Seriously the possibility of time travel is being investigated. They are trying to take advantage of quirks in the the quantised nature of SpaceTime to get information about events that will happen in the very close future.
This would be the first tiney step in any pursuit of Time travel. However it is also clear that any sustained movement though Time at any speed other than that to which we are accustomed requires a vast amount of energy.
The conservation of energy law is the bottom line and the kind of time travel machine of our imaginations would require a heavy diet of supernovas t power it.
presumably if time travel was possible in the future it'd be possible now? As our grandchildren would be returning to show us how. Or would it only be possible to travel forward? (Which, as Graham-W points out, we're doing already.)