Time is a curious dimension. Although we might be still in space, there’s no way for us to be still in time. And while we can explore every direction in space, time has a preferred direction: forward. We are constantly traveling through time, and for us we are going to the boring velocity of 1 second per second, but for an external observer who’s not moving at all we are traveling faster than that.
Our planet spins around the Sun, and the Sun moves around the centre of the Milky Way which in turn moves around in the Local Group (the name of the family of galaxies we belong to). Although these velocities are modest compared to the speed of light, time on earth is a fraction of a second (of the order of the million of a second) slower than in intergalactic space.
Traveling back to the future is easy. You need to be traveling fast. Very fast. If you want to jump an hour into the future, going at half the speed of light, it will take you 45 minutes. Although the technology to produce high velocities belongs in a somewhat distant future, they are perfectly allowed by what we know of the laws of nature.
Going back in time is the issue.
Past & Paradoxes
Time is a fearsome beast. Unmoved and unchanged no matter our powers and wishes. It remains almost inscrutable to us and yet we see its actions every instant.
According to most laws of physics, time should behave just like any other spatial dimension. But our experience is quite different. Time has a direction. And we can’t move through time like we move through space. This issue causes the fervor people have towards traveling to the past. Is it possible? Can we change things?
As far as we can tell, time travel towards the past doesn’t violate any conservation law. The universe, we believe is an isolated system. The fact that we haven’t found a fundamental law that says no to time travel, doesn’t imply that time travel is allowed. We know that we cannot accelerate past the speed of light, so traveling through time simply by going incredibly fast doesn’t work. Could there be another way? Mathematically speaking, there’s actually an allowed time traveling scenario:
Inside a black hole, time and space switch places. Space has only one direction (towards the singularity) while time can be navigated like our space. Within those event horizons, there are orbits that will take you on a closed time loop, making you encounter yourself; that’s if you’d been able to survive the gravitational force.
The other mathematical curiosity is a wormhole. A wormhole is a perfectly valid solution to the laws of general relativity, and it can connect points in space and time. Although wormholes are an unstable solution of Einstein’s equation, they are still valid. Their stability depends exclusively on the presence of negative energy. There are no known physical mechanisms that can produce negative energy, but there are a few theoretical ones (exotic matter, quantum foam, local variations of the zero-point energy). So we could create stable wormholes, unless there’s an as yet undiscovered limitation to time travel.
So if we could time travel, what about paradoxes? Could you kill your parents and survive? Change history? I’m not certain. What I know is that for every symmetric change in the universe there’s a conservation law. Symmetry in space, time, and under rotation correspond to the conservation of momentum, energy, and angular momentum. So, it wouldn’t be surprising if there’s a conservation of continuity. A set of laws that give a precise structure to time travel.
Unfortunately, until we find a physical time traveling mechanism, police boxes are just phone boxes, and DeLoreans are just cars.