vanhees71 said:
How else do you calculate planetary motion in Newtonian mechanics, if not assuming a force law. It was one of Newton's many great achievements to have found the universal law of gravitation, being the discovery of one of the fundamental interactions in Nature, as we call it today.
I added the edit (sorry I tend to do that, in hopes the answer isn't read immediately!) that I am talking about Hamiltonian or Lagrangian approaches. What I mean is, let's say Hamilton came along 100 years before Newton, and demonstrated his approach to calculating the motions of planets. Huge success, all of physics seems to now be deterministically accessible. Then Newton comes along and says, "hey you can understand all this if you invoke the existence of forces, including the force of gravity." Hamilton's followers accuse him of inventing philosophical fictions that can't be observed!
Or, what if Einstein in 1600 presents his approach to gravity in the form of an unknown parameter c that is too large to be observed. He also predicts the motion of the planets correctly to lowest order in v/c squared, not only without invoking any force of gravity, but with a theory whose form respects the equivalence principle (as well as Poincare covariance). If Newton then came along later and showed his theory that does not invoke a c parameter but is not Poincare covariant, would people see that as an improvement because it doesn't need an unknown large c parameter, or a fiction because it doesn't obey the key principle of Poincare covariance? Would they point out that Newton's theory is invoking a force that is expressly impossible to observe when there is an equivalence principle that is already regarded as a key symmetry, even though c is still unknown? Would that not still be the case
today, if it happened that c was so much larger than it actually is that we
still haven't been able to observe it? (I realize this is a hypothetical question because we have observed c so we know Einstein's theory is better than Newton's, but I'm framing this within the context of predictions that are the same in both theories at v scales where the differences are unobservable.)
Or consider Lagrange's approach that all of classical mechanics is described by minimizing action, such that the minimal principle is all processes have an action and that's it. No forces at all, they're all philosophical fictions! Throw in a Feynman like path integral interpretation to the reason that action is minimized, classical motions are now wavelike long before quantum mechanics. Even Huygens had a successful interpretation of Newtonian mechanics, is that the minimal way to look at it because it invokes a concept of interference of propagating signals rather than unobservable definite trajectories? I mean, what if wave mechanics was understood prior to particle mechanics, and then particle mechanics was seen as a duality based on some unobservably small and unknown h parameter, akin to the unobservably large c parameter in Einstein's gravity metric. Are those minimal interpretations because they don't need to invoke some unobservable fiction like particles following definite trajectories that are never actually observed (because one never observes a definite trajectory)? What if statistical explanations had been proposed long before determinism was a thing, would not determinism have to be regarded as a philosophical fiction if Newton suggested it later on?
vanhees71 said:
Of course you can clarify the question, which spacetime model is correct, by observation. That's, in fact, how it turned out that Galilei-Newton spacetime is an approximate description with a limited realm of applicability, while Einstein-Minkowski spacetime (and it's localized form in General Relativity) has been found to describe all observations correctly. This implies the Poincare invariance of all observables and thus a theory that's not obeying Poincare invariance is at best an approximation.
Well here my position is contingent on
@Demystifier's claim that the observations of relativistic quantum mechanics can also be predicted correctly with a form of BM that is not Poincare covariant. I don't know if that is actually true or not, so my logic is if it is true, then BM must be regarded as a successful interpretation of relativistic quantum mechanics by your own reasoning, and if it is not true, then we must fall back to the position that BM is a successful interpretation of nonrelativistic quantum mechanics, like you are arguing that the force of gravity is a successful interpretation of Newtonian mechanics. At issue is, if interpretation X successfully interprets theory Y, and if theory Y passes all the same observational tests as theory Y', then interpretation X also successfully interprets theory Y'. If one adds the further requirement that interpretation X is not successful unless it is minimal, then the Newtonian force of gravity is not a successful interpretation of Newtonian mechanics because the Hamiltonian, or Lagrangian, or Einsteinian with untested c parameter, or Huygensian with untested h parameter, approaches have no such object in them as anything but an unnecessary add on, like Bohmian trajectories.