Yes, but that type of time travel is not what we think it is from science fiction.
Imagine you have a basic downramp HotWheels track. Two to one drop over a few feet with twice the drop as a flat run and a block at the end.
Take a car and let it run the track. Pick it up from the end and do it again. Time Travel. You have just experienced a repeat of the past.
The repeat would not be exact because you didn't exactly position the car where it was before. Also, running the car the first time change the track and the car. Maybe it shifts a bit and micro levels of plastic shave off. The axles and wheels deform a teenty bit from the stresses and youb get another layer of the wear you see on the wheels of the car after time.
Now imagine that instead of picking up the car, you could push it back up the track in such a way that it reverses every process it went through rolling down the track. Every piece goes through reverse action. Every molecule passes through revers paths. Where bits shaved off, they rejoin. Where flexes and stresses broke weakened the material it reversed. The car is exactly in the precise state it was in before the first run. Now let it go.
This time, you get a rerun of the first event. But not exactly. First, let's account for and ignore that you only affected the car and the track, but not the air in the room, other objects, and even changes in the shape of the Earth that affect (in a teeny-weeny way) the gravitation field around the car and track. Quantum theory says you would rerun "time" (the dependent series of causes and effects), but some things are "random". Whether or not that means you would see the exact same event is up for debate.
If you added a tiny piece of paper to the track after you reset it, you would definitely see a different run. You can make this change because you were "outside" the scope of things that were "reset". And of course, all the other things outside that weren't reset would have the potential to change the second run.
This is an important difference between scifi and what Einstein, Penrose, and Hawking (and others, I'm just saying these three have slightly different takes on some of the details) discuss on this topic. Because you were outside the "reset" you can do things differently. And the things you do don't change your past. By "traveling through time" (you moving forward while other things "rest"), you have a different relationship with causality than the things. There is not time travel paradox (kill your grandpa and you don't exist) because nothing that happens in the second run affects "your past" (again, different people have different ideas about exactly how that happens, but they agree on the concept).
Now, instead of just "resetting" the track and the car, you "reset" everything in the universe except you (and some bubble around you for air, the equipment you are using to do it, and other necessaries). Now your presence, with a different line of causality than the rest of the universe, is the only thing different for the second run. That's the only thing that changes the run. And if in the second run, the car happens to jump the track, hit you in the temple, and kill you, there is no "paradox" … the universe just keeps on moving forward.
An interesting bit with this is that if we have no "time machine" doing this, if the universe in its entirety (whatever that means) just rolls "backward" occasionally and nothing at all is "outside" the action, we could actually be experiencing such a process all the time and never know it. It has strange implications on one side of the quantum argument if every time the universe "rolls forward" it does it differently. In fact, from that viewpoint, there's no reason the same effects wouldn't make the "roll backward" different than an exact reverse of the "roll forward".
If that is happening, one possible mechanism of time travel, other than forcing the entire universe to "roll back" except you, would be to pull yourself outside the "roll back" process and then "rejoin" the flow later.
Also, we discussed that just expending the (relatively) small amount of energy to "roll back" the car and track instead of the whole universe, would that be OK? Would you not mind the difference?
Well, you would. Something time travel scifi tends to leave out is if you "perfectly" move the track and car "back in time" it would not account for the movement of the Earth, so the track and car would end up somewhere in space (or possibly, inside the Earth, which technically is still somewhere in space). So you would need to move the whole Earth and deliberately move yourself since you are outside the "reset". But if you did that, you would greatly mess up the solar system dynamics. So you "roll back" the entire solar system. Now the question is are the interactions with the rest of the galaxy, or some subset of neighbours, or possibly other galaxies, going to cause a catastrophic problem (from our perspective) upon restart?
A question like that is a good place to stop. Plus, I have to go to work now.
discusses the limitations and challenges of working with a low-end 3Dprinter.
