole, then the mass of the black hole will increase by the photon energy divided by C².

To understand what stickiness or inertial mass means, let us compare two cases. One case is a massless photon moving with light speed and other case is a photon caught by a black hole. The former has the bounded area like in the Figure 1-(a) and the latter is the case that the bounded area of the photon will be the event horizon of black hole. At a time instance t0, lets assume the center of the bounded area is located at a point X0. In the former, the energy needed to move the center of the bounded area out of the point X0 to any direction is guessed to be zero because there is no stickiness at X0. On the other hand, in the latter case, a different story begins. To move the photon bounded within the event horizon of the black hole out of the event horizon some amount of energy is needed and it means the photon has a sort of stickiness or inertial mass. These two cases represent two extreme states; a massless particle with light speed and a massive particle with zero speed. Then what will happen in the intermediate course? I believe it would be natural to think that there is no sudden change in state such as mass, frequency.

I believe if the total energy of the photon must be conserved, the inertial mass can be calculated by the following equation:

$$E=hf_0=hf_1+m_1c^2$$

$$m_1=\frac{h\left(f_0-f_1\right)}{c^2}$$

To verify my model, I would like to propose an experiment as in the Figure 2.

Figure 2. The relation of mass and frequency of a photon. A massive photon bent within the gravitational force field.

I searched many sites to find the relation between mass and frequency of a photon but failed to find the one matched with my view. Anyway, based on my view, I argue that the frequency f2 of a photon at P2 will be higher than f1 at position P1. 

$$f_0>f_2>f_1$$

[Added 2015-08-29]

In my view, the concept of the stickiness or initial mass is closely related with the probability to find a particle within a bounded volume in space as I introduced in the previous post. I guess that it could be a ball shaped volume with a diameter of the plank distance.

If P is interacting with F so that it is forced to orbit around F, then the massless P gets massive. If the rate that P spend orbiting around F is increased, the probability to find P within the unit volume V where F centers is also increase.  So the mass of a photon could be rewritten as probability to find P within the volume V multiplied by photon energy E over c^2 if P is interacting with only a single rotational force element F. It should be noted that in some cases the bounded area of a photon pass through the the unit volume V of F with no interaction with F. In such case, there is no stickiness with F in V so no inertial mass. Even in such cases, if we can make the probability as the function of the interaction with F, then below equation would make sense.

$$m_f=P_f\frac{E}{c^2}$$

,where m_f is a mass in relation with F and P_f is the probability to find it within V in relation with F

If the bounded area of a photon interact with multiple rotational force elements, then the total mass of the particle would be integral of all force interactions.  

[Added 2015-08-29]

Additionally, to support my view, let me describe one more. I believe that the two slit experiment is actually showing the gravitational movement of a particle instead of wave like behavior. We all know that the light is bent near the sun due to the gravitational force. If two suns are located close at a short distance so that a photon pass through the narrow slit between two suns, what do we need to expect from the photon? Will it show the movement of a particle or wave? I think the photon must show a consistent behavior regardless of the scale difference. If it is confirmed that a photon is bent under the influence of gravitational force field, then we can accept that it need to be bent near at the slit wall because the wall also has a mass and the photon can pass at a very short distance from the wall. 

In Newton's law, force is proportional to mass and inverse square of distance. So even though the mass of the wall in ordinary two slit experiment is very small compared to the sun mass, very short distance will compensate the effect of the reduced mass. So in very short distance from the wall, photon will show the very same behavior with the space time curvature in the solar system scale or even larger. I will discuss this more in a separate post later.

[Series #4] What creates mass?

This post contains my personal view on the mechanism on the creation of mass. In my previous posts, I briefly mentioned that three rotational forces Fr,Fg,Fb acting on every location in our 3 dimensional space is the cause to get a massless packet of energy gaining or losing mass. For a particle, the sum of magnitude of active interactions with these three rotation forces is guessed to be proportional to the mass of it. I think this idea is the key to understand the mechanism about what makes mass and what is the gravity working well even in the subatomic scale world. For those who may feel difficult to accept this idea, it is right time to remind us all of Isaac Newton’s original view on inertia.

Classical view on Mass

Inertia is understood as the tendency of an object to resist a change in its state of motion. If an object stays at rest, it has the tendency to keep that position. To make some change in its rest state even if it has non-zero constant velocity, external force should act on it and so energy does. Simply to say, if we want to change the fate of an object into different direction against the path  which is destined to follow initially, with the assumption that we can predict its future motion using well established Newton’s law or whatever suitable, then we need to use some amount of energy. From this point of view, the mass of an object can be measured indirectly by measuring the energy consumed to make the change of the object as Einstein explained in his paper, “Does the inertia of a body depend upon its energy-content?”. The quote taken from it below shows it clearly and could be helpful to accept my idea briefly mentioned above.

“The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 × 10²⁰, the energy being measured in ergs, and the mass in grammes.” By A. Einstein

My personal view on Mass

The original expression of Energy-Mass relation used in Einstein’s 1905 paper may be written as the equation, “m=L/c²” provides a great insight about the true nature of Mass.

Firgure 1. Higgs mechanism? A mechanism about how a massless oscillating particle moving along x direction with speed of Light c can gain and lose mass depending upon the existence of interactions with the three rotational forces in the space.

To know what mass is and how mass can be measured, consider a scenario that a massless oscillating particle is moving from left to right along x direction with velocity of light c at x=x0 as depicted in Figure 1. At region 1, left side in Figure 1, it is assumed that there is no force at all for a particle to interact with so that the particle moving along x axis will show the translational symmetry which means the invariance of particle’s status such as velocity, periodicity and so on. It will soon move into the region 2 (centered in Fig.1) of which locations are filled with fluctuating forces due to the heavy mass at x=x2. These fluctuating forces which are believed to be created due to the Dark energy residing at the same position in space play key role in putting mass to the particle passing through.

It should be noted that the basic feature of matter is that we can find its location. If a ball is floating around in the ocean and happens to get close to strong swirl pulling anything nearby, it is easy to predict we would see the ball at the center of the swirl. If the ball is moving fast and the pulling energy of swirl is not enough to catch the moving ball, then the ball can escape out of the swirling area.

In my view, there are some sort of swirling forces in region 2 which are trying to hold any particle passing through. If the swirling forces acting on a bounded area is so strong enough to hold nearby particle, that means that there is high probability to find the particle at the position in the statistical point of view. This can lead to the following conclusion that if we want to move the particle to different location opposing the swirling forces sticking the particle to the same location of forces, some amount of energy is required. The necessary amount of energy to pull out the particle can be used to calculate the mass of particle. In this period, the particle is slow down a little bit due to the holding effect so its velocity v1 is less than light speed c.

If the particle is able to move into the region 3, it will lose its mass gained in the region 2 and restore its original masses state and the velocity of Light c.

It is almost impossible to measure the exact mass of a particle at a certain instance since the fluctuating forces are not distributed uniformly over the space and vary over time so the mass itself may vary upon its locations. Instead, it will be our best to get the average of mass over a period. So it will be very important to know what property or state of a particle system is time invariant because the time invariant properties such as energy can be only measured and verified over and over again.

Gravitational force

Newton stated that the force of gravity between two objects is attracting each other and works instantaneously at a distance. In Newton’s universal law of Gravitation, the strength of the force is proportional to the inverse square of distance r between two objects.

$$F=G\left(\frac{Mm}{r^2}\right)$$

In my view, the difference in the strength of swirling forces acting on two points can reason the gravitational forces.

Figure 2. An illustrative image to show how gravitational force work at a distance. The data used here is not correct and this picture is prepared to show the gradual decrements of gravitational force as distance is getting bigger. Blue curve is the sum of the swirling forces power and orange curve is the 2 power of blue curve which is guessed to be the probability to find the particle at distance r.

As shown in figure 2 which is prepared to show just a premature idea, the probability curve in orange color is continuously changing across distance and the gradual difference of the probability curve is guessed to be the cause for gravitational force. I chose this probability curve as a proper candidate to the correct answer with intention to understand the weirdness in dual slit experiment showing the diffraction pattern of particles.

[Added 2015-07-21]

Regarding Figure 2, the true meaning of the blue curve is the strength sum of all rotational forces only interacting with all objects involved in gravitational force. In fact, the strength varies over time because

the "mass" property of a moving particle in the force field full of fluctuating rotational forces is varying too. To get the data in Figure 2 which is time invariant, we need to depend on the statistical analysis which will help us to get such time invariant data. This issue will be discussed further when dealing with the periodicity of "strange attractor" later.

[/Added 2015-07-21]

Here comes my understanding how matters are attracted to each other within the force field. Let's assume that a particle with mass m is placed at distance r=r1 and a heavy mass M at r=0. As shown in Figure 2, the possibility to find a particle tend to increase as distance r is smaller. One additional assumption is that the minimum distance between two neighbor points should be Plank distance. Strong swirling forces at r=0 means there is high probability to find a matter at that point so in my view, the existence of the rotational force ( here I use swirling and rotational both as same) enable the creation of mass.

The probability difference between two neighbor position reasons the attracting force which fits with Newton's law - force proportional to the inverse square of r. This idea helps us to safely ignore the concept of "Spooky action at a distance".

Why gravitational force is the weakest one among all 4 forces?

As can be seen in Figure 2, the probability curve is not always increasing as distance r is getting shorter. Intervals where probability decrease as r goes to zero coexist with the intervals where probability is increasing and this is an interesting property of gravitational force. The existence of decreasing probability intervals makes it weaker than other 3 forces. 

To be continued ...

Reference

[1] DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT? By A. Einstein. 1905.

[Series #3] Energy-Mass relation and black hole

Purpose

I am not proving something here but trying to present a concrete framework and explanations helping readers to understand much intuitively about many weird things found in quantum mechanics such as Wave-Particle duality, measurement problem, and probability density.

This post contains my basic ideas about Energy and Mass relations which are missing in my previous post.

 http://kevino.tistory.com/entry/Series-2-A-introduction-of-a-Mother-function-governing-all-particle%E2%80%99s-movements

For smooth continuation of discussion, let me restate of the mother function which is introduced in previous post here again:

, where R is a dimensionless scalar value.

My fundamental assumption, described in my previous post, is that the dynamical system of every subatomic particle S can be defined as very much like to equation (1). The equation form is assumed to be a set of equations which are several coupled ordinary differential equations similar to the Lorenz equations so it is believed to show very same features which Lorenz equations can show such as deterministic behavior, sensitivity to initial conditions and etcetera.

Due to the lack of knowledge in the true nature, I do not know the exact equations for (1) yet but I believe that the similar behaviors discovered in study of the dynamical system showing strange attractor such as Lorenz attractor can be found too in the dynamical system of every subatomic particle. So I will focus my discussion to ensure people to see the close resemblances in behaviors found in between two different dynamical systems and hope everyone understand many weirdness in Quantum mechanics easily and intuitively with the help of knowledge in Chaos theory.

If we look at the stable trajectory in state space for a dynamical system S, S can be distinguished as one among three types: attractor of singularity, periodic and chaotic. The trajectory of each type will evolve over time and getting close into the fixed position, periodic orbit and strange attractor respectively if there is no change in the equations in the course of evolvement.

With regard to the dynamical system which can be converted into one showing strange attractor, below shows some features what I like to note especially, which are all described in the previous Chaos theory:

1.     The trajectory is bounded within finite volume in the state space. It is obvious that not only singularity and periodic attractors are bounded but also strange attractor.

2.     The center of bounded area is at one of critical points, normally at origin.

3.     The trajectory in form of strange attractor does not repeat itself so it seems to be non-periodic. In fact, it can be thought as a very long string with no intersection in the state space.

4.     Sensitivity to the initial condition. The nearby initial conditions in the state space diverge quickly so that predicting the future flow of the other trajectory starting at nearby point impossible.

5.     But the trajectories starting at nearby points are getting close to the same overall shape as time flows. For example of Lorenz equation, both trajectories eventually form a so called “butterfly” shape.

6.     Upon changes of environment or different configuration (refer to my previous post), the trajectory can be interchangeable between three different types of attractor. For example of Lorenz equations, it is known that the trajectory can have a certain behavior on the r dependence of the attractor. [1]

Fig 1. Various attractor types of Lorenz equation on dependence of r

As can be seen in figure 1, there are 3 types of attractors on dependence of r in the Lorenz equations. In (a) and (b), the trajectory starting at initial point(x0, y0, z0) is attracted to a single position. In (c), two different trajectories starting at different initial points (5, 1, 1) and (-5, 1, 1) occupy almost same region in the state space. It should be noted that each trajectory is actually something like an open ended string and the bounded areas of two which looks like butterfly shape are exact same one. The figure 1-(d) shows a periodic orbit.

Additionally, to fit every weird thing together in consistent manner, my intuition, mostly affected by string theory and chaos theory forces I to make few assumptions as like:

1.     From the famous Einstein equation E=MC², energy and mass can be interchangeable. That being said, a subatomic particle which is a basic building block of everything is assumed initially to be a massless lump of Energy E=hν ( Plank’s equation).

2.     In my view, even if a particle is in state of strange attractor (refer Fig 1-c) so its trajectory looks like non-periodic orbits, it is assumed to have a definite frequency. The more details for this will be provided in separate post.

3.     For a subatomic particle, the more interactions with the rotational forces within the nearby force field, the much heavier it gets. It means that some partial energy out of total energy turns into mass form. To meet the requirement for energy conservation, the following relation is necessary. Refer to Fig 2:

$$E=hν_1=hν_2+m_1v^2$$                      (2)

4.     If a particle get mass, then it is slowed down a little bit so its velocity is less than light velocity constant c.

5.     If the particle move fairly enough far away out of the field filled with rotational forces and almost no interaction with the rotational forces, then it will restore its massless state with initial frequency ν₁.

6.     The dynamical system of a subatomic particle can be into a state with singularity attractor which can be seen in Fig 1-(a), (b) under environmental changes.

7.     It is also possible that huge number of particle located in a bounded area in space can be resonated to have almost same singularity attractor type with a very same critical equilibrium point. It can be intuitively understood by looking at spin alignment in magnetic fields, although there is no clear evidence that they share a same mechanism. If they put together at a stable equilibrium point in space and grow more and heavier, it is possible for the crowded point like massive thing to become a black hole.

With the assumption above, I will try to explain counterintuitive everything which people are desperate to figure out so that they fit together in consistent way under given the single framework.

Black hole

Figure 2 shows my conceptual view on how energy of a particle is conserved. All size of rectangle area in different colors means total energy and is equal. In my view, with hint in Fig 1-a, it may happen for a subatomic particle to be in a state having singularity attractor and it eventually be attracted to a critical point of equation (1). For rectangle 2 colored in orange, it is assumed to be a particle with almost infinity mass and almost zero velocity. Because the velocity is not zero, so it is bounded with extremely small area but not zero space.

Fig 2. A conceptual image for how energy conservation works. Rectangle 1 represents a massless particle so it has frequency ν₁. Orange colored rectangle 2 means a particle with singularity attractor so it has zero frequency but its energy should be same with hν₁. Rectangle 3 has wave and particle like behavior at the same time.

If huge numbers of particles get attracted to a same point and grow bigger and heavier enough to pull nearby particles, it would become a black hole. The black hole can be thought basically as a particle with extreme heavy mass and gradually growing as eating up nearby particles. If there is another growing black hole coming and each is attracted, then it can be thought as a collision of two particles. Furthermore, if the collision of two black holes is so powerful enough to break the binding forces which are the source to keep the singularity attractor of all particles forming the black hole, then it will show super ultra-version far beyond the Large Hadron Collider or even more close to the Big bang.

References

[1] C. Sparrow. The Lorenz equations: bifurcations, chaos, and strange attractors. Applied Mathematical Sciences, 41, 1982.

[Series #2] A introduction of a Mother function governing all particle’s movements

CAUTION: This series is introducing my a lot of unproved ideas so many mistakes or just ridiculous story you can found. Although I think my view or descriptions correct, I do not guarantee anything written here until precise proofs are ready.

This post is continued from my previous article here. Here I will begin with introducing a framework which will explain many weird things happening at subatomic scale level. Initially I will provide a big picture and using that I will try to explain each detail one by one.

There is a single mother function Ω which is defined in 11 dimensional vector space and the Ω is the only one rule which determine every bit of time evolution of every state of any subatomic particle in our universe.

Ω( x,y,z,Fx, Fy, Fz, Fr, Fg, Fb,t, R)

Where x, y, z are three Cartesian position vector,

Where Fx, Fy, Fz are three directional forces defined in the position p=(x,y,z),

where Fr, Fg, Fb are three rotational forces along axis x,y,z, defined in the position p=(x,y,z),

Where t is time,

Where R is a scalar value.

So let’s assume that the following equation is only one correct root function governing whole future of any subatomic particle from now. It means that for a dynamical system, every state at any instance time t>0 are fully determined completely at t0 using the assumed mother function Ω.

Ω( x,y,z,Fx, Fy, Fz, Fr, Fg, Fb,t) = R    ---------- (1)

In fact, I assume that Ωshould have a form of several coupled ordinary differential equations similar to the Lorenz equations, a system of deterministic ordinary nonlinear differential equations introduced by Edward N. Lorenz.  [1].

Given the mother function Ω, the trajectory of the dynamical system governed by the equation (1) can be categorized into one of three types. And these types can be interchangeable by varying several parameters such as energy absorption/emission.

First type is singularity. The trajectory of the singularity type tends to evolve into a single point defined in the vector space.

Second type is simple periodic system. The trajectory of this second type shows a closed loop or repeated. Quasiperiodic orbits also belong in this type.

These two systems of singularity and simple periodic are related to R of same number category, rational number.

On the other hand, the third type is known as a system with non-periodicity and its trajectory as a strange attractor so far. But my observation is that this third type system seems to be actually a periodic system with irrational numbered period which need to be investigated further. This observation will be discussed more in another article which will follow soon.

Table 1. Symmetry. The relations between the trajectory type and R.

*: The details of the irrational numbered period will be provided in other separate article.

The figure 1 is an illustrative example of the force field in space to help readers to feel what I feel too. In every point P, there are 6 forces associated. 3 forces(Fx,Fy,Fz) mean the directional forces and other 3 forces(Fr,Fg,Fb) mean the rotational forces. If we accept the conventional knowledge from the Quantum mechanics, then the minimum distance between two different points in this space would be Plank constant length.

Furthermore I have an intuition that what add mass to a massless particle would be some interactions with 3 rotational forces Fr,Fg,Fb.  If a particle moving through this space S have some sort of interaction with one or all of these 3 rotational forces, then it seems to me that the interactions produce a holding effect to it at the position so is the reason why a massless particle gain mass out of the force field. If the particle can have more energy to overcome the holding effect at that position, then it will continue to move further escaping from the region where force affect around the point. This is just my imagination. The 6 forces can be thought as the combinational result of gravity, electromagnetic and strong/weak forces.

Figure 1. An illustrative example of the force field filled with 6 forces: Fx,Fy,Fz,Fr,Fg,Fb.

To help readers to understand what features the mother function Ω have, instead of using the correct equation form which makes difficult to visualize movements in high dimensional space above 3 dimensional space, it will be much convenient to use the famous Lorenz equations [1] which is believed to have same characteristics with the mother function Ωsuch as sensitivity to the initial condition, etc.

Features of the Lorenz equations

The famous Lorenz system is expressed as 3 coupled non-linear differential equations.

 , where σ, r, b are constant parameters.

Regarding equation (2), 3 things can be distinguished.

1.       The equation itself

2.       Initial values of state at t=t0. X0, Y0, Z0.

3.       Parametric coefficients such as σ, r, b. I will call a set of all coefficients as “parameter configuration” for later use.

This system has several characteristics.

1.       Depending on the “parameter configuration”, the system can show one of three different behaviors: Singularity, periodic, and chaotic. If there is a sudden change in the configuration, then there is possibility for trajectory to show a kind of quantum jump to whole different level depending on the amount of changes in the configuration.

2.       In case of chaotic configuration only, the system shows sensitivity to initial values of state. Small changes in the initial values of state can result quite different future of system state.

3.       The trajectory in the state space is bounded. This characteristic is similar to the orbital movement of an electron within a bounded area in atom.

4.       The overall shape (butterfly like) of the trajectory is invariant to the changes in the initial value of state X, Y, Z.

The characteristic 1 can be used to explain how an electron can do a quantum jump upon energy absorption or emission.

In the next article, I will discuss more about a kind of periodicity of the Lorenz equations which is believed to be found in the mother function Ω.

References

[1] Deterministic Non-periodic Flow. Edward N. Lorenz.