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Time invariance implies conservation of energy. Space invariance implies momentum convervation. What convervation law does the Lorentz invariance imply?
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 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:The Lorentz transformations by definition preserve the four-interval [tex]c^2t^2 - x^2 - y^2 - z^2[/tex].
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?
It is a funny answer... the position of the center of mass? Ok, in absence of external forces, the center of mass is a preserved quantity, so it makes sense, or sort of.