Time, the aspect of change. In time, the systems grow or die. Without time, we would be like a static painting, forever suspended in its frame. It's a mysterious aspect, hard to study and master, because its interaction with other aspects is usually defined as a process that better describes mechanics of other aspects in time, than the time itself.
Without further ado, we will study examples of mankind's achievements in the study of time.
For the beginners, we have 'Acceleration' and 'Deceleration' – spells responsible for altering the flow of time in the targetted system. As the names indicate, it can cause us to perceive time as moving slower or faster than the time of the environment. It's the most basic time spell that students of arcane can learn, but its form often varies, depending on a scale or how we define a target system. For example, you can cast it on your allies, enemies, or a specific device, while the world remains unaffected, or cast it in bubbles, it all depends on your rigorous approach.
What is important, is also the scale of an effect. There are two extreme cases, Infinite Acceleration, and Infinite Deceleration, but as we already know, it is hard to believe that perfect invocations exist, so they might not exist in nature.
The infinite acceleration leads to an absolute stop of time around the system, which is the holy grail of time-based spells, due to its immense combat effectiveness and research potential. It is claimed that such a spell was cast on numerous occurrences, but experts believe it always was just an extreme case of slowed-down time.
Infinite Deceleration is harder to achieve and makes the system perceive the time around it to move infinitely faster, which would mean it'll travel to the end of time in a single moment. Of course, we don't know If there's such a thing as an end to time, so perhaps the subject would be just frozen in a pin-point frame, just as it was in the case of Infinity-point Petrification. It's a very important parallel, that many researchers still try to decipher.
Now, time travel. At first, the future. Theoretically, it's possible to define the end of time as a point and limit the interval of infinite deceleration, which would help us achieve this effect, but that doesn't get rid of the body, which is frozen in process and must be maintained. To ensure the safety of the time traveler, one could theoretically transfer the spatial aspect of a system to limbo, which would make it appear like the traveler really hopped in time. We don't know the underlying mechanisms, but there is a strong connection between the passage of time and spatial limbo, which in theory, can exist in a different type of timeline, so in a perfect-perfect scenario, the body would remain there for exactly one or zero frames in time, achieving the most desired effect. It does sound plausible, but is harder to achieve, that's why for most time travelers, there is always a risk of a breach involved.
As for the travel to the past, the academy's stance is simple. Regardless of what you've seen or heard of, we firmly believe it's all utter nonsense. Be it time loops, links to future selves, multi-timeframe minds, and other temporal anomalies. To clarify, yes, the travel between timelines and different time mediums or structures is theoretically possible, but it's believed that they all exist in reference to each other, so there is a single mutual past-universe for their collection.
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How do we explain the time travel phenomena then? We have a saying in the academy when it comes to literature - Every loophole can be fixed with parallel worlds. That's the leading theory, when it comes to things we yet can't explain, but more often – you're subject to scam or advanced duplication magic.
Of course, there are factions opposing that theory and they bring one single exception to the table. The parallel worlds clustering. That is, when time travel would result in the creation of an identical parallel world, they claim, that no parallel world would be created and instead one or all of the original worlds would be used. The academy claims that it's utter nonsense, multiple identical parallel worlds can exist and have a rigorous scientific background. Their claims are dreamy philosophies that blatantly act against the law of entropy. In simpler words, their claim is, that it's possible to travel to the past, as long as you don't change the existing system in the whole interval of time, which means, that your travel to the past already happened in the target universe and that future actions of a time traveler, in the past, are pre-determined. In my personal opinion, it directly acts against free will... but there were some pseudo-scientific attempts to create theories that use objects without such.
You may ask, what about the time-loops? That's a subcategory of past travel and would simply be a massive production of parallel worlds.
Now, that we are done with examples, what else do we know about the nature of time? Is it continuous? Discrete? In theory, both mediums of time can exist. It can be an array of connected discrete states, which can act outside of what is perceivable, or exactly what we experience every day. Discrete timelines are an advanced branch of sciences and will not be the subject of this study.
We're close to the end, what else there is to say? We left the branching timelines untouched. While it is true, that in sense of parallel world clustering, past travel ceases to be theoretically viable, there still were some interesting findings. It's still a hypothesis, but the identical, and in rare cases even non-identical, branches might be able to 'synchronize' and form a single future timeline. Specifically, the synchronization of sapient bodies is interesting to consider, where the subject of a mental experiment, would become one body with two pasts and two sets of memories. We know that synchronization of systems in a single timeline is theoretically viable and the effect would be in its nature very similar, so we still don't reject that idea.
However, that's not everything. The timelines, theoretically... can be erased, or rather, stopped. Similarly, they can be created. Even so, you can create and destroy a timeline at an instant, creating what we call a time-point. Most of it though, due to lack of rigorous approach, would be similar to using global-scale infinite-point petrification... with weird properties. We already determined that travel to the past is impossible, so upon the destruction of the timeline you often can't go back to the point when it happened, and reviving it is not a trivial matter. You can cheat by creating parallel worlds, but that's not the same as reversing the effect. The biggest hope lies in the imperfections of a spell, which is the result of a lack of perfect rigorous cast. The biggest mystery though, is the souls, which in the case of the death of a timeline, seem to have properties parallel to existing outside of the time. These timeless properties allow us to fish for information and the soul's primitive compounds, which in theory, give room for attempts of embedding the soul fragment in any frame, since the future is undetermined.
What we said here, might be enough to exhaust the topic. I might repeat myself, but there is not a lot to say about the time and other studies often reiterate the points contained here. Due to that, there will be no homework assignment. The lesson is over, enjoy your free time.