Of course they're not. Anyone who seeks to supersede these theories (or any others, for that matter) with something else has the responsibility to explain why these theories have been so successful in explaining so much of what we observe, and how their new theory can do the same. Your description is near-perfect - Einstein didn't replace Newton, he extended Newton; i.e. showed that Newton's Laws work as a leading order approximation within his own new theory.
Any new theory would have to the same to QM and/or relativity - show that those theories still hold as a leading order approximations in the kinematic/dynamic realms in which we know their accuracy holds (a form of what Bohr referred to as the correspondence principle).
The old theory can be changed so far it is not recognizable. Adopting Hamiltonian mechanics or Gaussian coordinates will do that. However, since any such permutation will have to provide the same results that we see in daily life, in addition to new results, it may be said that the old theory has merely been extended in any and all cases.
Greetings!
I caught the replies early this morning but have been busy, so I thought about what I would say.
First, let me say this: If you went to a convention of physicists and stood on the podium and said "Einsteins GR is a refinement of Newtonian theory" you would hear wild applause. Mixed with the applause there would be strong boos and derision. Then the calculator folks would attack the slide rule folks and pandemonium would break out! Blood would flow and hi-iq brains splattered on the table! It'd be just like Braveheart! Magnificent!
:-}
Personally, depending on my mood, I might applaud or boo. Kinda depends on what the next followup conclusion would be.
The reason is the two methods that led to the theories. And while I am about to say things about Einstein that might put some folks panties in a wad, DON'T TAKE IT THAT WAY.
Newton had a fairly good set of observables. So when you start with observables and find a function that fits it, that's one thing.
But Einstein started with a proposition, basically that the speed of light was the same for all observers. Then he built/derived the necessary functions and forms that he needed to describe the space that resulted. IIRC, Einstein was a good friend of Hilbert.
So it may be that relativity was in fact a necessary result of his main proposition. It may be that if we took the fellow who picks up the garbage, zapped him with a super IQ beam and gave him the proposition, then a form very close to Einstein's results would come out.
I know I stated earlier that given any set of observables, there are an infinite set of models that fit. I am, today, however, rethinking that statement, I think it was wrong.
Given any FINITE, DISCONTINUOUS set of observables, I would say it is true. But given an infinite, continuous set, it's wrong because the derivative is know and measurable and if the derivative is fixed, the function is fixed.
Even if there are other models that seem to fit the observables RE: GR, it is PROBABLY true that they are all relativistic in nature. But still, not necessarily Einsteins results.
Now IMHO, we have touched on what I see as the heart of the matter. EPR.
From what I remember about the chapter(s) dealing in EPR in Einsteins and Rosens work, the end result is the promotion of a "hidden variable theory". Basically, we're not sure what the mapping is, but there exists a one-to-one mapping between the results as predicted by GR and the results as predicted by QM.
Nice idea. But wrong.
Bell proved conclusively that there can be no hidden variable theory.
Now I need to present a thought experiment of sorts. Imagine groups of people. In group 1, we have person A and person B.
Person A likes to wear red sunglasses. Person B likes to wear yellow sunglasses.
We could say that in a sense, person A and person B live in the same world.
Our next group is person C and person D. Person C likes to wear blue sunglasses. Person D likes to carry an umbrella.
In the sense that we are able to say A and B live in the same world, we are just as able to say that C and D do not.
I understand that this does not fit any sort of mathematical language rigidity requirements. But it is true nonetheless. And I am inclined to sometimes think that many are inclined to worship mathematics a bit too much. I could easily make a simple statement in English that would stretch the limits of math, for instance "It hasn't rained for three days".
Have at it! Sharpen your pencils! Put it in math form! No answers will be accepted if they don't also include complete descriptions of the relevent terms.
So now we have a really, really interesting situation. How can GR be true and QM be true? If there were some basic incompatability between the axioms (something like we find out that "velocity" as it relates to GR isn't the same as "velocity" as it relates to QM) then we could make adjustments and try again.
In the past I have described the multiverse theory. That there are in fact more universes than one, right here, right now. And I will close for the moment with giving an example of something that tries to explain.
We have available to us a rule book. On page 5 of the rulebook, we find the rules for seven card stud.
On page 6 of the book, we find the rules for chess.
Nothing on page 5 contradicts or confirms anything on page 6, and vice versa.
Toward the end of the book, say on page 213, we have the rules for GR. On page 217 we have the rules for QM. Same deal applies.
If we learn ultimately that QM and GR are really talking about two different universes, that is an exciting prospect. Either way. Perhaps the next great breakthrough will come from analysing what are the implications of not being able to merge all the theories.
Anyways I already know there are some things I thought about today that I missed, maybe I'll come back to the thread.