Time Dilated Particle Pairing- Closed Time Loop

In this experiment a highly advanced group sets up a paired particle generator. The generator is positioned in deep space in such a way that one end of the particle beam does a very wide orbit around a black hole, one that has relatively low or negligible time dilation, to their location (spaceship colony) without interference along the way, and the particle stream reaches them 10 years after being generated.

The other half of the paired particles are sent in the opposite direction, where they do a close loop around the same naked black hole, but still do not interact with anything else along the way.  The time dilation causes these particles to age slower from the perspective of the space colony (non-time dilated, outside observer), let's say to a factor of 1/10th the age, but from the paired perspective of the particles time continues moving at the same rate for each particle. They reach the space colony 10 years after being generated, from their own perspective, but 100 years after being generated, from the space colony's perspective.

When the 100 year trip particle beam arrives back, any changes made to them will be simultaneous with the 10 year particle beam, as the particle's perspectives are still linked, so from their point of view each trip took 10 years. So by adjusting the 100 year particle stream, the 10 year particle stream will be changed 90 years prior (when it first arrived back) from the perspective of the space station. If the observer has a way to measure those changes, and the way in which the particles has become changed can be translated into a binary code (shift "up" = 0, shift "down" = 1, let's say), then a calculation could be run and communicated after 100 years, with the output of the machine being communicated into the 100 year stream, but the measurement of those calculations would be received in the same location after only 10 years had passed, so 90 years before the calculations were transmitted. Once the 100 year beam arrives, the inputs of the machine would have already been adjusted by them for 90 years, which means 10 years after this machine is set up, it would be receiving information from the future, its own future state.

While this is difficult to wrap one's head around from the point of view of which perspective is valid, from a currently known mechanics perspective it is not difficult to comprehend. This experiment utilizes a function of quantum mechanics that states that any change to one particle of a paired set happens simultaneously to the other. This "simultaneous" action would necessarily happen from their own perspective rather than any outside perspective, as due to their lack of interaction with anything else, no other perspective possess validity from their own perspective when the change takes place. This experiment also leverages a principle in general relativity that states that time will dilate from a perspective moving at relative speed, or between perspectives in differing levels of gravity. Both of these points have been independently verified experimentally, this machine simply uses both concepts in the same experiment, marrying quantum mechanics and general relativity. While the outcome is foreign to our general ability to process what the result would be, as future information would link directly to past action, and would remain linked from that point forward for the duration of the experiment, this inability to process how this would look does not represent an incorrect conclusion but rather represents a new frontier of our lack of knowledge, if we can continue to claim that the elements of both theories (these specific elements of pairing/gravity, which are both fundamental claims of their respective theory, of quantum mechanics and general relativity) are valid. 

Let's say the colony ship is running a calculation of prime numbers via computer, a computer that originally starts from 0 and identifies primes up from there. The computer also uses the 10 year particles beam to inform its new starting position as that information is received and, once it is able, it communicates its findings with the 100 year beam. This would create a closed loop of calculation, allowing for larger and larger values to be communicated back immediately upon receipt of the 10 year beam, assuming there was no "choice" involved (take all variables like human decision and possible interference out of the equation). While I know it is tempting to assume that this would result in an infinitely large number being generated, an impossible outcome to envision, there are still limits on the output of this number. It is my belief that in this specific experiment you would receive information at that 10 year mark for the largest possible prime number to be communicated within the span of 90 years (give or take, accounting for actual processing speed of the computer). In that final iteration of the loop, the receiving version of the computer at 10 years could only receive the number, which would be unfathomably large but not infinite, with perhaps just enough time to verify it before that specific iteration of the loop was finished. In this way, even though time travel is utilized (in the closed loop sense), the additional time for information would not result in an infinite value presented. One could see that even if the timeframe were extended this would still be the case. Even if you somehow managed to chain these experiments together a limit would still be reached, and this limit is the ability to convey the information, which far exceeds our ability, in this scenario, to process it in a meaningful way. 

What is interesting to me in this scenario is that while it is hard to determine which perspective is valid during the experiment (as there are so many closed loops which contribute to the whole but are not present for the final iteration) what is valid at the end of the experiment, which would necessarily be the first beginning and full duration of the experiment from our perspective, is that afterward the processor could measure how many primes it had calculated, and the answer would only be one, the final one. In fact, it would only have calculated this prime in the sense that it had verified the number on that final pass, and at that point it would provide no new input to send back except possibly the verification signal to confirm the number. This would allow for significantly more "work" ("power"?) to be done than a processor could normally accomplish (let's say a processor was used that only had a couple/few hundred years of maximum output before it broke down, for example, if one added together all the loops needed to reach the final loop the time spent by the processor at maximum capacity would far exceed that), although the results of that intermediary work would not be known. Alternatively, one could encode into the stream all numbers uncovered up to the final number, but then the final number reached would be significantly less than the one referenced here, because an amount of time in the 90 year window available for communication, would be spent communicating the other numbers along with the final one reached.

I can also picture a scenario where this set up is used to alter the future. In the same way as described in the prime calculation, this could result in many iterations occurring at once. One could conceive of many intermediary steps where a suboptimal future would be communicated back, and in that communication a new suboptimal future would still be the result. At that point though the new suboptimal future would be communicated back to start another path, and this would continue. I imagine that at some point a threshold would be reached where the current future would be very close to the optimal future, from the perspective of those in the future. Once this threshold were reached, I imagine that adjustments would still be made, but the future perspective would likely not become erased as a result, but instead altered slightly enough to be retained. I imagine this path would be the first message sent back to the starting point from the starting point's perspective, and the first day would pass. If the intervals for messages were decided by days, both past and future would proceed one day, with the changes to the past, as communicated by the future, editing the future. The future would still be in a near optimal state, but would be different than it had been before sending the message back (just not different enough to feel like a reset, more like a shift in memory, I would imagine). I could see, based on human nature, that there may be other adjustments from this new state, things to try, as "optimal" would be a moving target, in contrast to the direct processing of prime numbers. So each day would proceed, perhaps with small things communicated back, but nothing that would alter the future so far as to make it unrecognizable. I imagine that for the future residents this would feel somewhat like deja va, but since they would know it was coming right after sending the message back they would be on alert for it, perhaps even having a method of measuring it and keeping records of how things had shifted, in order to provide greater stability to their timeline, the near optimal timeline, and understanding how to convey messages back to produce more fine tuned results. While I personally imagine that "optimal" may be a kind of fractal pattern, with many adjustments still being made so things do not become stagnant/fixed (entirely predetermined), this kind of beacon between future and past would be essential to making sure events moved toward this optimal fractal pattern.

I really like how this post turned out. I can truly picture this machine leading to an optimal reality, at which point more options could be seen, new frontiers. As a bit of an aside, based on something I have glimpsed in a sort of "core processing" state (aka "manic episode"), I believe that attention should be paid to the careful use of paired particles, as it feels like even on a fundamental level things that are connected feel that connection. If this method were used I would ask that a timely post experiment particle pair reconciliation method be established in some way, as it feels like we would find such a thing beneficial for the entire system at large.