Most of these timeline variants assume that the past state of all particles exists in the past (making up something of a trace/ribbon to today's particle state)

Most of these timeline variants assume that the past state of all particles exists in the past (making up something of a trace/ribbon to today's particle state), along the time dimension up to the current point. Kind of like a movie tape, except that they often assume a single-timeline self-consistent causality must exist, such that any version of events created in any timeline must be possible to arrive at without the time travel event to have happened. In other words, the trace can't be broken for any particle in the time traveler's past, or must be restored before the point of the time travel. Obviously that excludes time travel within your "light cone" from even being possible, as going back will sever at least one particle's "causality trace" within your own past. More reasonable assumptions are for example that you don't need to fold timelines together, so those branched time travel graphs made for just about every time travel movie would be what the actual time would look like, so only the time traveler's local causality matters (any change he makes in his past in his light cone does not affect him, it happens in a timeline parallel to the one he came from). Another is one where you essentially have a data tape where the the current time is like a writer head moving along the tape, writing down what happens. Time travel is to jump to another point and rewriting what happened. Multiple write heads may or may not be possible (likely impossible if you assume locally reversing the flow of time is possible, otherwise you'll get a real big mess). Then there's the one where time is a dimension like usual, but particles do not leave a trace in their past - going back or forth by jumping with a time machine puts you in empty vacuum with no end, not even with any cosmic background radiation (that too moves forward in time with all other matter). Perhaps gravity waves from the past would still be visible?