I created a great thought problem for astronomers, which I call the “time machine game”.
Some inventive genius creates a time machine that can take him either into the past or into the future. But unlike science fiction time machines, this one *doesn’t* move through space as well. With all the different speeds and directions we are traveling through space on spaceship Earth, all at the same time, when he materializes, his time machine is a long way away from where he started, most likely high up in the sky or inside the Earth, after even just a few seconds.
This means that either going back in time a year, or going into the future a year, the time machine is going to materialize out in empty space, the planet Earth no longer being where it was a year ago, or having not yet arrived at where it is going to be in a year.
But the question is: in what direction, in the past, or in the future?
To make things easier, just disregard the daily turning of the Earth, and since it is exactly one year in either direction, it will be in the same relative position around the sun.
But you need to figure out what direction the solar system is moving through the galaxy, and the galaxy is moving through the universe, to figure out where the Earth, and thus the time machine, was a year ago, and where it will be in a year.
That is, from the point of view of Earth, right now, you should be able to draw two lines into space, pointing in whatever direction the Earth was a year ago, and will be in a year.
Interestingly, if the time machine could *also* move in time relative to its location also, like a science fiction time machine, using some creative math, you could travel around the galaxy in your time machine by going into the past and the future, then *not* travel as you go in the other direction in time.
That is, say traveling into the past until where you want to be is where you are; then traveling into the future *with* that point in space until you are back in the present, but say, on the other side of the galaxy, which is where you traveled to is, in the here and now.
But to win the game, you should be able to look into the night sky, in the general direction of some stars, and say that that relative direction was where Earth was a year ago, and look at some other stars and say, and that is the direction where we will be in a year.
Now if you has a subcritical mass of plutonium in your time machine, and its mass increased as you approached the speed of light, would it at sometime become supercritical and destroy the time machine?
The biggest problem is that we DON’T KNOW which direction we are actually traveling. And in fact it really doesn’t matter (so says Einstein). Things like direction only come into play when you compare two objects. And even then if you’re comparing 3 or more objects, you need to use the same object as the reference for every other one.
As some people have already obliquely brought up. What if the universe is like a gigantic hall of mirrors? We each have a universe inside us which has a universe inside it and etc. And of course in the other direction as well. So many possibilities, and we only have a short time here to investigate them.
Would inertia be in effect for time travel? If so, we would keep moving in the same direction and speed (or in the case of going back in time, the reciprocal) while subject to the same gravitational forces, so in essence, we would stay in the same relative place.
Or not.