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Conservation and Symmetry 
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#1
Jul3110, 04:38 AM

P: 396

We say that conservation of linear momentum follows from the translational symmetry while conservation of angular momentum from directional (rotational) symmetry. Can anyone explain what exactly do we mean by these kind of symmetries and how they imply conservation of certain quantities?



#2
Jul3110, 11:36 AM

P: 239




#3
Jul3110, 12:56 PM

PF Gold
P: 691

There is a correspondence: when there is a symmetry in the theory then there is a correspondong conserved entity in that theory. For instance, given the definition of kinetic energy there is a correspondence between conservation of kinetic energy and symmetry with respect to time translation. So if you're curious whether some attempt at formulating a new theory will lead to a theory that implies conservation of energy it suffices to figure out whether the theory is symmetrical with respect to time translation. Our theories of motion have in common that for any system going through its motions (for example the solar system) the orientation in space is not a factor; there is no dependence on orientation; there is symmetry under shifts of orientation. According to the theorem there must be a corresponding conserved entity, and as we know that's angular momentum. In any derivation of conservation of angular momentum from the laws of motion the independence on orientation in space is part of it. For example, there is Newton's derivation of Kepler's law of areas from the laws of motion. Among the elements used there is the fact that the same reasoning applies for all orientations in space. 


#4
Jul3110, 01:25 PM

Mentor
P: 41,302

Conservation and Symmetry



#5
Jul3110, 11:51 PM

P: 239

t = FRsin = Iα 


#6
Aug110, 03:05 AM

P: 396

From Wikipedia Noether's theorem it states that the theorem doesnt hold for systems that can not be modeled with a Lagrangian. Isnt it possible that these systems can be modelled with some other way which still has some symmetry with time or space? 


#7
Aug110, 06:02 AM

Sci Advisor
PF Gold
P: 1,841




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