, ( )
- ( ),, - - T 2T 3T! t t! t 0 = t + T 2
주기적으로 반복되는 사건 공간적으로 반복되는 일정한 패턴 기하학적 대칭성 - 흔히 아름답다 고 인식하는 형태들이 기하학적 대칭성을 보이는 경우가 많음 Beauty is truth, truth beauty that is all Ye know on earth, and all ye need to know. - John Keats 3
? ( ) - ( )? - - ( ) + ( ) -?! 4
( :, ). - (symmetry) = (invariance) (?) - (?) - - - 5
* - (Noether s theorem) - :,, - - ( ), - - flavor SU(3) - - ( ) *. 6
- - F = ma - - - - 7
,. ( ), -? (= ). -..? 100? 10?. Enjoy (the symmetries) while you can! 8
= ( ) isotropy? Milky Way Galaxy -? - / / /?! artist s conceptual view - Again, enjoy the symmetry while you can! our Solar System 9
방향(회전) 대칭성 isotropy Planck 실험에서 관측한 우주배경복사(CMB) 분포: 거의 isotropic한 분포를 보여줌 평균 온도 2.7K를 기준으로 빨간색과 파란색의 차이는 10만분의 1도임 10
-. -. If we set c =1(perfectly allowable) t 0 = (t z) z 0 = (z t) t z 11
- - 19 - - Field strength tensor (?) r ~E = / 0 r ~B =0 r E ~ = @ B ~ @t r B ~ = µ 0 ~j + 1 @ E ~ c 2 @t 12
-. -, ( ).. (x) (p). H(q, p) = p2 2m + kq2 2 for SHO - Hamilton-Jacobi Poisson Bracket. - 20. F = dv dx = ma = x md2 dt 2 L = 1 2 mv2 V (x) H = p2 2m + V (x) df dt =[F, H] PB 1 i~ [, ]! [, ] PB d ˆF dt = 1 i~ h ˆF, Ĥi 13
?? Original Left Symmetry Right Symmetry... ( ). ( ), ( ),. ( ), ( ). ( ). - 14
?? (~ ). ( ).... 0. 0.. (Higgs). 15
대칭성의 자발적 깨짐 (예) 좌빵 우물 식탁에 빵과 물은 대칭적으로 놓여 있었다. 오른쪽 물컵과 왼쪽 물컵이 내 자리에서 정확히 같은 거리에 있다면 어느 쪽 물컵이 내 것인가? 누군가 우연히 오른쪽 컵을 잡으면 다른 사람들 모두 오른쪽 컵을 잡게 된다. 좌우 대칭성이 자발적으로 깨진다. 16
.,? -? -? -? 4 *. I cannot believe that God is a weak left hander. - W. Pauli * 17
Parity violation 18
Quark model 1960 3 (u, d, s). SU(3) Flavor-SU(3). 1970 6. (u, d, c, s, t, b) 6 Flavor-SU(6).? Flavor-SU(3) u, d, s.. Flavor-SU(3). 19
?, (classical mechanics) - (simple harmonic oscillation) - : 3 (!). -? F (x) = kx F (r) = k/r 2 20
. ( )?
?. Gauss law... 1/r 2. F (r) = kqq 0 /r 2 E(r) = kq/r 2 I ~E d~a = Q in 0 r ~E = / 0. 22
? 20.. 23
? 20...... 24
? 4. 4 [F = q(e + v B)]. 4 (linear). chaos. (non-linear)??? 25
the unreasonable effectiveness of mathematics (Eugene Wigner) COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, VOL. XIII, 001-14 (1960) The Unreasonable Effectiveness of Mat hematics in the Natural Sciences Richard Courant Lecture in Mathematical Sciences delivered at New York University, May 11, 1959 EUGENE P. WIGNER Princeton University The universe is both rationally transparent and rationally beautiful (John Polkinghorne) 26
If you stop to think about it, all this is very odd. Mathematics, after all, is just abstract thinking, but it turns out that some of the most beautiful patterns that the mathematicians can think up are not just airy-fairy ideas, but they actually occur, out there, in the structure of the world around us. Dirac s brother-in-law, Eugene Wigner, (himself also a Nobel prize winner) once called it the unreasonable effectiveness of mathematics. He also said it was a gift that we neither deserved nor understood. I do not know about deserving it, but I would certainly like to understand this strange property that makes theoretical physics both possible and greatly rewarding. The universe is both rationally transparent and rationally beautiful. The first fact makes science possible, the second gives scientists their deepest satisfaction, the sense of wonder at the marvelous order revealed to our enquiry. (J. Polkinghorne) 27
There is a story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former classmate, The reprint started, as usual, with the Gaussian distribution and the statistician explained to his former classmate the meaning of the symbols for the actual population, for the average population, and so on. His classmate was a bit incredulous and was not quite sure whether the statistician was pulling his leg. How can you know that? was his query. And what is this symbol iere? Oh, said the statistician, this is n. What is that? The ratio of the circumference of the circle to its diameter. Well, now you are pushing your joke too far, said the classmate, surely the population has nothing to do with the circumference of the circle. Naturally, we are inclined to smile about the simplicity of the classmate s Let me end on a more cheerful note. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure even though perhaps also to our bafflement, to wide branches of learning. The writer wishes to record here his indebtedness to Dr. M. Polanyi E. Wigner 28
,? ( ).,,. (frame)..,... 29
Epilogue 30