I'm in a mood for this game right now, so I'll have a go this once.
This simple Newtonian explaination shows that the apples potential energy is stored in its density.
Nope. A kilogram of lead has the exact same gravitational potential energy as a kilogram of feathers. This has been experimentally proven.
Density is just a measure of the distribution of mass. For any object, its density is its mass divided by its volume, and has dimensions [mass]/[length]
3.
It only wants to reduce the potential difference between itself and the water in the bucket.
Nope. The potential energy of an apple in air, and the same apple in the same location but inside a bucket of water, is the same. So is the density of the apple, too. While this does require somewhat costly equipment (due to immersion in water instead of air!), it is not difficult to prove experimentally.
In order to say the uniform rotation of atmoic structure is a store of energy is to say that every atom should be constantly losing energy and everything stops.
No, the two are completely separate concepts.
Anything rotating is a store of energy. In rotating systems, angular momentum is conserved, including in large weather systems like tropical cyclones.
Atoms do not rotate by themselves, electrons do not rotate around atomic nuclei. Electrons do not form an atmosphere around atoms. The terms "electron orbital" and "electron cloud" refers to the basic shape of the electron wave function, and have nothing to do with atmospheric phenomena.
It should be remembered that gravity has been confirmed as a wave, waves can only propagate by changing a quantity.
No. Gravity is not a wave.
Gravitational waves refer to a phenomena where the spacetime itself contracts and expands like a wave on the surface of a pond. This happens, when very heavy, very small objects accelerate or decelerate. The ones we have thus far detected are from colliding neutron stars or similar or heavier stellar objects.
What it means, is that spacetime itself is something that can carry a wave, just like the surface of the water –– or more aptly, like sound waves in a medium like air. It is not a static fixed coordinate system like Newtonian mechanics would imply: it is something much more malleable. Albeit it takes a lot of energy to cause such effects.
Simply put, it is called "gravitational wave" because the
cause is related to accelerating steep gravity wells; it is spacetime itself that carries the wave.
volume happens to be a key component of the inverse square LAW
No, it isn't. Volume would actually correspond to a cubic or inverse cubic law, because we have three spatial dimensions.
That is, we measure volume using units of [length]
3, not [length]
2.
a magnetic helical wave that generates a potential difference when rotated
No, that's just word salad you hoped was complex and wonderful enough to cover the lack of understanding. I did something similar as a child, when I wanted to impress others. Then I found out the universe was vaster and more complex than I could ever understand, and stopped doing that, because it occurred to me that actual observations and scientific experiments are more interesting than any fiction. The fact that I do not understand everything is a given, and the starting point; any understanding gained is a win, and we find out most effectively if we apply the scientific method and cooperate – that includes no more fibbing and hiding behind jargon.
Magnetic fields have both strength and direction. The direction, magnetic flux, has no start or end, and only form continuous loops. (That is what ∇·B=0, Gauss's law for magnetism, means.) In vacuum, the strength H is related to the flux via H = B/µ₀, where µ₀ is vacuum permeability. Outside of vacuum, it depends on the magnetization and permeability. Because of this, the flux cannot "cross" itself: the field strength would increase dramatically there, and something would need to cause it –– in pure vacuum, it cannot happen.
How would you describe the magnetic flux B in a "magnetic helical wave"? Preferably mathematically, so that it can be reproduced and properly examined in all four dimensions –– remember, it's supposed to be a wave, not a static magnetic field.
I'll give you a hand. "Magnetic helical waves" do not exist, because it would require infinitely twisted magnetic field, or magnetic monopoles. Neither has ever been discovered in probably millions of practical experiments. If you try to save that idea by using
two oppositely twisted magnetical helical waves, you end up with intersecting field lines, which in turn means unphysically high field strengths. If you invent a structure of helices that avoids intersections, you still have the problem of exactly what is causing the magnetic field; and that in the near-vacuum of space, there just isn't anything that could cause such.
Finally, "a helix that when rotated, generates a potential difference" is a non-starter. By definition, an uniform helix has axial-rotational symmetry, such that both rotating it and moving it forwards or backwards by a suitable amount, the exact same shape repeats. Thus, rotation is no different from propagation when helices are involved. Besides, "when rotated", how? By hand? No, seriously.
It is most useful to concentrate on finding out how things happen. This is the core of physics: modeling practical reality, so that phenomena can be described and results predicted to an useful degree. Thinking up hugely complex mechanisms of why things happen, then covering the
how part with mushy descriptions, can be fun, but is not useful physics. It's just like in software: there are millions of people who have the best idea since sliced bread, and just need a typist-programmer to type it for them for a couple of hundred of dollars, to become millionaires! But the darn programmers are so uppity and full of them that they refuse, probably just to keep their own salaries up. No, the truth is that the idea is worth nearly nothing, because the implementation requires a lot of hard work. Similarly, the soft mushy adjective-y descriptions as in post #843 describe an idea with no reliable, reproducible details on
how.
We don't use math to describe the details because we are so uppity; we use it because it is the best language we have for such descriptions. If you don't want to use math for these descriptions, you should ask yourself why.