We consider a theoretical twin paradox experiment in which the "twins" are in fact two entangled quantum systems (electrons, protons , atoms whatever may be the case ).
Accordind to a "reliable" source as Wikipedia, all processes—chemical, biological, measuring apparatus functioning, human perception involving the eye and brain, the communication of force—are constrained by the speed of light. There is clock functioning at every level, dependent on light speed and the inherent delay at even the atomic level. Biological aging, therefore, is in no way different from clock time-keeping. This means that biological aging would be slowed in the same manner as a clock.
Then this should also apply to decoherence time , as related to quantum measurement. So if we measure quantum system A and it decoheres into state S after measurement (this is the static "twin") , then we know that its entangled twin (the entangled "twin" in motion ) , quantum system B will eventually decohere into state S'.
The entangled twin returns home . So now we end up with two quantum systems in the same spacetime region, quantum system A already in state S (the static "twin ") , and quantum system B which we know it will decohere into state S' (that's the entangled "twin" in motion, which will decohere into state S' sometime in the future ). It didn't decohere yet into state S' yet because of relativistic effects, the decoherence time is affected like any other "clock".
What if we deliberately affect the decoherence process of the quantum system B, and put it in quantum state P' instead ? Does it mean that quantum system A will change its (decoherence ) course , jumping into anothe quantum state P at an earlier time? Of course, as long as no information about quantum system A is leaked into the environment in between the two moments in time .
Does this mean that we can transfer information (a bit of information in this case ) back in time?
Where is the flaw here, I checked the math, but maybe I misunderstood something ? Is it in keeping the information about system A from leaking into the environment, or something else?
Question. This is a thought experiment, the practical implementation details might solve this apparent "paradox' (by making it practically infeasible), but before thinking about practical experimentation, is this train of thought theoretically correct from a mathematical perspective?
