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All the visual explanations I know work in some kind of "If you are moving relative to something A, while inside A something is moving, the stuff in A has to move slower due time dilation and therefore the mass has to increase so the impact(and momentum) stays the same."

Since all moving objects and not only the ones inside of moving objects have their mass increased I have big trouble understanding why these kind of pictures should lead to any understanding.

Could I argue that if A was moving his whole point-of-view would be moving?
As if everything already would be inside of something moving?
This sounds very wrong and just raises more questions in my head.
You could simply determine who was moving if that would be true, so it isn't.
Or is it?

I don't know where my thoughts got messed up. Hopefully you do.

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If you describe it in such a vague way, it's going to be confusing of course.

There are two reference frames, say A and B. The reference frames are moving with respect to each other. The same phenomon X is described from the point of view of each reference frame. X might be a rocket travelling from some point to another. Clearly, X is a moving object. The only reference frame in which X would not be moving, would be a reference frame that is comoving with X.

Relativity says that some aspects of phenomenon X will be frame-dependent, like the speed of X. While others, will not be. For instance the rest mass of X is an invariant.

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Mostly I don't understand how to explain why mass increases in an example like yours. In the Feynman Lectures it is explained with 2 balls colliding at some angle, but not zero. While viewed from someone moving relatively to them. But since they are not inside a moving object they can't be slowed down? Or are objects slowed down if viewed by someone moving relatively to them? I always thought only the moving time inside the moving object would be slowed down. Not the speed it travels at. I seem to be quite confusing, but I'm quit confused myself. I'm sorry for that. – Fabian Gerhardt Mar 4 '12 at 13:42
Mass doesn't change, it's one of the invariants of the theory. However, in older expositions of relativity, it was customary to introduce a concept of "relativistic mass", which would depend on speed. (Formula: $m=\frac{m_0}{\sqrt{1-v^2/c^2}}$ ) This terminology has been largely abandoned I think. Maybe you should post the exact chapter of the Feynman lectures you are refering to in your question. We could then address this. – Raskolnikov Mar 4 '12 at 14:07
It's chapter 16.4 of the volume mechanics, radiation, and heat. I have the german "definitve edition" 5. edition if that matters. I didn't know it would be that outdated. But I still think the stuff he said there should make sense somehow. Maybe looking into the chapter can help you understand me. To repeat my problem. I think the vertical witch is mentioned in the chapter, shouldn't be changed by horizontal movement. But maybe I misunderstood everything. – Fabian Gerhardt Mar 4 '12 at 14:51

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