Time Paradox
In theory, it is possible to travel back in time while navigating Hyperdimensional Space. But as much as that idea is attractive, going back into the past is considered a very bad idea. Doing so could create a time paradox, which could have disastrous consequences for everyone involved.
How it Happens
To understand how this happens, it is important to realize how the universe determines how things are "supposed" to be. Every moment that passes is automatically "saved" into the universe's record of "how things are supposed to be." The reality that exists right here, right now is considered "the original timeline" and used as a template in case something goes wrong (see "Consequences" below).
A time paradox occurs when one who has traveled back into the past alters it in any way. This effectively creates a "separate timeline" in which the individual's actions have altered the present in some major way.
If the paradox is particularly egregious (for example, someone talks to their parents in a time before they were born), the paradox can become even more severe. In this case, reality itself may break as the universe tries to correct itself.
Consequences
The universe is self-correcting. When faced with a time paradox, the universe will use any and all means necessary to get back to the original timeline. That means any and all changes made to the timeline will eventually be erased.
Usually, this is a rather smooth process; the universe just quietly cleans up the illicit changes and moves on. But with bigger paradoxes, the backlash can be... extreme, to say the least. And by "extreme," I mean, "anything and anyone who exists because of the paradox will be violently glitched out of existence." This can end in whole swaths of people and places being retroactively erased from existence.
The universe eliminates every trace of the paradox, including memories (though those are the last to go). The timeline will be reset to how it was before the incursion, with no lasting damage to reality.
Traveling into the Future
Going into the future does not cause time paradoxes. As soon as one travels back to the present, any changes made in the future are automatically erased without fanfare. Hence, it is considered much safer to travel to the future than to the past.
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