Patients with schizophrenia have often been considered to be "in their own world". However, this casual observation has not been proven by scientific evidence so far. This can be explained because scientific research has usually addressed cognition related to the processing of external stimuli, but only recently have efforts been made to explain thoughts, images and feelings not directly related to the external environment. This internally directed cognition has been called mind wandering. In this paper, we have explored mind wandering in schizophrenia under the hypothesis that a predominance of mind wandering would be a core dysfunction in this disorder. To this end, we collected verbal reports and measured electrophysiological signals from patients with schizophrenia spectrum disorders and matched healthy controls while they were presented with segments of films. The results showed that mind wandering was more frequent in patients than in controls. This higher frequency of mind wandering did not correlate with deficits in attentional, memory or executive functioning. In addition, mind wandering in patients was characterized by a different pattern of Electroencephalography (EEG) complexity in patients than in controls, leading to the suggestion that mind wandering in schizophrenia could be of a different nature. These findings could have relevant implications for the conceptualization of this severe mental disorder.