 Markus Hanke

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• swansont

1. No, linear momentum is the conserved quantity that arises from spatial translation invariance via Noether’s theorem.
2. SR is far more general than just a relationship between inertial frames; it describes how events are related in regions of spacetime where gravity can be neglected. As such, it applies to any type of reference frame, not just inertial ones - it’s just that the relationship between inertial frames takes on a particularly simple form (Lorentz transformations), since the world lines of such local frames represent the longest possible separation between given events. Of course it also works with accelerated frames, but naturally the relationship between such frames has a more complicated form than a simple Lorentz transformation (i.e. such frames are in general not symmetric). To “derive” SR, all you need to know is that the metric of spacetime is diag{-,+,+,+} or diag{+,-,-,-}.
3. I am unsure what you mean by “amount of movement” - you would have to provide an exact mathematical definition of this term. In general though, you can obtain the equations of motion for a system from its action by plugging the action into the Euler-Lagrange equations. Solving the equations of motion then gives you the “movement” of the system, in the sense of some quantity changing with respect to some other quantity. This general approach is often used for field theories of various kinds. To answer your original question - no, the relationship between action and “motion” is somewhat more complicated than a simple gradient.
4. Yes, dimensional reduction on small scales is a distinct concept. I don’t know what - if any - observable consequences would arise from such a small scale structure, on macroscopic scales. Note that dimensional reduction is not what the OP suggests here, though.
5. Macroscopic spacetime being (2+2)-dimensional can be ruled out on a number of observational grounds (over and above the obvious fact that there are evidently three spatial dimensions that we can observe). To give just one example - in such a spacetime, electrons would not be stable particles, and would decay rather quickly. This is evidently not what we observe.
6. Of course it does not physically exist - it‘s just a mathematical artefact of the fact that GR is a purely classical model, and hence cannot account for quantum effects.
7. We already have such a framework: quantum field theory.
8. Yes, it is invariant under rotation about some real-valued angle (i.e. under a U(1) symmetry); the corresponding conserved current in Noether‘s theorem is called the probability current.
9. The angular momentum of a black hole is a property of the entire spacetime, and not of the singularity (which only arises in our models in the first place because we can‘t yet account for quantum effects). Furthermore, while spin can be considered a form of angular momentum, it is quite different from the one of macroscopic bodies.
10. A geometric relationship between reference frames in spacetime. In the simplest case of inertial motion, two reference frames being in relative motion quite simply means that they are rotated by a (hyperbolic) angle wrt each other in spacetime. Motion is purely a geometric phenomenon.
11. The gravitational field in the interior of a mass distribution such as a galaxy is not equivalent to the sum of gravitational interactions between discrete point masses arranged in a disk pattern. Also, I am pretty sure that General Relativistic effects cannot be neglected in this scenario, so Newtonian gravity is not the right theory to use. The model’s basic assumptions are fatally flawed, which is why no one in the scientific community is using it.
12. It’s battery operated (as I suspected), so the green light indicates that the battery is fully charged.
13. Distinction between what?
14. Yes, the magnitude and precise direction of the frame dragging effect does depend on the mass and the total amount of angular momentum of the central mass. It also depends on the exact shape of the central body, since rotating bodies are not perfectly spherical.
15. The big bang reveals a problem with the materialistic view

No. Causation does not imply intention. But then, it also does not preclude intention either - the question of whether or not there is a creator deity is outside the domain of the natural sciences. It is seldom a good idea to try and conflate fundamentally different domains of enquiry.