At absolute zero, gas particles do not completely stop moving; instead, they exhibit behavior consistent with Bose-Einstein Condensates. As the temperature approaches absolute zero, the particles' movement decreases, but due to the Heisenberg Uncertainty Principle (HUP), their positions become less defined, leading to a "smearing out" effect. This means that while their kinetic energy is minimized, they retain a quantum state that prevents them from being completely at rest. The discussion emphasizes the importance of understanding quantum mechanics in relation to temperature and particle behavior. Overall, gas particles at absolute zero still possess motion, albeit in a unique quantum state.