Now, is total momentum conserved in an "inelastic collision" between two carts on an air track (in the impulsive collision approximation), or not? There is a "yes" or "no" answer to this question. Do you know what it is? Can you answer this year 11 physics question correctly, or can't you?
For an observer who is isolated with the carts (comoving), and assuming they can ignore a few things, yes. But it isn't true for a remote observer who sees momentum transferred out of the "isolated system".
Let's try, for argument's sake, to connect a pair of carts sticking together on an air track, to two electrons, one in a detector, the other being detected. How does the apparently irreversible change around the electron in the detector, if that's how it gets measured, say the system is isolated?
Momentum is conserved, but kinetic energy is lost when an electron 'hits' a screen. Now there is something you can print copies of; the electron is lost along with an amount of heat it generated, leaving a mark, in a sort of permanent-ink way. You should now, according to Bennet and Landauer, consider what it would take to erase all evidence of this mark having been made.
You already have no possible information in your future concerning the electron that left this mark, . . . in the case of two carts, the analogy is the heat and sound the collision made, these can in principle 'leave a mark' if you can record them, like with electrons.
I should add the obvious, if you're in a lab and you hear two carts colliding, you remember it. For long enough the "mark it left behind" stays coherent; in signal-processing terms.
So say the scenario is, you do the carts on an air track experiment. You finish up and the professor asks you, did you hear a sound when the carts collided inelastically?.
You say, yeah, and he says, then you weren't in the comoving frame, you only saw momentum conserved because in that frame there are only two carts, no air track, and no sound. You can choose which cart to be comoving with, of course, but it doesn't make a difference to what you're constrained to observe.
In short, if you're a cart momentum is always conserved--there are no inelastic collisions, even when you suddenly become two carts. Unless you're the kind of cart who responds to second or higher order effects of a collision.