Symmetries in the Physical Laws

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SP2171 Lecture
Symmetries in the Physical Laws
Kuldip Singh
15 February 2002
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An operational definition
Herman Weyl (1885-1955)
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Operations and Symmetry Operations
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Symmetry Transformation
Combination of transformation is also a
transformation
Identity transformation
Inverse transformation
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noncommutative
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I want to know how God created this world. I am
not interested in this or that phenomenon, in
the spectrum of this or that element. I want to
know His thoughts,the rest are details.
A.Einstein.

• Symmetry operations in Physical Laws
• Translation in space
• Translation in time
• Rotation through a fixed angle
• Uniform velocity (Lorentz transformations)
• Reversal of time
• Reflection in space
• Charge conjugation (matter-antimatter)
• Quantum mechanical phase
• (gauge symmetry)

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Reference Frames
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Translational Invariance
Newtons law is the same in both frames
Isaac Newton (1643-1727)
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Rotational Invariance
The components of the force transforms as
Newtons law is the same in both frames
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Galilean Relativity Principle
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Covariance of Physical Laws
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Length Invariance under Galilean Transformations
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Time-interval Invariance under Galilean
Transformations
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Addition of Velocities
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Noethers Theorem If a system has a continuous
symmetry property, There are corresponding
quantities whose values are conserved in time.
Symmetry under spatial translations
Momentum Conservation
Energy Conservation
Symmetry under time translations
Angular momentum Conservation
Symmetry under rotations
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