When cats look like they are staring at nothing, they are most likely responding to something that they see, hear, feel or smell that is not apparent or cannot be sensed by a watching human. Cats perceive objects through sight in much lower light intensity than humans.
Cats are much better than humans at noticing very slight movements. When a cat appears to be staring at nothing, it may actually have noticed movement not apparent to its owner because of low lighting or minimal movement by a small object.
Cats may also stare at an area where they can perceive a sound, even though they may not have seen anything. Cats can hear higher pitched noises than humans. Additionally, they can better hear and locate sounds than humans. If a cat is staring at an area, it may actually be focusing its ears to hear a sound imperceptible to its owner.
Cats have a more sensitive nose than humans. When it pivots its head to look at something, it may be because it smelled something interesting in that direction.
A cat may also be sensing movement through vibrations through its whiskers. If the cat perceives an object moving, it may then turn to its eyes, ears or nose to better identify the source of the movement.