Symmetry and Nature are related on the deepest level . The Conservation
laws of Physics can be derived from considerations of symmetry of
different types . This means that since our Universe has certain kinds
of symmetry THAT IS WHY it has the corresponding kinds of conservation
Law of conservation of linear momentum is related to linear symmetry
or putting it in other words : conservation of p is related to
symmetry about x .
Law of conservation of angular momentum can be derived from
rotational symmetry . conservation of L is due to symmetry of theta.
In other words : since space has no preffered direction and is homogeneous
so it causes these kinds of conservation laws .
Law of conservation of Energy is because all eqns of physics are
same when we add or subtract time from them . conservation of E
is bacause of symmetry wrt t .
Also notice that these conservation,symmetry pairs cannot be measured
at the same time ie the Heisenberg’s uncertainty principle applies
to them .
so u cannot measure x and p at the same time .
u cannot measure E and t at the same time .
All the other conservation laws too are due to some or the other
symmetry . The conservation of charge for example , is related
to something called gauge symmetry .
See how deep symmetry is embedded in the fabric of the universe !!!!!
And that is the end of the Conservation Laws Week .