Conservation laws

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Online jeffreyH

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Conservation laws
« on: 28/02/2015 03:57:08 »
Can there ever be a situation in which conservation laws are violated?

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Offline PmbPhy

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Re: Conservation laws
« Reply #1 on: 28/02/2015 04:25:40 »
Not really. If it was possible then it wouldn't be called a law. However there are instances when only part of a system has a conserved quantity. Here are some examples

1) Violation of Conservation of Law of Energy

If there was a mechanical system for which the potential energy was a function of time then the total energy would also be a function of time. E.g.

Let

[tex]V = V(r, t)[/tex]

Then since the total energy E of a system is the sum of potential energy and kinetic energy we have

[tex]E = K + V(r, t)[/tex]

which means that the energy is now a function of time. Since its a function of time its no longer constant meaning its no longer conserved. How can we do this in real life? Simple. We place two large metallic plates very close to each other and parallel to each other. In between the plates we place electrons. We connect the plates to a oscillating electric source where the voltage is stepped up to a high voltage using a transformer (i.e. such as the 60 Hz wall outlet) and place the whole thing in a vacuum. When we plug it into the wall outlet the electrons between the plates will oscillate with the voltage. The energy of the charges will not be conserved.

2) Violation of Conservation of Law of Momentum

If we apply a force to a system of particles then the total momentum of the system will be violated.

3) Violation of Conservation of Law of Charge

Place some charge into a system in which the total charge was zero. The amount of charge will then change. :)

Pretty simple, huh?  [:o)]
« Last Edit: 28/02/2015 04:32:30 by PmbPhy »

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Online jeffreyH

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Re: Conservation laws
« Reply #2 on: 28/02/2015 04:56:32 »
That is the sort of answer that helps clarify things. Thanks. Can you tell that I am reading up on conservation laws and symmetry principles.

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Offline PmbPhy

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Re: Conservation laws
« Reply #3 on: 28/02/2015 05:43:45 »
That is the sort of answer that helps clarify things. Thanks. Can you tell that I am reading up on conservation laws and symmetry principles.
Yep. I saw you post something about Noether's theorem.

There's a great book out that you should pick up called Emmy Noether's Wonderful Theorem by Dwight E. Neuenschwander

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Online jeffreyH

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Re: Conservation laws
« Reply #4 on: 01/03/2015 22:09:49 »
I've ordered the book. A very informative page on Lagrangians and Noether's theory is this.

http://math.ucr.edu/home/baez/noether.html