Imagine the current time we all exist in as a single line on a sheet of paper where every single moment is located on certain distance of the beginning of the line. This line does not get longer or anything, it is with fixed length (one you can not know if you are on that very line) - every moment of existence is on that line and "time" is at what place you are on that line.
Now how do we travel in time? First comes the problem with the "speed" of time. It is rather useless in this explanation, since no matter how fastly we move through the line we would experience the same effects from it and time would seem the same. Lets step aside for a moment. Say we are only looking from aside to this line and time flows normally for us as observers but its not moving on the line. The current "time stamp" remains on position X - time has stopped. If you are on that line you wouldn't experience the time stopping. Nothing would happen and there is no way of recording or observing this while on the line. So the speed you increment the timestamp doesn't matter. Speed does not exist unless you are observing. The only important thing is to go through each time stamp as incrementing from the previous.
Having this idea of time stamps and line of existence set here is how I imagine time travel to work without creating any of the paradoxes.
Let's say the line we all exist on is named "A" (for easier reference) and take the current timestamp as "20" where 0 is the beginning of time/line. At that very moment/location you manage to time travel into the future to timestamp "100". All cool, you move to the footer and things remain well, no room for paradoxes here. What happens if you want to move to the post though..
Here comes the fun part of how time travel paradoxes are "fixed". Moving before timestamp "20" to lets say "10" means that you might meet with your past-self, screw up with events and kill yourself. Here is a paradox where if that happens you would never reach to the "20" timestamp and travel in the first place. But what if you duplicate this "A" timeline to "B" while time traveling? So you just jump into that copy "B" and don't touch "A" at all. Any change of events there wouldn't matter, because you originally come from "A" and alternating "B" won't create paradoxes. If you kill yourself in "B" you can countinue to exist, because you would exist also in "A" for the same time stamp which will allow you to time travel back in time. From your point of view "B" is complete copy to "A" so it looks like you stay in the same line.
If you want to get back to "A" timeline you could do that only if its after your jump - after the timestamp "20". One "counter" must be added to measure and fix those paradoxes though. You can never go before your latest timestamp you have been on a certain line. Meaning if you travel to the end of a line you will not be allowed to step on it ever again. Same goes for any copy. The creation of copies is infinite.
So as summary the time machine you would need has to be able to do the following:
- Read the line ID
- Create duplicates from the current line
- Read and be able to move to given timestamp ID
- Make sure it never goes to timestamp before the highest in which you have been on the specific line. If that is the case duplicate the current line and jump there.