PHY 4460 RELATIVITY

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PHY 4460RELATIVITY

• K Young, Physics Department, CUHK
• ?The Chinese University of Hong Kong

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CHAPTER 1INTRODUCTION
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Objectives

• Physics independent of coordinates
• Rotation of coordinates
• Index notation
• Principle of relativity
• Experimental basis
• Applications

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Physics Independentof Coordinates
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Physics independentof coordinates

• Physics is absolute
• Coordinates are arbitrary

• Physics independent of coordinates

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Coordinate Transformations
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Rotation leads to vectors
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Moving coordinates leads to Special Relativity
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General transformation leads to General Relativity
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Rotation of coordinates

• Linear relationship
• Vectors and matrices
• Rotation matrix

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3D notation
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3D notation
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Coordinates are relative
End point x
Study coordinate transformations
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Index Notation
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Index notation
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Summation convention
Repeated index (dummy) summed over allowed values
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Properties of rotation matrices
Addition theorem for sin, cos
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Addition theorem
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Orthogonal
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Principle of Relativity
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Physical law different observers

• Variables covariant
• Equation invariant
• Depends on linear transformation

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Physical law different observers
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Principle of relativity

• All valid laws of physics should take the same
  form in different coordinates systems invariance
• All terms in valid equation must transform in the
  same way covariance
• How do they transform? scalars, vectors, tensors

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Experimental basis

• SR Michelson-Morley experiment The speed of
  light is the same for all observers
• GR All objects fall at the same
  acceleration in a gravitational field
• Both known to great precision
• Thought to be exact

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Applications
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Applications

• Relativistic kinematics and dynamics
  collisions
• Mass-energy equivalence
• Relation between E M
• Theory of gravity

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Applications

• Astrophysics
• Cosmology
• Global Positioning System (GPS)
• Constraining other laws of physics

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Relativistic kinematics dynamics
Only need to do this once and for all
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Mass-energy equivalence
From relativistic kinematics dynamics, new
concept of E, P, m
Important for nuclear physics high energy
physics
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S
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Gravity

• If ao g, cannot tell apart
• If we understand transformation to an
  accelerating frame, then we understand gravity??

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BUT
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Astrophysics gravity important

• Uniform body
• Compact body

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Universe
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• M fixed

Black hole Schwarzschild radius
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Black hole heuristic derivation
Escape?
Mixture of Newtonian relativistic Not really
legitimate OK for order-of -magnitude estimate
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Global Positioning System (GPS)
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GPS
Accuracy 10 m
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GPS
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Cosmology

• Depends on gravity
• In detail Einstein's theory

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Constraining other laws of physics

• Laws must be invariant
• Limited possibilities

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Objectives

• Physics independent of coordinates
• Rotation of coordinates
• Index notation
• Principle of relativity
• Experimental basis
• Applications

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Acknowledgment

• This project is supported in part by the Hong
  Kong University Grants Committee (UGC) Teaching
  Development Grants (TDG) 3203005 and 3201032
• I thank Prof. S.C.Liew for software
• I thank Prof. M.C.Chu and Dr. S.S.Tong for advice
• I thank Miss H.Y.Shik for design