FOM: Precision and Turing-computability

[Paul LE MEUR]

We can't measure any physical magnitude with an infinite precision.
I'm not a physicist but this seems widely admitted.

Another hypothesis that seems reasonable, probably less than the first though, 
but that I've seen enounced:
For any given finite precision, any physical phenomenon can be predicted by a 
Turing machine with this precision.
(like an instance of the N-body problem)

Then if both are true, there can exist no machine that computes a non-Turing-
computable function.

My questions are:
What are the current opinions on these two hypothesis?
And, if true, do you agree they prove Church-Turing thesis?

Thank you.

Paul Le Meur