Now the general idea behind this chapter is that all the important equations of physics are built from the simple formula of Area = LxW. But equations of physics may be masked with various different geometries and compounded by areas. For example, the Area in Euclidean geometry is just simply A = LxW, but the area in Elliptic geometry is Area = pi x r^2 and the area in Hyperbolic geometry involves the logarithm Ln function.
So for example, the Malus law of physics is area in elliptic geometry of I =I' cos^2 a where the cosine squared is evidence of area in Elliptic geometry.
Now Ohm's law of physics is a example of area in Euclidean geometry where we have V = iR, or simply Area = Length x Width. Now, however, we complicate Ohm's law to render superconductivity by replacing Resistance R with Malus law, for resistance in superconductivity is polarization where the angle allows all the messenger waves to go through unscathed, meaning, a alignment of the angle of polarization.
So when we replace R with Malus law in V = iR we end up with a more complicated equation for superconductivity, or, even for conductivity in general such as the flow of electrons in copper or silver or in a semiconductor. A insulator would have cross alignment in polarization and no messenger photons or neutrinos get through.
So here we begin to see the what I call the "flavor of equations in physics." And what I mean by that, is that all the important equations of physics are fractals of Area = LxW, or Area = pixr^2 or Area involving logarithm.
Now let me give another example of the Coulomb law for it is Gauss's law where we have F = (k x q1 x q2)/ r^2
So we have Fxr^2 = k x q1 x q2, so that charge times charge is a Elliptic geometry area.
Now look at another famous equation of physics in that of E = mxc^2 and we immediately recognize it as a area in Elliptic geometry, just as the Malus law is area in Elliptic geometry.
Now an example of area in Hyperbolic geometry is entropy in thermodynamics of S = -k (lnP) . Another example is radioactive decay rates involving logarithms.
The important message that I am conveying is that all important equations of physics are built up from roots of Area = L x W. Where we simply compound a root equation, such as the diffusion equation and build up to the Schrodinger Equation. From the Schrodinger Equation we replace some of the terms with areas and we end up with the Dirac Equation.
Now why is Physics so easy and simple, like this, in that all its important equations are compounded area formulas? And the reason it is, because the Maxwell Equations such as the Coulomb law is a area formula, and since all of physics is derived from the Maxwell Equations, then all of physics important formulas end up being compounded Coulomb formulas.
Google's New-Newsgroups halted a proper archiving?of AP posts, but Drexel's Math Forum has my posts in ?sequential archive form as seen here: