# What convervation law is required by the Lorentz Transformations

1. Jul 9, 2005

### metrictensor

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

2. Jul 9, 2005

### dextercioby

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

Daniel.

3. Jul 9, 2005

Staff Emeritus
The Lorentz transformations by definition preserve the four-interval $$c^2t^2 - x^2 - y^2 - z^2$$.

4. Jul 9, 2005

### pervect

Staff Emeritus
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.

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

5. Jul 9, 2005

### metrictensor

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.

6. Jul 9, 2005

### George Jones

Staff Emeritus

Regards,
George

7. Jul 9, 2005

### Berislav

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

8. Jul 9, 2005

### dextercioby

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

Daniel.

9. Jul 19, 2005

### yogi

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?

Last edited: Jul 19, 2005
10. Nov 1, 2007

### arivero

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.