Day 5: Conservation Laws and Symmetry

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 . 

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