Several days later at Lyra's home, Twilight was teaching Lyra the basics of time-traveling, drawing diagrams on a board while doing so.
“Let's call 'soul' that which is preserved every time I die, and not be concerned about what exactly it's made of. It could be simply be a part of my brain made of physical material, or some special nonphysical thing that interacts with my brain in some way, or just a special mathematical pattern of my brain.
Now, when I'm still alive in a world, my soul is connected to the world, experiencing it through a body. But every time I die, my soul is disconnected from this world, and immediately connected with a world that, other than my soul, is exactly the same as the world that I was first connected to, up to the reset point.
Just how many worlds are there? Possibility one: every time I disconnect from a world, that world stops existing. This way, there is no simultaneous existence of worlds. There is always at most one world existing at any moment.”
Twilight drew a diagram on the board.
“But there's a problem with saying 'two worlds exist at the same time', since it seems to require a way to measure time outside of the worlds. We have to imagine all the worlds as floating around in some hyper-world, and that there is a hyper-world time, with which we can meaningfully say something like 'This 4 o'clock happened before that 4 o'clock.' That sentence would mean, 'In hyper-world, this world's 4'clock happened at the hyper-world's 14 o'clock, and that world's 4 o'clock happened at the hyper-world's 19 o'clock.'”
Twilight ran her hoof along the “Time” arrow on the top of the diagram, “Here, we are showing the time in hyper-world as a straight line, along which the many worlds are arranged. And we see that in this model, no two worlds exist at the same time.
Now, consider the following question. When I die in world A, does the magic create a world B that is an exact copy of the world at reset point, and put my soul into that world? If that is so, what happens to world A? Does it get immediately destroyed, so that when seen in the hyper-world, there is no world A beyond that time? Or it just goes on without me, and my friends mourn my death in world A while I keep on living in world B?”
“Either way, what about the other souls? They have no continuity, unlike my soul. Anypony other than me does not remember anything from the previous worlds. They always begin exactly as the ponies in the first world I was in, and no change in one world would carry over to the next world.
Suppose other souls exist and are made in the same way as my soul. My soul might be unique – or copied, but there's no way for me to tell unless I could see it in hyper-world – but their souls must be copied.”
Lyra asked, “How did you know that?”
Twilight replied, “I have made experiments to systematically probe the extent of soul-copying, in the following manner: I took a map of Equestria and chose by random twenty cities. I then traveled to these cities and made friends and acquaintances in these cities, of all species – pony, griffin, and others – then I revisited them in the next lives to see whether there is any recollection from their past life. There was no retention of events beyond the reset point. I also checked if they would have memories and personalities that are different with their previous life, for example, I would ask them if they went to a certain school when they were 6 years old, or ask about the details of some pivotal event in their life that occurred before the reset point. There were almost no inconsistencies. The inconsistencies that did occur were minor and could be attributed to memory errors.
Thus, I determined that the soul-copying applies to all souls everywhere, and the copying is practically perfect, and they are always copied from the original at the reset point.
This seems extremely unlikely, for such a spell I made to always copy all the souls in the world repeatedly. It would be far more likely for the spell to affect only me personally.”
Lyra asked, “'Unlikely'... Why is that?”
Twilight replied, “It's a principle of magic theory, that is hard to experimentally verify, but makes intuitive sense, and explains a lot of phenomena. It's called 'The Locality-Energy Correspondence', and it states that the 'extent' affected by a spell is proportional to the 'effort' required to cast it. For a spell to affect a large area, such as all of Equestria, requires the power of at least a thousand ponies. I performed the spell alone, so I have reason to believe it only affected me specifically.
So let's assume that the spell does not affect any souls except my own. Then where did all the extra worlds come from? Maybe in the hyper-world, all possible worlds already exist. Like in a giant garden, all the worlds are trees that grow higher and higher as their history unfolds. The spell simply transports my soul across them.”
Twilight drew another diagram on the board.
“But then, suppose upon the death in world A, my soul is transported to world B, at the reset point, then what happened to world-B-Twilight's soul? Did her soul get destroyed? Lost in the hyper-vacuum between the worlds? And if that were the case I must have killed hundreds of alternative-Twilight's souls by now, that means the spell can kill a very large number of souls across the hyper-world. Thus the spell has an extremely powerful and non-local effect, which as I said, is very unlikely... Or maybe not. Metaphorically speaking, maybe this spell has made my soul a kind of mobile parasite.”
Twilight dragged her hoof along the arrows on the diagram.
“After I experience death in world A, I split free, swim across the hyper-vacuum to an uninfected world B. Then I find the reset point in world B, kill the oblivious world-B-Twilight, then attach myself. This is certainly too much metaphor, but at least it makes it at least possible to think of this as a model of how the spell works while also assuming that the spell can affect only my soul, and maybe a little bit of space and time around me.
But this can't be true either, for, suppose I died in world A at 2 years after reset time, then I must swim to world B, then crawl backwards in time for 2 years before injecting myself into world B at reset point. Now, what would happen to the 2-year-long chuck of world B's history after the reset point? Did it just get chopped off, since, after my injection, world B's history after reset point will unfold in a different way?”
“Maybe there is only one world-tree in the hyper-world that has branches everywhere, each branch starts a different way the future can unfold. Yesterday, I bet a coin throw with a pony, and at that place, the world-tree branched into many branches. In some branches, I win the coin, in others, they win the coin, and in yet others, the coin rolls away.”
Twilight drew another diagram.
“In this case, the world-tree must have the ability to constantly generate new branches. A simple coin throw makes many branches, and the tree must branch out enough to allow them all to happen in some branch. The world is copied all the time, the souls are copied all the time. It's now a thing that the tree does, not my spell.
Every time I experience death, I detach from the branch I'm one and attach myself at the reset point. The tree then grows a new branch at the reset point, and I would kill the alternative-Twilight, which was just copied in that branch, and inject myself.”
“This is where I have gotten so far. It stands better than all the other hypotheses. It involves only local effects, and explains copying as an inherent ability of the world itself.”
After Twilight gave Lyra a rough sketch of the theory and practice of time-loop traveling, to Twilight's satisfaction, Lyra enthusiastically agreed to become a time loop traveler, so she took her under her tutorship.
One day, a few months into the tutelage, Twilight was lecturing to Lyra about implications of the spell on Lyra.
“Suppose Twilight and Lyra are currently in world K, at time '+5 years after reset point', and Lyra casts the spell on herself. Then what will happen? Lyra will live on for a while, then she would die, and her soul would go back to world K, at her reset point here, and get a branch of the world, leap onto the newly-copied Lyra's soul, kill her, and inject herself into there.
What would Twilight observe? Well, the moment after Lyra's reset point, the world splits into many branches, and it would depend on luck what future branch this Twilight would go down. Assume that there is equal probability that Twilight end up on a certain branch, then the probability that she end up in a branch that contains 'time-traveler Lyra' is N1/(N1 + N2), where N1 equals number of new branches of the universe created by Lyra's time-traveling, and N2 equals number of universes that would have branched at that moment if Lyra doesn't time-travel.”
Lyra asked, “Aren't N1, N2 both infinite?”
Twilight replied, “Let's ignore time-traveling for a moment, and just consider how the world should branch. From each state of the world, shouldn't there are an uncountably infinite number of possible worlds that could follow? For, if a coin can land 1 mm to the right or 2 mm to the right, shouldn't it also be that it can also land with any distance in between? Thus, the number of possible worlds should be at least the number of real numbers, so N2 is uncountably infinite. But Lyra, since she can only travel back in time for a countably many number of times, N1 is countably infinite. So...
N1/(N1 + N2) = 0
In other words, Twilight almost certainly will not meet a time-traveler Lyra. She will find herself going into a universe where Lyra has time-traveled exactly 0 times.”
Lyra asked, “So... you think that, just after I cast the spell, you will find yourself meeting a Lyra that is quite clueless and unsure if the spell had worked?”
Twilight nodded, “Exactly.”
Lyra looked at her suspiciously, “But I thought you said you wanted to teach me because you wanted to find somepony that can truly understand you.”
Twilight replied, “Yes, but I also want to help you find your adventure. Besides, maybe my calculations were wrong and I could meet you with positive probability. We have to give it a try to know.”