On 03/10/2018 14:23, Chris L Peterson wrote:
On Wed, 3 Oct 2018 10:23:50 +0100, Martin Brown
wrote:

Conjugate variables in Heisenberg's uncertainty principle is the most
obvious counter example. You cannot simultaneously know the momentum and
position of a particle in phase space to arbitrary precision.

Yes, but that's a triviality.

No. It isn't.

It is because it isn't what I'm talking about as "knowability". There
are certainly "things" we can't know. That's not important. The
question is are there rules of nature we can't know? I don't see
evidence of that. I think our understanding of nature can be complete.

In practice there are potentially whole regions of physics at ultra high
energies and very short length scales where we can never know what
really happens since it is not possible to probe them experimentally.
(and never will be)

We can make conjectures about the underlying structure but never test
them in any meaningful way so it will be impossible to choose between
any competing physical theories that make the same predictions for all
of the things that we can actually measure.

The Godel incompleteness theorem probably also applies to the real world
every bit as much as it does to mathematics. There are always some true
things that can't be expressed in any formal grammar or world model.

Succinct explanation of the incompleteness theorem for others:
https://blog.plover.com/math/Gdl-Smullyan.html

You should also recall that every time some eminent physics has stood up
at a major event and said "physics will be solved in the next twenty
years" some new observation has completely up turned the apple cart.

Last time was when radioactivity and relativity were discovered.

Science is always an approximation to reality that is as good as our
mathematical models will permit but since physics rests on mathematics
and we know mathematics can't describe everything you are always in a
position where there could be true statements about the universe that we
cannot know and will remain forever inaccessible.

--
Regards,
Martin Brown