In science, the idea and the reasoning behind insisting that time travel is impossible are subordinate to the measurements. It doesn’t matter how good an explanation is; if the data disagrees with it, then it is the explanation that is wrong.
It is done this way is to apply objectivity to subjective human reasoning. Human reasoning is subject by default because we automatically assign meaning and interpretation to any data our brains receive so that we can function. While this is necessary and incredibly useful, it leaves us vulnerable to accepting things as accurate, which is not real.
Even the tools we use to discipline our reasoning are affected by this. Mathematics and logic are subjective because the output depends on the input. An equation will reliably produce a result based on its structure, but what is included in the comparison is still dependent on human reasoning. The same is valid for logic. The only way to apply objectivity to the process is to have something utterly objective as a reference to allow us to see where reasoning is wrong. There is nothing more accurate than a measurement. The only thing that can affect an analysis is the precision of the device taking the size. But one measure is not enough because the device making the measurement will have a range of inaccuracy and provides too small a dataset to know the extent it applies. A larger body of measures covering as broad a range of appropriate circumstances is always more reliable than less. When scientists talk about the data, they are still referring to a body of measurements.
For a few decades, it looked like time travel might be possible because general relativity used time as a spatial dimension. But there has been a persistent lack of data and quite a bit of relativistic math that either disagrees with this possibility or show impossible energy requirements. All this work, of course, is still subjective because of the lack of data.
This has been a persistent problem in relativity theory, because while the math does work better than anything else we have for a range of problems, and we can confirm the relationship between energy and mass, that there is an underlying geometry to existence (detected gravity waves). We can confirm the rate of atomic vibration can be contracted and dilated at least to some extent (we use these to regulate clocks and GPS has to account for the difference to function) we have never detected any form of time travel. Any spacial dimension should offer this as naturally as moving in the three spatial dimensions we know. After all, we do have an experience of traveling forward in time but never in any other direction.
“The General Theory of Relativity” has another way to travel back in time. Or at least back to the moment in time, where we invent this “way.” This method is messier and much more complex than the time dilations mentioned above and would require its own set of articles to explain alone. It involves traversable wormholes and, again, velocities near the speed of light. And for this method, we first need to create wormholes. We know how to, just not technically how.
Once this device is created, it will allow us to travel back to the point it was first turned on, but not further back. It does not help us now, but it gives comfort knowing it might someday.
Nevertheless, if we were to suppose that we are in some sort of digital reality where the pixel size is Plank’s length and what we understand as quantum mechanics is the interface that spins out our experiential reality. Then what we interpret as “material reality” is better understood as “agreement reality,” which is the state data stored by the system that is accessible to all of the players (that’s us). Any Many Worlds concept would cause the amount of data necessary to represent the state of agreement reality to explode exponentially at the will of the players, whereas the players experientially cannot move from one agreement reality map to another. The fair play would mean that any player could, but the resource cost, if we were attempting to build such a game, would be higher than just the data required because new players would have to be recruited to provide the conscious will to all of the players in each map. So, beyond the limits of space, time, energy, and information, the ultimate limit is the number of player consciousnesses available to animate each map. This is not good game design, the number of players you have is pretty much fixed at any one point in time. Thus any offering that worked as an MW model would necessarily be populated by NPC’s, and you would be the unique unitary player of this universe. This is lonely from a perspective but certainly possible, but then it makes me an NPC, and I wouldn’t say I like that as much. The point of “agreement reality” is that it enables the existence of an MMORPG, and thus the maintenance of singular “agreement reality” is a feature of the system, not a bug.
So a lot of work has been done on this, and newer research on the underlying geometry of space from different angles by different groups of researchers, keeps coming up with that time may not be a spatial dimension at all and isn’t needed as one for existence as we know it to exist. This has led to the idea that time might be an effect of the geometry, much like gravity is an effect of the geometry. Built-in but limited by the mechanism in the geometry it emerges from.
If that turns out to be the case, that is, if the data agrees with this reasoning and math, then time travel would be completely impossible.