Is time travel possible?
In my opinion, anything is possible. But it will most likely be centuries before we even have the technology for it. And even when we do develop it, it will probably be too dangerous to do at first. Time travel is a touchy subject and you will probably get many answers on it. But here is a tip that you can use anywhere: always be open to multiple ideas and opinions, even if you're convinced it's right.
A few thoughts...
Some forms of time travel are not only possible but unavoidable. For example, we are always travelling into the future.
We can affect the rate of travel by the use of accelerating frames or strong gravitational fields.
For example, if you were able to construct a spacecraft that could accelerate/decelerate constantly at the rate of
Travelling backward in time is a very different problem. It almost unavoidably violates causality and results in all kinds of problems. One way around this is a many worlds interpretation of quantum mechanics. In that theory, if you were successful in travelling backwards in time, then the time to which you travelled could be on a separate branch of reality from the branch you set out from. Then you would not violate causality.
Some forms of time travel are not only possible but always happening.
Newton say time an an independent variable. Time ticks at the same rate for everyone and there is an arrow of time pointing from the past to the future. Unfortunately this model is wrong.
The theory of relativity says that different observers experience time passing at different rates. If two spacecraft are travelling apart at high speed, an observer on either spacecraft will experience time passing at the normal rate. The observers will also both observe that time is passing slower on the other spacecraft! Crazy?
This means that if a spacecraft leaves the Earth and travels at 95% of the speed of light they will experience normal time. On return to Earth, for every year the astronauts were travelling, Earth would have experienced 6.28 years. Effectively, this means that we can travel into the future, using a fast spacecraft as a time machine.
Relativity redefines time from being an absolute ticking clock to a dimension in four dimensional spacetime. Arguably time doesn't exist as such. Everything is travelling from one point in spacetime to another at the speed of light! We are all travelling in time. Interestingly the photon which has zero mass and always travels at the speed of light experiences no time.
As for travelling to the past, there are theories which allow it, including wormholes. If some kind of time machine could be constructed which allowed travel to the past, it would be impossible to travel back to before the machine was created.
We already know that our physics can't explain things like black holes. Maybe future discoveries in physics will change our understanding completely.