Here is the plan for a simple time machine. Consider the drawing at left.
A projector, at the lower left corner of the box, shines a light up to a mirror, on path “a” where it is reflected down to the detector at the lower right along path “b”. The total distance the beam of light travels is thus a+b.
Now suppose the box moves so fast that it is able to complete a journey during the time that the beam of light is traveling from the projector to the detector. In the drawing below, the middle position shows the box at a time exactly in the middle of its journey, just as the beam of light strikes the mirror. On the right we see the box at t3, the end of its journey. Now we ask, how far did the beam of light travel? Was it not the distance e+f?
It must be, because when the journey started at t1, the projector was in the leftmost position, and in order for the beam of light to be detected at all, it had to arrive at the far right position at time t3, where the detector ended up.
How could the beam of light travel the whole distance e+f in the same time it took to travel the shorter distance a+b when the box was stationary? This should not be possible because the speed of light never changes. In the laws of physics, it is a constant, known as c.
To travel a longer distance in the same amount of time, the only possibility is that time slowed down while the box was moving, giving the light more time to make the longer journey at a constant speed. Thus the box is now displaced in time with respect to the rest of the world, literally “living in the past.”
Perform that same sequence again, and the box falls even farther back in time. Cycle the experiment rapidly, and the box steadily recedes farther and farther back in time.
Put an easy chair in the box between the projector and the detector, settle into it, and you could take a ride into the past, as far back as you wanted to go. Unfortunately, you could never return to the present, so take a sandwich and a beer.
With suitable controls, you could stop the machine and get out of the box anytime you liked. After exploring that period of history, you could get back in and go even farther back into the past.
It’s so simple, you could build it in your garage!