The world turns quickly in Lincoln Center Theater’s exhilarating production of Tom Stoppard’s “Voyage,” the first installment of his “Coast of Utopia” trilogy about Russian intellectuals in the 19th century dreaming of revolution.

It isn’t simply the industriously employed revolving stage of the Vivian Beaumont Theater, where the play opened last night, that gives the heady sense of an entire culture about to spin off its axis. As directed by Jack O’Brien and performed with freshness and vigor by an immense and starry cast led by Ethan Hawke and Billy Crudup, “Voyage” pulses with the dizzying, spring-green arrogance and anxiety of a new generation moving as fast as it can as it tries to forge a future that erases the past.

The play may have been written by a man in his 60s, and its principal performers are at least into their 30s, yet even more than in its London incarnation at the National Theater, where I saw it four years ago, “Voyage” is paced and defined by the quicksilver changes of mood and conviction that come from being young in a time of flux — by the feeling that everything and nothing is possible. It’s a work infused with the metabolism that lets college students talk furiously until dawn about big thoughts they are sure have never been thought before.