User:RC711/sandbox

The problem with learning and Wikis in their current form.

The equation on Wikis, and most of the Internet, just sit on the page. They do nothing themselves, but require humans to read, resolve dependencies, and convert to some action such as calculation or simulation or comparison or cabration or design).

If every use of numbers for calculations, either in the presentation or potentially in the future, is within a framework where


 * Each symbol is clearly identified
 * Each symbol is identified by its value and units
 * Each equation is stored as a computable object so it can actually do the calculation, simulation, modeling, calibration, or symbolic manipulation implied
 * All equations and symbols can be brought into a complete collection, in a working environment, where engineers, scientists, mathematicians, muscians, artists, managers, designers, ANYONE can use them as needed.
 * The same is true of all 2D and 3D and 4D technologies where manipulation of complex stored objects is required - manufacturing, design, 3D printing, and most of our current technologies. That includes most biological, chemical, financial, social and economic areas.

The time to learn something, in the quantitative areas and where complex tasks are stored or could be stored on computers, is weighted heavily to memorization and look-up of basic properties of the equations involved. It takes months or years to absorb and use some tools. You have to read them off the page, look up what the author presumably knew (what each piece is called, its units and dimensions, and the various supporting models that explain or model its behaviors), then you have to find a programming or modeling environement, manually transcribe the equation or data structure to that new environment, speed weeks or months just getting it to work, before you can see if it is close to what you need. Then you find that it was from an unreliable source, has big holes and assumpltions the authors did not reveal or know, and you have to throw it all away and start over again.

Example: Suppose you want to build an electron microscope to look at some defects on the surface of a new kind of glass you need for an experiment, or just for a new kind of nanoscopic art project. You know they have been done before many times, and can find 15 million entry points from your search on the web. You need to walk through what parts are needed, and want to simulate them first, so you don't waste much money and time just getting started. If only a few hundred people have designed and built this before, you really do not have the time to spend years going over the basics again. You do not want to become an expert on electrodynamics and quantum mechanics, especially as there are so many copies (many incomplete or simply wrong) on the web. You do not want to become an expert on vacuum techniques, many of which were memorized from the earliest days and no longer applicable. You need to bring together a few dozen modules, put them into a simple framework, set boundaries on what you want to try to begin, and then interact with the model/simulation and see what it can do. It might be that the virtual simulation answers your question, or need for a particular type of image or 3D video segment for something you want to try. So you run a sensitivity analysis of the model, within certain bounds, and then check to see if it either makes a new reality, or matches the real world - by comparison to a standard data collection of the type you want to work with.

If $$\eta$$ is constant, this reduces to the vector heat equation


 * (1)    $$\frac{\partial \mathbf{B}}{\partial t} = \eta\nabla^2 \mathbf{B}(\mathbf{r},t) + \nabla \times ( \mathbf{u\times B} )$$

=


 * (2)    $$\mathbf{u\times B} = (uB_x, uB_y, uB_z)  =  (u_yB_z - u_zB_y), (u_zB_x - u_xB_z), (u_xB_y - u_yB_x)$$


 * (3)    $$

\nabla \times ( \mathbf{u\times B} ) =  \nabla \times (uB_x, uB_y, uB_z)  =  \left(\frac{\partial uB_z}{\partial y} - \frac{\partial uB_y}{\partial z}\right), \left(\frac{\partial uB_x}{\partial z} - \frac{\partial uB_z}{\partial x} \right), \left(\frac{\partial uB_y}{\partial x} - \frac{\partial uB_x}{\partial y} \right) $$


 * (4)    $$\eta = \frac{1}{\mu_0 \sigma_0}$$


 * (5)    $$\sigma_0 = \frac{n_ee^2}{m_e\nu_c}$$


 * (6)    $$c^2 = \frac{1}{\epsilon_0\mu_0}$$


 * $$e = $$ electron charge
 * $$m_e$$ electron mass
 * $$\mu_0 = 4 pi \times 10^{-7} = 12.566370614 \times 10^{-7}$$, magnetic constant, Newtons/Ampere^2
 * $$c$$ speed of "light and gravity"
 * $$\sigma_0$$ electrical conductivity
 * $$\epsilon_0$$ electric constant, vacuum permittivity
 * $$N_A = 6.022140857 \times 10^{23}$$  Avogadros Number, Particles/mole
 * $$n_e$$ electron density
 * $$\nu_c$$ collision frequency


 * $$\epsilon_g$$ gravitational energy density, Joules/kg
 * $$\epsilon_B$$ magnetic energy density, Joules/kg
 * $$\epsilon_E$$ electric energy density, Joules/kg
 * $$m_g1$$ graviton mass 1, Joules/kg
 * $$\epsilon_g = \frac{g^2}{8 \pi G}$$
 * $$\epsilon_g = \frac{g^2}{8 \pi G}$$


 * $$\epsilon_B = \frac{B^2}{2 \mu_0}$$


 * $$\epsilon_E = \frac{\epsilon_0 E^2}{2}$$


 * $$m_{g1} = \frac{\epsilon_g}{N_A c^2} = \frac{g^2}{8 \pi G c^2 N_A}$$


 * $$g = B \times \sqrt\frac{4 pi G}{\mu_0} = B \sqrt{10^7 G} = B \times 38.70831762$$


 * B Magnetic field in Tesla
 * E Electric field in Volts/meter
 * g Acceleration field from any source in meters/second^2 (m/s2)
 * \epsilon_g, \epsilon_B, \epsilon_E are the energy densities for the gravitational, magnetic and electric fields.

The magnetic, electric and gravitational fields at very low frequencies all overlap to some degree. They are each derived from the same underlying potential, and they each can be expressed in their traditional field value and units. Or their potentials can be combined in energy per unit mass, or energy per unit volume, or other convenient units.

This last equation shows that where the gravitational and magnetic energy density are known or assumed to be equal, the magnetic field in Tesla is equal to a universal constant times the acceleration. For example, if g is 9.8 meters/second^2, then the equivalent magnetic field is 9.8 m/s2 times 38.70831962 Tesla per m/s2 or 379.341512676 Tesla. I leave the full decimal representation so it can be checked in a testing and verification process that ultimately will be out to 12 digits or more.

The collision of neutron stars in August of 2017 (see GW170817) showed that the speed of light and gravity are identical to many decimal points. This could not be true, unless they share the same underlying potential and mechanisms, the same underlying vacuum process.