I have several comments with respect to your post, if I may:
- Bohr model is wrong. It has been replaced by quantum mechanics.
- Maxwell equations and Newton mechanics are also known for ages to be not compatible. This is why we needed special relativity. It is not an error.
- And of course, electricity is known today not to be a gas.
Thanks for contributing, it is very much appreciated. Let me briefly go through the points you make:
Your first point, as I see it, is exactly what I am saying. Perhaps, if there has to be a difference, it could be that the way you state it shows that you are happy with the solution QM provides, whereas for me the issue is not solved with absolute certainty.
Your second point, is also partly what I am saying; it is a long known incompatibility. For me however it is absolutely an error because if two particles exert a force on each other the combined force on the combined particles has to be zero for if they were not inanimate things could suddenly start moving which is something entirely unknown to all science. Also I studied relativity at university level and I do not see how this solves this issue. Perhaps you could refer me to a paper/theory on this?
Then your third point... When you read popular science publications everything is presented as if we know it all, while if you go to a university and talk to any professor on that subject you will find that there are as many theories as there are unanswered questions. Only in math you will find certainties, in physics and other sciences there are none.
Take data. All microscopic physics data. But all. They all agree with QM. Which means that whatever is the true theory of nature, it has to reproduce the predictions of QM very well concerning the 100 years of data we have.
An incompatibility is not an error. Those are different things. The problem with maxwell equations and Newton mechanics is that the time is absolute. Maxwell equations are not invariant under Galilean transformations, but they are under Lorentz transformations. This is what I meant. Take any textbook It is in there.
And for the final point, an theory is a very nice thing, but a theory in agreement with data is better. Including all possible source of uncertainties on the predictions.
Thanks for your prompt reply. I agree with your 1st and 3rd point, but I am afraid I did not get the problem that I see with Maxwell's equations across. It is not the issue you mentioned, which is a known and solved issue, and therefore not or no longer an error.
Look at this picture from my colleague Koen van Vlaenderen:
J(x) and J(x') denotes the current in a conductor,
fr() denotes the forces as given by Maxwell and f() as given by Newton.
All our experiences and logic dictates that Newton's forces represent the actual situation implying that Maxwell gives the wrong answers in this particular case.
Sorry for my late answer. I was without any computer for a few days. If you refer to the theory of Vlaenderen, it is questionable as charge is not conserved in his theory. To me, this is sufficient to prevent me from further thinking about it as we have here an apparent failure of his theory.
Koen did put a version online that still contained an error, but I believe that even in that version conservation of charge is not violated. Anyway his most recent and peer reviewed version can be found here. Many people, much more clever than I, have now reviewed it and I am pretty sure it is correct.
Besides that, it is completely obvious that the forces in the above image as given by Maxwell can not possibly be correct, even if Koen's theory would be completely flawed. It is a recognized and known error and there are some more theories, besides Koen's that intend to correct it.
This journal is not considered as a serious journal. It is mostly spamming scientists to publish with them. Therefore, the peer-review process is questionable.
Concerning your picture, I need the full context. Where is the conductor? etc...
Ok, you have made your point.