Indeed, phase symmetry provides conservation of charge. In fact and this is one of the most amazing things in physics, if you demand the system to be invariant under a change of phase everywhere, a symmetry called U(1), you will automatically find electromagnetism! A fundamental force of nature is a consequence of symmetry.
This is the unifying principle of physics as we know it: the Standard Model. Except of course for gravity on one hand and the fact that everything has mass on the other hand (which these symmetries forbid). That is why the search for Higgs boson is so important. It provides a way of breaking symmetries so particles can have mass but still interact with various forces. (The reasons why symmetry forbids massive particles are complicated).
You've piqued my interest here with the linking of symmetry to the fundamental forces and symmetry breaking to the existence of the Higgs boson. Thanks to you and drostie for your intriguing posts.
This is the unifying principle of physics as we know it: the Standard Model. Except of course for gravity on one hand and the fact that everything has mass on the other hand (which these symmetries forbid). That is why the search for Higgs boson is so important. It provides a way of breaking symmetries so particles can have mass but still interact with various forces. (The reasons why symmetry forbids massive particles are complicated).