While exploring the Gamma Quadrant in the Defiant, Sisko, Dax, Bashir, and O'Brien are shocked when a planet appears where none existed before. They are contacted by a woman named Seltin, who invites them to join her people on their world for a meal. During the feast, Seltin explains that the planet, Meridian, shifts between this dimension and another, where they exist as pure consciousness. When they return to this dimension, it is as if no time has passed for them even though decades have gone by in reality. Dax is intrigued by a Meridian named Deral, who explains to her that the periods when his planet exists in this dimension are getting shorter — this time, they will only be visible for 12 days, after which Meridian will shift back into its non-corporeal state for 60 years. Those intervals returning to Dax's dimension will soon be cut to a matter of minutes, after which the planet will become too unstable and simply cease to exist.
Sisko volunteers to help find a way to stabilize Meridian's dimensional shifts. Dax notices a possible anomaly in the sun's fusion cycle, and a probe is sent to investigate. While awaiting the readings, Dax and Deral take a long walk through Meridian's landscape, during which they give in to their growing attraction and kiss.
Dax soon discovers an imbalance in the sun's core is triggering the dimensional shifts. Unfortunately, while it is possible to equalize the time between shifts, it cannot be accomplished before the five days Meridian has left remaining in this dimension. Dax and Deral realize they will not see each other again until his planet returns in 60 years. Unwilling to lose her, Deral decides to leave Meridian and his people in order to go with Dax to the Alpha Quadrant.
Seltin is thrilled to hear that the next time Meridian returns to this dimension, it will remain for 30 years, allowing the group to have families and expand the settlement. But she is less than thrilled with Deral's announcement that he is leaving with Dax. He knows that the small society can't afford to lose a member, but remains determined to be with the woman he loves. Noticing Deral is torn, Dax presents an alternative — having her molecular structure altered in order to survive the dimensional shift. Realizing it's the only way they can be together, Dax decides to do this so she can remain on Meridian with Deral.
As the shift of Meridian begins, Dax's presence interferes with the process, making the planet unable to completely enter the other dimension. Trapped, Dax is left unable to breathe, but is then beamed aboard the Defiant. Sisko informs her that Meridian shifted successfully after her disappearance, letting Dax know that Deral is alive, but lost from her life for the next 60 years.