# conservation laws

Discussion in 'Physics & Math' started by ecclesiastes, May 2, 2006.

1. ### ecclesiastesRegistered Senior Member

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82
how exactly did they arrive at the conservation laws? say,conservation of mass-energy for instance...
(i did read about how one arrives at the conservation of strangeness while doing elementary particles but thats evaporated).
so someone give me an explanation for conservation of mass energy.please?

3. ### DaleSpamTANSTAAFLRegistered Senior Member

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1,723
Most of the classical conservation laws stem directly from Newton's laws. E.g. momentum is equal to the integral of the force over time. Using that fact and Newton's 3rd law we see that any time the "action" object has a momentum change the "reaction" object has an equal and opposite momentum change. Therefore momentum is conserved. I think that the relativistic conservation of four-momentum is derived the same way and, conveniently, automatically includes the classical conservation of mass and energy.

-Dale

5. ### Tom2Registered Senior Member

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726
Noether's theorem states that for every symmetry of a physical system there is a corresponding conserved current.

Examples:

* Invariance under translation implies conservation of momentum.
* Invariance under time translation implies conservation of energy.
* Invariance under rotation implies conservation of angular momentum.

I take it that by "mass energy" you are referring to the rest energy E=mc<sup>2</sup> from Special Relativity. If that's the case then that quantity isn't conserved in general. You can see this by studying electron-positron annihilation, for example. But energy--and even more generally 4-momentum--is conserved. Noether's theorem covers relativistic physics, too.