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## Main Question or Discussion Point

Time invariance implies conservation of energy. Space invariance implies momentum convervation. What convervation law does the Lorentz invariance imply?

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Time invariance implies conservation of energy. Space invariance implies momentum convervation. What convervation law does the Lorentz invariance imply?

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Angular momentum. Immediate by Noether's theorem for classical fields.

Daniel.

Daniel.

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selfAdjoint

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Conservation of angular momentum is generated by spatatial rotation invariance. Space rotation invariance is indeed part of the Lorentz group. But I suspect the original poster was interested in the symmetries related to the Lorentz boost, not by the spatial rotation part of the Lorentz group.dextercioby said:Angular momentum. Immediate by Noether's theorem for classical fields.

Daniel.

I seem to recall that this question was discussed before, but I don't recall the conclusion that we came to.

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I was thinking the same thing but there are many 4-vector invariants in SR. Energy-momentum, space-time. The classical conservation laws have one specific quantity conservered not a variety.selfAdjoint said:

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George Jones

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Read the stuff here.metrictensor said:Time invariance implies conservation of energy. Space invariance implies momentum convervation. What convervation law does the Lorentz invariance imply?

Regards,

George

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Thinking by analogy, shouldn't it imply conservation of the stress-energy tensor?

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Nope, stress- energy tensor is linked to space-time translations.

Daniel.

Daniel.

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This should be a straightforward question with an obvious answer - but authors seem to skirt the issue

spatial displacement symmetry - conservation of momentum

temporal displacement symmetry - conservation of energy

isotropic symmetry - conservation of angular momentum

When gauge symmetry is applied to Maxwells's em equations, one consequence is conservation of charge - isn't conservation (invariance) of the spacetime interval also consequent to gauge symmetry?

spatial displacement symmetry - conservation of momentum

temporal displacement symmetry - conservation of energy

isotropic symmetry - conservation of angular momentum

When gauge symmetry is applied to Maxwells's em equations, one consequence is conservation of charge - isn't conservation (invariance) of the spacetime interval also consequent to gauge symmetry?

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arivero

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