What is the time complexity gain when using an oracle machine over a standard Turing machine?
Compared to a standard Turing machine, the time complexity gained when using an oracle machine is not well-defined, as it depends on the problem being solved and the oracle being used. In general, an oracle machine can solve specific problems faster than a standard Turing machine, but this depends on the computational power of the oracle. Therefore, the concept of an oracle machine is often used in theoretical computer science to explore the limits of computation and to study the relationships between different complexity classes.

However, it's important to note that oracle machines are a theoretical construct and do not exist in physical reality. A real-world algorithm would never have access to an oracle that can solve problems instantly, so the time complexity gained when using an oracle machine is not directly applicable to real-world computing.
So is it fair to say that in real world its not possible to have complexity gain over oracle machine as all of them are theoretical construct. And what are some example of in theory where oracle beats the turing?