To omit from consciousness; shut out of the mind: I can just zone everything out and keep going(1960s+)
The Dictionary of American Slang, Fourth Edition by Barbara Ann Kipfer, PhD. and Robert L. Chapman, Ph.D. Copyright (C) 2007 by HarperCollins Publishers. Cite This Source
Idioms and Phrases with zone out
Stop paying attention, dissociate oneself from a situation. Also, engage in a mindless activity. For example, When Felicia starts talking about her ailments and her friends' ailments, I totally zone out. This idiom also occurs in the passive,
be zoned out. It originally alluded to narcotic intoxication and then was broadened to other kinds of dissociation. For a near synonym, see tune out, def. 2.
[ ; second half of 1900s