Watch closely what is happening when two people cling to each other at the gate, because the physics of it is far stranger than the sadness. No two objects in this universe actually touch. The atoms in her arms and the atoms in his back never make contact; their outer electrons repel each other through the electromagnetic force, so what she feels as a fierce embrace is really that repulsion pushing back, a field standing in for the flesh it will not let her reach.
She has never once touched him. She is feeling a force at arm's length and calling it holding.
Then he walks down the jet bridge, and here the numbers turn merciless. As his plane climbs to cruising altitude and accelerates away, time itself dilates between them, just barely, a few billionths of a second stretched across the flight. When he lands, he will be very slightly younger than he would have been beside her. Not enough to notice. Enough to be true.
And the atoms doing all this waving and weeping, the calcium in the bones of the raised hand, the iron reddening in the blood behind the wet eyes, none of it was made here. Every heavy atom in both of them was forged in the core of a dying star and flung across the galaxy before the Earth existed.
So this is two clouds of ancient stellar debris, briefly assembled into people, generating a repulsive field they mistake for contact, standing in a terminal, unwilling to let the distance grow.
She waves until the plane is a point. The point is already redshifted, its light stretched imperceptibly longer by its motion away from her: the universe's oldest and most literal signature for the word goodbye.