Traveling forward into the future or backward into the past is impossible. Neither can be done. And here’s why.

One can only exist in the present. Past events are done deals; they no longer exist. Future events are yet to unfold; they don't yet exist. There is only the present. Like you reading this answer and scratching your...whatever.

Those who cite time dilation as a means for traveling into the future are misinterpreting the effect. According to both theories of relativity (special and general) the rate of unfolding events commonly known as the passage of time slows down from normal dT to a slower time rate dt < dT when a platform k goes some speed v relative to a designated static frame K according to the special theory of relativity or approaches a source of gravity according to the general theory of relativity.

The so-called special theory of relativity by Einstein shows how the two rates are related by dt = dT sqrt(1 – (v/c)^2); where v is the speed of k relative to K. c is the speed of light in a vacuum; also relative to K. The general TOR shows that dt = dT sqrt(1 - (Rs/R)); where Rs = 2GM/c^2 is the so-called Schwarzschild radius at which black holes are formed around a gravity source M. We'll focus on time dilation due to relative speed.

Note that the two rates are the same rate when k’s speed relative to K is v = 0. That means k and K are both static. In a true sense, k becomes K; so its rate of time is the same as K’s. My point is that k must be moving relative to K for time dilation to occur due to relative speeds.

While k is moving, the difference in rates dT - dt = e is that dilation (stretching) of time we are talking about when we cite “time dilation.” So if you have a twin who stays behind on K while you run off on moving reference frame k at some speed v relative to K, your time rate is dt while your twin's is dT > dt.

And there you are. Your static twin on K (e.g., Earth) is aging faster than you are. So when you return, you will find that your twin is dT - dt = e units of time older than you are...both chronologically, as your clock was running slower, and physiologically, as your bodily events, the metabolic functions, were also running slower than your twin's.

So for grins let's say your calendar on k (e.g., a spaceship) showed December 1 when you landed at the space port to meet your twin for the upcoming Holidays. And because relative time at the port was running faster than yours while aboard the ship, your twin's calendar showed December 12. Some will claim that you traveled 11 days into the future when you stepped off the ship onto the tarmac at the port.

Not so. All you did was catch up with the present time on Earth. You lived your present while on the ship and that put you at December 1 when you landed. But that's your personal present time only while traveling aboard the starship. December 1 is on your calendar hanging on the bulkhead of the ship. If December 12 were your future, that would be December 12 on the bulkhead, not December 1.

Now you are back on Earth and are living its present time, which is K’s December 12; it’s not your future at all. December 12 is on your twin’s calendar. Your future December 12 never happened as that would have unfolded if and only if you had stayed aboard the ship and continued going v speed.

And that's why they are called theories of relativity...time is relative. Aboard k, the moving ship, time ran a slower dt when compared with (or relative to...get it?) time dT > dt back on Earth. And while the ship is moving, k is the reference frame for its personal present time, which is the slower dt. But when the ship lands at the port, it joins or becomes K, the static reference frame, and the ship’s rate of time automatically becomes the faster rate dT, not dt.

But, this is important, both dt and dT are the present rates of time. Both twins are living in the present, their own personal presents. And when the traveling twin stops to visit the static one, the two present rates become the same rate…the present or current rate of time for the static reference frame.

So as I assert, one cannot travel in either direction, past or future. In either direction those events do not exist; only the present time determined by ongoing events exists. But the present rates of time are relative; so each reference frame has its own present rate of time and it most likely is not the same rate as other reference frames.