# Is momentum conserved in all inertial frames?

1. Nov 4, 2005

### MichaelW24

and is the momentum of a particle the same in all inertial frames?

Thanks for any help

2. Nov 4, 2005

### pervect

Staff Emeritus
In the context of special relativity, the momentum of a particle or a system of particles is conserved in any inertial frame. (Frames that include gravity sources would not be inertial by defintion).

The momentum of a particle however is not the same in all inertial frames, the momentum is obviously dependent on the velocity of the particle, and the velocity of the particle depends on the choice of the frame.

3. Nov 4, 2005

### pmb_phy

If the particles interact through fields then there is momentum transferred into the fields. In that case its the the total momentum of particles + field that is conserved.

Pete

4. Nov 4, 2005

### pervect

Staff Emeritus
Yep, good point.

5. Nov 4, 2005

### masudr

In fact, (in classical field theory) we normally say a system is "sufficiently isolated" when the Lagrangian of a system is transationally invariant, and so gives rise to a conserved canonical energy-momentum tensor (i.e. implying total momentum and energy is conserved).

6. Nov 4, 2005

### MichaelW24

sorry, I am specifically talking anout special relativity; my lecture notes say that momentum must be conserved but I dont understand why this is nessecary to validate the first postulate, can somebody explainm why if momentum isnt conserved them the first postulate is invaudatted?

Thank you very much again for your help!
Micahel.

7. Nov 4, 2005

Staff Emeritus

Postulate I says physics is the same in all inertial frames.

My rest frame is an inertial frame.

That moomentum conservation is true is part of the physics in my rest frame.

Therefore momentum conservation is true in all inertial frames.