Good day to everyone, I would love to ask You a question about the computational power of a hypothetical Turing machine.
Lets imagine a world, where the laws of physics don't prohibit FTL communication and there exists a mean of instantaneous communication across arbitrary distance. What would be a computational power of TM inside such world?
I know that this question is vague, but I got into an argument with a friend of mine who believes in ESP (extra senzory perception) where one can send thought instantaneously across arbitrary distance. Now I am skeptic when it comes to ESP, but I wonder how would such phenomena increase the computational possibilities. Could computers (modeled by TM) in such hypothetical scenario reach nontrivially into Arithmetical hierarchy? Encompass it whole? Reach nontrivially into projective hierarchy?
Thank You for kind answers.
It would probably be able to compute the same thing as a classical Turing Machine (the same laws apply to the atomic steps of computation) but everything can be computed in constant time as FTL communication means you can send message in the past.
So just send the result in the past once its computed. But you still need to spend energy and time for the computation after the result is received (otherwise, it's a paradox, but then, you wouldn't have received any result).