If theoretical physics can find a complete model of all particles and spacetime, and we can show that a Turing Machine can emulate it, then that would suffice.
If you can write down the Turing machine for anything, then a person with pencil and paper can simulate its execution. That direction doesn't appear to be the way to go. Despite the generality of what I wrote above, the only feasible counterexample would be one that people can do on paper but a Turing machine somehow can't.
>If you can write down the Turing machine for anything, then a person with pencil and paper can simulate its execution
What you're describing is the reverse direction, simulating a TM with pencil and paper, and this is doable so long as you are allowed two stacks of paper to work with, and an unlimited supply of pencil/paper. The question of simulating TMs in the real world really doesn't have anything to do with the Church-Turing thesis, though.
>Despite the generality of what I wrote above, the only feasible counterexample would be one that people can do on paper but a Turing machine somehow can't.
If some dimensionless measurable physical constant were a non-computable number, then the Church-Turing thesis would be false. In fact, if we think that certain quantities are in some sense random or arbitrary, rather than something that could be written as an equation, we should expect the Church-Turing thesis to be false with probability 1.
> What you're describing is the reverse direction, simulating a TM with pencil and paper
That's what I'm describing, but what is it the reverse of?
You wrote: "If theoretical physics can find a complete model of all particles and spacetime, and we can show that a Turing Machine can emulate it", to which I added "then a person with pencil and paper can simulate its execution", so putting these together a person with pencil and paper can simulate your complete physics model. How does that suffice as a counterexample to the Church-Turing thesis?
Right, I don't think physics is advanced enough yet to say whether anything can be measured with infinite precision. In the case of distance, our current understanding of quantum physics says this can't be done (or rather, the notion of distance is not meaningful beyond a certain precision), but I don't think there is any known limitation on generating quantum states of the form a|0>+b|1> where a and b are non-computable, in which case measuring these states over time could give a (probabilistically) infinite measurement.
