Time travel

The idea that space and time are similar suggests that it might be possible to move backwards and forwards in time just like it is possible to move backwards and forwards in space. And indeed in the partial differential equations that define general relativity, it is formally possible for the motion of particles to achieve this, at least when there is sufficient negative energy density from matter or a cosmological constant. But even in this case there is no real progression in which one travels backwards in time. Instead, the possibility of motion that leads to earlier times simply implies a requirement of consistency between behavior at earlier and later times.