a blind alley
A metaphorical path that leads nowhere; a dead end. After spending years trying to prove his hypothesis but failing to get the results he had hoped for, the physicist feared that he had wasted too much time heading down a blind alley.
blind alley
A dead end; a position without hope of progress or success. For example, That line of questioning led the attorney up yet another blind alley. This term alludes to a street or alley that has no outlet at one end. [Mid-1800s]
blind alley, (up) a
A dead end, either literally (a street or passage with only one entrance) or figuratively (a situation without hope of progress). The term dates from the sixteenth century.