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By the "absolute center of mass" I mean the center of all the matter that exists in a given moment. My friend asserted that today and it intrigued us very much but since we only have a CS degree and not very well versed in modern physics we couldn't be sure about that claim.

It is based on the observation that; the total momentum of a given system never changes. Am example; considering a hypothetical situation where an astronaut is floating in the space, to change his speed, he needs to push an object against the direction he wants to move. He gains as much momentum as the object gains in the opposite direction, net momentum is zero and center of mass doesn't changes.

Applying this principle to the beginning of our universe, we arrive to the aforementioned conclusion. Is this true? If not, why?

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Well, I would say no. Why?

Because an absolute center of mass would require a uniform covering (coordinate system) over the whole manifold, which, even if it exists, will probably not be on the manifold itself.

An analogy would be the center of mass of a spherical surface/manifold. It would be exactly on the center of the sphere (i.e not on the sphere surface/manifold).

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