I am working on a science fiction role playing game. One of the features of the setting is very fast travel, but never faster than the speed of light. This is my one big handwave, I am not particularly interested in explaining how it works. I guess it is a type of wormhole, but I would be just as happy calling it magic. My purpose in having such a device is to avoid unbelievably high tech engines, body smashing accelerations and time travel.
In order to travel quickly, the characters enter a machine called The Orrery. Each major planet has at least one Orrery entry point, either in orbit on a space station or on the surface of the planet, if possible. The properties of the Orrery are such that each trip takes exactly 20 hours, no matter how far or close you are traveling. Passage is one way, so a traveller must cross the threshold of the door on the other end before turning around to go back to the place they left. A round trip journey like this would take 40 hours. Another property of the Orrery is crossing the threshold of the doorway causes the person to vanish. The will not be seen again until 20 hours pass and the door is opened on the far end. The traveller can open the door themselves, it isn't locked. Interestingly, there is a window of time where multiple people can enter and travel as a group. It's short, like 30 seconds. Otherwise, everyone travels alone.
Obviously, using the Orrery to commit crimes in one place and escaping to someplace else won't work. A radio message would outrun the escapee by a good margin.
People's sense of time in the Orrery is highly subjective, some people would say the trip was minutes long while other experience the full 20 hours. This almost seems like a user choice, but is vaguely unpredictable.
With such a device, would there be any possibility of actual time travel?