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.

Magnets and Spin

Every chemist learns about the electron spin and magnetism. The so called magnetic field is just the propensity for electrons to 'curl' to borrow a term from vector calculus. So from the North pole of a magnet to the South pole of another magnet the curl will tend to align. The curl will also tend to make a round trip. The electrons curl on the way into one pole of a magnet and they curl on the way out of the other end of a magnet.

So what of electric generators and motors? We set up a field of curling electrons and we expose a coil to the field.The tight curl of electrons begs for the coil to conserve angular momentum. There are tight swirls due to the magnet and an induced larger swirl that constitutes the current that makes up the voltage presented in a generator.

As a generator turns it exposes itself to more and more of the curled field of electrons. Then as the generator coil moves past pi radians the process reverses itself. This can be characterized by Maxwell-Faraday's law but also invokes Lenz's law. These two laws or relationships can be explained as one idea but I will reserve this explanation for another post.

The reason magnets attract different poles is due to a mess of electrons rotating in opposite directions. At the boundary between electrons moving one way and another (magnetic field lines in opposing directions) there are many collisions. These collisions will at as a relative low pressure zone pulling the magnets towards each other. The sheer pressure of the electrons puts a mechanical force on the rotor of the generator.

Conversely, when two like poles are put next to each other the spin of their electrons does a tight loop to its opposing pole. This looping of electrons draws in matter and causes the two like poles to push away from each other. The same phenomenon is at play in Ampere's laws of attraction.

The Idea of Electron Pressure

Pressure is measured in force per unit area. Do we allow that electrons carrying mass can exert force on a cross section of a wire? Certainly we observe electromigration of mass through wires. The electrons seem to push through resistances without too much interaction. Electrons seem to spring through a lattice of copper like putty through sand.

If the electrons in a mass are dense from the standpoint of small masses travelling at 1% of the speed of light. Then as we bend the medium to make a sphere or a cube the electrodense inside will push electrons outwards. The outwards push will be fast compared with the pull back for charge balancing. All of the negative charge lost is filled with returning mass.

One of the thoughtful mistakes that might be made is assuming that electron pressure is less than it is. Electrons seem to be the light cloud that surrounds the real mass of the nucleus. In fact electrons moving at 1% of the speed of light exert a pressure that adds up to gravity. Internal electron pressure is greater than outer electron pressure causing a charge inversion. The balance of charge and mass is a push inwards towards the center of mass.

Magnets and The Economist

So I was just reading The Economist and this publication was reporting that complicated magnets were getting easier to manufacture into mechanical pieces with tolerances of 1 mm or less. Oak Ridge National Laboratories is working on building stators for motors and generators.

Lets review how magnets work. Electrons often spin and engage in circular motion around the atomic nucleus. The electrons will have angular momentum a physicist will say. If an electron is spinning in a circular manner inside the lattice of a magnet it will leave the lattice or interact with electrons outside of the lattice. The angular momentum will propagate along magnetic field lines until it re-enters the magnet at the other pole of the magnet. The angular momentum will have to add up.

Therefore, we have net spinning of electrons inside a magnet's lattice and around the lattice of the magnet in the air around the magnet. If one puts a piece of paper on the magnet and sprinkle iron filings on the paper the iron filings will line up with the magnet's so called 'field' of spinning electrons.

The radius of the spin of the electrons should be of great focus. Perhaps the new X-Ray machines, developed at the accelerator labs, will shed a light on statistics for electron movement relating to magnetic effects.

The interactions between any two electrons must be viewed statistically. Looking at a small magnet the interactions between any two electrons can be modeled statistically as a Poisson arrival. If we look at fields of spinning electrons around a magnet there will be regions where the electrons move together and regions where the electrons react with each other more violently.

Where electrons are spinning in opposite directions we have many and more violent interactions. Electrons will scatter and they will take the positively charged ions with them. This kind of interaction happens where magnetic field lines of one direction are very near to magnetic field lines pointed in the opposite direction.

All of the scattering allows the air to tend towards vacuum and the magnets pull together. If the magnets do not pull together air quickly back fills itself such that no observable vacuum of any sort develops.

Reverse Galton Box and Electromagnetism Causing the Gravitational Effect

You may have observed a Galton box. These contraptions knock beans back and forth until they settle into a binomial distributed bell curve. Imagine turning the contraption upside down and watching what happens to the electrons as the beans fall.

If electrons are accelerated from the center of mass by like-charge repulsion along the electric field lines there will be a drift velocity for these charges. The electrons move at a speed about 1-5% of the speed of light. Lots of kinetic energy is involved when n electrons push outwards from the center of mass. These electrons will bounce like Galton objects in the Bean Machine box. Ultimately many Beta particles will radiate from the Earth's atmosphere.

As I've said on previous blog posts the sheer number of events where a build up of negative charge cause an electron to be accelerated rapidly towards a region of lower density. Due to the massive velocity imbalance between electrons and their associated nucleus we see a tendency towards outward acceleration (slower) mass is accelerated towards the center of mass.

The Poisson equation helps us understand how gravity works. At a certain distance from the center of mass there will be lambda excess accelerated electrons outwards from the center of mass. Lambda is said to be the rate parameter. Therefore, lambda to the power of the mean number of excess electrons accelerated from that position multiplied by Euler's constant to the power of negative lambda. Divide all this by the factorial of the mean number of electrons and presto one has the probability in one interval that force is generated away from the center of mass. Of course we know Newton's laws and for every action there is an equal and opposite reaction. Large mass is accelerated inwards in what we normally call gravity.

Observing at Particles in Large Numbers

What can we say about the observation of particles in large numbers. It is easy to observe a vortex or a tendency to spin. When a large number of particles sheer past each other there is a tendency to spin towards a vortex.

Positively charged is an interesting way of looking at a population of particles. Conversely negatively charged particles implies particles with an abundance of electrons that are moving at a high rate of speed around the larger particles. Did earlier scientists simply mistake differing speeds of particles with the concept of positive and negative charge.

The speed of a large number of particles are often observed to be much slower than the sum of the instantaneous speeds measured. The root mean squared speed of a gas is far faster than the observed speed which may be zero. The root mean squared speed of electrons in a conductor is very fast. Further, electron accelerations due to the electromotive force is fast as well. The real drift velocity of a group of electrons in a conductor is altogether slow.

The terminal velocity of a mass is inevitably linked to a group velocity of the particles. So an accelerated mass is slowed by a building pressure will terminate in a velocity. Likewise a group of electrons accelerated by an electromotive force will collide with the lattice of a conductor and develop a group velocity or drift velocity.

Accelerating large numbers of particles often results in a group velocity.

Is Gravity a One Way Force?

Gravity seems so simple. It pulls forcefully towards the center of large bodies of matter. In previous blog posts it has been suggested that the force of gravity is simply a large additive force that is equal and opposite to ejected electrons that find themselves repelled from each other because of their negative charge and their high velocity. Larger bodies made of neutrons and protons find themselves inevitably pulled towards the center of mass.

The electromagnetic pull of gravity is a direct result of the fact that electron charge surrounds the more positive and slower ions that make up so much of the matter we observe. The question then becomes is gravity a one way force: down. Certainly when we look at large bodies of over thirty molecules or atoms gravity seems to fit. Gravity is ultimately an equal and opposite reaction to the multitude of accelerations due to the charged electrons coming together due to a three dimensional shape.

How then do we explain an atmosphere? A lower density surrounding to a higher density planet. Nitrogen and Oxygen diatomic molecules seem to have no problem hovering above the Earth's surface. If gravity is the culmination of billions of electron interactions then the outward collisions must be additive and significant. A clear buoyancy of gas molecules hangs above a more dense solid planet. Buoyancy and relative density play a role.

As the electrons try to fire away from other electrons and a dense core; protons, neutrons and electrons are drawn in to fill a mass and charge gap. A spherical planet will have a natural electron pressure develop towards the center of mass and continuing outwards. The sheer root mean squared velocity of the electrons and the energy involved in their collisions will, using Markov statistics, allow for a build up of kinetic energy in certain electrons with a regular statistical frequency.

The law of large numbers causes the Markov statistics to settle over billions of atoms to a gravity force that is very stable given the mass of large protons and neutrons that are drawn towards the center of mass.

Is gravity a one way force? Certainly not. Buoyancy and rising heat are examples of counter gravitational force. Electrons moving at extreme speeds will also experience a fly against gravity. The very equal and opposite reaction force to the electrons flying away is the gravitational force.

Two - Mass and Charge Exploration

My son's favourite number is two. I explore number theory at work to maximize safety and availability and two is a number with some interesting properties. For example between Gauss and Franklin charge has been built into two categories - positive and negative. Electrons and nucleus-es have other dichotomies of light and heavy as well as fast and less fast. What is the energy balance between an electron and its nucleus if the electron contains a higher ratio of its energy as kinetic energy and the nucleus contains a relatively higher ratio of its energy in mass (times the speed of light squared).

Charge is an interesting concept. The interaction of two categories of particles has given us a model that we term positive and negative. These charges repel like and are generally attracted to unlike charges. This may be a little over-simplified. We know that on Earth mass is attracted to mass through developed theories such as the London Forces and Gravity. Under this kind of intense pressure electrons will fill an important role being observed by their interaction with nucleus-es. These negative charges move at extreme speeds of over one percent of the speed of light at times. The number of interactions that an electron will have with various nucleus-es is hard to calculate without a well considered stochastic model.

Add to the hypothesis that two sets of particles are heavy and light. It is rare to see a well developed comparison of the momentum of these two types of particles. If we look directly at conventional physics a nucleus will contain more energy in the form of mass through the e=mc squared equality. The root mean squared speed of this more massive nucleus is only a small fraction of the speed relating to the mighty mouse styled electron.

Finally, electrons are fast. It is highly likely that no matter how tightly you bond your Rutherford model to the nucleus; electrons will find their way around a large mass quickly. Free of any nucleus, as we find in the plasmas of space, the electron will tend to travel straight without the torque of its opposing charge. The speed these particles travel at is extreme. Alpha, Beta and Gamma particles all fly at extreme speeds and behave like a ray. Why wouldn't they? There is not enough interaction between the particles to cause torque and the behaviours we witness on Earth.

More thought has to be given to the relativistic quantities observed in the interaction of atoms. The electron's energy in contained in kinetic, mass and charge models. How does this change as speeds begin to approach the speed of light? All questions worth answering as we take steps towards a deeper understanding of the physics of electromagnetism.

Gravity is Not Magnetic

"Well of course gravity is not magnetic" any respectable scientist would say. Physics and Wikipedia specify a law for gravity and a set of functions describing magnetism as a subset of the field of electromagnetism. The truth all discerning scientists will discover is that gravity and magnetism are both ionic - velocity related forces relying on the statistics of large numbers to exert force from one body to another.

Magnetism works through electrons spinning around atoms in a regular pattern. This large school of spinning electrons protrudes into the dielectric material surrounding a magnetic body. The electrons follow the 'magnetic' field lines around to backfill the electrons in the magnetic material. The spins must line up and if you trace the magnetic field lines you will find they do. A diagram is included in a previous blog post.

The 'magnetic' fields of spinning electrons attract and repel magnetic bodies with beautiful symmetry. This symmetry is well documented through Maxwell's Equations specifically the Ampere-Maxwell equation. What isn't well documented are the physics of the actual attraction and repulsion. To explore magneto-attraction more I would refer the reader to a few previous blog posts where I explore the matter in more detail. Clearly the magneto-attraction involves the spin of many electrons concurrently as well as the collision of electrons and ions causing the attraction or repulsion of mass between the two magnetic bodies.

Gravity also involves large numbers of electrons and ions moving in particular ways to provide attractive force. The only concept that may be seen as a repulsive analog to gravity is the Biefeld–Brown effect but this effect is poorly documented. The gravity force is the result of the statistical tendency of electrons to be accelerated one way and then to be attracted back in the opposite direction due to charge balancing. This concept is explored in many of this blog's previous posts.

Contrasting the ionic statistical movements of gravity and magnetism is well worth thinking about for any physicist or chemist. The root mean squared speed of electrons is extremely high compared with the RMS speed of the ions they surround. This means that the electrons will seem to reach out and exert a force on surrounding material in the case of gravity and magnetism.

Telegraphers' Equations Revisited

Today I'll revisit the telegraphers' theory. It all seems so obvious nobody stops to ponder the particle (electron) dynamics of the telegraphers view of electricity and how it moves around. The equations were advanced by Heaviside and apply to power distribution as much or more as they apply to information signal distribution. This model applies to small traces on printed circuit boards as well as integrated circuits and long distance power transmission lines between cities.

A power or signal electrical transmission line can be modeled by series resistances measured in ohms per meter. In series with the resistance the telegraphers' model specifies an inductance. We shunt a capacitance and a conductance. Briefly, the resistance represents electrons resisting flow as they smash into the lattice of the transmission line. Inductance has classically been thought of the generation of a magnetic field by moving electrons. Capacitance between the transmission wire and the return stores energy in the electric field. Conductance is the flow of electrons between the transmission wire and the return. In the case of a differential signal both wires are transmission wires.

Resistance is the impedance to the flow of electrons through a wire. The electrons are accelerated by a classical electrical field. These electrons often travel at a fraction of the speed of light. At this high rate of speed the electrons often slam into a copper nucleus which has a mass ten thousand times higher than the offending electron. The vibration imparted to the copper nucleus causes heat in the copper lattice. The electrons accelerate each other through more interactions and the power of the electrons propagates down the wire.

Inductance may be the least well understood impedance ever. Inductance infers an induced magnetic field if you believe in magnetic fields. I'll submit that the induced field is simply (simply is a bad way to state it) a field of curling or spinning electrons. A certain statistical amount of all the electrons that are traveling down a wire each meter will eject themselves from the wire and spin out into the dielectric. The dielectric could be a polymer or simply the air. All of these dielectric substances contain molecules that the 'hot' electrons can orbit. The nature of these orbits has not been well characterized by physicists. It is most important to note that a certain percentage of electrons ejected from a wire each meter will orbit in the dielectric and end up right back on the wire creating the characteristic 'paddle wheel' or 'magnetic' energy storage effect.

Capacitance is another energy storage mechanism whereby electrons ejected from a wire will store energy. The build up of electrons in the dielectric region between the transmission wire and the return wire of any electrical system. Capacitance in Farads per meter represents the electrons that leave the transmission wire (and or return wire) but don't make their way toward the return wire in the case where they left the transmission wire. These electrons just hang out in the dielectric outside the transmitting or conducting zone.

Finally, conductance shows us that electrons are definitely ejected from 'hot' wires. These electrons make their way, statistically, to fill holes on the return wire assuming the transmission wire was negatively charged in the first place.

There are currently no good statistics showing what the path looks like for an electron that experiences the inductive spin, the capacitive hang or the conductive path form wire to wire. Capacitance and inductance involve an electron leaving one wire and landing back on that self same wire whilst resistance and conductance in the telegraphers' equations refer to an elongated path or a shortened path for electron travel in the case where the electromotive force has exerted itself on a group of electrons traveling over some sort of transmission line.

Spherical Warping and Gravity

Imagine for the sake of example a flat Earth. Many layers of flat ferrous, silica and carbon making up a flat Earth. We bend the flat layers one at a time to turn the flat layers into a sphere. The electrons on the concave side will tend to repel each other. These electrons will tend to push outwards as the material bends. Given that the root mean square speed of electrons at room temperature may be one one hundredth the speed of light. It is highly likely that the electrons will pop out of the convex side at a high velocity. Charge balance will tend to pull electrons in to fill the void.

The pop or acceleration of inside electrons is countered by the charge balance that must bring these particles back. The force of gravity permeates everything as it is composed of the basic neutron, proton and electron combination.

When the flat earth model is bent the electron concentration tends to be higher on the inside or on the concave side. Electrons move extremely fast and they will balance themselves quickly.

Gravity and London's Force

I've blogged about the propensity of a mass to emit electrons. The resulting equal and opposite reaction force that is gravity is caused when an electron is emitted from the center of mass. Trying to dissect this force leads us to the atomic level where we encounter the London forces.

The London force is easiest to picture when we consider the noble gasses as these atoms don't make complicated bonds. Diatomic molecules tend to stick together but will still have inter-molecular interactions with the material that surrounds them. More complicated molecular structures will tend towards a balanced state that will have London forces of their own.

Imagine two helium atoms coming together with a certain amount of kinetic energy. Current models have it that these atoms will have electrons on their outskirts that are moving at a real fraction of the speed of light (aprox. 1%). The electrons will interact first and will not want to share space. It is relatively likely that one of the electrons will take off and the rest will attempt to balance charge and momentum.

As an electron takes off from the local center of mass the rest of the mass will be pushed in the opposite direction so as to conserve momentum. This push will happen throughout a mass. The push tends towards the center of mass because the electron is carrying momentum in the opposite direction. At least this is a tendency. This tendency may be repeated many trillions of times in a mass. The net result is a force called gravity.

The 'Magnetic Field' and Spinning Electrons

The biggest mystery I see in the physics of electromagnetics and electrical engineering concerns Heaviside's four equations representing Maxwell's equations in vector calculus form. The Gauss-Maxwell equations dictate the shape of the fields as they were observed before Bohr's model of the atom took hold. The Ampere-Maxwell equation dictates current flow and it's relationship to the 'magnetic' field. The magnetic field was a construct necessary before we could understand how a lattice of metal ions related to free electrons and bound electrons. Finally the Faraday-Maxwell equation describes the first derivative of the Ampere-Maxwell with respect to time. This is critical for understanding how the electromotive force is generated.

The Ampere-Maxwell and Faraday-Maxwell equations seem to work both ways. That is to say the Ampere-Maxwell equation is often made reference with respect to the magnetic field forming around a conductor. But the curl of the current of an electromagnet also produces the straight portion of the magnetic field. Likewise with the Faraday-Maxwell equation the curl of an electron field produces a change in the magnetic field. The opposite is true. The change in a a magnetic field causes a curl in the electric field. We use this equation to explain electric generators and electric motors.

Many of the applications where we see magnetic fields set up are around conductors. Conductors are the most common place to find free electrons carrying charge. We know from the telegraphers' equations that there are parasitic leaking of charge from the conductor in the form of conductance and I will add capacitance and inductance. In the case of inductance the parasitic electrons eddy out around the dielectric surrounding the conductor. This creates a curl of the electron field surrounding a conductor with a net drift velocity of its electrons.

The curl vector from vector calculus of the electron field is proportional to the magnetic field lines. Magnetism is just electrons moving in a curling manner. Previous blog posts sought to explain how the curl of the electrons leads to attraction and repulsion of magnetic solids or current carrying wires. Explaining magnetic phenomenon any other way may be difficult enough to prove truth to the circulating electrons. Perhaps X-ray imaging of time lapsed magnetic phenomenon can answer questions at the Government Labs in Oakridge, Switzerland or Sandia.   

Using the Biefeld-Brown Effect to Measure the Ion Acceleration Distribution,and Ion Quantity

The Biefeld-Brown Device (BBD) is an electric condenser which normally uses the electromotive force to accelerate electrons from the anode of the condenser towards the cathode. The cathode has been found to be more efficient when it has a large surface area. The telegrapher's equations jump to mind quickly as the conductance parameter (G) will measure the ion exchange with the environment outside the BBD. Specifically the electrons will travel through the air and ultimately interact with the air to give levitation. L and C parameters will begin to describe the flux of the flow of ions around the BBD.

There will be a real difference between the telegrapher's parameters at the anode and the cathode of the BBD as they are oriented differently with respect to the ground and they have a different mechanical shape. Electrical properties with respect to the emission of electrons and the propensity to accept electrons at the anode compared with the cathode.

But what can we use this BBD to do in order to understand the electromagnetic properties of gravity and how ions behave to give us the gravitational effect described in previous posts? If a BBD is able to levitate in a YouTube video we have to wonder what the ion exchange looks like on either side of a BBD levitation. We have the ground 'firing' electrons one way and we have the condenser at 30 kV or above firing electrons in the opposite direction.

The anode is well hidden by being smaller helping more of the cathode's emitted electrons counter those electrons coming from the Earth.

What is of real interest is that the electrons leaving the cathode do so in a discrete manner. What does the discrete distribution of electron emissions look like? How many electrons leave the cathode over what period of time? Over a small and discrete period of time how many electrons leave the cathode? It would seam that the Poisson distribution would be a good place to start for any analysis. If we knew what sort of ion distribution levitated a BBD we would have clues to the nature of gravity's electron launch and ion pull described in previous posts.

The Poisson distribution tends to fit behaviour that is discrete. Also as one breaks the time scale into increasingly smaller slices all events should fit in a separate slice of time. The rate of electron emission taken to the power of the number of electron emissions observed in a time period is multiplied by Euler's constant to the negative power of the rate of electrons emitted from the cathode. Now we divide by the factorial of number of electrons emitted from the cathode in the observed period. That is the Poisson distribution applied to the BBD cathode.

Also, important data points are the speed and acceleration profile of the electrons as they leave the cathode. For the exact same reason our interest in the distributions of ions leaving the cathode of the BBD we want to know how the BBD accelerates electrons into a drift velocity in the air underneath the device or in the ground.

The distribution of electron emission from the cathode of the BBD, the acceleration, drift velocity of electrons of a BBD would help us understand how gravity really works.

Safety of a Biefeld–Brown Type Device

In electrical discipline of the transportation industry it is necessary to get the potential hazard rate below the tolerable hazard rate of ten to the negative nine hazards per hour. Can this potential hazard rate be achieved using a Biefeld–Brown effect type device as an aircraft. Two questions may be asked: are Biefeld–Brown effect devices safe for travel with people on board and are Biefeld-Brown remote controlled drones safe for use at all according to North American or British case law.

Any practical Biefeld–Brown device that was able to carry a person will require in excess of 50 kV to 200 kV with the anode pointed up. The apparatus is really a condenser with a power supply and an electric generator. This blog post will limit its scope to the most safety critical items the subsystem containing the high voltage electrostatic generator and the condenser assembly itself.

It is so critical to note that if the device has a person on board they will be very close to a high voltage negative condenser plate which may or may not be spinning (see Searle effect). Compounding the problem, Biefeld–Brown devices aren't exactly heavy lifters. It would be hard enough to fit the requisite generation equipment on-board with a pilot. How would such an apparatus lower its hazard of touch potential under cramped circumstances?

A strong dielectric material would help but, again, fitting everything is such a cramped space would yield a potential touch potential hazard rate well in excess of the transportation tolerable hazard rate of ten to the negative nine hazards per hour. MIL-STD-882E specifies the safety requirements and method for achieving a suitably low hazard rate for an aircraft or aircraft subsystem. The condenser may require Electronics Parts Reliability Data data to infer rates that would allow compatibility with 217Plus:2015.

So would a remote controlled drone work? This machine could be lighter as it does not need to carry a person or the associated fuel. A lighter aircraft could use a lower condenser voltage. This voltage would still need to be 30 kV to 80 kV and would be hazardous if the drone were to crash. This type of high voltage drone should not be used in areas with any population density. 

References:

https://en.wikipedia.org/wiki/Biefeld%E2%80%93Brown_effect

United Sates of America Department of Defense, System Safety: Standard Practice MIL-STD-882E, Ohio, U.S.A., 2012.

RiAC, Electronic Parts Reliability Data-2014, Up-state New York, U.S.A., 2014.

RiAC, 217Plus:2015, Up-state New York, U.S.A., 2015. 

Gravity and Electron Emission from Mass

The Poisson distribution might just be the right distribution to model the occurrences of high linear velocities of electrons in a small volume within a mass. The mass will seem to emit electrons in a direction generally towards the periphery of the mass at a high rate of linear speed rather than the Bohr type angular rates of speed of electrons surrounding a nucleus generally travel at within the mass.

The Poisson distribution would specify a discrete number of electron jumps from a mass or from a small volume within a mass. The rate parameter of the Poisson distribution will reflect how many jumps per unit volume will occur during a given nanosecond. Due to negative charge density the jump will tend to be from the center of mass toward the periphery of the mass.

If we break a mass into layers from the center of mass to the periphery of the mass we will find the same thing as we examine each layer. The interior side of the layer will have a higher negative charge density than the exterior. Electrons will tend to want to pop or accelerate outwards towards areas where there is less particulate mass.

This acceleration of electrons almost looks like an electromotive force. If electrons are pushing outwards then what of the return path? Electrons likely return in a drift velocity that is much slower and more orderly than the outward pushing or popping electrons. This effect can be modeled as a dieract delta function being propagated down a thin strip-line on a printed circuit board. The voltage/current waveform hits the termination or load and returns to the power supply along a wide ground plane. The forces on a printed circuit board are most often negligible but it is important to understand the fast-signal slower-return dynamic associated with electronics.

It is not known how this would even be measured at the present time. Because gravitational masses are so large and involve so many counter-balanced interactions it is very hard to pick them apart. One might have to imagine a smaller mass suspended in space. Regardless of the imagined mass, the interactions will follow a similar pattern. How would we compare the number of electron accelerations within a cm cubed at the Earth's surface vs. the number of electron accelerations one meter deeper.

The gravity force comes from an acceleration of charge (electron) away from the center of mass. Electrons, with their much smaller mass, will tend to fly off compared with a proton or a neutron. The return of mass and charge will seem to happen instantaneously. Mass will be dragged down to back-fill the escaped electron. Furthermore, charge balance will dictate that electrons will be attracted back into the place of the escaped electron.

I'm having trouble putting equations into the blog.

[1] Faraci, V., Spares Optimization Algorithm for Calculating Recommended Spares, J. RiAC, Third Quarter, 2008.

[2] www.wikipedia.org, Poisson Distribution, August, 2016.

Bar Magnets

It is much easier to draw a bar magnet with magnetic field lines surrounding it than helices of electrons traveling largely in a circular fashion. Well here is a drawing.

This drawing is a poor way to convey the circular path an electron takes around a bar magnet. Between the two magnets there are interactions between the two curling fields of electrons moving with opposing curls. It is likely that these fields interact and scatter matter such that a negative relative pressure is created. This lack of pressure pulls the two bar magnets together.

The Maxwell-Gauss magnetism equation traditionally defines this elliptical field. That is to say if we take the vector calculus curl of the electron movement fields we arrive at the magnetic field strength and direction. That vector field can be related to the Maxwell-Gauss magnetism equation. Otherwise, the Maxwell-Gauss magnetism equation is simply a vector calculus identity to be found in any vector calc text book.

Between the two bar magnets, in the gas or vacuum, there is likely to be centrifugence where the electrons leave the bar magnet and centripetence where the electrons enter the opposing bar magnet.

It will be harder to draw like poles of bar magnets repelling.

Electric - Magnetic Model for a Planet

We know that electrons move at a rate of speed many, many orders of maginitude faster than an iron nucleus. The electron moves with a root mean squared speed of 1% the speed of light. Electrons can move much faster than half the speed of light if they can get going in a straight line for any length of time. We now have to ask ourselves what this does to the momentum of the electron and how to model this in a large mass.

Electrons are incredibly hard to picture. They are extremely small. They have an ability to travel at extreme speeds. When an electron flows away from the center of a mass it has a higher ability to accelerate and it travels faster in general. This might be modeled as a collection of thin wires leading from the center of a planet out to the cold plasma surrounding the planet. In fact, it comprises all of the particles within the 'sphere' of gravitational and 'magnetic' influence. Small wire - fast electrons - with a greater ability to accelerate.

In reality one electron does not begin and continue to accelerate from the center of mass. Due to the size of the electrons and their more loose bonding to their surroundings electrons will have an ability to drift outwards with an instantaneous velocity. This velocity likely increases towards the periphery of a large mass as the density of the material is likely less due to the weaker force field of gravity.

If electrons flow from the center of a mass to the periphery they much regain charge balance through another process. This process is different. Imagine fewer thicker, heavier gauge, wires funneling current back towards the center of mass from the periphery. These wires become thinner as they get closer to the center of mass. At the center of mass we can likely look to the London Dispersion Forces to get a clearer picture of what is going on. This is a post that has already been written to this blog.

Thinner wires at the center of a large mass with thicker return wires compared with 'hot' wires on the way out. This model shows us that differing impedances can exist within one, very large, electrical system. The force imbalance leads to an equal and opposite force imbalance that we know as gravity.

Ground Equals Zero Volts

One of the fundamental teachings of electrical engineering is that we reference all circuits to what we call a common ground and that we call that 0 V. This means that there is zero potential energy difference along the common ground.

Well wouldn't you know that I spent the last two days of my life considering that ground may not be 0 V after all. In a great number of cases the ground is not 0 V. These cases usually involve some amount of distance. This distance may be greater than 25 m. Over a distance of 100 or 200 m there may naturally occur in the soil and between soil layers a potential difference of a few volts. With heavy machinery or lightening about the potential difference across a few hundred meters can be significant.

The downside of potential differences between different points is that if one is trying to communicate over this distance and the ground rises the communication will fail.

It turns out that the solution to this problem has been to divide large buildings up into different grounding zones. These zones are kept electrically separate without any conductors between them. Any communication between different grounding zones must be done with differential signalling.

Static Magnets - The Basics

When the North end of a magnet is close enough to the South end of another magnet electrons will spin out of one pole and spin towards the opposing pole. It is very important to note that the opposing pole is also inverted with respect to its counterpart. This is why the spinning electrons line up. The curl speed of the electrons is probably much higher than the drift speed of the electrons from one magnet to the other. This means that the drift direction matters less than the curl of the electron field.

Implicit in the last paragraph is that the electrons flowing between magnets have a return path. The path is from the outside poles of the magnet. The vector calculus calculated curl of the electron field will line up with the so called 'magnetic field lines' of antiquity.

So why does the North pole attract the South pole in paragraph number 1? When the electrons are spinning from one magnet to the next there will be a boundary between the electrons curling one way and the return path curling the opposite way. The matter at or near the boundary will interact with collisions and cause matter to evacuate the space between the two magnets. This is what causes the attraction.

The opposite happens when a South pole is put next to a South pole. Electrons will work hard to get in between the two magnets pulling in matter. The buoyant feeling of matter stubbornly not evacuating the space between the two magnets in this case.

The Maxwell-Ampere equation backs this up. Substituting del cross I for B with a proportionality constant adjusts the equation so that one does not have to use the magnetic field idea.

Equation for Electron Induced Gravity

There is certainly a tendency in any object large or even small for the electrons traveling away from the center of mass to have more kinetic energy. Objects tend to radiate. To balance charge the electrons must settle back towards the center of mass with a particular drift velocity.

The electrons moving out from the center of mass will have divergence in their vector field and will have a decreasing divergence per unit volume as we observe from the center of mass to the periphery of the object and beyond.

Representing this relationship as an equation involves calculating the force of gravity using the surface integral over the area of interest. The divergent vector field will yield a type of  buoyancy that forces objects towards the center of mass. The turn or curl closer to the center of mass will be greater than that further away.

A more complicated model involves the density of all materials as to which way the net 'force' points. Buoyancy can push one way while electron buoyancy might point in the opposite direction.

Due to the comparison this electron gravity has towards stress and buoyancy the natural reaction might be to try and use tensors. Integrating the tensor over the area in question may yield a model for calculating force due to gravity. I wonder weather using tensors isn't too complicated to be accurate.

The Photon Field

There is no ether but the photon field is worth exploring. Photons permeate explored space. According to Bloomberg (not the greatest science reference) a sunbather is hit at a rate of ten billion photons per second by stars outside our solar system. The same sunbather is hit ten to the power of 23 times by photons from our own sun.

These photons permeate a large amount of space around the earth and throughout our solar system. These photons and other frequencies of background radiation must play a real role in the propagation of electromagnetic signals.

The background radiation provides more than a noisy environment for signals. Without ether it provides the medium for signal to propagate.

Magneto Attraction

None more mysterious than the attraction of opposed poles of a magnet. Conversely, like poles repel. We can look at the curl of the electron field and note that opposing poles with opposing orientations in space have electron fields that add constructively in curl.

How does a constructive or additive curl cause magneto-attraction? It is interesting to note that the magnetic force acts similarly in a gas as in a vacuum. I have challenged the whole notion of a vacuum when a magnet or two are present in previous blog posts.

Writers make a big deal of poles never being separated. If poles just represent the orientation of spinning or curling (vector field) of electrons then why does it surprise us that the poles can never be separated? It becomes a trivial statement. This fact is described by the Maxwell-Ampere equation where curl is related to magnetism and movement of electron-charges.

Back to the attraction between magnets. The opposing poles with opposing orientations in space will have additive curl. Electrons will move from one pole to the other but note that the direction doesn't matter. The return path will be through the magnetic material and around the outside of the magnet with the vector curl of the electron field following what we call the magnetic field lines. Both the direct path and the return path for the curling electrons add constructively for attraction.

The curl from the mass of the magnet to the center between the two opposing poles relaxes the curl of the electron field. The field wants to stay together but the mass is loose in the gas or vacuum between the magnets so the electrons spiral outwards. At the same time the return path is curling the other way pushing the electron vector curl field inwards. Eventually the mass of one or both of the magnets seeks to fill the void where the curl is loose (less) and trending towards more.

This phenomenon may be best described by tensors or vector calculus of many dimensions. I will reserve this analysis for another blog post.

The Drift Velocity of a Magnet

What is the drift velocity of a magnet under equilibrium? A quick and safe answer is zero. The net velocity of the magnetic lattice is zero. But what the Ampere-Maxwell's relation points out is that there exists a curl to an electron field when the magnetic force is said to exist.This relationship between force, on particles, and the net flow of electrons is also less obvious in Lorentz's equation relating the movement of a particle in the presence of curling electrons.

There are particle accelerations and velocities at play in electromagnetics that have been described in previous posts. I'd like to explore drift velocity and electron acceleration with respect to magnetic phenomena in this post. Under what conditions do we expect to observe accelerated electrons while dealing with magnets?

The Ampere-Maxwell's relation shows us half of what goes on when electrons start moving around. Because of effects that generally have to do with Bohr's model of the atom, electrons seem to eddy around the nucleus of either one atom or many atoms. This gives a field of traveling electrons a drift that can curl. The drift angular velocity is what produces the magnetic field by the Ampere-Maxwell relation. This mechanism by which this happens is explored in other posts. My focus is on the velocity of electron flow, the flux of the flow and the curl of the electron flow.

In a given current carrying wire, the drift velocity is radically slower than the root mean squared velocity of the electrons. The electrons, therefore, can carry information or power radically faster than the drift velocity. This is good because the drift velocity can be quite slow. The current in a conducting medium is always going to have a telegrapher parasitic profile. The shunt conductance and capacitance and the series inductance are all caused by electrons moving in the dielectric (maybe in some cases curling in the conductor itself). An induced curling field, as electrons eddy out in the dielectric is interesting. It would appear that the field would have a drift angular velocity under steady-state Ampere-Maxwell conditions. When an electromotive force is setting up a circuit, di/dt, and charge is accelerating the 'magnetic' or electron curl field would accelerate as well.

Imagine that the curl is not just localized to a small space but the curl of an electron field is continuous throughout a given three-space around a conducting medium. The acceleration and drift velocity of a rotating point charge starts to take on a complicated pattern.

The Faraday-Maxwell equation shows us how circuits behave under accelerating conditions. When a rotating body with an angular velocity swings through a curling field of electrons there will be sinusoidal acceleration and velocity. This acceleration leads to the electromotive force in generators. This force is generated and take direct advantage of the angular drift velocity of electrons around a permanent magnet or an electrified coil.

Maxwell's Equations

Are Maxwell's equations fundamentally flawed. What if we considered currents free of fields. That is to ask do vector fields really help us understand electromagnetism or do they cover the truth with nice looking math equations that don't explain the physics completely?

Let's start with the Maxwell-Gauss electrical equation. The divergence of the electric field is equal to the charge contained within a volume. This describes electric fields. What if you don't like vector calculus or you want to understand the Maxwell-Gauss concept free of field theory. In this case we can say charges accelerate towards or away from other charges. The field doesn't exist but it forms a convenient representation of the truth.

Second, we have the Maxwell-Gauss magnetism equation. This equation states that there is no divergence to a magnetic field. Magnetism lovers know that the magnetic field is always elliptical in nature. But what if you don't like field theory or magnetic fields. I mean what if magnetic fields don't exist? Magnetism could well be an interaction between a lattice and curling electrons. More on that topic later (and in previous posts). It is most important to examine this equation. If a magnetic field is just the curl of current then the Maxwell-Gauss equation becomes the common vector identity: the divergence of a curl always equals zero. The Maxwell-Gauss magnetism equation is just a vector calculus identity.

The Maxwell-Ampere equation follows the previous equation well. The curl of the magnetic field is equal to the sum of the current and the displacement current. Again, if we realize that the so-called magnetic field is a curl in the group electron movement then we see that the curl of the curl is equal to the current. Imagine a wire with electrons curling off of the wire. They eddy out around the surrounding molecules and atoms in the dielectric material. The curl puts you on the magnetic field lines and the curl of the curl puts you right back on the wire.

It is rarely described in the Maxwell-Ampere equation that the curl of the current or the displacement current produces a straight magnetic field. This is the theory behind an electromagnet but the Maxwell-Ampere equation doesn't describe it specifically.

Finally we consider the Maxwell-Faraday equation. The curl of an electric field is equal to the negative first derivative of the magnetic field. Change the magnetic field and the electric field must curl. A curling electric field gives rise to a changing magnetic field. This equation is really saying that when negative charge is accelerating the curl (derivative) of the current will change. This is a circular equation because it looks at the acceleration of curling charge in terms of the acceleration of curling charge. This equation looks at the dynamics of how the charge moves. Acceleration of charge is very important in electric motors. As some of my previous posts have noted, there are better ways of understanding motors than the Maxwell-Faraday equation.

Fundamental Question in Electromagnetism: Voltage

What is voltage? Text books give a non-answer; something to do with electromotive force. Fuck off. I mean please explain to me what's going on with voltage. What is it and what are it's properties in physics. The fact that we don't have an easy time answering this question leads me to believe we have rather poor understandings of inductance and capacitance too. But that has been the subject of other posts.

Voltage is always given as a potential difference. There is always a system with some amount of energy that will be compared to produce a potential difference. I'll repeat my question: what is this energy difference? What causes it? Let's start with the units. Volts are Joules per Coulomb. This means that six times ten to the power of eighteen electrons in two different places will have an energy difference of one Joule. But what causes this energy difference?

I know all these questions are annoying but it annoys me even more that we can't just pick quick answers off of Wikipedia. Shouldn't Stanford and the DoE's X-Ray lab be looking at this stuff? Let's describe what we do understand. Voltage has been related to tension and pressure in the past as analogies. Those analogies may or may not hold. I'm not as interested in analogies as I am in the physical truth.

Previous posts have shown electric generators to whip electrons onto a return wire sucking electrons from the hot wire creating what we call positive charge. There is now a deficit of electrons on the hot wire that is being back-filled by the load. Electrons move at about 1% the speed of light so they can back-fill fast but they tend not to. The drift velocity of an electric circuit is almost always radically lower than the root mean squared velocity of the electron. So an electron surplus or deficit may contribute to a negative or positive voltage respectively.

That may not be all that is going on. I'll leave out parasitics related to the telegrapher's equations. What about the root mean squared speed of the hot side of the circuit related to the root mean squared speed of the electrons on the return side of the circuit. These quantities are hard to measure. Electrons move quickly and I'm not aware of any laboratories working on characterizing them.

Finally, a contributor to voltage may be hot carriers. Very few, fast moving electrons that can devastate transistors and provide a visible spark show.

Scientists studying the upper atmosphere talk about density and temperature of charge to characterize particles. That helps us only a bit with the characteristics of low voltage and high voltage electric circuits here on Earth.

A deficit or surplus of electrons relative to the nuclei in wires may cause an electric voltage relative to other wires. The root mean squared speed of electrons as it differs from another point in a circuit may cause a voltage. The drift velocity may be a measure that correlates to voltage. Hot carriers may also be a cause of voltage.

Electrostatic Acceleration and Newton's Third Law

Gravity and electromagnetism have not always been linked. It does seem hard to imagine that with so many atoms, molecules and especially electrons that something must be working to keep things down. Specifically objects or mass is attracted to other mass. Often we only look at gravity in planetary terms. The Moon pulls the tides the Sun pulls on the Earth.

So what causes the attraction? It may be that the mysterious dance of electrons and the nuclei they surround can cause an attractive force. Imagine particles in towards the center of mass. The electrons are going to be in abundance and we know from electrostatics that they repel each other. Often enough this repulsion from the center of mass will be enough to accelerate the electron for a while. The acceleration can be seen all the way from the center of mass to the periphery of the mass in a sort of electron buoyancy.

Electrons will be accelerated from the center of mass and they will also be attracted back to maintain charge balance conditions. The attraction back to the center of mass may happen with a drift velocity as the electron bangs from atom to atom - molecule to molecule on the way back down.

I've tried to present this in a diagram shown below. At the center of the circular mass electrons, marked e, accelerate away from the center of mass with a centripetal force. The equal and opposite reaction acts on the molecules around the accelerating electron. The force, F, is dense and acts in a uniform manner. The force at the periphery of the mass turns the electron back towards the center of mass. In reality many particles will fly off into space. The force at the periphery pushes some matter away but this force is diffuse compared with the force towards the center of mass at any point.

The diagram shows X3 at the center of mass so that the number of electrons at the center and at the periphery balances out.

Coils as Electron Structures

The previous post didn't address coils as a part of electron structures. Coils are certainly important as they factor into generators, motors and inductance of magnetic fields. These fields add up as the coil turns we find the measured inductance increase.

In the beginning a long straight wire requires a magnetic field to be set up. The telegraphers' equation show a series inductance as one of the parasitic parameters impeding signal and power propagation along any transmission medium. As the post yesterday pointed out long thin structures tend to have more inductance.

The telegraphers' equations point to four parasitic parameters. Conductance and inductance factor into coils. Conductance tells us that without a doubt electrons leak out from conductors. Electrons are small and extremely fast so this should be no surprise. Electrons have a high propensity to spin around nuclei outside the wire in the dielectric. This forms the inductance signal and power engineers seek to avoid.

As the number of turns in an inductor increases so does the interaction and the additive curl of this spinning electron field. If the curl of the electron field is substituted for the magnetic field we have a clearer picture of what is really going on. These facts are complicated by topics from other posts. Notably, the Ampere and Faraday equations that Maxwell used complicate things with differing eddy current directions.

This happens due to Lenz's effect. More on that later.

Electron Structures

Mechanical structures of conductors with their surrounding dielectrics have a profound influence on electromagnetic signal and power propagation. This post explores some of these mechanical conductor structures and the influence on electron flow.

Microstrip capacitors occur when, relative to the wavelength of the propagating wave, the microstrip widens considerably. Often microwaves are manipulated using microstrip capacitors. Electrons will be trapped momentarily causing the capacitive effect. Electrons will slow down their drift velocity in the wider capacitive microstrip though the group velocity of the electromagnetic wave may not slow down at all.

Microstrip inductor is created to, relative to the wavelength of the propagating wave, the microstrip narrows considerably. Microwaves can be manipulated with microstrip inductors. Electrons will accelerate and move faster through the narrow space. Some of the electrons will jump off the conductor and eddy out. This phenomenon is known as inductance and is used as a linear circuit element in microwave circuits.

Brushes are an old electron structure. They have been used to build high voltages. Excited electrons will find themselves traveling down a conducting brush towards the end. Electrons have been observed to fire very well off the end of conductive brushes no doubt creating some amount of inductance along the way (Ampere-Maxwell's law). Plasma discharge is observed from the ends of brushes as large amounts of electrons fire off the ends of the bristles.

Spike or electron wick is used for electrostatic purposes. When a surface builds up too many excess electrons such as on the wing of an airplane or on the international space station it has to find a way to shed the excess charge. If the charge is not neutralized to the surroundings communication noise or arcing could be a dangerous result. Spikes or wicks can be a tuned electron structure that allows for some inductance or eddy electrons that keep the flow of electrons from the aircraft or the spacecraft. The spikes will act as an electron trap as the conductivity and inductance will propel electrons from the craft but it is far less likely that an electron will spontaneously jump back onto the spike.

Xe charge balance mechanism allows the fuselage of the international space station to reach charge balance with the surrounding orbital plasma if the station finds itself short on electron or positively charged. The station might accelerate Xe nuclei into the surrounding plasma. The electrons that were orbiting the Xe nuclei before they were accelerated will diffuse through the chassis of the station causing a relative match in charge balance with the surrounding plasma.

Resonant cavities are a topic I should attack some other time. These structures are used on microwave frequency radiation to provide bandpass linear effects. Someone has even proposed harvesting thrust from an electromagnetic resonant cavity. More on this some other time.

Circuits Within a Planet or Mass

The force field due to gravity is characterized by a function in i, j and k that has negative components. The gravitational constant, G, is multiplied by the mass of the two objects being attracted to each other. This is divided by the distance between the two masses squared. The result is a force field that points towards the center of mass.

This blog has been exploring what likely happens from an electromagnetic perspective to create the force field known as gravity. We know that electrons move so fast (ten to the sixth power m/s or faster) that the root mean squared speed of protons and neutrons looks like it is effectively zero. Electrons in a dense space will likely experience acceleration due to an effect like buoyancy. The forces on the electrons closer to the center of mass will be greater.

If electrons are propelled out from the center of mass by a force that diminishes with respect to distance (r) squared they will accelerate at a lower rate.These electrons can only continue to accelerate as long as they don't interact with an atom. That means on the way back to the center of mass the electrons might well jump through the shadows of the ions in the mass to balance charge at the center of mass or wherever the negative charge is needed. It is likely that the trip from the atmosphere to the center of mass is a velocity compared with an acceleration on the way from the center of mass outwards.

The acceleration shall be less and less as the electrons move away from the center of mass. A relative velocity (zero acceleration for most of the trip) is likely on the return. The gravity circuit electrons accelerating on the way out and pushing inwards on the way back.

Turning of an Electron Field

Electrons move so quickly they have to be looked at as a vector field or fluid that flows. This field turns and has many statistical properties. The reason it is important to understand the turning of the field of electrons is that turning of a field causes lift. That is to say that every action has an equal and opposite reaction. So every turning field has a centripetal force caused by an object or another field. The equal and opposite reaction is lift. This is known as the Newtonian explanation for lift.

This lift is useful in understanding electrons and their involvement in gravity. Relative to the speed of electrons protons and neutrons can be seen to be standing still. Under dense circumstances electrons in the presence of other electrons will acquire kinetic energy and head for areas of less electron density with some stochastic frequency. At some point the electron will turn around and may make the trip back towards the center of mass again due to statistical interactions with other particles.

Notice that electrons will turn at the center of mass and head outwards away from the center of mass. It is also require for charge balance that electrons be at least modeled as turning around and heading back towards the center of mass. It is important to note that these two turns happen in different places in a gravitational mass. One turn happens in a high density place and one in a lower density place. A model for this could be one electron headed out from the center of mass and two electrons headed back at half the velocity of the electron heading out.

If we look at the dense set of electrons turning at the center of mass we can draw the electrons' centripetal force vector pointed away from the center of mass. Slower particles are causing the 'modeled' 180 degree turn and thus a force is exerted on them with a downwards (towards the center of mass) vector. Every action has an equal and opposite reaction. The opposite is happening far away from the center of mass the electrons have a centripetal force vector pointed downwards. These vectors are less dense meaning that gravity will always prevail as the counter-force to the turning of electrons under the extreme density at the center of a mass.

High density low volume turning vs. low density high volume turning leading to a force imbalance we call gravity. Lift and buoyancy can be analogies that help us understand how matter works in large quantities.

Electrons and Gravity

Electrons at high density near the center of mass are going to acquire kinetic energy and head towards a lower density in much the same way as buoyancy works. The force of an abundance of electrons will seek to distribute the charge. The electrons headed away from the center of mass will seek charge balance equilibrium and will head back towards the center of mass. Electrons travel so quickly they may be modeled as a flow rather than an abundance of particles.

The electrons far away from the center of mass will seek charge balance and will bump down towards the center of mass at a lower group rate compared with the rate they moved out at. There will be more electrons moving slowly towards the center of mass pushing and pulling matter along with it. The turnaround point at the center of mass where a particle has no choice but to head outwards needs a net force acting from the center of mass outwards. For every action there is an equal and opposite reaction and matter will be pulled inwards towards the center of mass. As well, a sphere or most shapes mass that mass takes will see more electrons away from the center of mass converging inwards adding to an electron ‘traffic jam’ as these particles seek the charge balance condition.

Imagine a three lane road with cars moving in one direction and another road with one lane with cars moving in the opposite direction. A set number of cars move along these roads and no car enters or exits the system. The single lane will jam and move slowly while the three lane road will move quickly.

The road system in the previous paragraph is analogous to the path electrons take on our planet or about any mass. The three lane road is the fast path out from the center of mass. The single lane is like the more crowded path back towards the center of mass.  

Reverse Buoyancy Key to Understanding Gravity

Buoyancy is an interesting concept. Today I might suggest that it applies to more than just helium balloons and Styrofoam floating on water. There are a lot of concepts of density and many of them may be additive. That is to say the more atoms and molecules we have the more of this force we observe. We know that the buoyancy of very large objects such as cargo freighters is so solid it resembles the ground itself.

But what of electrons and ions? They have relative densities that correlate with the density of the matter itself at any point. The sheer number of particles can be impossible for the human mind to comprehend. Ten to the twenty particles is an amount of matter that is hard to think of on a particle by particle basis.

So if we have electrons that are bond but not always rigidly bound to an internal nucleus then what do we find as a part of a larger mass? The electrons will float up and even bring a small number of light ions with them. The heavy will sink - gravity - therefore.

When we consider a helium balloon rising we like to focus on the helium - less dense - rising. We don't focus on the fact that the Nitrogen in the air is falling. This is not gravity but it may make up a small part.

Electromagnetism fills in the gaps. There is a circuit like nature to a large mass such as our planet. Electrons rise quickly and fall back towards the center of mass in a step by step manner.

Gradients and Velocities

The highest electron pressure on Earth will be found at the center of mass for the planet. There electrons will be interacting. The slight over-pressure of electrons will cause some of these particles to want to escape. Given that electrons tend to travel at speeds that are about 1% of the speed of light these particles speed outwards.

The electron will want to move along a gradient that is from high density to low density. Given the relative spacing of atoms in the lattice of the earth's core an electron might make it quite far. The main takeaway is that the fast moving particles are moving fast.

If particles are leaving the Earth's center of mass they will be quickly replaced. The replacement will not be in quite the same manner as the outward bound electrons. The replacement electron will likely slide in from a nearby atom or molecule. Just like stepping down a ladder the electrons will backfill the electron that left. Eventually the electron that left rapidly will slow down and become one of the electrons that backfill.

So we have light fast moving particles that move from the center of mass towards the periphery. This movement causes a counter-movement of mass towards the center of mass. This is analogous to the return path of an electric circuit. In this case the return electrons drag positively charge nuclei with them. This creates an overwhelming slow pull inwards towards the center of mass. This is gravity.

Telegrapher's Equations Revisited

Oliver Heaviside presented his version of electricity to humanity as the vector calculus version of Maxwell's nine equations. Heaviside also introduced us to the telegrapher's equations. The telegrapher's model for conductors remains with us to this day. Series resistance added linearly to a series inductance with a shunt resistance and a shunt capacitance.

Let's look at what this means as far as I learned in school as an electrical engineering student. The series resistance is easy to explain. Any conductor, copper for example, is made up of a lattice. as electrons traverse the lattice they accelerate and then slam into nuclei that make up the lattice. Electrons must also, critically, interact with one another. Traditionally we will say that some of the electrons repel each other when they come close to each other. All this bumping and grinding causes resistive loses.

Inductance tradition would tell us comes from the fact that every current carrying conductor has a magnetic field around it in the shape of an ellipse according to Gauss and Maxwell's magnetic equation. The magnetic field must be induced when the current starts to flow hence induction. The opposite happens when the current stops flowing.

I was taught that capacitance refers to the capacity of an electric field to store energy. For every telegraph line there is a return path for electrons. Phone and telegraph circuits work best when the return circuit is a conductor like the signal path. Capacitance is the representation in the telegrapher's model of the electric field. The electric field must be set up and it will unload its electrical energy when the circuit is de-energized.

Shunt conductance is the most ignored of the four elements of the telegraphy model. I'm not sure it should be. The conductance represents straight leakage from the signal path to the return path. Sounds simple but we ignore it to our peril in understanding how electric circuits really work.

Inductance and capacitance should be understood in terms of the shunt conductance; at least as far as the telegrapher's equations go. These two elements of the model store energy and then give it back.

Inductance should be explained without the use of a mythical magnetic field. Electrons accelerated down a conductor are going to pop off the conductor and statistically will make their way through any dielectric cladding. Electrons also have a massive propensity to spin in the presence of molecules. The spin or curl of the electron field is what has fooled humanity into believing in a mythical magnetic field. The spinning electrons in an eddy field will store energy regardless of how we want to perceive Maxwell and Heaviside's equations.

That leaves us with another highly statistical behaviour of capacitance. Some electrons that are accelerated off the signal wire will spin while others won't. The electrons that don't spin form the capacitive part of the telegraphers model. When the line is de-energized the electrons come back to the signal wire completing the capacitive model.

To summarize, electrons pop off the wire when there is an abundance of these elementary particles. Some electrons make it to the return wire forming conductance. Some electrons spin and this is represented by the inductive part of the telegrapher model. Other electrons pop off the line and don't make it to the opposing voltage line. This is capacitance.

More London Forces Excitment

How exciting are the London Forces? These forces exert themselves on the polarity of both atoms and molecules. UCLA's chemistry department points out that all atoms and molecules exhibit the London Force. The strength increases with the number of electrons. If only this University would elaborate.

What are the trends as molecules or atoms become larger? How fast do the London Forces grow? Do the London Forces diminish in growth as a molecule or grouping of molecules grow?

It looks to me like there is a fundamental disconnect between chemistry's understanding of atoms and the reality of particles under the influence of gravity. Do electrons have clouds? Maybe through probability theory but realistically those electrons are moving fast. So fast do electrons move that one might even call their combined interactions more of a fluid than a cloud surrounding a nucleus. I distinguish between atoms under planetary gravitational influence and atoms that aren't. There is evidence that near the earth plasma's set up in low gravity. The plasma may have very particular properties. Lots of electrons or lots of 'positive' ions.

So the London Force adds up with diminishing exponential growth of the force.We can add a lot of what looks like an electron fluid and call it gravity. A mass of any size is going to have shifting forces that ultimately pull towards the center of mass. The electrons at the center of a mass will have an outward exertion at 1% or more of the speed of light. This out-push of electrons will eventually attenuate in velocity and kinetic energy. Other less kinetic electrons will take the out-pushed electrons place. The result is gravity.

London Forces are Linear and Additive - Multiplicative

London forces are fairly basic forces. They represent a fairly geometric positive-negative view of the world. No self-respecting physicist would ever believe the truth to be that simple but we all must rely on models. Here our model is clear. An abundance of fast moving negative charge will exhibit self repulsion. This will propagate negative charge into diverse places. The charge balance will re-establish itself eventually and the return path of lower energy electrons and the process will begin again.

So if we consider a mass of any size or shape we end up with an additive or multiplicative force of attraction that causes the mass have a tendency to clump and stick together. This is the basis of gravity and it has an electrical analog. The proximate electrons at the center of a dense space are 'hot' and these electrons make their way towards the periphery of the mass. The electrons eventually make their way back through the return path down towards the center of the mass.

The nucleus follows or does the opposite of the electrons. Remember that the root mean squared speed of electrons is way faster than the the rms speed of the nucleus which carries so much mass. This is the electro-chemical basis for the so called weak force of gravity.

London Forces and Electromagnetic Conduction

This blog may be the first look at these two seemingly disparate topics. Chemistry has this oft hidden topic of the London forces. Part of the van der Waals series of forces they attempt to deal with what ionic and covalent bonds cannot tackle.

My problem is that I think I have a fairly good idea of what Dr. London was getting at when he wrote about these attractions years ago. There seems to be very little written about the London dispersion force. What is written almost makes it sound simple. Add a little Poisson Stoichastics and additive theory or considerations of linearity & additive Gaussian functions and this dispersion force is anything but simple! There is reason to think that this type of interaction may have broad ranging applications from one end of the universe to the other (big wink on that last statement)

To know more about the far reaching possibilities of the London force please take a look at my past posts about electromagnetism and gravity. I must digress to the London force and conduction.

The London force seems to deal strictly with instantaneous or dipoles that arrange themselves for small periods of time. Statistically when ten to the fifteen atoms are involved I would hardly say theses types of interactions are few and far between. To ditch the pejorative I would simply state these forces are a big deal in any system with more than ten to the fifteenth number of atoms. I mean what if it can be proved that the additive property of these forces add to gravity?

So if an electromagnetic is propagating most quickly at the border between the conducting metal lattice and the dielectric what can we say about the London forces at this junction. I know these topics are disperate and maybe not always be associated but follow me please. The excess negative charge present at the boundary is going to polarize the atoms at the boundary of the conductor and the dielectric.

While these forces can hardly be said to be London forces they certainly do add up and should be considered in the propagated electromagnetic wave from a conductor or an antenna if the conductor is exhibiting antenna-like properties. Another blog post will have to explore how these early statistical diploles manifest themselves and then propagate. They originate in the power supply through a whipping and then pumping (regulation) action by the various rotor, stator and then semiconductors in the signal path.

Electro-chemistry and Electromagnetism

Fusing the laws of electro-chemistry and electromagnetism seem elusive. We have a lot of tools at our disposal from CERN to the Oakridge colliders. Seeing the relationship and patterns between ions and electrons will certainly be one of the next century's major endavours. Though expensive, statistical research into the interaction between electrons and their more massive and less massive particle friends.

Let's consider the interaction between two helium atoms coming at each other with kinetic energy. Two electrons find themselves somewhere near each nucleus. It is unlikely that the two nuclei will come together first. Instead, more likely, two electrons will interact causing one or both of them to accelerate in what might look, on such a small scale, as a violent way. This interaction will scatter the two electrons more than the two nuclei or the other two electrons.

If the universe contained only these two helium atoms, then the electrons would fly off until they were attracted back to a nucleus through the acceleration due to the electric fields of the imbalanced nuclei. Remember that there are only two atoms in this make-believe universe.

Important to note in this little scenario is that the hot path is the screaming mutual acceleration of the two hot electrons the return path is the less violent return of the electrons to their valence position outside their respective helium atom.

Why, pray-tell, do I present this scenario? It is important to understand this small scenario before exploring how trillions more atoms and molecules behave in a bunch to create gravity using what we most often call electrostatic or electro-statistical attraction.

Generators Interacting with the Field

Conventionally generators inject mechanical work and take electrical energy to a load such as a light bulb or a clothes dryer. A so called 'magnetic' field is gener
ated with permanent magnets or electromagnets.

Maxwell's equations tell us that electrons spiral around magnetic fields. It seems to me that magnetic fields are just the curl of a dense electron field. This being the case, how does a generator work. The Maxwell-Faraday equation lets us know that the spatial curl of the electron field - as it changes in time - is equal to the curl in the electric field or the acceleration of electrons. As the generators rotor spins the coil has a changing view of the curl of electrons. The greater in change of the exposed curl to the coil the greater the electric field or voltage presented to the electrical load. The following diagram attempts to explain.

I've shown the direction of the electrons at the fringe of the electron field but the electrons, in fact, permeate the diagram between the two poles of the magnet. The diagram shows the rotor's coil at zero pi radians were the coil is aligned to minimize coupling from the electron field to the coil. The change in the electron curl exposed to the generator's coil accelerates the electrons causing a voltage at the electrical load.

The diagram above shows the generator's rotor at pi over four radians. The amount of electron angular velocity that the coil is exposed to is actually decreasing compared with the preceding figure.
The angular velocity of the electrons countered by the angular velocity of the rotor creates an acceleration of electrons in a sinusoidal manner.

Now what if we were to look at things in a more traditional manner. Lets look at the two diagrams above with the 'magnetic' field instead.

In the diagram above the rotor is at zero radians and there is said to be no flux linkages or coupling between the magnetic field and the rotor coil.

In the diagram above the rotor coil is at pi over four radians and the flux linkages of the 'magnetic' field are coupling with the coil of the rotor. The Maxwell-Faraday equation tells us that as the flux linkages change so does the voltage at the load end of the coil.

Gravity Models Starting with Electrostatics

Gravity exerts a force on an object towards the center of the largest mass in the vicinity of that object. Gravity is usually, in our experience, exerted by the Earth, the Moon and the Sun. The masses under observation will tend to act somewhat like the small charges they are made of.

Important to note the similarities between the universal gravity equation between two masses and the charge equation detailing the force between two charges. These similarities have been seen for a very long time but they have yet to be explained. We can chalk these similarities down to clues to how our universe might behave.

If gravity were like a game of Jenga then a block from the bottom would be put on top. Holes would be left in the bottom. In the case of gravity the holes are filled in Jenga the building eventually collapses. Negative charges are more likely to be in the vicinity of other negative charges towards the center of a mass due to simple geometry. Electrons will be ejected from the tight core of the center of mass with an excess of kinetic energy.

Electrons with excess kinetic energy are like the Jenga blocks from the bottom that are taken out to be put on top. This kinetic electron eventually interacts with other atoms and molecules and eventually slows down and joins with an atom or molecule. The slow down and joining to an atom or molecule is like the Jenga block being put on the top of the Jenga structure.

This is where gravity differs from a Jenga game. The electrons near to the ejected electrons are going to move in to back-fill the ejected electron with excess kinetic energy. So there is a circuit. The low voltage side is the high kinetic electron moving away from the center of mass. The return path is the electrons that back-fill that highly kinetic electron by moving in to charge balance the system. This happens continuously creating the widely observed gravity effect.