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In classical mechanics, a center of mechanical momentum frame can always be found for a system of particles interacting with one another locally. For an electromagnetic system where the charges interact non-locally via the electromagnetic field, a center of total momentum can likewise always be found. I have two questions:

When can a center of mechanical momentum frame exist for an electromagnetic system?

When is this frame also inertial?

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The answer is always. What you should be asking is when is the center of mechanical momentum frame an inertial frame. –  David H Apr 15 '13 at 19:27
    
@DavidH OK, I've added the your suggestion. I would have thought the relativity of simultaneity would make it impossible for it to be generally true. We're summing the non-local mechanical momentum in one frame at the same time, and then boosting to another frame where they're no longer simultaneous. Rather than using the comments here, it might be better if you could answer the question, so we can use the comments under it ;) –  Larry Harson Apr 15 '13 at 21:01

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