I can totally prove 'theories' of mechanics (including planetary mechanics) using calculus-based physics, given a writing instrument and some notepaper; prior to centuries of that then-evolving thing we now take for granted (math, in its advanced forms, including multivariable calculus, differential equations, polar geometry, modern trigonometry, modern algebra (the grad-level stuff), that would not be possible. Though, likely since as long as humans have walked the planet, they had seen 'proof' with their own eyes (collision physics, metabolism, bulldings not falling down randomly).
But stuff like black holes, special relativity, etc, are like phenotype vs genotype: the former you can witness and deduce, and prove, and witness the proof. The latter, you can witness instruments, hypothesise, use math, use instruments, deduce... you aren't really witnessing the stellar event though; you are merely witnessing instruments and playing matching games.
Humans will probably never ever be able to measure or witness what would really happen if you tossed a Cabbage Patch Kid into a black hole, no less an exoplanet or whatever. We will almost certainly never be conscious and anywhere near an accretion disk, nor even have cameras that can show us them, nor be able to toss that Cabbage Patch Doll in. Yes, we can hypothesise and 'sorta prove' there is a whole lotta denseness going on, but our ability to really understand it IS somewhat limited to numbers.
Theories are theories until proven multiple times. But even when we prove them, that doesn't always mean the theories we built around them are also right. For instance, maybe there are things that can seem like supermassive black holes that are something else entirely.
There may be a language-barrier issue here, because you've already used an uncommon term. You also put 'theories' in quotes, as if they are not actually called theories? Are you thinking of theorems in mathematics?
A physical theory is, at its core, a mathematical model of some set of physical phenomena. It gets judged on two main grounds: how well its predictions match what we already observe, and whether it can successfully predict new things that can then be tested...
It is also worth being clear about what a physical theory is not. A mathematical proof establishes the truth of a conclusion given certain axioms, and that is that. A physical theory, however well-supported, remains permanently open to revision by future observations. That is not a weakness. It is the defining feature of a science that is actually trying to describe the world rather than merely exploring abstract structures.[6]
> I can totally prove 'theories' of mechanics
I don't think you can. We know that orbits and ephemera can be calculated to a high degree of accuracy, and there's abundant evidence of that. But even here, the three-body problem exists, and perturbation theory is actually a theory. If you extrapolate your pencil-and-paper calculations for the orbit of Europa, for example, 3,000 years into the future, you'd have discrepancies. Our formulas are not proofs but approximations, even still.
Proofs can be written for purely mathematical aspects--even the math in theoretical models--but a mathematical proof is guaranteeing the equation and the soundness of the mathematics; it is proving a theorem, not "proving a theory".
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven.[a][2][3] The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.
I don't see that. GPS actually takes into account both special relativity and general relativity, in different ways, and thereby confirming predictions made by these theories.
"Black hole" is simply a conventional name we've given to a prediction arising from general relativity. General relativity has been a robust theory, with predictions confirmed, and with no significant falsified predictions.
> Theories are theories until proven multiple times.
This makes no sense at all.
> But even when we prove them, that doesn't always mean the theories we built around them are also right.
You've doubled down on the nonsensical. We've lost the plot here.
But stuff like black holes, special relativity, etc, are like phenotype vs genotype: the former you can witness and deduce, and prove, and witness the proof. The latter, you can witness instruments, hypothesise, use math, use instruments, deduce... you aren't really witnessing the stellar event though; you are merely witnessing instruments and playing matching games.
Humans will probably never ever be able to measure or witness what would really happen if you tossed a Cabbage Patch Kid into a black hole, no less an exoplanet or whatever. We will almost certainly never be conscious and anywhere near an accretion disk, nor even have cameras that can show us them, nor be able to toss that Cabbage Patch Doll in. Yes, we can hypothesise and 'sorta prove' there is a whole lotta denseness going on, but our ability to really understand it IS somewhat limited to numbers.
Theories are theories until proven multiple times. But even when we prove them, that doesn't always mean the theories we built around them are also right. For instance, maybe there are things that can seem like supermassive black holes that are something else entirely.