A cardboard box is a manipulable object that is light and easy to carry in the Normal Dimension. It becomes as heavy and uncarriable as a safe in the Heavy Dimension and thus can used to activate Mass-to-Electricity converters. It can be blown by fans in the Normal Dimension as with safes in the Fluffy Dimension.
They are also sometimes used to interrupt blue trip lasers. While most objects in Quantum Conundrum are too heavy to carry outside the fluffy dimension, cardboard boxes' ability to be carried normally allow them to be used in conjunction with the Slow Motion Dimension to block trip lasers that don't have a solid surface beneath them to leave the box on.
Additionally some puzzles require the player to use the slow motion dimension to catch cardboard boxes thrown from DOLLIs before they reach a trip laser and trigger something detrimental to the player's progress.
The player can not collide with the cardboard box, as in the player cannot stand on it.