Thread: Conservation of energy - Energy-Momentum Tensor in SI units

1. I've succesfully derived the symmetric Energy-Momentum tensor for electromagnetism in free space in SI units.

However, I find that while my expressions for the energy density etc are correct, I cannot then go on frrm there to derive conservation of energy and momentum. I was wondering if anyone knew which technique to use?

I have been using Classical Electrodynamics by Jackson and have taken his expressions in Guassian units and converted to the SI unit system.

This wikipedia article has the same results which I derived:
http://en.wikipedia.org/wiki/Electro...-energy_tensor

Does anyone have any suggestions as to how to proceed in proving conservation of energy and momentum?

Cheers, sox

2.

3. Originally Posted by sox
I've succesfully derived the symmetric Energy-Momentum tensor for electromagnetism in free space in SI units.

However, I find that while my expressions for the energy density etc are correct, I cannot then go on frrm there to derive conservation of energy and momentum. I was wondering if anyone knew which technique to use?

I have been using Classical Electrodynamics by Jackson and have taken his expressions in Guassian units and converted to the SI unit system.

This wikipedia article has the same results which I derived:
http://en.wikipedia.org/wiki/Electro...-energy_tensor

Does anyone have any suggestions as to how to proceed in proving conservation of energy and momentum?

Cheers, sox
Conservation of energy and momentum can be derived from Noether's theorem and the symmetry associated with time translation (energy conservation) and spatial translation (momentum conversation).

4. Thanks for the response.

I've only managed to have a brief look at the theorem you suggested so haven't actually been able to try and work with it, but I noticed that it works with the Lagrangian.

I've only recently been introduced to the Lagrangian, so if I can prove energy conservation with this theorem, the Prof should be impressed!

Thanks!

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