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

laws .

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 .