A Brief Review of Special Relativity

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A Brief Review of Special Relativity

• Jian Wu
• Dec. 2, 2004

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OUTLINE

• Basic Principles of Special Relativity
• Mathematical Forms
• Four Vectors
• Tensor
• Application in Electromagnetic Field and Its
  Physics Interpretations

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Basic Principles of Special Relativity

• Galilean Transformation
• Two Hypotheses (1905)
• Relativistic Principle
• Invariance of light speed

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Basic Principles of Special Relativity

• Lorentz Transformation
• Time and Space are correlated
• Time and Space are symmetric
• Inverse transformation (v ?-v)

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Basic Principles of Special Relativity

• Lorentz Transformation

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Basic Principles of Special Relativity

• Useful Deductions
• Time Dilation (Same Position)
• ?t ? ?t
• Length Contraction (Same Time)
• ?x ?x / ?
• Beaming Effect (u c)
• ?? 1 / ?

• Aberration of Light (? p / 2)
• cos ? v / c
• Doppler Effect
• ? ? ? (1 v cos?)
• Acceleration (u 0)
• a ?3 a
• ap ?2 ap

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Mathematical Forms

• Four Vectors and Tensors

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Mathematical Forms

• Useful Four-Vectors

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Mathematical Forms

• Useful Tensors

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Mathematical Forms

• Functions of ?µ?, ?µ? and dµ?

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Mathematical Forms

• Tensor Analysis

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Mathematical Forms

• Lorentz Invariants

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Application in Electromagnetic Field

• Four-current

• Four-potential

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Application in Electromagnetic Field

• Electromagnetic Tensor

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Application in Electromagnetic Field

• Covariance of Electrodynamics
• Invariance of Maxwells Equations by
  transformation between inertial frames
• Tensors are Lorentz covariance

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Application in Electromagnetic Field

• Electromagnetic Tensor

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Application in Electromagnetic Field

• An Example

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A Brief Review of Special Relativity
THE END