Symmetry and Symmetry Violation in Particle Physics Who

Symmetry and Symmetry Violation 对称 in Particle Physics 违反

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. Particleantiparticle 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 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 . n n a io T t n c a e i r i T d e y z i n n a g o m c o e r r f o e t m y a s s a e e h s t i It ooks l t I

Mount Fuji in Japan 富 士 山

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 US Postage Stamps 600 Symmetric with respect to rotations of nx 60 o

Kaleidoscope万花筒 随机 模形 Start with a random pattern 反射 Include a reflection te 0 a t ro 45 by 魅力 Use mirrors to repeat it over & over The attraction is all in the symmetry 对称

自转 对称 Rotational symmetry qq 2 1 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

Timetranslation symmetry r 时间 平移 对称 in music in a g a t a pe re t a e p e & in a g a

开普勒 伽利略 Prior to Kepler, Galileo, etc 上帝是完善 自然必须相称 God is perfect, therefore nature must be perfectly symmetric: 星球轨道 完善的圈子 Planetary orbits must be perfect circles 神圣对象 Celestial objects must be perfect spheres 完善的球形

Kepler: planetary orbits are ellipses; not perfect circles 椭圆 开普勒 完善的圈子

Galileo: There are mountains 伽利略 on the Moon; it is not a perfect sphere! 完善的球形

Galileo got into trouble 异端 for publishing “the heresy that the Earth moves. ”

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 软禁 • He was kept under “house arrest” from June, 1633, until he died in 1642

Dec 25, 1642 25 yrs later (1687): Isaac Newton is born 牛顿 Isaac Newton’s laws of motion describe gravity & how planets move around the Sun

Newton’s Law of motion: : 牛顿 运动法则 2 r d F=ma=m 2 dt Implicit assumptions: 隐含 给定 • Same law holds everywhere • Works the same for every direction • Same for all times, past & present

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 Law of motion: : 牛顿 2 r d F=ma=m 2 dt Implicit assumptions: 隐含 给定 • Same law holds everywhere Space translation symmetry 空间 平移 对称 • Works the same for every direction • Same for all times, past & present

对称 自转 rotational symmetry F=ma F Same rule for all directions a (no “preferred” directions in space. ) a F Newton’s laws have rotation symmetry

Newton’s Law of motion: : 牛顿 2 r d F=ma=m 2 dt Implicit assumptions: • Same law holds everywhere Space translation symmetry 空间 平移 对称 • Works the same for every direction Rotational symmetry 对称 自转 • Same for all times, past & present

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; 已有的事， 后必再有。 and that which is done is that which shall be done: 已行的事， 后必再行。 and there is no new thing under the sun 日光之下并 无新事。

Newton’s Law of motion: : 牛顿 运动法则 2 r d F=ma=m 2 dt Implicit assumptions: 隐含 给定 • Same law holds everywhere Space translation symmetry 空间 平移 对称 • Works the same for every direction Rotational symmetry 对称 自转 • Same for all times, past & present Time translation symmetry 时间 平移 对称

恢复了 Symmetry recovered 自然规律 Symmetry is in the 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 I L=Iw = constant w Iw

Conservation of angular momentum Iw I w

Emmy Noether 诺特 Symmetry: Conserved There must be something that quantities: relation between stays the same things that symmetry and throughout a stay the same conservation laws. process throughout a process 1882 - 1935

力学 Review of Lagrangian Mechanics gy 能 r 动 ne e c i t e n i K 势能 al e ti n ote gy r ne P Law of motion 运动法则

Lagrangian mechanics “generalized” force 广义力量 “generalized” momentum: pq 广义动量

Some examples of Linear motion vx m x v angular motion r q m “generalized” momentum 广义动量

Rewrite Lagrange Equations 方程 =p q j d Pq = j dt V q

Rewrite Lagrange Equations II V is to c ri j et q m in m s sy ge an ch d V P qj = dt qj if =0: V q j. P qj d Pqj = 0: dt = constant P qj is d! e v r e cons

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 on R e c n e d n No depe tude i n g a m r • eithe n o i t c e r i d • or mi R Distant observer ri rij Total momentum & Total angular-momentum stays constant

Symmetries Conservation laws Conservation law Symmetry Rotation 自转 角动量守恒定律 对称 Space translation 时间 平移 对称 Momentum 动量守恒定律 空间 平移 对称 Time translation Angular momentum Energy 能量守恒定律

Noether’s discovery: Conservation laws are 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 “Discrete Symmetries” 离散 奇偶 • Parity • P (x, y, z) (-x, -y, -z) • Charge reversal • C (+, -) (-, +) • Time reversal • T (t - t)

Gravity is Parity symmetric P : change: xi - xi yi -yi and zi -zi (for i, j &k) xi 2 (-xi)2 xi 2 then: ri (xj -xk)2 (-xi +xk )2 (xj-xk)2 and rjk unchanged V is unchanged parity symmetry

Parity transformation y z x y -y z -z x’ z’ y’

Left – right handed coord systems

Man holds razor in right hand Image holds razor in left hand Man P Man

Parity: left right y Left handed system z x Right handed system y -x y -y z -z x’ z’ y’

threads 传统 image By convention, engineers Mirror usually only use Right-handed threads, although Left-handed ones would function just as well. Right handed thread left handed thread

Sometimes they need both Turn one way F -F Left thread Right thread

Basketball rules have parity symmetry Yao’s right-handed “hook” shot is legal So is his left-handed “hook” shot

Basketball Left-Right symmetric An example Basketball strategy If this is allowed so is this

Baseball rules violate Parity 3 rd Base batter pitcher 2 nd Base 1 st Base When the batter hits the ball, he runs to 1 st base (not 3 rd)

Allowed forbidden

Not Left-right symmetric Only right-handed people can play these positions

Parity in Quantum Mechanics 量子力学 Wave function: y(x, y, z) P 波函数 y(x, y, z) = y(-x, -y, -z) P 2 y(x, y, z) = P y(-x, -y, -z) P 2 y(x, y, z) P P = y(x, y, z) = +1 y(x, y, z) 2 = I 特征值 恒等式 算子 ”identity” operator eigenvalues = ± 1

Parity in Quantum Mechanics Even Wave function 偶波函数 Y(x) Parity: P Y(x) Y(-x) = +1 Y(x) “even parity state”

Y(x) changes but parity stays even 偶

Odd Parity Odd wave function 奇波函数 Y(x) Parity: P Y(x) Y(-x) = -1 Y(x) “odd parity state”

Y(x) changes but parity stays odd 奇 If V(x) = V(-x), parity is conserved Left-right symmetry conservation law

Multi-electron atom - - +Z - - - ri rjk - Construct the Potential energy

Charge reversal symmetry + + + -Z + + C: + ; + ri + + rjk + V remains the same! “Charge-reversal symmetry”

Charge reversal operator 电荷 反转 算子 C (+, -) (-, +) C 2 (+, -) = C (-, +)= (+, -) C 2(+, -) = +1 (+, -) C 2 = I 恒等式 ”identity” operator C eigenvalues = ± 1 特征值

Time reversal symmetry Newtons’s law t -t Charged particle In an Electric-field t -t no change Time reversal symmetry

t -t with a magnetic field t - t : different?

B-fields are produced by electric currents Electro-magnetic force: t - t symmetric

Lecture 1 Summary • Symmetries are an important aspect of nature. • Laws of nature are rotation, spacetranslation & time-translation symmetric. • Symmetries imply conservation laws – Rotation symm conserv. of angular momentum – Space trans. symm. conserv. of momentum – Time transl. symm conserv. of energy

Lecture 1 Summary (cont’d) • Classical physics also has discrete symmetries: – Parity (Left-right) symmetry (x, y, z) (-x, -y, -z) – Charge reversal symmetry (+ -) – Time reversal symmetry (t -t )