Random Thoughts About Time Travel

It's just a thought that occured to me once when I had to get a taxi somewhere; what was the earliest I could arrive at that destination, supposing that I could travel at any speed? The earliest I could arrive would surely be at the exact same time I departed. But then, I wondered, what if I travelled even faster than that? Would I arrive before I departed?

I don’t know anything about physics but I googled what you wrote and I got this information on the physics forum Physics. stack exchange:

“Your mass doesn't increase when you move at relativistic speeds. Nothing changes at all. You feel exactly the same. Although the world around you will appear distorted, nothing endogenous to your spaceship feels any difference. This is in fact the fundamental idea of relativity”.

And here’s what another poster wrote:

“Sometimes, when people are trying to explain relativity, they say that your mass increases when you go faster. Einstein said this, and you can find it in books as late as the Feynman lectures, perhaps later. Unfortunately, while it is possible to use this idea responsibly, it is subtle and not especially helpful, so that by now most physicists do not use it any longer. First, it is easily misunderstood by thinking that the changing mass is happening to the astronaut. Not so. It is just an artifact of different observers in different frames of reference. It is a bit like velocity - different people on different planets might look at the spaceship and claim that it has different velocities. They could even say "the velocity of that spaceship increases when it is moving near the speed of light", which sounds silly but is essentially the same thing as saying the mass increases. Of course, from the astronaut's point of view, he's just sitting around in his spaceship unmoving. Similarly, from his own point of view his mass is just the normal mass.

Additionally, if we say that the mass increases, it leads to separate ideas for mass in the direction of motion and mass perpendicular to the motion. This is confusing and unnecessary, so the idea of increasing mass is best left alone.

When you read a physics paper and it refers to a particle's mass, it means the "rest mass", the mass it has in its own reference frame. The old idea of changing relativistic mass is really just energy. People took the equation E=mc2, noticed that the energy of the astronaut increases as they move faster, and said that means the mass increases as well. A better way to do it is to write the new equation E=γm0c2 and say that as the astronaut moves faster and faster, the mass m0 is constant, but it is multiplied by a Lorentz factor called γ equal to 11−v2/c2√”.
I hope this is true because I really like the idea of my Time Travelling Rabbit.

Oh well, it could be a tachyon, it doesn't have to be a rabbit or perhaps a rabbit made of tachyons.