Gravity and Maxwell's Equations

Previous blog posts have looked at gravity as a combination of electromagnetism and geometry. Maxwell's equations are the vector calculus description of electromagnetism so it might occur to a physicist that Maxwell's equations can explain gravity. This is only partly true.

The two Maxwell-Gauss equations explain static fields and can get us part of the way towards explaining gravity. Maxwell's equations don't explain the fast moving root mean square speeds observed in electrons and nuclei.

Maxwell-Gauss' electricity equation explains how the fictional electric field works. The field lines in an exaggerated sphere will tend to diverge as the observer moves from the center of mass.

Maxwell-Gauss' magnetism equation explains how the fictional magnetic field works. In reality the magnetic field simply represents the spinning of electrons as they travel through space. The field lines in an exaggerated sphere will tend to have a density that is lower as the observer moves from the center of mass.

Where electric fields converge we find a complicated mix of alternating positive and negative fields. Electrons in close proximity will tend to flee the relative convergence of a dense portion of matter near the center of a mass. Towards the periphery of a mass the opposite is true. Mass tends to seek charge balance and gravity takes the form of particles spinning back towards the center of mass. It is highly likely that the return to the center of mass happens more slowly and with more bumps than the ejection of particles; most notably beta particles.

Magnetic fields are orthogonal to electric fields. Where the magnetic field lines are found to be more dense we find an environment that is ready to impart potential energy to particles. This will happen, most readily, to the small and fast electrons rather than the ions in the nucleus. The ejected beta particles will eventually collide with other electrons or, less likely, with the nucleus of a particle.

The electrons will travel away from the center of mass. The resultant pull due to the charge balance of the mass will yank particles of both 'charges' back towards the center of mass. It is this constant pull that constitutes the gravitational pull that we experience every day on Earth.

Depletion Layer and an Air Gap

It is interesting to consider the differences and similarities between the depletion layer or transition layer in a semiconductor and an air gap. This is important because for decades the mechanical relay used an air gap to produce an 'open circuit' output that would break the circuit and inhibit current flow. Now semiconductors can do the same thing using the depletion layer but exploring this part of a semiconductor takes a bit more imagination.

Imagination is needed because there aren't great descriptions of how the depletion layer works beyond a smoothing of the charge balances between 'positive' and 'negative' doped semiconductor regions. How do those charges jump around? Like the charge discussed in my posts on gravity, the depletion layer may see spark-like charge jumps and fuzzy-Gaussian charge movement akin to the boil seen in a kettle.

The spark-like carriers I write about are often termed hot carriers and although the Poisson - Gaussian statistical movements are not termed cool carriers, The term shot is often used in noise theory and has also been related to the Poisson arrivals in mathematics. Thinking hard about what electrons are doing statistically leads quickly to words like fuzzy vs. spiky.

Let us consider, more closely, the depletion layer of a standard Si diode that does not have Schottkey properties. The standard theory states that there is charge smoothing through the depletion layer. Doped Si on either side of of the p-n junction swaps sides causing the depletion layer to exhibit a neutral or opposing charge.

I'd like to see more research in this area of Poisson vs. Gauss statistics in the p-n junction. How does 1/f noise factor into the analysis? The p-n junction may have a kettle boil of charge that traverses the junction with a statistical equilibrium that causes the diode action. The incoming charge comes in hot and crosses the diode to the junction where it either piles on to the depletion layer or in fires right through relatively hot (though nothing like the Schottkey diode). Diodes behave differently depending on whether or not they are forward or reverse biased.

A full comparison to the air gap in a relay will have to wait for a future blog post. It is enough to say, right now, that when the incoming carriers pile into the diode they are under what people our size might term - incredible pressure. At the electron feature size particles behave differently. The growth of the depletion layer due to incoming carriers leads to what I would estimate is a Gaussian or fuzzy electron distribution. This kettle boil keeps the reversed biased diode 'gaped from conduction'. The depletion layer is not an air gap where arcs are prevented. The depletion layer provides a push back that mimics the air gap of an electro-mechanical relay.

Turbulence and Electron Flow

As stated on a previous post, turbulence and laminar flow are terms usually reserved for aerodynamics. Electrons flowing through a circuit might be said to exhibit turbulent or more graceful flow. During the graceful flow of molecules or electrons density can go up as the electrons are very well ordered. A turbulent flow of electrons consumes more space and draws in positive ions. This is the magnetic push observed between like poles of a magnet.

Question of the day: Can a proper Poisson related (shot pattern of multiple Poisson arrivals) cause light gravity to shift if the right number of electrons are moving with respect the the mass ratio of the electron to nucleus ratio? Light gravity could move shift and swirl without affecting heavy gravity. This would result in two different gravity constants for the same point of space close to a large mass such as a planet. Gravity could then not be said to be simply 9.8 m/s^2.

Maxwell-Faraday Equation - Does It Even Say the Right Thing?

So those who like electric motors and generators look to the Maxwell-Faraday equation to get direction and relative motion of current right. Curling electric fields and changing magnetic fields, described by this equation, give us the logic we use to run millions of machines world-wide. What's more this equation works.

We can do much better. The Maxwell-Faraday equation doesn't capture the complexity of what is really going on with the curl in the currents. This equation instead uses some vector calculus to explain the big picture of what is really going on. The equation tells us that a curling electric field and thus a curling current due to a changing magnetic field. Now why might that be?

The magnetic field is often a tight curl of individual electrons that emanates from one pole of a magnet and terminates in the opposite pole of the magnet with the same total curl to preserve the conservation of angular momentum. The Maxwell-Ampere equation shows us the relative polarities and spin of the electrons and how that relates to an electron current. The curl of a magnetic field is equal to the displacement and volume charge current. The curl of a current field is proportional to a magnetic field at some distance from a coil or a current carrying wire.

Once the polarities have been sorted out we can dive into the Maxwell-Faraday equation. Starting with the right side of the equation we find the changing magnetic field. A changing magnetic field involves a tight spiraling field of electrons. As this tight spiraling field approaches the point under analysis by the equation the field gets tighter and the number of spinning electrons becomes greater. When we observe a point under analysis that is conductive we find that the tight curls accelerate the electrons in the conductive material.

Conservation of angular momentum (some have written conservation of energy) and other electrons in the conductive material find themselves in a larger curl oriented in the opposite direction. For this reason the left side of the Maxwell-Faraday equation shows the large counter-curl of the electrons as a curl of an electric field.

Can Physics Do Better Than the Maxwell-Heaviside Equations

Heaviside's version of Maxwell's Equations are a history lesson. There have to be better ways of describing electric phenomena and magneto attraction. Running through Maxwell's equations tells us the basics of the way electromagnetism works using the concept of fields, flow of fields and the flux of the flow of these fields. Specifically a branch of physics examines the flux of the flow of magnetic fields to describe how magnets will behave and electric flux of the flow describes how charged particles will behave. In addition to Maxwell's equations the Lorentz force equation provides additional information on the behaviour of charge in the presence of the above mentioned 'fields'.

The Gauss-Maxwell electric field equation describes a volume charge can be represented as a diverging electric field. This is a convenient representation of electric phenomena and it seems to hold at a high level. Is this equation accurate at a microscopic or nanoscopic level?

The Gauss-Maxwell magnetic field equation is simply a vector calculus identity. The electrons turbulently fly off any given wire and curl. This is especially true for natural magnets. The normal of this curl is what Maxwell and Heaviside termed the 'magnetic' field in this set of equations.

The Maxwell-Ampere equation states that a magnetic field curls around a volume current density or a changing displacement current. It is important to note that when the electron field curls the magnetic field lines up as well as in the case of an inductive coil electromagnet. These two relationships reflect that when there is turbulence in a field of moving electrons the spinning electrons interact with the laminar flow of current in a manner described by the inductance equations.

The Maxwell-Faraday equation should be rewritten. There is a lot going on when we relate the change in magnetic field to a curl in the surrounding electric field. Specifically Lenz's law shows us that opposing eddy current show up when a magnetic field is presented. The magnetic field sets up and increases in a tight fashion. What this equation is really saying is that conservation of angular momentum of electrons causes a large curl of electrons to set up when a tight curl of electrons in a magnetic field is presented. The whole truth of electromagnetic induction with respect to curls of currents and counter-curls of current are not being told using this equation or any other popular equation.

Finally, Lorentz's equation shows us what direction a particle will travel in the presence of electric and magnetic fields. A moving charge will be deflected by a magnetic field or turbulence in a field of moving or curling electrons. Charge will see a force by other charge and the equation sums this up neatly.

Maxwell's Equations Revisited

In previous blog posts I've stated the Gauss' law of magnetism is just a vector calculus identity. Ampere - Maxwell equation simply states that electricity moving in a circular or turbulent motion is what we call magnetism. The magnetic field is the normal vector of the circulation or turbulence of the electron flow.

Now I look at the Maxwell - Faraday equation and relate it to Lenz's law. The tight circulation of magnetic field or curling electrons is observed by its counter-rotating motion of other electrons working to conserve angular momentum. It is the counter-rotation that we observe in an electric generator and we normally attribute that to the Maxwell-Faraday equation. In the Maxwell-Faraday equation the change in magnetic field magically creates a curling electric field.

Laminar and Turbulent Flow

The link between fluid dynamics and electron flow is incomplete and a bit on a stretch for most physicists but what better place to explore the topic than a blog? Laminar and Turbulent flow are two fluid concepts. Current and inductance are analogs. A turbulent flow that wraps back on itself stored energy in the same way as an induced curl field in a circuit. The telegraphers' equations specify the current as the series linear circuit elements R and L.

Viscosity is the propensity of the fluid to resist deformation. If an electron is injected into one side of a copper wire does one pop out the other side? Certainly yes though the turbulence of the route the electron takes is questionable. Now if you tried to push a Coulomb of electrons into the wire the capacitance specified by the telegraphers' equations would have to absorb all of the charge save the bleed off due to G.

In effect the ratio of R:G tells us something about how electrons behave in an electronic circuit. What is the ratio of electrons that push through to the load vs those that end up back at the electromotive force source having not delivered energy to the load. The probability that the electron will not deliver energy to the load is R:G.