Symmetry and Conservation
Physics 100
Chapt 7
Temple of heaven (Beijing)
Snowflakes
600
Rotational symmetry
qq2 1
No matter which way I turn a perfect sphere
It looks identical
Space translation symmetry
Mid-west corn field
Timetranslation
symmetry
in music
Time-translation symmetry in the Bible
Ecclesiastes 1.6-7
Prior to Kepler, Galileo, etc
God is perfect, therefore nature must
be perfectly symmetric:
Planetary orbits must be perfect circles
Celestial objects must be perfect
spheres
Kepler: planetary orbits are
ellipses; not perfect circles
Galileo:There are mountains
on the Moon; it is not a
perfect sphere!
Critique of Newton’s Laws
Law of Inertia (1st Law):
only works in inertial reference frames.
Circular
Logic!!
What is an inertial reference frame?:
a frame where the law of inertia works.
Newton’s 2nd Law
F = ma
?????
But what is F?
whatever gives you the
correct value for
ma
Is this a law of nature?
or a definition of force?
But Newton’s laws led us to
discover Conservation Laws!
• Conservation of
Momentum
• Conservation of
Energy
• Conservation of
Angular Momentum
Newton’s laws implicitly assume
that they are valid for all times
in the past, present & future
Processes that we see
occurring in these
distant Galaxies
actually happened
billions of years ago
Newton’s laws have time-translation symmetry
The Bible agrees that nature is
time-translation symmetric
Ecclesiates 1.9
The thing that hath been,
it is that which shall be;
and that which is done
is that which shall be done:
and there is no new thing
under the sun
Newton’s laws are supposed to
apply equally well everywhere in
the Universe
Newton realized that
the same laws that
cause apples to fall
from trees here on
Earth, apply to planets
billions of miles away
from Earth.
Newton’s laws have space-translation symmetry
rotational symmetry
F=ma
F
Same rule for
all directions
a
(no “preferred” directions
in space.)
a
F
Newton’s laws have
rotation symmetry
Symmetry recovered
Symmetry resides in the laws of nature, not
necessarily in the solutions to these laws.
Emmy Noether
Conservation
laws are
consequences
of symmetries
1882 - 1935
Symmetries Conservation laws
Conservation law
Symmetry

Angular momentum
Space translation

Momentum
Time translation

Energy
Rotation
Noether’s discovery:
Conservation laws are a consequence
of the simple and elegant
properties of space and time!
Content of Newton’s laws is in their
symmetry properties
Have a nice weekend
Enjoy the full moon
(& the mid-autumn festival)