In my last post, I mentioned that I am finding the most difficult proofs to be proofs of physics and not proofs of mathematics.
First off, it me detail that idea. For when we axiomatize physics, we thence have logical proofs in physics. In Old Physics, they had no axioms, and a proof in Old Physics was a experiment. In New Physics, we have two methods of proof, experiment and logical deduction from the Maxwell Equations as axioms.
Now let us take some of the most difficult proofs of mathematics as an example of how easy they are compared to proofs of physics.
The Fundamental Theorem of Calculus is so easy, that even a college student would ask why we need a proof at all, since the derivative is the hypotenuse of the triangle atop the rectangle and the integral is the area of the picketfence, so you cannot have one without the other.
The 4 Color Mapping Problem is a one paragraph proof when borderlines are seen as necessary to the statement and without borderlines, it is philosophy or psychology and not mathematics.
Fermat's Last Theorem is as easy as Infinitude of Primes proof in New Math, for in both, the borderline of finite to infinity is 1*10^603 and we simply ask, are there at least 1*10^603 primes between 2 and 1^10^1206? If there are, then there are an infinite set of primes. There are an infinite set of perfect-squares, but perfect cubes is a universal finite set. So in New Math, the question of infinite sets becomes a question of density of that characteristic. Are primes characteristic form a dense set? Does perfect squares form a dense set compared to perfect cubes? It is only commonsense that no-one is going to ask if tigers and whales are infinite set, for they lack density and are rather "rare", whereas even the question of are microbes an infinite set may be appealing to ask here on Earth for they do seem to be dense but when we ask that over the vastness of Space, do you think we would have 1*10^603 microbes?
The Fermat's Last Theorem was proven a long time ago in mathematics and takes only a one page proof, for there are no Pythagorean triples in 1 to 1^10^603 for exponent 3 or exponent 4 and none for any higher exponent.
You see, when mathematicians clean up their science of the borderline between finite and infinity specified, then all of their statements of mathematics and their proofs of mathematics require only a one page proof.
But now, physics is a different and superior science for it is the top science. Some of the statements and proofs of Physics are the most difficult of all, and I happened to land on one of those most difficult.
Calculus of mathematics teaches us that there are no curved lines in mathematics at all, but rather, what we think is a curved line is a composite of tiny straightline segments. This is a direct result of there being a borderline between finite and infinity which causes there to be tiny holes or gaps in space of empty space gaps. Those empty space gaps are what creates length for a line and no length for a point. Those empty spaces creates internal area for the integral. But those empty spaces also creates the non existence of curves in math and in physics.
So I need to prove in Physics that the Maxwell Equations do not allow for curves to exist. That what we think are curves, are actually a strung together tiny straight line segments.
That is tough, extremely difficult.
I have one very important supporting evidence, that lightwaves must travel in a straightline, and when entering a new medium, the lightwave as it refracts, does not form a curve but forms a new straightline.
I also have another important supporting evidence of quantum mechanics itself, in that quantum mechanics means physics is discreteness and not continuity. Discreteness favors tiny straightline segments.
And finally, I have another major supporting evidence in the force laws of physics. We call them interactions between two bodies, mediated by a third body. So in physics, a force is 2 bodies mediated by a 3rd body.
So here the argument for Coulombs law or EM-gravity, of their inverse square force law, is that if you had just 2 bodies and no 3rd body interacting, then you can have Space and Physics with curved lines. However, since you have to have a 3rd body, the photon interacting with the electron to proton, then you cannot have the motion of the electron as a curve but only as a collection of tiny straightline segments. The interaction of the photon as it goes from proton to electron, tells the electron "go in this tiny straightline now" then the photon goes back to the proton and tells the proton "go in this tiny straightline now" then back to the electron and back and forth.
So in Physics, there can be no curved lines but only tiny straightlines compounded together to form a straightlinecurve overall. The Maxwell Equations require the charged particles of proton and electron but also require the noncharged particle of photon in the Coulomb law. (Many in physics today, never realized that quantum mechanics was not borne in early 1900s with Planck and Bohr, but actually was borne in 1861 when Maxwell put together the Maxwell Equations.)
If Physics requires out of necessity 3 bodies to form a force of physics, those 3 bodies interacting cause there to be straightline segments and curves cannot exist when 3 bodies are interacting.
More than 90 percent of AP's posts are missing in the Google ?newsgroups author search archive from May 2012 to May 2013. Drexel ?University's Math Forum has done a far better job and many of those ?missing Google posts can be seen here: