So which of today's accepted theories are in error? Quantum Mechanics and General Relativity do not agree so at least one must be incorrect yet both are widely if not completely accepted.
Isaac Asimov wrote a really great essay about this, in which he pointed out that some people thought the Earth was flat. And it is flat, on a local scale. Then people thought it was round. And it is round, just not exactly. Then it was considered an oblate sphere. And it is an oblate sphere - just not exactly.
The main theme of his essay is to point out that a theory can be wrong, but pretty accurate. Enough for rough work. And the one that replaces it can also be wrong, but even closer. Etc. So all theories in succession can be wrong. The real question is how wrong a theory is, and how useful it is.
Here's the essay:
And whilst one can say these, one may note something like say letting blood can cure disease it is not. Hence talking is ok. But actually using it …
More precisely, they are incompatible if you treat them as fundamental theories of everything. But neither QM nor GR claims to be any such thing.
That is a key difference between our current theories and schemes like Aristotelian physics, or for that matter Newtonian physics. Both Newton and Aristotle thought their theories were theories of everything. We know that neither the QM we currently have nor the GR we currently have are theories of everything; they are just models valid within particular domains. Those domains are very wide, but (a) neither one covers everything, and (b) there is virtually no overlap between them, and where there is (for example, quantum field theory in curved spacetime) we have ways of meshing them that work well enough.
It's not the same kind of error. Because science is based on factual observation, it tends to agree with the facts of reality.
> Quantum Mechanics and General Relativity do not agree so at least one must be incorrect
That's not so. It's not a binary choice at all. Both are accurate - both accurately predict certain phenomena and they will continue to do that. Someday, hopefully, someone will come up with an explanation that encapsulates both of them.
That seems more likely than the thing that happened last time repeating itself. Basically we just need Grothendieck’s ideas to percolate to the physics people.
Or not.
Have you any examples showing recent convergence between quantum & relativity?
Sure we don't have a single theory of everything yet, but our mental model is asymptotically converging to our observations.
I'm asking for facts, hope doesn't come into it.
> ...our mental model is asymptotically converging
Which is not what I'm picking up, so have you any evidence to change my mind? TIA
I said our overall mental model of reality is converging with reality. We're zeroing in on the truth. One day that might include a unified theory.
> So which of today's accepted theories are in error? Quantum Mechanics and General Relativity do not agree so at least one must be incorrect yet both are widely if not completely accepted.
You (FredPret) responded
> We're certainly zero-ing in on the truth though, which is extremely exciting
I had to read that as you implying closing in on some resolution of QM with relativity. Hence my confusion.