Have I mentioned that I despise the fictional concept of Time Travel?
It basically treats Time as if it were a separate dimension instead of recognizing that the concept of a dimension is abstract and fictional. Everything that exists is in motion. That’s the core of Relativity.
The concept of dimension certainly is abstract, but it is not
fictional. You can demonstrate dimensionality with effects like
the intensity of light as distance from its source increases.
Mathematicians arbitrarily invent the concept of an X axis, which doesn’t exist, a Y axis, which doesn’t exist, and a Z axis, which doesn’t exist, in order to mathematically model an object’s position at a given instant, which doesn’t exist, and then creates an artificial model of motion as a series, which doesn’t exist, of instants, that don’t exist, and calls that fictional series “Time”, which doesn’t exist.
Axes are fictional, but space-time exists. What we call time might be an emergent property of motion through space-time, but that doesn't mean time doesn't exist. Similarly, temperature is just an emergent property of the motion of particles in a delimited area, but it still exists. You can measure it. It has tangible effects. Just because it's made up of components doesn't mean the pattern doesn't exist.
Anyway, there is no single "concept of time travel." Fiction has lots of different ideas about time travel, many of which are contradictory. Some of them go the way you've gone in despising time travel: they say that time travel could work if you recognize that space and time are just abstractions with which we filter our perception of reality, and if we can remove those filters we can see all the infinite timelines of the universe and manipulate them. (See Douglas Adams's Mostly Harmless and the concept of the Whole Sort Of General Mishmash.) Others go in exactly the opposite direction and suggest that all one has to do to travel in time is to manipulate mathematics itself to have tangible effects on the universe, including altering one's location in time and space. (See Doctor Who, "The Shakespeare Code." I also reference the never-quite-published role-playing game Narcissist, in which the inventor of time travel did so by manipulating mathematics so deftly that he just appeared somewhen else. This isn't quite spelled out in the pre-release version of the game, but I've had conversations with the author, where he described this idea for me.)
Even Star Trek isn't consistent on how time travel works.
Slingshot around a star or imploding planet. Step through an alien
device that has no origin. Have your body "prepared" and step
through a doorway. Hang around with aliens that exist outside of
time, then leave at any point in history or the future. Time
cannot be rewritten, time flows around nexus points that can
change the future, any casual change in time can have major ripple
effects, no one remembers changed history, our heroes remember
changed history, everyone remembers changed history. To try to
analyze the physics of a word by Okrand when the franchise itself
is completely muddy on the subject would be folly.
-- SuStel http://trimboli.name