While en route to their planned destination, sensors pick up a lone shuttlecraft drifting through empty space, with no power or fuel reserves. When Worf and Riker use the tractor beam to bring it into the shuttlebay, they find it has the same name (El-Baz, named for Egyptian born geologist and engineer Farouk El-Baz) and registry as the neighboring shuttle. Inside is a double of Captain Picard, barely clinging to life.
After the double is brought to sickbay for treatment, Data and La Forge power up the shuttle, but only after a lengthy period of trial and error. It is then discovered that the shuttle's internal clock is about six hours ahead of the ship's chronometer: this means that the shuttle, and therefore Picard's double, is from six hours into the future. They recover a very poor quality sensor log video that shows the Enterprise falling into an energy vortex and being destroyed.
Dr. Pulaski determines that the incoherent double's biological functions are out of sync, but are improving as the future Picard draws nearer to his own time. Picard orders that his future self be revived, but is unsuccessful in extracting any information from him. Picard is disquieted at the idea that he would abandon his ship and its crew.
As the crew members talk about what they need to do to avoid their destined destruction, they decide simply to let nature take its course. They encounter the vortex, but are unable to move away despite running warp engines at maximum, and only become drawn in further. They send a probe into the vortex which explodes upon impact. Beams emanating from the vortex that scan the Enterprise seem to concentrate on Picard, leading him to understand that his double had left the ship to draw its attention, an unsuccessful maneuver. It is theorized that the vortex may be a form of life.
At this point Picard's double, now almost completely aware and coherent, sets out to escape the Enterprise as he had done before. Picard follows him and attempts to learn the solution to the predicament. The double only mumbles about how impossible the solution is. As the double is boarding the shuttlecraft, Picard proclaims that the cycle will be broken, and fires at him with a phaser. It is not established whether he is dead or merely stunned, but the sound from Dr. Pulaski's tricorder made the flatline sound heard in previous instances when the tricorder scanned dead individuals.
Picard returns to the bridge and orders that the Enterprise fly straight into the center of the vortex; the Enterprise comes through the other side into normal space. The doubles of Picard and the shuttlecraft disappear. The Enterprise resumes its course.