mathematic

The physics of the earth and moon orbits is completely different from what happens inside an atom. The celestial orbits are governed by Newton's laws of gravity (or General Relativity to be precise). The interactions describing the atom are described by quantum mechanics. These relationships should not be viewed as orbits in the same way as the celestial. Instead the description is in terms of quantum states.

Not much today, but the future could bring some surprises.

The weak force as a function of distance is nothing like the strong force. Look at chart in the following: http://en.wikipedia.org/wiki/Fundamental_interaction

You can simplify by 2x/(x+1) = 2/(1 + 1/x), so you can get the limit directly.

The usual method of extra-solar planet detection is by fluctuations in light intensity due to the planet passing in front of the star.

It is very simple - there is no theoretical or experimental evidence for such a thing.

Looks fine to me.

Quantitatively it is impossible. The sun itself is producing far more neutrinos than anything that could ever be made by ordinary mortals. Furthermore most of them pass right through the sun without interacting.

Could you be specific as to what you are referring to? There was some discussion of a "Glasma", which is at a lower temperature than a quark-gluon plasma.

Mother nature's trick is to use the laws of physics.

Your first sentence is completely wrong. All that is known is that the universe (immediately after the big bang) was a high temperature collection of photons and other stuff, all of which could interact. It took a little while (fraction of a second) to settle down into a plasma made up of photons, protons, neutrons, and electrons. Further along other light nuclides (H2, He, Li) formed. After about 300,000 years things cooled down enough that atoms formed. All other elements were formed in stars, a much later development.

Entanglement and double slit experiment are not optical illusions.

Gluons exert forces on quarks. Presumably right after the big bang it was a "quark-gluon soup". http://en.wikipedia.org/wiki/Quark%E2%80%93gluon_plasma

I am not sure what point you are trying to make. However the strong force is essential to holding atomic nuclei together. If it wasn't there, there would be no universe as we know it.

What is your point?

Your other post says you want to use epsilon-delta definition, but no specifics, so my answer is still I guess so.

Star formation results essentially from gas clouds (primarily hydrogen, not water) condense due to internal gravity. If there is enough matter so that the internal pressure heats up the gas sufficiently (becoming plasma), it will start shining. Water is irrelevant.

Atomic "orbits" and gravitational orbits are two completely different things. Quantum theory describes how atoms are put together. Gravity is described by general relativity.

It doesn't take an infinite amount of energy to separate two quarks (in particular a quark anti-quark pair). However when trying to separate them, a lot of energy is needed. When they are finally apart, the extra energy gets converted into another anti-quark attached to the original quark and another quark attached to the original anti-quark.

I guess so, but I don't see any δ or ε in your description.

You need to clarify your question. Give an example of what you have in mind by the second sentence. What is "greater forms of energy"?

1+x^2 has a minimum at x = 0, so 1/(1+x^2) has a max at x = 0 with the value 1. Net result: your last expression is bounded by |a-x|(a^2 + 3|a| + 2).

The value you got for the square root of i looks correct, assuming the part you elided ends in i. The exact value is (1 + i)/√2.

Expansion of the universe is effectively anti-gravity and is seen by galaxies moving apart. At a microscopic level the other three forces define what is going on.

I am not an expert. However, as I understand it Aspect's experiment has to do with Bell's inequality (quantum entanglement). I have no idea how this connects to the idea of the holographic universe.