Group Theory of Symmetry in Physics Conservation Laws (in Energy, Momentum), Quantum Physics in unifying the 3 (out of 4, except Gravitational) universal Forces.
Tag Archives: Symmetry
The Simple Math Behind Our Expanding Universe
Plant Leaves Symmetry
Mathematician Emmy Noether changed the face of physics
Symmetry, Algebra and the “Monster”
Very good introduction of Modern Math concept “Group” to secondary school math students by an American high school teacher.
Summary:
- Symmetry of a Square
- Isometry (*) or Rigid Motion (刚体运动) = no change in shape and size after a transformation
- What is a Group (群 “CAN I” ) ? = Closure Associative Neutral Inverse
- Monster Group = God ?
- String Theory: Higgs boson (玻色子) aka “God Particles”
Note (*): “保距映射” (Isometry），是指在度量空间 (metric space) 之中保持距离不变的”同构“关系 (Isomorphism) 。几何学中的对应概念是 “全等变换”。
Group is Symmetry
Landau’s book “Symmetry” explains it as follow:
Automorphism = Congruence= 叠合 has
1). Proper 真叠合 (symmetry: left= left, right = right)
2). Improper 非真叠合 (non-symmetry: reflection: left changed to right, vice-versa).
Congruence => preserve size / length
=> Movement 运动 (translation 平移, rotation about O )
= Proper congruence (Symmetry)
In Space S, the Automorphism that preserves the structure of S forms a Group Aut(G).
=> Group Aut(G) describes the Symmetry of Space S.
Hence Group is the language to describe Symmetry.
Positron Symmetry
Positron is the anti-matter of Electron, born by symmetry of universe.
It disappears the moment it is created, to neutralise to nothingness.
Application in medicine: ‘PET‘ scanning (P= Positron).
Positron is smaller than electron, so can scan smaller tumor than CT Scan machine.
Maxwell Equation: Symmetry
Maxwell Equation
Maxwell boldy derived from Faraday experimental results by symmetry to get the Maxwell Equation for Electro-Magnetic Fields:
1) rot E = -1/c ∂H/∂t
div H = 0
By symmetry (swap E <-> H )
2) rot H = +1/c ∂E/∂t
div E = 0
Note:
E = Electric Field
H= Magnetic Field
c = Speed of light
Noether Theorem: Symmetry
Symmetry (hence Group) explains :
1. Conservation of Energy;
2. Conservation of Angular Momentum;
3. Periodic Table;
4. Laws of Thermodynamic.
Emmy Noether Theorem (1918): Conservation Laws owes to Symmetry :
1. In Linear motion
=> Conservation of Momentum
2. In Angular movement
=> Conservation of Angular Momentum
3. In Time
=> Conservation of Energy
Math Online Tom Circle 