If one would use something like the Time Stone from the MCU to move someone along their own timeline, would they have all of the memories that they would have made if they had lived out their lives until that point in their timeline, i.e. would everythimg that would have happened in the intervening time if the device had not been used happen if it is used? For example would one be able to use this device to change a 20 year old into his 70 year old self and ask him which stocks to invest in?
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The Time Stone is particularly problematic because unlike a traditional time machine which transports one person around in time, the Time Stone changes time in local bubbles. The user of the Time Stone does not move through time, nor does anything outside the bubble. This offers all sorts of opportunities for contradictions.
We see the Time Stone (as the Eye of Agamotto in Dr Strange) do contradictory things. It can alter the flow of time in specific locations, like around an apple, which is fine. But we then see Dr Strange use the Eye to advance time around the apple causing the apple to be eaten. Then he reverses time causing the apple to be uneaten.
But there's nobody inside the time bubble eating and uneating the apple! When Dr Strange moves time forward, who is taking bites out of the apple? Does the apple "know" it will be eaten by Dr Strange despite him not being inside the bubble eating it? Does this apply to every object?
If Dr Strange took a bite out of an apple, set it on a table, reversed time on the apple to just before the bite, and then left the apple alone, would he see a bite being taken out of the apple shortly after? Does this "remembering" history apply without the Time Stone? Or is it only when the Time Stone is in use?
He again demonstrates this by locally reversing time around a book to restore the torn out pages. But there's nobody within the time bubble restoring the pages. And the torn out pages still exist! Now there are two sets of the same pages.
This implies that objects have a single history, forwards and backwards. That when you move an object back and forth through time it will be as if all the same effects happened to it, despite it sitting on a table in completely different circumstances. That once eaten the apple will always be eaten even if it moves independently back and forth through time with nobody eating it. In that case, yes, if you advanced a person forward 50 years they would remember all the things that happened including stock trades... but will those things happen again?
What if Dr Strange reversed time on the eaten apple, causing it to be whole again, and then cut it in half? When he forwards time again will it also be eaten? But Dr Strange ate a whole apple, not a half one. How does that work?
Like the apple being eaten despite nobody eating it, your aging stock broker might report on events that happen in a different timeline.
Another problem is in the case of the apple he first eats the apple, reverses time to uneat it, then advances time and it's eaten again. He's replaying events which have already happened to the apple. Take your stock broker. If you advance them forward 50 years, will they remember just standing in front of you for those 50 years while the world moved in slow motion? Or will they somehow remember 50 years as a stock broker that didn't happen to them inside or outside the Time Stone's bubble?
As another example, let's say your friend is shot and mortally wounded. You use the Time Stone to reverse time for them to when before they were shot. They're healed, hooray! Once you release the Time Stone bubble, will bullet wounds appear in their body again?
If your friend remains healed then an object's history diverges once out of the Time Stone's bubble. Your stock broker's tips will come from a different 50 years in the future than the timeline you're now on. But if your friend dies of bullet wounds again once outside the Time Stone bubble, their future is written in stone. They're fated to die, but your stock tips will be perfect. Kind of a monkey's paw situation.
You decide what sort of story you want.