Is time travel possible?

The answer laid out by Professor John D Norton of Pittsburgh University (more here):

Is time travel possible?

YES

The "yes" is intriguing, but there is a catch. The question did not ask if there really is time travel; it asked only if it is possible. Something can be possible without actually happening. It is possible for our earth to have two moons. In fact it has only one.

While we have no evidence that time travel actually occurs, all our latest work in theories of space and time tell us that it is entirely possible. Broadly speaking, there are two senses of time travel, both possible.

1. The first sense is the the H. G. Wells sense. This one is named after the author of the most famous story about time travel in which a voyager hops into a machine and travels about in time. Special relativity has room for something close. If we had things that traveled faster than light, then, for some observers, they would travel backwards in time. These faster than light objects are "tachyons." For some observers, they would leave today and arrive yesterday.

The effects that bring this about are closely related to those that lead to the slower aging of rapidly moving astronauts. That effect depended on rapidly moving clocks not behaving as we expected. The time travel effect arises from anomalies in how observers in rapid motion set their clocks at different places in space

Of course how we could get ourselves to travel faster than light is an unsolved problem! We cannot accelerate through the speed of light. But is there some way to recreate ourselves traveling faster than light? If so, some observers would judge us to be traveling backwards in time.

"There was a young lady named Bright,Whose speed was far faster than light.She set out one dayIn a relative way,And returned home the previous night."--Arthur Henry Reginald Buller.

2. The second sense is more topological and has been called "Goedelian" (by John Earman) in honor of the great logician Kurt, Goedel, who was a friend of Einstein's and did pioneering work on spacetimes that admit time travel.

We can imagine space and time as forming a huge sheet of paper. the vertical line is the complete history through time of a person, experiencing the years ..., 1980, 1981, ... etc.

What Einstein did in 1917 was to get us to wrap up the sheet of paper in the spatial direction so travel in the direction "left" is wrapped around to meet travel in the direction "right". That way we always end up where we started.

What Einstein's theory also allows is that travel into the future of time can be wrapped around to connect with the past, so that if we persist long enough in time we end up back at the present.

 

This is not a type of time travel that we create with a machine. There's no device we can build that could somehow turn our spacetime into one that has this global structure. The best adviceto someone who wants to travel in time this way is that they should be sure to be born into the right universe! However there are special circumstances that might bring about the wrapping around of future into the past at least locally. It might happen near black holes generated by gravitational collapse. It also may happen if we get very dense, very rapidly rotating matter.