For a given set of fast-moving objects in empty space, the maximum mass-energy t

Question

For a given set of fast-moving objects in empty space, the maximum mass-energy that can be extracted by using only interactions between objects in the set (e.g., colliding all of them together) is identical to the relativistic mass-energy that an observer would see when residing in the center-of-mass inertial frame for that set. (You can trust me on that or prove it yourself; it's not difficult.)

This is why a proton colliding with earth at ?=10 velocity does not cause a catastrophic release of ten earth's worth of energy. Since the mass of the proton is entirely negligible in comparison to the earth, the mass-energy available by colliding all objects in the set {earth, proton} is very close to the mass of earth plus ten times the mass of the proton.

Thus for any set of objects that are isolated in space, the center-of-mass inertial frame is the only special relativity frame for which the observed mass-energy of all parts is identical to the available mass-energy. More energy can of course be extracted, but only by bringing in objects that were not in the original set. The center-of-mass inertial frame thus is both "distinguished" and unique with respect to that set of objects (only).

Now here's the fun part: Define the set to include all objects in the universe. Since you have just placed all your eggs in one basket, so to speak, there are no longer any objects to bring in from outside to alter the result, even in principle. Next, calculate for "distinguished" inertial frame for this set. (For a pretty good guess, try the CMB.)

My question is this: Doesn't the above argument imply that under the rules of special relativity the universe really does have a single, unique, and non-trivially distinguished inertial frame, that being its center-of-mass inertial frame?

Addendum 2012-05-30.20:220 EST

Angular momentum

I skipped over angular momentum in defining the set of objects used to define the minimum energy SR frame. Unlike linear momentum, residual angular momentum in a set of object of course cannot be resolved simply by resetting the frame. Always interesting, angular momentum, since if it exists it necessarily "points" to additional matter that exists outside the current set, at least if you believe in absolute universal conservation of it (which I certainly do). Its energy can be quantified locally, though.

"Center of mass" in curved spaces

@Lubo

Explanation / Answer

It's true that the CM frame of a set of objects is distinguished with respect to that set of objects. But that doesn't qualify it as a preferred rest frame, as far as special (or, locally, general) relativity is concerned. After all, the laws of physics will still hold just as well whether you're in the CM frame of any particular set of objects or not. So there's no contradiction with relativity there.

This is kind of like a case of spontaneous symmetry breaking, in fact. The theory itself works the same no matter which reference frame you're in, but the system that the theory applies to does look different from different reference frames. So the system "spontaneously" selects a particular "natural" reference frame, the CM frame, for you.

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