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].
metrictensor said:Time invariance implies conservation of energy. Space invariance implies momentum convervation. What convervation law does the Lorentz invariance imply?
George Jones said:
The conservation law required by the Lorentz Transformations is the conservation of energy and momentum. This means that the total energy and momentum of a system remains constant in all inertial reference frames.
The conservation of energy and momentum is important in the Lorentz Transformations because it is a fundamental principle of physics that helps us understand the behavior of particles and systems in different reference frames. It also helps us make accurate predictions and calculations in relativistic situations.
The conservation of energy and momentum applies to the Lorentz Transformations through the equations for energy and momentum in special relativity. These equations take into account the effects of time dilation and length contraction, ensuring that energy and momentum are conserved in all inertial reference frames.
If the conservation of energy and momentum is not satisfied in the Lorentz Transformations, it would mean that there is a violation of the fundamental laws of conservation in physics. This would indicate a flaw in the calculations or assumptions made, and further analysis would be needed to correct the error.
There are no exceptions to the conservation of energy and momentum in the Lorentz Transformations. This principle holds true in all inertial reference frames, regardless of the relative velocities of the observer and the observed. However, in non-inertial reference frames, such as accelerating frames, the conservation laws may not hold true and additional factors need to be considered.