If one accepts the feasibility of engineering negligible senescence, the benefits of the endeavor depend on when it succeeds. Many of those who would like to benefit from engineered negligible senescence will likely perish before it can be accomplished. There is, however, a potential "safety net" for such individuals, which can be called medical time travel. It is based on one fact and two assumptions. The fact is that at the boiling point of liquid nitrogen, changes in biological systems are generally agreed to be negligible for periods of hundreds to thousands of years. The first assumption is that it is possible to cool a human being to such a temperature without fundamentally destroying the essential information in the brain. The second assumption is that medical and scientific progress will continue until medical resuscitation technology is limited only by physical law. If these assumptions are correct, the memories and personalities of people preserved by today's methods should be intact after revival by future technology, and medical time travel can be used as a bridge to a time in which senescence can be controlled. Based on presently available information, the evidence in support of both assumptions of this proposal appears to be strong.