Kirk and the derelict starship Defiant vanish into a spatial interphase between universes. To rescue him, Spock must maintain position despite a growing, violent hysteria aboard the Enterprise, like that which destroyed the Defiant's crew, as well as a force field being laid around the Enterprise by Tholian patrol ships.
Did You Know?
This is the first time we see Lt. Uhura's quarters in the broadcast order. The first time via production order is in Star Trek: Elaan of Troyius
(1968), when the room was occupied by Elaan, Dolman of Elas, on the way to her wedding. See more
We don't know anything about what Kirk experienced when he was trapped in limbo. It seems as though his ghostly appearance was a way of him trying to break through the barrier to either warn or call for help. When he's seen on the bridge, he is soundlessly mouthing something directly to Spock.
However, all this goes completely unacknowledged by the end of the episode, even by Kirk himself. He somehow knew he was to be declared dead because he mentions the last taped orders. See more
[regarding the development of an antidote
The urgency requires your personal attention in the laboratory.
My staff is working around the clock. My being there will not affect the biochemistry of any of the tests. This service requires my personal attention, Mr. Spock.