Well, remember that traveling to the past is, as far as we know, pretty much impossible. But you can kind of wink that away as a trope and pretend it's doable anyway. Still, it's good to at least pay lip service to scientific accuracy, so as I said, your system needs to take into account the Earth's orbit and the fact that it won't be at the same place in the past as it is when you travel back in time in the present.
This is technically true but I only know of two stories that actually mention that, Macroscope and Timescape. You can get away with not mentioning it and if after your story is published some
pedantic idiot enthusiastic fan brings it up, you can say "oh, well, I didn't want to get too detailed and techy, but the programming inside the machine takes care of all of that. It even knows when Daylight Savings Time was started in what area, so it can always tell you what time to set your watch to."
Aren't we underneath eight-minute old sunlight every day though?
Yeah, so ... ?
(I know you're getting at SOMETHING here, but I dunno what)
As a fan of Diana Gabaldon's novels, I have to say that I think a time portal is more believable than a time machine. Think of a doorway rather than a material object which transports you from here to there. Or should I say from now to then.
Well, as the younguns these days say, "whatever." It might as well be a Tardis.
Yeah, but the problem with a multiverse is that it's always going to be different, isn't it? So it's more or less traveling into an alternate time period rather than the one in our universe. For instance, you may decide to travel back to the time of World War II, but instead, in that universe, America loses the war.
Well, not neccesarily. You could have America lose in the alternate universe if it moves the story forward, but there doesn't have to be anywhere near that big of a change for it to be an alternate universe.
According to one quantum physics interpretation, alternate universes are created at the rate of zillions* per second, and many are so close to identical you can't tell the difference (a BIG difference would be a coin flip landing heads up rather than tails up) .
What the alternate universe thing does is allow time travel without a
causality violation (look what that link forwards to!). If you go back and kill a grandparent before your parents were conceived, then you 'no longer exist' and were never born in that universe. But your grandparents lived on in the universe you came from.
The thing is, we don't know how to change to other universes. At least, not that we know of (I'm thinking of a Larry Niven story where they've been using transporters on Earth, but the MC works for a company experimenting with transporting between Earth's surface and Earth orbit).
You can read a few (dozen) books to educate yourself on some of the known and speculated-on science, as well as SF that uses time travel to see how it's often done, but I think you might as well "just write it" (some section of your story where time travel is actually done), post it to SYW and take suggestions about what to change or how to do it.
But if you want to learn some of the ways it's been done before, here's some fiction that includes time travel that I think might be instructive:
"
A Sound of Thunder" Ray Bradbury. Short story (really!), I strongly suggest you click the link and read it.
"The Number Of The Beast" Robert Heinlein
"Timemaster" Robert L. Forward
"Timeline" Michael Crichton
I know I've read quite a few others that don't immediately come to mind.
* Zillion is actually a technical term. A very technical term. You can trust me.