Vacillating time: a metaphysics for time travel and Geachianism

'Past vacillators' believe that what was once the case may change over time. This has obvious applications to the possibility of changing the past via time travel. 'Future vacillators' believe that some things will happen and yet, later, will not. Further to issues in time travel, future vacillation has applications when it comes to 'Geachian' views about the open future. This paper argues that if you deny that the 'earlier than' and 'later than' relations are converses of one another then you can develop metaphysical systems underpinning the possibility of such vacillation.