Nice, present the paradox with a possible paradox of your own, I like the way you think. Well, I would think that if the simulations can be run forward, they can be run backwards all the same. It just depends which way you run the tape. If something is recording, then you can take that recording and play it backwards, just like cassette tape or reverse something digitally. Therefore, you can go backwards if you can go forwards. Now the real question is, can you go side to side? Can you create other dimensions and explore these dimensions, or are they merely able to be observed through their interaction with the objects moving forward and backward? We already know that light isn't all we need to see. You can detect vibrations, that's sound. You can feel the heat given off by the interactions between things that produce energy, the same goes for sensing pressure (which of course is inexorably linked to heat).
My original idea about time travel was that everything happens in cycles, so presumably you could go so far forward in time that you witness at least one of the cycles of what could have happened in the past. However, what if you could take the probability of whether it was how it happened the first time out of the picture altogether? Quantum physics suggests to me that after the big bang, everything existing does so as a result of a lot of miniature bangs. Each time a moment of time occurs, things explode into existence from a state before existence. You could call it inexistence, or you could call it a super state in which all matter and therefore energy retracts into itself and then spits back outwards until it reaches a limit of potential that is achieved solely because the existence of other bits of energy and matter. The interaction between the opposing particles would thus allow for an existence of reality in a wave like pattern much like we can observe with light in the double-slit experiment. Until the next explosion happens, the next "calculation" if you will, you won't know what happens next, until you can observe particles, or single points of energy or matter. The further you try and investigate exactly where a singular piece of energy/matter/whatever is, the less likely you are to know where it will wind up, and vice versa. The uncertainty principle. The mind is like a computer with a monitor attached to it, if you will, that draws in all the information together at regular intervals and pieces the otherwise random interaction of forces, particles, energy, and matter, and strings it together into something meaningful, what we know as the flow of time. We already know that the mind waits until it gathers enough information before forming a final picture to make up for the time lag between say, feeling something touch our nose and something touch our foot, or for us to see something, decipher it, and hear something, and decipher it. The distance between neurons and the brain and the speed of electricity are factors in this that must be taken into account. It then displays this information quickly enough at regular intervals that it appears simultaneous. Much like how a CPU of a computer works, it can only ever perform a single calculation at a time, it just does so at a rate that is imperceptible to us and thus it seems to be processing multiple things at once. Therein lies the beauty of the brain: multiple processors with 3 dimensional transistors, cells/neurons. It allows for immense calculation speed. What happens in between those segments of explosive existence is as far as we are able to comprehend, incomprehensible. It may be an eternity as we would know it before things explode back into existence in what we call seconds, but it would be totally unbeknownst to us.
The question then is, if we can piece it together forward, can we piece it together backward, or does it even matter? Would we know the difference? We already see things upside down, technically, and the brain flips it right side up to make sense of it. If you give humans goggles that flip the image back upside down again, eventually the brain flips the image again to make sense of it. Could it even change the course of events if we do play it backwards? Would it cause unpredictable results like the formation of new multiverses or dimensions or black holes if we ripped spacetime apart like that? Perhaps that is what stars do. All very interesting stuff.
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