In terms of experimental design I don't think you would be able to design an experiment to prove the information processing theory is correct, at most you would only be able to prove that the information processing theory is *not incorrect*.
Since the theory hinges on the operation of three different components, the sensory register, short-tem memory and long-term memory, you would have to 'test' whether actual mental behaviour is consistent with the predictions of the theory, i.e. information passes from the sensory register to short term memory and from short term memory to long term memory and from long term memory to short term memory.
