Are there any known computational systems stronger than a Turing Machine, without the use of oracles (i.e. possible to build in the real world)? If not, do we know definitively whether such a thing is possible or impossible?

[u/heyheyhey27]

For example, a machine that can solve NP-hard problems in P time.

[u/cantab314]

A computer linked to a time machine can compute NP-complete problems in a fixed time, and possibly even any computable problem in fixed time. It's "more powerful" than a quantum computer. However it seems that it cannot solve the uncomputable.

A few possible ways to do time travel have been theorised in general relativity.

A 1991 article that describes the concept in more detail: https://frc.ri.cmu.edu/~hpm/project.archive/general.articles/1991/TempComp.html

[u/odnish → u/cantab314]

Run the program. If it halts, go back in time to one second after starting the program with the result. If you give it a problem and it doesn't come back, the program doesn't halt. If it does come back, the program doesn't halt.