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## Symmetry and Symmetry Violation in Particle Physics

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**对称**违反 Symmetry and Symmetry Violation in Particle Physics**Who am I?**Stephen L. Olsen Experimental Particle Physicist University of Hawaii Visitor to IHEP (高能物理研究所) 2007-2008**What am I famous for?**I have had many very excellent students (Including Prof. Zheng Yang Heng) 郑 阳 恒**My tentative plan for this class is as follows:**Lecture 1. Definition of symmetry, why they are important in physics. Symmetries of the laws of nature. Relation of symmetry and conservation laws. Discrete symmetries C, P & T. Violation of parity (P) in beta-decay Lecture 2. Antimatter, and matter-antimatter symmetry. Quark content of hadrons & discrete symmetries of hadrons. Particle- antiparticle mixing. Lecture 3. CP violation in K decay. Difficulties with incorporating CP violation into a physics theory. KM 6-quark model for CP violation. Role of B mesons in the theory Lecture 4. Studying CP violation in the B meson system. Experimental techniques and results. What is left for the future. Lecture 5. Exam**Today**• Definition of symmetry, why they are important. • Symmetries of the laws of nature. • Relation of symmetry and conservation laws. • Discrete symmetries C, P& T.**地标**Beijing’s beautiful landmark**天坛**It is easy to recognize Tian Tan. It looks the same from any direction**富**士 山 Mount Fuji in Japan**Hokusai 1760-1849**24 views of Fuji View 18 View 20**Hiroshige 1797-1858**36 views of Fuji View 4 View 14**Symmetry**If you can change a parameter of a system without making an observable change, the system is “symmetric” with respect to that parameter change**Snowflakes**600 US Postage Stamps Symmetric with respect to rotations of nx60o**Kaleidoscope万花筒**随机 模形 Start with a random pattern 反射 Include a reflection rotate by 450 魅力 The attraction is all in the symmetry Use mirrors to repeat it over & over 对称**对称**自转 Rotational symmetry q1 q2 No matter which way I turn a perfect sphere It looks the same**空间 平移 对称**Space translation symmetry Mid-west corn field**Time-translation symmetry in music**repeat 时间 平移 对称 repeat again & again & again**开普勒**伽利略 Prior to Kepler, Galileo, etc God is perfect, therefore nature must be perfectly symmetric: Planetary orbits must be perfect circles Celestial objects must be perfect spheres 自然必须相称 上帝是完善 星球轨道 完善的圈子 神圣对象 完善的球形**Kepler: planetary orbits are ellipses; not perfect circles**完善的圈子 椭圆 开普勒**Galileo:There are mountains on the Moon; it is not a perfect**sphere! 伽利略 完善的球形**Galileo got into troublefor publishing “the heresy that**the Earth moves.” 异端**The church is wrong?**Galileo on trial by the church (June, 22 1633) Painting by Castiano Banti 1857) Galileo’s discoveries got him arrested**Galileo’s Punishment**取缔 • All his published works were banned • He was kept under “house arrest” from June,1633, until he died in 1642 软禁**25 yrs later (1687):**Dec 25, 1642Isaac Newton is born 牛顿 Isaac Newton’s laws of motion describe gravity & how planets move around the Sun**Newton’s Laws**d2r dt2 Law of motion:: F=ma=m 运动法则 牛顿 • Implicit assumptions: • Same law holds everywhere • Works the same for every direction • Same for all times, past & present 隐含 给定**Newton expected his laws to apply equally well everywhere in**the Universe Newton realized that the same laws that cause apples to fall from trees here on Earth, apply to planets billions of miles away from Earth. 空间 平移 对称 Newton’s laws have space-translation symmetry**Newton’s Laws**d2r dt2 Law of motion:: F=ma=m 牛顿 • Implicit assumptions: • Same law holds everywhere • Works the same for every direction • Same for all times, past & present 隐含 给定 Space translation symmetry 空间 平移 对称**对称**自转 rotational symmetry F=ma a F Same rule for all directions (no “preferred” directions in space.) a Newton’s laws have rotation symmetry F**Newton’s Laws**d2r dt2 Law of motion:: F=ma=m 牛顿 • Implicit assumptions: • Same law holds everywhere • Works the same for every direction • Same for all times, past & present Space translation symmetry 空间 平移 对称 Rotational symmetry 自转 对称**Newton assumed that his laws are valid for all times in the**past, present & future Processes that we see occurring in these distant Galaxies actually happened billions of years ago Deep space exposure from the Hubble Space Telescope 时间 平移 对称 Newton’s laws have time-translation symmetry**圣经**The Bible agrees that nature is time-translation symmetric Ecclesiates 1.9 The thing that hath been, it is that which shall be; and that which is done is that which shall be done: and there is no new thing under the sun 已有的事， 后必再有。 已行的事， 后必再行。 日光之下并 无新事。**Newton’s Laws**d2r dt2 Law of motion:: F=ma=m 运动法则 牛顿 • Implicit assumptions: • Same law holds everywhere • Works the same for every direction • Same for all times, past & present 隐含 给定 Space translation symmetry 空间 平移 对称 Rotational symmetry 自转 对称 Time translation symmetry 时间 平移 对称**恢复了**Symmetry recovered 自然规律 Symmetry is inthe laws of nature, not necessarily in the solutions to these laws. 对自然规律的解决办法**Conservation Laws**守恒定律**动量守恒定律**Conservation of momentum**Conservation of momentum**Initial momentum canoe = 0 boy = 0 Total = 0 final momentum canoe = mcvc boy = mbvb Total = 0**Conservation of angular momentum**角动量守恒定律 Iw L=Iw = constant Iw Iw**诺特**Emmy Noether Symmetry: something that stays the same throughout a process Conserved quantities: things that stay the same throughout a process There must be some relation between symmetry and conservation laws. 1882 - 1935**力学**Review of Lagrangian Mechanics 势能 动能 Potential energy Kinetic energy 运动法则 Law of motion**Lagrangian mechanics**“generalized” force 广义力量 “generalized” momentum: pq 广义动量**“generalized”**momentum Some examples of 广义动量 vx m Linear motion x v r m q angular motion**Rewrite Lagrange Equations**方程 =pq j d dt V qj Pq =- j**Rewrite Lagrange Equations II**d dt V qj V is symmetric to changes in qj Pqj= - d dt V qj if =0: Pqj = 0: Pqj is conserved! Pqj = constant**Noether’s theorem**诺特 定理 If a system is symmetric with respect to changes in a coordinate, the generalized momentum associated with that coordinate is conserved. Symmetry Conservation Law 1882 - 1935**Potential Energy of the solar system**mi ri MQ mj rjk mk**the solar system from far away**• No dependence on R • either magnitude • or direction mi ri R rij Total momentum & Total angular-momentum stays constant Distant observer**Symmetries Conservation laws**Conservation law Symmetry Angular momentum Rotation 角动量守恒定律 自转 对称 Space translation Momentum 动量守恒定律 空间 平移 对称 Time translation Energy 能量守恒定律 时间 平移 对称**Noether’s discovery:**Conservation lawsare a consequence of the (simple and elegant)properties of space and time!**The conservation laws that are “derived”**from Newton’s Laws of Motion do not originate from the details of the laws. Rather, they are a consequence of the “implicit assumptions” that Newton made about their space-time symmetries. Symmetries play a central role in our current understanding of nature**Other symmetries**离散 • Parity • P (x,y,z) (-x,-y,-z) • Charge reversal • C (+,-) (-,+) • Time reversal • T (t - t) 奇偶 “Discrete Symmetries”