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Suppose a hypothetical universe is created with only two objects in it, A and B, of equal mass M, separated by some distance and initially stationary relative to each other. Of course at this point they will start to gravitate towards one another. Let’s suppose that just before they smash into each other B is approaching A with a velocity V. If we use the inertial frame of reference that is the center of mass of the two objects when we do the computation, the total kinetic energy of objects in the hypothetical universe just before they collide is M(V/2)^2/2 + M(V/2)^2/2 = MV^2/4. But if we use A, a non-inertial frame of reference, the total kinetic energy of objects is MV^2/2. How can the difference in the energies be explained? Or, perhaps putting it another way, does the different answer obtained using the non-inertial frame of reference invalidate using it as a frame of reference?

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  • $\begingroup$ Kinetic energy isn't Lorentz-invariant, so it'll be different even between two inertial frames. $\endgroup$ – probably_someone Jul 8 '17 at 7:35
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The first point I need to make is that your use of the word "inertial frame" and "non-inertial frame" isn't quite correct, but I think I see the underlying question.

The response given above is correct - Kinetic energy is reference-frame dependent just like velocity and length are (in relativistic situations such as this).

I'm not sure exactly how to "explain" the difference in kinetic energies. However, most physicists write the difference off as being due to the fact that kinetic energy depends on your reference frame, just like length contraction and time dilation are written off by the fact that time and length are reference-frame dependent.

Hope this helps.

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