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Imagine a reference system where a certain proton is standing still in front of us. We measure its energy and we realize it's very low, so that the strong coupling constant $\alpha_s$ is pretty high and the quarks within necessarily seem to be confined. Consider now a system which is boosted to nearly the speed of light with respect to the previous one. When measuring the energy of the proton from this new system, its energy will seem to be very high, so that $\alpha_s$ will appear very small and one would then think the quarks inside are asymptotically free. How is this possible?

This looks like quite the contradiction to me, and seems to break Lorentz invariance, so that this lead me to think that perhaps what we refer to as energy scale (especially in the context of running coupling constants) is not just the energy of a system from a certain reference frame, but actually a Lorentz invariant quantity that is somehow related to it. Is this actually the case?

SeedHeartA
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This is effectively the same as Why am I not burned by a strong wind? In both cases what matters is the internal energy of the system not the translational energy of its centre of mass.

For elementary particles what matters is their kinetic energies in the centre of mass frame. For a single proton the COM frame is just the rest frame of the proton and in this frame the KE of the proton is zero. However if we consider two protons colliding in the Large Hadron Collider the rest frame is stationary (because the protons have equal and opposite velocities) but the total kinetic energy is $14~\mathrm{TeV}$.

John Rennie
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