Old Twentieth by Joe Haldeman

The twentieth century lies hundreds of years in humanity’s past. But the near-immortal citizens of the future yearn for the good old days—when people’s bodies were susceptible to death through disease and old age. Now, they immerse themselves in virtual reality time machines to explore the life-to-death arc that defined existence so long ago. Jacob Brewer is a virtual reality engineer, overseeing the time machine’s operation aboard the starship Aspera. But on the thousand-year voyage to Beta Hydrii, the eight-hundred member crew gets more reality than they expect when people entering the machine start to die.