Symmetries in the Physical Laws

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SPS SYMPOSIUM 1
Symmetries in the Physical Laws
Kuldip Singh
9 January 2001
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An operational definition
Herman Weyl (1885-1955)
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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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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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Relativistic Invariance The basic laws of
physics are identical in all reference
systems which move with uniform (unaccelerated)
velocity with respect to one another.
It is physically impossible to tell which one of
two observers in relative motion at constant
velocity is actually moving.
Galilean Transformations
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Wave Nature of light
Maxwells Equations in free space
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1. The laws of physics are identical to all
uniformly moving observers. 2. The velocity of
light in the vacuum, c, is independent of
the motion of the source and the motion of
the observer.
? Galilean Transformations need revision!
Joes frame
Moes frame
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Lorentz Transformations

• Implications
• Length Contraction
• Time Dilation
• Energy-mass Equivalence

H.A. Lorentz (1853-1928)
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Law of Reflection Angle of incidence angle of
reflection
Snell (1580-1626)
Law of Refraction
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Fermats Principle The actual path taken light
from source S to an observer O is among all
geometrically possible paths the one
corresponding to the shortest travelling time.
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Lagranges action principle
Variational Principle
(Equations of motion)
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A physicist dream of writing down the design of
the universe on a piece of napkin. .adapted from
Fearful Symmetry by A. Zee
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Noethers Theorem To every continuous symmetry
in the action there results a conserved quantity.
Symmetry under spatial translations
Momentum Conservation
Energy Conservation
Symmetry under time translations
Angular momentum Conservation
Symmetry under rotations
Symmetry under gauge transformations
Charge Conservation
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Quantum Mechanics Special Relativity Diracs
Equation
(1929)
Twice as many solutions as Schrodingers
equation
Diracs Equation
Solutions (particles antiparticles )
This new solutions (antiparticles) admitted had
opposite charges. (Charge Conjugation)
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1. Fearful Symmetry by A. Zee, Princeton
University Press 2. Six Not-so-easy Pieces by
R.P. Feynman, Perseus Books 3. Symmetry
Discovered by Joe Rosen, Dover Publications 4.
Symmetry by Hermann Weyl, Princeton University
Press
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http//sps.nus.edu.sg/kuldip/